Abstract

Here, an all-optical switch is modeled in the form of fiber Bragg grating (FBG) based on electromagnetically induced transparency (EIT) phenomena dealing with a three-level EIT silicon (Si) nanocrystalline medium. The EIT consists of two fields, namely a strong control and weak probe fields that interact with the medium. Fast-optical switching of the probe is achieved by applying a pulsed control field, which relies on both steady-state and transient density matrices. The effects of four significant parameters of interest, i.e., Rabi frequency of the control field, EIT nanocrystal density, FBG length, and spontaneous decay rate, have been extensively investigated to optimize the probe transmission. Subsequently, the time-dependent density matrix is solved to obtain the response time of the FBG-EIT switch. Eventually, FBG is modeled such that low index layers contain EIT material and the high index layers do not. The FBG-EIT switch satisfies the criteria of maximum transmission and minimum rise time to give out the optimal operational condition. Despite the optical switching is in OFF mode at Ωc=0 THz demonstrating a high FBG reflectance, the reflectance suddenly vanishes at a certain $\mathrm{\Omega }_c^s$ to satisfy the equivalence of low and high refractive indices (switching ON). Therefore, a fast-optical switch is envisaged operating as large as 100 GHz in theory. The future applications of the FBG- EIT include the fast Q-switching of fiber lasers, ultra-fast modulation, optical quantum communication, and high speed optical processing and computation.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Optical achievements are often made by producing new materials with suitable properties. The coherent effects demonstrate a new way to the dramatic alteration in the optical properties of the medium. A modified optical response of an atomic medium, based on the laser induced coherence of the atomic states, results in the quantum interference between the excitation pathways to control the optical response. As a consequence, the absorbance suddenly drops and the optical material promptly switches to transparency at the resonant frequency of transition. The EIT attractive properties address the nonlinear quantum effect to demonstrate notable switching applications. The importance of the EIT arises from the fact that high non-linear susceptibility can be achieved within the spectral region of induced transparency associated with steep dispersion [13]. Regarding the EIT quantum interference phenomenon, the electromagnetic field can control the optical response of the material. In fact, the absorbance of the multiple-level atomic ensembles disappears by using an electromagnetic control (coupling) field [1,4,5]. This effect may enhance the nonlinear properties of the photonic crystal cavities, based on the optical characteristics of the nanocrystals [6,7]. Recently, there is a great deal of interest in the EIT context of three- and multiple-level systems [8]. A number of its nonlinear optical applications include slowing light [1,9], optical switches [2,4,10], data storage [11,12] and the wavelength converter [13]. Furthermore, one tunes the output power of the probe field at a certain wavelength in the master oscillator fiber power amplifier (MOFPA) using EIT based on FBG as an example of an all-optical adjustable fiber laser. The tunability of output power of a CW DC Yb:Silica laser fiber has been investigated, using a CW control field. The output coupler reflectance varies with control field from zero to high reflectance [14].

All-optical switching, as the main component of the network in data processing of optical signals, have been widely studied during the last decades. The capabilities of optical switches and storage by making use of the EIT effect of Rubidium (Rb) and Strontium (Sr) atomic gases have been previously reported [4,11]. Similarly, an all-optical EIT switch dealing with phase and control field regulations were reported in 85Rb in a four-level structure [12,13]. Furthermore, EIT in some rare-earth ion doped crystals, metal composite nanocrystals and semiconductor multiple quantum wells have been also proposed for the implementation of all-optical switching [7,1522].

On the other hand, the acousto-optic modulators (AOM) and various saturable absorbers are widely used as Q-switching elements in fiber lasers [2329]. However, current Q-switched (Q-SW) lasers suffer from high cavity losses degrading the beam quality. Furthermore, the application of various saturable absorbers may enhance the complexity of the system. Therefore, it is a challenge to develop an all-fiber optical alternative for purpose of fast Q-switching performance. [30,31]

Moreover, the use bulk components for intra cavity switching elements in the fiber lasers cause a beam quality degradation alongside the addition of high cavity losses, resulting in a decrease of laser performance and efficiency reduction. Thus in order to scale up laser output, the use of larger pump powers are essential [32,33]. Moreover, the bulk components require fine alignment and good mechanical stability, which complicates the design of a practical device. Q-switching of a fiber laser using an all-fiber intensity modulator employs an all fiber acousto-optic-based attenuator as cavity loss modulator [34]. Furthermore, the application of piezoelectric transducer in AOM may increase the complexity against all optical FBG-EIT switch.

Incorporation of fiber coupled FBGs with optical modulators enables us to achieve the facile, compact and robust Q-SW fiber laser cavities. Furthermore, the ability to tune the Bragg wavelength may enhance polarization selectivity and fast switching. There are few examples of all-fiber actively Q-SW lasers using FBG wavelength tuning according to the thermal or mechanical strain methods via electro-mechanical transducers. For instance, exposing the magnetic field to magnetostrictive material, the rod periodically stretches/relaxes to impose the grating wavelength shifting thereby altering the Q-factor of the cavity [35].

Furthermore, an all-fiber optical switch was demonstrated in an Yb based fiber laser. Strong stable pulses are developed to obtain Q-switching up to 200 kHz [36]. Moreover, the modeling of a typical Q-SW Yb:silica MOFPA has been carried out regarding the numerical solution of coupled time-dependent rate equations. Moreover, there are several articles available in the context of fiber laser modeling [3739]. The master oscillator is modeled in various rise times to investigate its effect on the output peak power and pulse duration [27,40,41].

In this work, the effect of EIT in Si nanocrystals is investigated. There are several articles available to address the application of Si nanocrystals for EIT process [7,14,4244]. An all-optical switch EIT implementation on FBG i.e., FBG-EIT structure is proposed via the significant change in transmission of probe field under the desired control field tuning. At first, the Hamiltonian/density matrix has been solved to demonstrate EIT susceptibility in both stationary-state and time-dependent modes. Consequently, the effect of four parameters of interest; i.e., control field Rabi frequency (Ωc), EIT nanocrystal density (N), length of FBG medium (L) and spontaneous decay rate (${\mathrm{\gamma }_{31}}$) on the probe field transmittance are extensively inspected. According to the results, the optimal all-fiber switch condition is obtained using MATLAB software to find the maximum probe transmission with minimum rise time. In fact, the performance of optical switch at a high rate strongly depends on control field Rabi frequency to promptly change FBG reflectance to null at a certain Ωc. This nature of FBG-EIT is extensively studied here. Consequently, this optical switch exhibits high potential to be employed in the fiber lasers. Despite there are a few articles available addressing the optical EIT switches [45,46], however, to the best of our knowledge, the context of EIT doped FBG has rarely been inspected so far.

2. Theory

2.1 EIT mechanism

The theory of EIT can be simply described using quantum mechanics whose details are given in Supplement 1. Figure 1 illustrates three-energy-levels of $|1\rangle $, $|2\rangle $ and $|3\rangle $ respectively. In fact, $|1\rangle $ and $|2\rangle $ represent ground states, and $|3\rangle $ denotes the excited state. Transitions $|1\rangle \leftrightarrow |3\rangle $ and $|2\rangle \leftrightarrow |3\rangle $ are allowed, while $|1\rangle \leftrightarrow |2\rangle $ is a dipole forbidden. The three-level system is called Λ-type due to its shape. It is irradiated by a couple of laser pulses namely the probe and control fields, at angular frequencies ${\mathrm{\omega }_\textrm{p}}$ and $\; {\mathrm{\omega }_\textrm{c}}$, respectively. When the control field is turned on, a narrow transparency window promptly opens. The detuning of the probe and control frequencies, based on the corresponding transitions, are given by [4750]:

$$_{{\Delta _p} = {\omega _{31}} - {\omega _p}}$$
$$_{{\Delta _c} = {\omega _{32}} - {\omega _c}}$$
where, ${\omega _{31}} = \frac{{{E_3} - {E_1}}}{\hbar }$ and ${\omega _{32}} = \frac{{{E_3} - {E_2}}}{\hbar }$, Ej and Ei ascertain the energy of states $|\textrm{j}\rangle $ and $|\textrm{i}\rangle $, respectively. The ${\Delta _\textrm{p}}$ and ${\Delta _{\textrm{c}}}\; $ denote to be the angular frequency differences (detuning) between the corresponding states, accordingly.

 figure: Fig. 1.

Fig. 1. Typical Λ-type EIT system with Rabi frequencies Ωp and Ωc driven by probe and control fields respectively. Note that the spontaneous decay rates ${\mathrm{\gamma }_{\textrm{ij}}}$ labels the transition $|\textrm{i}\rangle $ and $|\textrm{j}\rangle $ states and Δp and Δc ascertain the detuning of the probe and control fields [49]

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A couple of laser fields are applied considering the transitions $|1\rangle \leftrightarrow |3\rangle $ and $|2\rangle \leftrightarrow |3\rangle $. The interaction of atom-laser is expressed by Rabi frequency. Here, Ωc and Ωp denote to be Rabi frequency of control and probe lasers respectively, written as below [47,48,5052]:

$${\Omega _c} = \frac{{{\mu _{23}}{E_c}}}{{2\hbar }}$$
$${\Omega _p} = \frac{{{\mu _{13}}{E_p}}}{{2\hbar }}$$

Here, ${\mathrm{\mu }_{\textrm{ij}}}$, Ep and Ec ascertain the electric dipole of ij transition in EIT ions, the amplitude of probe and control electric fields, respectively.

${\mathrm{\gamma }_{\textrm{ij}}} = {\mathrm{\gamma }_{\textrm{ji}}}$ are the decay rates between the states i and j, composed of the radiative decay rates due to the spontaneous emission and the dephasing rates. The spontaneous decay rate ${\mathrm{\gamma }_{\textrm{ij}}}$ is obtained from the quantized theory [53,54] where the electromagnetic field is also treated quantum mechanically. For N similar species, the time-dependent population of excited state 3 is given by:

$${N_3}(t) = {N_3}(0)\textrm{exp} ( - 2{\gamma _{31}}t)$$
and, the corresponding spontaneous decay rate is written as below [53]:
$${\gamma _{31}} = \frac{{\omega _p^3{e^2}\mu _{13}^2}}{{3\pi {\varepsilon _0}\hbar {c^3}}}$$

Note that ${\mathrm{\gamma }_{31}}$ is a cubic function of probe frequency (ωp).

The complex susceptibility through the matrix elements is written as follows [47,51,55]:

$$\chi = \frac{{N\mu _{31}^22{\rho _{31}}}}{{{\varepsilon _0}\hbar {\Omega _p}}} = \frac{{N\mu _{31}^2}}{{{\varepsilon _0}\hbar }}\frac{{ - ({\Delta _p} - {\Delta _c}) + i{\gamma _{21}}}}{{\Omega _c^2 + ({\gamma _{31}} - i{\Delta _p})({\gamma _{21}} + i({\Delta _p} - {\Delta _c}))}}$$

Therefore, the time-dependent susceptibility according to is obtained, namely [50]:

$$\chi = \frac{{N\mu _{31}^22{\rho _{31}}}}{{{\varepsilon _0}\hbar {\Omega _p}}} = \frac{{N\mu _{31}^2}}{{{\varepsilon _0}\hbar }} \times \left[ {\frac{{i{\Omega _p}{e^{i{\Delta _p}t}}(({\gamma_{21}} + i({\Delta _p} - {\Delta _c}))}}{{\Omega _c^2{e^{i2{\Delta _c}t}} + ({\gamma_{31}} + i2{\Delta _p})({\gamma_{21}} + i({\Delta _p} - {\Delta _c}))}}} \right]$$

Thus, the susceptibility holds almost all information regarding the propagation of light in the medium. The absorption coefficient, transmission and refractive index can be obtained according to the following Eqs. [51,54,56]:

$$\alpha = {\mathop{\rm Im}\nolimits} (\chi ) \times L$$
$$T = \textrm{exp} ( - {\mathop{\rm Im}\nolimits} (\chi ) \times L) = \textrm{exp} ( - \alpha )$$
$$n = \sqrt {\frac{{n_0^2 + {\textrm{Re}} \chi + \sqrt {{{(n_0^2 + {\textrm{Re}} (\chi ))}^2} + {\mathop{\rm Im}\nolimits} {{(\chi )}^2}} }}{2}} $$
where, L and n0 are the absorbing medium length and initial refractive index when no control field is applied. Moreover, it is worth noting that α and T, in Eqs. above are determined via linear susceptibility χ to envisage steady state and transient EIT behaviors.

The model is based on three-level lambda system of atomic vapor (where n∼1), however it is developed to Si nanocrystals in SiO2 host having large refractive indices [7,14,4244]. The proposed structure of EIT based modulator is analyzed here. The element is designed according to all-optical switching of FBG basis relying on the EIT phenomenon. The sequential modeling steps of EIT doped FBG are given in the Supplement 1.

FBG as a periodic microstructure with typically few millimeters-length can be photo inscribed along the core of a single mode fiber. This is done by transverse illumination of the fiber using a UV laser beam via a phase mask to generate an interference pattern along the core. This consists of spatial periodic modulation in the form of low (nL) and high (nH) refractive index-layers, respectively. The effective refractive index leads the reflection of light along the core of an optical fiber within a narrow spectral range for which a Bragg condition is satisfied. The central Bragg wavelength is given by [57]:

$$\lambda = 2{n_{eff}}\Lambda $$
where, λ, Λ and neff denote to be vacuum wavelength, grating period and effective refractive index of the fiber, respectively. In fact, the effective refraction index is dependent nL/nH and the central wavelength slightly varies with neff and grating period. Figure 2 illustrates (a) a three-energy-level diagram of Λ-type EIT nanocrystal and (b) EIT material incorporated in FBG as a number of periodic (nL, nH) layers.

 figure: Fig. 2.

Fig. 2. a) Energy diagram of a three-level Λ-type EIT nanocrystal b) EIT material incorporated in FBG as a number of periodic (nL, nH) layers. Note that nL/nH stand for the layers alongside FBG for low / high refraction indices in FBG and Λ denotes to be the grating period. The control field in terms of successive ultra-short pulses irradiate whole FBG length (L) to attain the adequate laser intensity required for EIT process. Typical values of the parameters are given as below: nL=1.4415, nH=1.4589, Λ = 375 nm, L=75 µm.

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Figure 2(a) depicts the energy diagram of a three level Λ-type EIT nanocrystal. The silicon nanocrystals were previously used for EIT process [7,14,4244]. Note that nL/nH layers are considered along FBG length where nL layers are made up of (Si nanocrystal: SiO2) with refractive indices ranging 1.4415-1.4589. This varies against control field intensity (control Rabi frequency), whereas nH layers are not made of EIT material to be invariant under the control field having a certain refractive index (typically 1.4589). Despite, the nL is sensitive to the control field, however it would nonlinearly increase to become equal nH at a certain Rabi frequency. Similarly, the absorption (imaginary part of the refractive index) approaches to negligible value at large control fields. Furthermore, the periodic nL/nH layers look like a grating alongside FBG length according to Eq. (12), allowing high transmission of the narrow band probe field at a desire wavelength. Note that, the beam profile of control field covers whole FBG length through a cylindrical lens to attain the adequate intensity requires for EIT process.

Note that, the Gaussian and Sech2 profiles can be used as well as step functions. The Sech2 function has exponential wings and the wings of the Gaussian one plunge steeply downwards. Naturally, in any experimental situation, the wings ultimately end in the noise background and Sech2 function fits better that Gaussian one. Here, the nature of EIT time response is estimated in order of 10 ps, hence the pulses with several femtosecond durations, act as a step function against the EIT time response.

3. Results and Discussion

3.1 EIT properties

There are several methods available to implement the EIT medium to realize a typical FBG based optical switch coupled with the fiber laser. One may rely on the doping of semiconductor quantum dots/nanocrystals as multi-level atoms into a selected region of FBG. The latter is made up of typical fiber with a certain grating period. Here, Si nanocrystals are doped within periodic low index layers in silica (SiO2) core as the FBG host. The transmission of probe pulse is modulated by the control (coupling) field according to Eqs. (9,10). Moreover, Table 1 tabulates the typical value of the parameters involved in the model [14]. Subsequently, the equations are numerically solved in MATLAB software according to the given parameters. Finally, FBG architecture is predesigned to simulate the transient (switching) effect.

Tables Icon

Table 1. Typical EIT parameters used in the FBG modeling [42,55]

The optical properties of species are fundamentally tied to their intrinsic energy-level structures. The linear response of an atom to the resonant light is described by the first order susceptibility including the dominant EIT features. Figure 3 depicts the real part (phase shift) and the imaginary part (absorption) of the linear susceptibility versus probe pulse detuning ${\mathrm{\Delta }_\textrm{p}}$. In the absence of the control field (Ωc=0), the susceptibility χ obeys a Lorentzian function. In contrast, at the attendance of the control field for instance typically (Ωc=1 THz), Autler-Townes splitting takes place and the profile splits into two parts [49]. It is supposed small Rabi frequency of the control field leads to a sharp spectral transmission window whose linewidth approaches to that of EIT at Ωc=0 [4]. One recognizes that Im($\mathrm{\chi }$) undergoes a destructive interference over the region such that the coherently driven medium becomes transparent to the probe field according to Eq. (9). The results resemble to be in good agreement with the findings given in Refs. [17,19,22,45,47,48,50,54,58].

 figure: Fig. 3.

Fig. 3. a) absorption and b) phase shift versus probe pulse detuning under two distinct cases, i.e., Ωc=0 (no control field) and at the attendance of control field Ωc=1 THz (typical)

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3.2 Steady-state EIT transmission

At first, the steady-state property of the optical switch is studied. Four involving parameters are examined at various probe pulse detuning, demonstrating an EIT-FBG optical switch in the presence of the control field. The parameters include the Rabi frequency of control pulse (Ωc), Si nanocrystals density (N), length of FBG medium (L) and the spontaneous decay rate (${\mathrm{\gamma }_{31}}$) to achieve the maximum transmission of the probe. Let assume a grating period of 375 nm; hence, in the case, the number of FBG pair layers changes from 100 to 700, then the FBG length would vary from 37.5 to 262.5 µm.

Figure 4(a) displays the transmission of the probe field in terms of detuning. Note that the variation of Rabi frequency of control pulse is carried out ranging 0–3 THz, regarding data given in Table 1. When Rabi frequency elevates, then this parameter enhances and the corresponding bandwidth enlarges too. Regarding EIT, the transmission of the probe field at line center increases, in favor of larger control field intensity. Figure 4(b) plots this parameter versus the Si nanocrystals concentration. In fact, EIT nanocrystal density notably affects the probe transmission. It is elucidated that this parameter undergoes large values at low EIT concentrations. Figure 4(c) depicts the variation of transmittance versus different FBG lengths. Not only the transmission peak reduces with EIT concentration, but also it decreases against FBG length. However, the width of spectral window in which an EIT medium appears transparent remains invariant in terms of N and L parameters. These parameters play an important role in the applications of EIT comprising between fiber length and EIT concentration. In fact, a long fiber can be used in low concentration or a short fiber requires an adequate dense concentration. Finally, Fig. 4(d) demonstrates the transmission of the probe in terms of the spontaneous decay rate. This slightly levels down at higher decay rates, as if it is less sensitive to ${\mathrm{\gamma }_{31}}$. This arises from the fact that transmittance usually takes small values regarding $|1 \mathop \leftrightarrow \limits_{} |3 $ transition. Furthermore, the transmission coefficient obtains maximum value at center line due to the constructive interference.

 figure: Fig. 4.

Fig. 4. Spectral transmission in terms of detuning versus, a) Rabi frequency of control field (N=1×1021 m−3, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), b) dopant concentration of EIT nanocrystals (Ωc=1 THz, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), c) FBG length (Ωc = 1 THz, N=1×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.24$ THz) and d) spontaneous decay rate (Ωc = 1 THz, N=1×1021 m−3, L=187.5 µm) in steady-state mode.

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As a consequence, the control field intensity causes to elevate the transmission, whereas conversely the other parameters such as concentration, length and ${\mathrm{\gamma }_{31}}$ level down the probe transmittance. Therefore, the higher transmission is envisaged using large Ωc at low EIT concentration in short FBG length according to the present model. Furthermore, the results of Figs. 4(a)-(d) attest to be consistent with Refs. [19,45,48,50,59,60].

3.3 Time-dependent EIT transmission

When the control field is switched on (Ωc≠0), the instantaneous transmission response of EIT material against Ωc, N, L and ${\mathrm{\gamma }_{31}}$ would sensibly change to demonstrate a fast optical switch property through parametric characterization. The rise time (trise) as an indication of EIT temporal response demonstrates the time required to reach the maximum transmission peak value (Tmax) according to Eqs. (8) and (10).

Figure 5 shows the transient variation of probe transmission in terms of (a) control Rabi frequencies, (b) EIT concentrations, (c) FBG lengths and (d) spontaneous decay rates, accordingly. After a few picoseconds, transmission reaches the maximum value. According to Figs. 6(a)-(d) insets, the rise time linearly decreases with Ωc ranging 4 −11 ps, following a nonlinear growth versus N and L as well as a plateau in terms of ${\mathrm{\gamma }_{31}}$ that slightly drops to another plateau at larger ${\mathrm{\gamma }_{31}}$. In addition, one reminds that ${\mathrm{\gamma }_{31}}$ is a cubic function of ωp according to Eq. (6), assuring reliable tunability of probe frequency takes place.

 figure: Fig. 5.

Fig. 5. Time-dependent transmission versus (a) Rabi frequency of control at (N=1×1021 m−3, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), (b) nanocrystal concentration at (Ωc=1 THz, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), (c) FBG length at (Ωc = 1 THz, N=1×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.24$ THz) and (d) spontaneous decay rate at (Ωc = 1 THz, N=1×1021 m−3, L=187.5 µm). The insets display the variation of rise time in terms of four varying parameters of interest, respectively.

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 figure: Fig. 6.

Fig. 6. Typical transmission and rise time in terms of, a) Rabi frequency of control (case I: N=6×1021 m−3, L=262.5 µm, ${\mathrm{\gamma }_{31}} = 0.3$ THz; case II: N=1×1021 m−3, L=37.5 µm, ${\mathrm{\gamma }_{31}} = 0.05$ THz), b) EIT concentration (case I: Ωc = 1 THz, L=262.5 µm, ${\mathrm{\gamma }_{31}} = 0.3$ THz; case II: Ωc = 3 THz, L=37.5 µm, ${\mathrm{\gamma }_{31}} = 0.05$ THz), c) FBG length (case I: Ωc = 1 THz, N=6×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.3$ THz; case II: Ωc = 3 THz, N=1×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.05$ THz) and d) decay rate in Si nanocrystals (case I: Ωc = 1 THz, N=6×1021 m−3, L=262.5 µm; case II: Ωc = 3 THz, N=1×1021 m−3, L=37.5 µm). Note that case II values are determined at large Ωc, low N, short L where as ${\mathrm{\gamma }_{31}}$ is not very sensitive to trise.

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We elucidate despite trise is shortened with Ωc and ${\mathrm{\gamma }_{31}}$, however, the rise time of probe increases at larger values of N and L. The peak transmission usually approaches to steady-state conditions after ∼ 10 ps. Tmax and minimum trise are considered as the criteria for optimal parameters in transient conditions of an FBG-EIT based optical switch. According to Fig. 2, four values of interest are examined within a selected range i.e., Ωc (0–3 THz), N (1×1021−6×1021 m−3), L (37.5−262.5 µm) and ${\mathrm{\gamma }_{31}}$ (0.001–0.3 THz). In fact, it is worth noting a variety of thousands of cases have been examined to find the optimal parameters among them. According to the criteria, two typical extreme cases are chosen to represent graphically. In order to inspect the effects on probe transmission as well as probe rise time, it is essential to vary a single parameter and keeping the others fixed. As a consequence, the optimal values are assessed for the reliable operation. Figure 6 indicates the behavior of Tmax and trise in terms of those parameters considering steady-state and time-dependent modes.

Figure 6(a) demonstrates the transmission and rise time in terms of control Rabi-frequency such that Tmax increases and trise decreases at higher Rabi frequency. This assures a short rise time takes place at maximum transmission and large Rabi frequency. Figures 6(b) and (c) illustrate the same transmission behavior as to Tmax takes places at low concentration and short FBG length leading to desirable rise time. Finally, Fig. 6(d) displays the transmission and rise time versus decay rate which both linearly reduce at larger decay rate. Note that maximum transmission and minimum rise time meet the optimum criteria as expected.

In summary; the coupling field must be strong enough to separate the two peaks of the Autler-Townes splitting [19]. So, the elevation of Ωc provides the possibility to increase the peak and width of spectral of transmission, thus the time required to reach the maximum transmission peak value (rise time) reduces. On the other hand, the absorption notably changes with concentration which can significantly affect on the EIT window. Finally, the dephasing rate of the spin arises from the photon interactions. A higher dephasing rate leads to the smaller ground state coherency and a weaker EIT effect [59,60].

3.3 FBG-EIT architecture

FBG-EIT can be coupled with the fiber laser to operate both as a fast modulator and an output coupler at the same time. According to Fig. 2(b), the high refracting index layers are chosen to be made up of a non-EIT material, invariant under various control fields, whereas the low index layers contain EIT material as we discussed in previous sections. Notice that maximum transmission and minimum rise time are criteria for better performance of an all optical rapid switch [61,62]. One may carry out a desired FBG-EIT architecture according to the optimal conditions to meet the criteria above. For instance, let FBG runs at λp = 1080 nm (ωp=1.746×1015 Hz), so maximum reflectance would naturally take place at the Bragg wavelength. Subsequently, the optimal values of ${\mathrm{\gamma }_{31}}$ would be determined at λp whose optimal value gives out to be ${\mathrm{\gamma }_{31}}$=0.002378 THz (point P). Figure 7(a) plots the probe wavelength in terms of ${\mathrm{\gamma }_{31}}$ according to Eq. (6): ${\mathrm{\omega }_\textrm{p}}\sim \mathrm{\gamma }_{31}^{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 3}} \right.}\!\lower0.7ex\hbox{$3$}}}$. Then, the FBG length is obtained based on the following relation, namely L=Λ×pair layers. Here, 200 pair layers are selected and for a grating period of Λ=375 nm, then FBG length is determined to be L=75 µm. Subsequently, the optimal dopant concentration is chosen N=1×1021 m−3.

 figure: Fig. 7.

Fig. 7. a) Probe wavelength (and ωp) versus decay rate ${\mathrm{\gamma }_{31}}$ (Eq. (6)), b) Low index (nL) and FBG reflectance (Eq. (1)1 and 13) in terms of Rabi frequency of control, inset: nL versus under whole range of Ωc, a portion of nL is highlighted in the interval of 0.7–1.2 THz, c) corresponding EIT absorbance versus Ωc, d) probe wavelength of FBG versus Ωc. Note that nL increases to equate nH in terms of Ωc at point Q where FBG reflectance entirely vanishes. Simultaneously, the probe wavelength slightly shifts from 1.08 to 1.09 µm at Q.

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On the other hand, by making use of a pulsed control field, the probe transmission can be modulated regarding transient behavior. Hence, the control pulse duration adjusts the switching time. As a consequence, in the absence of a control field Ωc=0 (switching OFF mode), then the refractive low/high index layers are typically set to 1.4415/1.4589, respectively. In the presence of a control field (Ωc≠0), the low index of FBG is elevated in terms of the external coupling field (Ωc) according to Eqs. (7) and (11). When nL=nH, then FBG reflectance becomes nearly null and the whole probe field is allowed to traverse through FBG-EIT switch. According to the Eq. (11) and using the optimal parameters, N=1×1021 m−3, L=75 µm and ${\mathrm{\gamma }_{31}}$=0.002378 THz, the optimal control field at switch mode is determined to be $\mathrm{\Omega }_\textrm{c}^\textrm{s}$ = 1.1 THz such that the condition ${\textrm{n}_\textrm{L}} = {\textrm{n}_\textrm{H}}$ holds.

Moreover, according to Eqs. (3) and (13);

$${I_c} = \frac{1}{2}c{n_L}{\varepsilon _0}E_c^2$$
and Rabi frequency $\mathrm{\Omega }_{\textrm{c}}^{\textrm{s}}$ required to trigger the switch is estimated Ic ∼ 105 W/cm2 [14,51]:

On the other hand, the FBG reflectance can be given by the following relations [63,64]:

$$R(L,\lambda ) = {\tanh ^2}(\gamma L)$$
$$\gamma = \sqrt {{\kappa ^2} - \Delta {\beta ^2}} $$
$$\kappa = \frac{{\pi \Delta {n_{eff}}}}{\lambda }$$
$$\Delta \beta = \beta - \frac{\pi }{\Lambda }$$
where L, $\kappa $, $\mathrm{\Delta }\beta $, $\beta $, and neff ascertain to be the total length of FBG, coupling coefficient, wave vector detuning, fiber core propagation constant, and effective refractive index, respectively. When λ= λp, the probe wavelength is set to be equal to center Bragg wavelength, thus no wave vector detuning takes place, i.e., $\mathrm{\Delta }\beta = 0$.

Figure 7(b) depicts the variation of nL and FBG reflectance as a function of Ωc, indicating the optimal switching condition occurs at point Q. This attests the reflectance levels down to vanish at ${\textrm{n}_\textrm{L}} = {\textrm{n}_\textrm{H}}$. Fig. 7(b) inset shows the refractive index in terms under whole range of Ωc. A portion of nL is highlighted in the interval of 0.7–1.2 THz. Figure 7(c) demonstrates corresponding EIT absorbance versus Ωc. Note that the absorbance becomes negligible at $\mathrm{\Omega }_c^s$. Moreover, Fig. 7(d) represents the probe wavelength λp in terms of Ωc regarding Eq. (12). In fact, probe wavelength shifts of ∼ 10 nm takes place at $\mathrm{\Omega }_c^s$.

According to the model, we have proposed an FBG-EIT micro-structure including L=75 µm, N=1×1021 m−3, ${\mathrm{\gamma }_{31}}$=0.002378 THZ and $\mathrm{\Omega }_c^s$=1.1 THz to trigger the optical switch at point Q efficiently.

Figure 8(a) reveals time-dependent transmission at the optimal values of four parameters of interest to activate switch ON mode ON at $\mathrm{\Omega }_\textrm{c}^\textrm{s}$ alongside a minimum rise time of 10 ps. The duration of the control pulse (${\mathrm{\tau }_{\textrm{cp}}}$) may vary from ns to fs according to the type of laser. Figure 8(b) displays the temporal response of EIT doped FBG switch assuming identical rise/fall times, total switch duration at ON mode is given by; $\mathrm{\tau } \cong 2{\textrm{t}_{\textrm{rise}}} + {\mathrm{\tau }_{\textrm{cp}}}$. However, in practice depending on the pulse repetition rate of the control field ($\textrm{P}.\textrm{R}.\textrm{R} = \frac{1}{\mathrm{\tau }}$), it is feasible to achieve 100 MHz at 1080 nm employing a nominal mode locked laser as the control pulse. However, the switch is capable of operating up to 100 GHz in theory.

 figure: Fig. 8.

Fig. 8. a) Time-dependent transmission of probe field, b) Temporal transmittance of FBG-EIT by applying a short pulse of control field to model the fast switching performance. Note that trise, tcp and tfall denote to be rise time, duration of control pulse and fall time, respectively.

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4. Conclusion

All-optical switches have attracted much attention as key devices for high-speed optical data processing and optical communication systems. In fact, ultrafast all-optical switching also yields notable progress in other research areas such as nanophotonics, integrated optics, nonlinear optics, material science, and optical communications. Here, a model is developed to realize the optical switching of an FBG based on the EIT effect. An optical fast switch is designed based on the assumption where the low index layers of FBG are filled with EIT nanocrystal dopant and the high index layers do not contain EIT material. The cascade-type three-level scheme of Si is modeled by solving the Liouville equation including Hamiltonian/density matrices. At first, the maximum transmission of probe pulse is obtained against different parameters of interest such as Ωc, N, L and ${\mathrm{\gamma }_{31}}$ in a steady-state condition. The transmission peak of the probe decreases at larger concentration, longer FBG length and high values of the spontaneous decay rate. Conversely, the transmittance elevates with Rabi frequency of control. Secondly, the time-dependent transmission is determined, under these parameters of interest. Despite the rise time levels down in terms of Ωc and ${\mathrm{\gamma }_{31}}$, however it increases with N and L.

A periodic nL/nH FBG micro-structure is envisaged such that nH index layers contain ordinary material, whereas nL index layers are made up of EIT nanocrystals. Typical FBG-structure, characterizing nL/nH repetitive stacks, operates as both an output coupler and an FBG-EIT switch. Since nL material obeys EIT properties, at the onset of applying a certain control Rabi frequency ($\mathrm{\Omega }_\textrm{c}^\textrm{s}$), nL value notably increases to reach nH, let initially assume a high reflectance FBG-EIT. Subsequently, the total reflectance of FBG-EIT undergoes a prompt changeover to maximum transmission of the probe signal at the optimal control field $\mathrm{\Omega }_\textrm{c}^\textrm{s}$. Simultaneously, the FBG reflectance becomes null just to realize a fast optical switch with a prompt time response. Despite the imaginary part of the EIT refractive index (absorbance) suddenly disappears, however the real part (dispersion) elevates to reach nH activating to switch ON.

As an example, for the operational wavelength 1080 nm as the probe signal, then the optimal parameters are obtained to be $\mathrm{\Omega }_\textrm{c}^\textrm{s}$=1.1 THz (equivalent to Ic ∼ 105 W/cm2), N=1×1021 m−3, L=75 µm and ${\mathrm{\gamma }_{31}}$=0.002378 THz. This benefits the maximum peak of probe transmittance 99.9999 and minimum rise time of 10 ps according to the model.

As a fast switch, the temporal response of FBG-EIT transmittance is modulated by the transient properties of the control field to runs up to 100 GHz theoretically.

Disclosures

The authors declare no conflicts of interest.

Supplemental document

See Supplement 1 for supporting content.

References

1. S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990). [CrossRef]  

2. S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Physical review letters. 81(17), 3611–3614 (1998). [CrossRef]  

3. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001). [CrossRef]  

4. K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991). [CrossRef]  

5. N. Hayashi, A. Fujisawa, H. Kido, K. I. Takahashi, and M. Mitsunaga, “Interference between electromagnetically induced transparency and two-step excitation in three-level ladder systems,” J. Opt. Soc. Am. B 27(8), 1645–1650 (2010). [CrossRef]  

6. M. Soljacic, J.D. Joannopoulos, and L.V. Hau, “Using electro-magnetically induced transparency in photonic crystal cavities to obtain large non-linear effects,” Google Patents, (2006).

7. G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012). [CrossRef]  

8. S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

9. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999). [CrossRef]  

10. A. N. Tuan, D. Le Van, and B. N. Huy, “Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity,” J. Opt. Soc. Am. B 35(6), 1233–1239 (2018). [CrossRef]  

11. B. S. Ham, M. S. Shahriar, M. K. Kim, and P. R. Hemmer, “Frequency-selective time-domain optical data storage by electromagnetically induced transparency in a rare-earth-doped solid,” Opt. Lett. 22(24), 1849–1851 (1997). [CrossRef]  

12. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003). [CrossRef]  

13. H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” Appl. Phys. Lett. 76(22), 3173–3175 (2000). [CrossRef]  

14. V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018). [CrossRef]  

15. B. S. Ham, S. M. Shahriar, and P. R. Hemmer, “Electromagnetically induced transparency over spectral hole-burning temperature in a rare-earth–doped solid,” J. Opt. Soc. Am. B 16(5), 801–804 (1999). [CrossRef]  

16. P. C. Ku, F. sedgwick, C. J. chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29(19), 2291–2293 (2004). [CrossRef]  

17. B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. 144(4-6), 227–230 (1997). [CrossRef]  

18. Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008). [CrossRef]  

19. H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002). [CrossRef]  

20. S. M. Sadeghi, “Spatial modulation of electromagnetically induced transparency in quantum wells using monolayer growth islands,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1275–1282 (2006). [CrossRef]  

21. L. Silvestri and G. Czajkowski, “Electromagnetically induced transparency in asymmetric double quantum wells in the transient regime,” Phys. Status Solidi (c) 5(7), 2412–2415 (2008). [CrossRef]  

22. A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003). [CrossRef]  

23. L. Luo and P.L. Chu, “Passive Q-switched erbium-doped fibre laser with saturable absorber,” Optics Communications 161(4-6), 257–263 (1999). [CrossRef]  

24. H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998). [CrossRef]  

25. F. Seguin and T. K. Oleskevich, “Diode-pumped Q-switched fiber laser,” Opt. Eng. 32(9), 2036 (1993). [CrossRef]  

26. A. Chandonnet and G. Larose, “High-power Q-switched erbium fiber laser using an all-fiber intensity modulator,” Opt. Eng. 32(9), 2031 (1993). [CrossRef]  

27. N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020). [CrossRef]  

28. S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

29. G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997). [CrossRef]  

30. A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013). [CrossRef]  

31. V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

32. R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

33. P. Pérez-Millán, A. Díez, M. V. Andrés, D. Zalvidea, and R. Duchowicz, “Q-switched all-fiber laser based on magnetostriction modulation of a Bragg grating,” Opt. Express 13(13), 5046–5051 (2005). [CrossRef]  

34. D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000). [CrossRef]  

35. N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002). [CrossRef]  

36. T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006). [CrossRef]  

37. M. Ilchi-Ghazaani and P. Parvin, “Distributed scheme versus MOFPA array on the power scaling of a monolithic fiber laser,” IEEE J. Quantum Electron. 50(8), 1–11 (2014). [CrossRef]  

38. M. Ilchi-Ghazaani and P. Parvin, “Impact of cavity loss on the performance of a single-mode Yb: silica MOFPA array,” Opt. Laser Technol. 65, 94–105 (2015). [CrossRef]  

39. M. Ilchi-Ghazaani and P. Parvin, “Temperature Effect on Yb-Doped Silica Fiber Laser Performance,” IEEE J. Quantum Electron. 56(5), 1–7 (2020). [CrossRef]  

40. S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013). [CrossRef]  

41. P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009). [CrossRef]  

42. K. X. Guo and Y. B. Yu, “Nonlinear optical susceptibilities in Si/SiO2 parabolic quantum dots,” Chinese J. Phys. 43(5), 932–941 (2005).

43. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010). [CrossRef]  

44. H. Tang, H. L. Zhou, J. Xie, L. Lu, and J. Chen, “Electromagnetically induced transparency in a silicon self-coupled optical waveguide,” J. Lightwave Technol. 36(11), 2188–2195 (2018). [CrossRef]  

45. Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014). [CrossRef]  

46. B. D. Clader, S. M. Hendrickson, R. M. Camacho, and B. C. Jacobs, “All-optical microdisk switch using EIT,” Opt. Express 21(5), 6169–6179 (2013). [CrossRef]  

47. J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019). [CrossRef]  

48. J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018). [CrossRef]  

49. T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: Two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010). [CrossRef]  

50. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005). [CrossRef]  

51. D. Bejan, “Electromagnetically induced transparency in double quantum dot under intense laser and magnetic fields: from Λ to Ξ configuration,” Eur. Phys. J. B 90(3), 54 (2017). [CrossRef]  

52. J. T. Verdeyen, “Laser electronics,” laser electronics (1989).

53. R. Loudon, “The quantum theory of light,” OUP Oxford (2000).

54. K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997). [CrossRef]  

55. M. O. Scully and M.S. Zubairy, “Quantum optics,” 1999, American Association of Physics Teachers.

56. P. W. Milonni, Fast light, slow light and left-handed light, (CRC Press, 2004).

57. https://www.rp-photonics.com/fiber_bragg_gratings.html.

58. L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

59. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995). [CrossRef]  

60. R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980). [CrossRef]  

61. Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45(9), 2058–2071 (2006). [CrossRef]  

62. Y. Wang and C. Q. Xu, “Switching-induced perturbation and influence on actively Q-switched fiber lasers,” IEEE J. Quantum Electron. 40(11), 1583–1596 (2004). [CrossRef]  

63. R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016). [CrossRef]  

64. A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

References

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  1. S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
    [Crossref]
  2. S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Physical review letters. 81(17), 3611–3614 (1998).
    [Crossref]
  3. C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
    [Crossref]
  4. K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
    [Crossref]
  5. N. Hayashi, A. Fujisawa, H. Kido, K. I. Takahashi, and M. Mitsunaga, “Interference between electromagnetically induced transparency and two-step excitation in three-level ladder systems,” J. Opt. Soc. Am. B 27(8), 1645–1650 (2010).
    [Crossref]
  6. M. Soljacic, J.D. Joannopoulos, and L.V. Hau, “Using electro-magnetically induced transparency in photonic crystal cavities to obtain large non-linear effects,” Google Patents, (2006).
  7. G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
    [Crossref]
  8. S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).
  9. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
    [Crossref]
  10. A. N. Tuan, D. Le Van, and B. N. Huy, “Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity,” J. Opt. Soc. Am. B 35(6), 1233–1239 (2018).
    [Crossref]
  11. B. S. Ham, M. S. Shahriar, M. K. Kim, and P. R. Hemmer, “Frequency-selective time-domain optical data storage by electromagnetically induced transparency in a rare-earth-doped solid,” Opt. Lett. 22(24), 1849–1851 (1997).
    [Crossref]
  12. M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003).
    [Crossref]
  13. H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” Appl. Phys. Lett. 76(22), 3173–3175 (2000).
    [Crossref]
  14. V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
    [Crossref]
  15. B. S. Ham, S. M. Shahriar, and P. R. Hemmer, “Electromagnetically induced transparency over spectral hole-burning temperature in a rare-earth–doped solid,” J. Opt. Soc. Am. B 16(5), 801–804 (1999).
    [Crossref]
  16. P. C. Ku, F. sedgwick, C. J. chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29(19), 2291–2293 (2004).
    [Crossref]
  17. B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. 144(4-6), 227–230 (1997).
    [Crossref]
  18. Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
    [Crossref]
  19. H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002).
    [Crossref]
  20. S. M. Sadeghi, “Spatial modulation of electromagnetically induced transparency in quantum wells using monolayer growth islands,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1275–1282 (2006).
    [Crossref]
  21. L. Silvestri and G. Czajkowski, “Electromagnetically induced transparency in asymmetric double quantum wells in the transient regime,” Phys. Status Solidi (c) 5(7), 2412–2415 (2008).
    [Crossref]
  22. A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
    [Crossref]
  23. L. Luo and P.L. Chu, “Passive Q-switched erbium-doped fibre laser with saturable absorber,” Optics Communications 161(4-6), 257–263 (1999).
    [Crossref]
  24. H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998).
    [Crossref]
  25. F. Seguin and T. K. Oleskevich, “Diode-pumped Q-switched fiber laser,” Opt. Eng. 32(9), 2036 (1993).
    [Crossref]
  26. A. Chandonnet and G. Larose, “High-power Q-switched erbium fiber laser using an all-fiber intensity modulator,” Opt. Eng. 32(9), 2031 (1993).
    [Crossref]
  27. N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020).
    [Crossref]
  28. S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).
  29. G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
    [Crossref]
  30. A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
    [Crossref]
  31. V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).
  32. R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).
  33. P. Pérez-Millán, A. Díez, M. V. Andrés, D. Zalvidea, and R. Duchowicz, “Q-switched all-fiber laser based on magnetostriction modulation of a Bragg grating,” Opt. Express 13(13), 5046–5051 (2005).
    [Crossref]
  34. D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000).
    [Crossref]
  35. N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
    [Crossref]
  36. T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
    [Crossref]
  37. M. Ilchi-Ghazaani and P. Parvin, “Distributed scheme versus MOFPA array on the power scaling of a monolithic fiber laser,” IEEE J. Quantum Electron. 50(8), 1–11 (2014).
    [Crossref]
  38. M. Ilchi-Ghazaani and P. Parvin, “Impact of cavity loss on the performance of a single-mode Yb: silica MOFPA array,” Opt. Laser Technol. 65, 94–105 (2015).
    [Crossref]
  39. M. Ilchi-Ghazaani and P. Parvin, “Temperature Effect on Yb-Doped Silica Fiber Laser Performance,” IEEE J. Quantum Electron. 56(5), 1–7 (2020).
    [Crossref]
  40. S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
    [Crossref]
  41. P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
    [Crossref]
  42. K. X. Guo and Y. B. Yu, “Nonlinear optical susceptibilities in Si/SiO2 parabolic quantum dots,” Chinese J. Phys. 43(5), 932–941 (2005).
  43. X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
    [Crossref]
  44. H. Tang, H. L. Zhou, J. Xie, L. Lu, and J. Chen, “Electromagnetically induced transparency in a silicon self-coupled optical waveguide,” J. Lightwave Technol. 36(11), 2188–2195 (2018).
    [Crossref]
  45. Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
    [Crossref]
  46. B. D. Clader, S. M. Hendrickson, R. M. Camacho, and B. C. Jacobs, “All-optical microdisk switch using EIT,” Opt. Express 21(5), 6169–6179 (2013).
    [Crossref]
  47. J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019).
    [Crossref]
  48. J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018).
    [Crossref]
  49. T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: Two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010).
    [Crossref]
  50. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
    [Crossref]
  51. D. Bejan, “Electromagnetically induced transparency in double quantum dot under intense laser and magnetic fields: from Λ to Ξ configuration,” Eur. Phys. J. B 90(3), 54 (2017).
    [Crossref]
  52. J. T. Verdeyen, “Laser electronics,” laser electronics (1989).
  53. R. Loudon, “The quantum theory of light,” OUP Oxford (2000).
  54. K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
    [Crossref]
  55. M. O. Scully and M.S. Zubairy, “Quantum optics,” 1999, American Association of Physics Teachers.
  56. P. W. Milonni, Fast light, slow light and left-handed light, (CRC Press, 2004).
  57. https://www.rp-photonics.com/fiber_bragg_gratings.html .
  58. L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).
  59. A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
    [Crossref]
  60. R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980).
    [Crossref]
  61. Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45(9), 2058–2071 (2006).
    [Crossref]
  62. Y. Wang and C. Q. Xu, “Switching-induced perturbation and influence on actively Q-switched fiber lasers,” IEEE J. Quantum Electron. 40(11), 1583–1596 (2004).
    [Crossref]
  63. R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016).
    [Crossref]
  64. A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

2020 (2)

N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Temperature Effect on Yb-Doped Silica Fiber Laser Performance,” IEEE J. Quantum Electron. 56(5), 1–7 (2020).
[Crossref]

2019 (1)

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019).
[Crossref]

2018 (4)

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018).
[Crossref]

H. Tang, H. L. Zhou, J. Xie, L. Lu, and J. Chen, “Electromagnetically induced transparency in a silicon self-coupled optical waveguide,” J. Lightwave Technol. 36(11), 2188–2195 (2018).
[Crossref]

A. N. Tuan, D. Le Van, and B. N. Huy, “Manipulating multi-frequency light in a five-level cascade-type atomic medium associated with giant self-Kerr nonlinearity,” J. Opt. Soc. Am. B 35(6), 1233–1239 (2018).
[Crossref]

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

2017 (1)

D. Bejan, “Electromagnetically induced transparency in double quantum dot under intense laser and magnetic fields: from Λ to Ξ configuration,” Eur. Phys. J. B 90(3), 54 (2017).
[Crossref]

2016 (1)

R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016).
[Crossref]

2015 (1)

M. Ilchi-Ghazaani and P. Parvin, “Impact of cavity loss on the performance of a single-mode Yb: silica MOFPA array,” Opt. Laser Technol. 65, 94–105 (2015).
[Crossref]

2014 (2)

M. Ilchi-Ghazaani and P. Parvin, “Distributed scheme versus MOFPA array on the power scaling of a monolithic fiber laser,” IEEE J. Quantum Electron. 50(8), 1–11 (2014).
[Crossref]

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

2013 (3)

B. D. Clader, S. M. Hendrickson, R. M. Camacho, and B. C. Jacobs, “All-optical microdisk switch using EIT,” Opt. Express 21(5), 6169–6179 (2013).
[Crossref]

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

2012 (2)

G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
[Crossref]

A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

2010 (3)

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: Two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010).
[Crossref]

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
[Crossref]

N. Hayashi, A. Fujisawa, H. Kido, K. I. Takahashi, and M. Mitsunaga, “Interference between electromagnetically induced transparency and two-step excitation in three-level ladder systems,” J. Opt. Soc. Am. B 27(8), 1645–1650 (2010).
[Crossref]

2009 (1)

P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
[Crossref]

2008 (2)

L. Silvestri and G. Czajkowski, “Electromagnetically induced transparency in asymmetric double quantum wells in the transient regime,” Phys. Status Solidi (c) 5(7), 2412–2415 (2008).
[Crossref]

Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
[Crossref]

2006 (3)

S. M. Sadeghi, “Spatial modulation of electromagnetically induced transparency in quantum wells using monolayer growth islands,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1275–1282 (2006).
[Crossref]

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45(9), 2058–2071 (2006).
[Crossref]

2005 (3)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

P. Pérez-Millán, A. Díez, M. V. Andrés, D. Zalvidea, and R. Duchowicz, “Q-switched all-fiber laser based on magnetostriction modulation of a Bragg grating,” Opt. Express 13(13), 5046–5051 (2005).
[Crossref]

K. X. Guo and Y. B. Yu, “Nonlinear optical susceptibilities in Si/SiO2 parabolic quantum dots,” Chinese J. Phys. 43(5), 932–941 (2005).

2004 (2)

P. C. Ku, F. sedgwick, C. J. chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29(19), 2291–2293 (2004).
[Crossref]

Y. Wang and C. Q. Xu, “Switching-induced perturbation and influence on actively Q-switched fiber lasers,” IEEE J. Quantum Electron. 40(11), 1583–1596 (2004).
[Crossref]

2003 (2)

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003).
[Crossref]

A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
[Crossref]

2002 (2)

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002).
[Crossref]

2001 (1)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref]

2000 (2)

H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” Appl. Phys. Lett. 76(22), 3173–3175 (2000).
[Crossref]

D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000).
[Crossref]

1999 (3)

L. Luo and P.L. Chu, “Passive Q-switched erbium-doped fibre laser with saturable absorber,” Optics Communications 161(4-6), 257–263 (1999).
[Crossref]

B. S. Ham, S. M. Shahriar, and P. R. Hemmer, “Electromagnetically induced transparency over spectral hole-burning temperature in a rare-earth–doped solid,” J. Opt. Soc. Am. B 16(5), 801–804 (1999).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

1998 (2)

S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Physical review letters. 81(17), 3611–3614 (1998).
[Crossref]

H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998).
[Crossref]

1997 (4)

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

B. S. Ham, M. S. Shahriar, M. K. Kim, and P. R. Hemmer, “Frequency-selective time-domain optical data storage by electromagnetically induced transparency in a rare-earth-doped solid,” Opt. Lett. 22(24), 1849–1851 (1997).
[Crossref]

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. 144(4-6), 227–230 (1997).
[Crossref]

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

1995 (1)

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref]

1993 (2)

F. Seguin and T. K. Oleskevich, “Diode-pumped Q-switched fiber laser,” Opt. Eng. 32(9), 2036 (1993).
[Crossref]

A. Chandonnet and G. Larose, “High-power Q-switched erbium fiber laser using an all-fiber intensity modulator,” Opt. Eng. 32(9), 2031 (1993).
[Crossref]

1991 (1)

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

1990 (1)

S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

1980 (1)

R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980).
[Crossref]

Abi-Salloum, T. Y.

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: Two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010).
[Crossref]

Afzali-Kusha, A.

G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
[Crossref]

Agger, S.

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

Álvarez-Tamayo, R.I.

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

Andersen, T. V.

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

Andrés, M. V.

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

P. Pérez-Millán, A. Díez, M. V. Andrés, D. Zalvidea, and R. Duchowicz, “Q-switched all-fiber laser based on magnetostriction modulation of a Bragg grating,” Opt. Express 13(13), 5046–5051 (2005).
[Crossref]

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

Bajcsy, M.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003).
[Crossref]

Bananej, A.

P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
[Crossref]

Behroozi, C. H.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Bejan, D.

D. Bejan, “Electromagnetically induced transparency in double quantum dot under intense laser and magnetic fields: from Λ to Ξ configuration,” Eur. Phys. J. B 90(3), 54 (2017).
[Crossref]

Boller, K. J.

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

Camacho, R. M.

Cao Long, V.

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

Chandonnet, A.

A. Chandonnet and G. Larose, “High-power Q-switched erbium fiber laser using an all-fiber intensity modulator,” Opt. Eng. 32(9), 2031 (1993).
[Crossref]

Chang, S. W.

chang-Hasnain, C. J.

Chen, J.

Chikh-Bled, M.

A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

Chu, P.L.

L. Luo and P.L. Chu, “Passive Q-switched erbium-doped fibre laser with saturable absorber,” Optics Communications 161(4-6), 257–263 (1999).
[Crossref]

Chuang, S. L.

Clader, B. D.

Clarkson, W.A.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Codemard, C.A.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Cruz, J. L.

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

Czajkowski, G.

L. Silvestri and G. Czajkowski, “Electromagnetically induced transparency in asymmetric double quantum wells in the transient regime,” Phys. Status Solidi (c) 5(7), 2412–2415 (2008).
[Crossref]

Dai, Z.

A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
[Crossref]

H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002).
[Crossref]

Deng, C.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Díez, A.

Dinh Xuan, K.

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

Dong, C. B.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Dong, L.

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

Duchowicz, R.

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

P. Pérez-Millán, A. Díez, M. V. Andrés, D. Zalvidea, and R. Duchowicz, “Q-switched all-fiber laser based on magnetostriction modulation of a Bragg grating,” Opt. Express 13(13), 5046–5051 (2005).
[Crossref]

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

Duran-Sánchez, M.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Durán-Sánchez, M.

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

Dutton, Z.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Eilchi, M.

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

Espinosa-Martínez, M.

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

Fang, A.

A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
[Crossref]

Feng, X.

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

Field, J.

S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

Forchel, A.

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Fujisawa, A.

Ghafoorifard, H.

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

Glódz, M.

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

González-García, A.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Guina, M.

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Guo, K. X.

K. X. Guo and Y. B. Yu, “Nonlinear optical susceptibilities in Si/SiO2 parabolic quantum dots,” Chinese J. Phys. 43(5), 932–941 (2005).

Habibiyan, H.

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

Hakulinen, T.

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Ham, B. S.

Harris, S.

S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Physical review letters. 81(17), 3611–3614 (1998).
[Crossref]

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref]

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Harris, S.E.

S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

Hau, L. V.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

Hau, L.V.

M. Soljacic, J.D. Joannopoulos, and L.V. Hau, “Using electro-magnetically induced transparency in photonic crystal cavities to obtain large non-linear effects,” Google Patents, (2006).

Haus, J. W.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Hayashi, N.

He, Y.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Hedara, R.

A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

Hejaz, K.

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

Hemmer, P. R.

Hendrickson, S. M.

Huang, D. W.

D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000).
[Crossref]

Huy, B. N.

Ibarra-Escamilla, B.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

Ikhlef, A.

A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

Ilchi-Ghazaani, M.

M. Ilchi-Ghazaani and P. Parvin, “Temperature Effect on Yb-Doped Silica Fiber Laser Performance,” IEEE J. Quantum Electron. 56(5), 1–7 (2020).
[Crossref]

N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Impact of cavity loss on the performance of a single-mode Yb: silica MOFPA array,” Opt. Laser Technol. 65, 94–105 (2015).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Distributed scheme versus MOFPA array on the power scaling of a monolithic fiber laser,” IEEE J. Quantum Electron. 50(8), 1–11 (2014).
[Crossref]

P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
[Crossref]

Ilchi-Ghazani, M.

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Jacobs, B. C.

Jain, M.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref]

S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

Jang, J.N.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Jayarubi, J.

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019).
[Crossref]

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018).
[Crossref]

Jiang, H.

Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
[Crossref]

Jiang, Z.

Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
[Crossref]

A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
[Crossref]

H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002).
[Crossref]

Joannopoulos, J.D.

M. Soljacic, J.D. Joannopoulos, and L.V. Hau, “Using electro-magnetically induced transparency in photonic crystal cavities to obtain large non-linear effects,” Google Patents, (2006).

Kasapi, A.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref]

S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

Kee, H. H.

H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998).
[Crossref]

Keiding, S. R.

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

Kido, H.

Kim, M. K.

Kivistö, S.

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Kowalski, K.

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

Ku, P. C.

Kuzin, E. A.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Kuzin, E.A.

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

Kwong, D. L.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
[Crossref]

Lali-Dastjerdi, Z.

P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
[Crossref]

Larose, G.

A. Chandonnet and G. Larose, “High-power Q-switched erbium fiber laser using an all-fiber intensity modulator,” Opt. Eng. 32(9), 2031 (1993).
[Crossref]

Le Van, D.

Lee, C. W.

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019).
[Crossref]

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018).
[Crossref]

Lee, G. P.

H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998).
[Crossref]

Lees, G. P.

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

Li, T.

Li, X.

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

Li, X. M.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Liang, Q.

Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
[Crossref]

Liu, B.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Liu, C.

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref]

Liu, W. F.

D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000).
[Crossref]

Loudon, R.

R. Loudon, “The quantum theory of light,” OUP Oxford (2000).

Lu, L.

Lukin, M. D.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003).
[Crossref]

Luo, L.

L. Luo and P.L. Chu, “Passive Q-switched erbium-doped fibre laser with saturable absorber,” Optics Communications 161(4-6), 257–263 (1999).
[Crossref]

Luo, Z. F.

S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

Macfarlane, R. M.

R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980).
[Crossref]

Madanipour, K.

R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016).
[Crossref]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

Maya-Ordoñez, F.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Milonni, P. W.

P. W. Milonni, Fast light, slow light and left-handed light, (CRC Press, 2004).

Mitsunaga, M.

Mohammadian, S.

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

Mora, J.

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

Newson, T. P.

H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998).
[Crossref]

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

Nguyen, B.

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

Nilsson, J.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Okhotnikov, O.

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Oleskevich, T. K.

F. Seguin and T. K. Oleskevich, “Diode-pumped Q-switched fiber laser,” Opt. Eng. 32(9), 2036 (1993).
[Crossref]

Palinginis, P.

Parvin, P.

N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Temperature Effect on Yb-Doped Silica Fiber Laser Performance,” IEEE J. Quantum Electron. 56(5), 1–7 (2020).
[Crossref]

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Impact of cavity loss on the performance of a single-mode Yb: silica MOFPA array,” Opt. Laser Technol. 65, 94–105 (2015).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Distributed scheme versus MOFPA array on the power scaling of a monolithic fiber laser,” IEEE J. Quantum Electron. 50(8), 1–11 (2014).
[Crossref]

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
[Crossref]

Pérez-Millán, P.

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

P. Pérez-Millán, A. Díez, M. V. Andrés, D. Zalvidea, and R. Duchowicz, “Q-switched all-fiber laser based on magnetostriction modulation of a Bragg grating,” Opt. Express 13(13), 5046–5051 (2005).
[Crossref]

Pesrson, G.N.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Peter, A. J.

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019).
[Crossref]

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018).
[Crossref]

Philippov, V.N.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Poozesh, R.

R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016).
[Crossref]

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

Pottiez, O.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

Powers, P. E.

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Ram, R.

H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” Appl. Phys. Lett. 76(22), 3173–3175 (2000).
[Crossref]

Richardson, D. J.

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

Rößner, K.

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Rostami, A.

G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
[Crossref]

Rostami, G.

G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
[Crossref]

Russo, N. A.

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

Sadeghi, S. M.

S. M. Sadeghi, “Spatial modulation of electromagnetically induced transparency in quantum wells using monolayer growth islands,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1275–1282 (2006).
[Crossref]

Sahu, J.K.

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

Schmidt, H.

H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” Appl. Phys. Lett. 76(22), 3173–3175 (2000).
[Crossref]

Scully, M. O.

M. O. Scully and M.S. Zubairy, “Quantum optics,” 1999, American Association of Physics Teachers.

sedgwick, F.

Seguin, F.

F. Seguin and T. K. Oleskevich, “Diode-pumped Q-switched fiber laser,” Opt. Eng. 32(9), 2036 (1993).
[Crossref]

Shafii Mousavi, N.

N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020).
[Crossref]

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

Shahabadi, M.

G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
[Crossref]

Shahriar, M. S.

B. S. Ham, M. S. Shahriar, M. K. Kim, and P. R. Hemmer, “Frequency-selective time-domain optical data storage by electromagnetically induced transparency in a rare-earth-doped solid,” Opt. Lett. 22(24), 1849–1851 (1997).
[Crossref]

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. 144(4-6), 227–230 (1997).
[Crossref]

Shahriar, S. M.

Shelby, R. M.

R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980).
[Crossref]

Silvestri, L.

L. Silvestri and G. Czajkowski, “Electromagnetically induced transparency in asymmetric double quantum wells in the transient regime,” Phys. Status Solidi (c) 5(7), 2412–2415 (2008).
[Crossref]

Soljacic, M.

M. Soljacic, J.D. Joannopoulos, and L.V. Hau, “Using electro-magnetically induced transparency in photonic crystal cavities to obtain large non-linear effects,” Google Patents, (2006).

Szonert, J.

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

Takahashi, K. I.

Tang, H.

Tang, J.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Taverner, D.

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

Tuan, A. N.

Varmazyari, V.

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

Vatani, V.

R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016).
[Crossref]

Verdeyen, J. T.

J. T. Verdeyen, “Laser electronics,” laser electronics (1989).

Wang, H.

Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
[Crossref]

P. C. Ku, F. sedgwick, C. J. chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29(19), 2291–2293 (2004).
[Crossref]

Wang, J.

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

Wang, T.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Wang, Y.

Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45(9), 2058–2071 (2006).
[Crossref]

Y. Wang and C. Q. Xu, “Switching-induced perturbation and influence on actively Q-switched fiber lasers,” IEEE J. Quantum Electron. 40(11), 1583–1596 (2004).
[Crossref]

Wong, C. W.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
[Crossref]

Xie, J.

Xu, C. Q.

Y. Wang and C. Q. Xu, “Modeling and optimization of Q-switched double-clad fiber lasers,” Appl. Opt. 45(9), 2058–2071 (2006).
[Crossref]

Y. Wang and C. Q. Xu, “Switching-induced perturbation and influence on actively Q-switched fiber lasers,” IEEE J. Quantum Electron. 40(11), 1583–1596 (2004).
[Crossref]

Xu, H.

A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
[Crossref]

H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002).
[Crossref]

Yamamoto, Y.

S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Physical review letters. 81(17), 3611–3614 (1998).
[Crossref]

Yan, W.

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

Yang, C. C.

D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000).
[Crossref]

Yang, L.

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

Yang, X.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
[Crossref]

Yannoni, C. S.

R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980).
[Crossref]

Yin, G. Y.

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref]

S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

Yu, M.

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
[Crossref]

Yu, Y. B.

K. X. Guo and Y. B. Yu, “Nonlinear optical susceptibilities in Si/SiO2 parabolic quantum dots,” Chinese J. Phys. 43(5), 932–941 (2005).

Zalvidea, D.

Zhang, L.

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

Zhao, M.

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

Zhou, H. L.

Zibrov, A. S.

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003).
[Crossref]

Zubairy, M.S.

M. O. Scully and M.S. Zubairy, “Quantum optics,” 1999, American Association of Physics Teachers.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

H. Schmidt and R. Ram, “All-optical wavelength converter and switch based on electromagnetically induced transparency,” Appl. Phys. Lett. 76(22), 3173–3175 (2000).
[Crossref]

Chinese J. Phys. (1)

K. X. Guo and Y. B. Yu, “Nonlinear optical susceptibilities in Si/SiO2 parabolic quantum dots,” Chinese J. Phys. 43(5), 932–941 (2005).

Electron. Lett. (2)

H. H. Kee, G. P. Lee, and T. P. Newson, “Narrow linewidth CW and Q-switched erbium-doped fibre loop laser,” Electron. Lett. 34(13), 1318–1319 (1998).
[Crossref]

G. P. Lees, D. Taverner, D. J. Richardson, L. Dong, and T. P. Newson, “Q-switched erbium doped fibre laser utilising a novel large mode area fibre,” Electron. Lett. 33(5), 393–394 (1997).
[Crossref]

Eur. Phys. J. B (1)

D. Bejan, “Electromagnetically induced transparency in double quantum dot under intense laser and magnetic fields: from Λ to Ξ configuration,” Eur. Phys. J. B 90(3), 54 (2017).
[Crossref]

Eur. Phys. J. D (1)

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well in the influence of laser field intensity,” Eur. Phys. J. D 73(3), 63 (2019).
[Crossref]

IEEE J. Quantum Electron. (4)

M. Ilchi-Ghazaani and P. Parvin, “Distributed scheme versus MOFPA array on the power scaling of a monolithic fiber laser,” IEEE J. Quantum Electron. 50(8), 1–11 (2014).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Temperature Effect on Yb-Doped Silica Fiber Laser Performance,” IEEE J. Quantum Electron. 56(5), 1–7 (2020).
[Crossref]

Y. Wang and C. Q. Xu, “Switching-induced perturbation and influence on actively Q-switched fiber lasers,” IEEE J. Quantum Electron. 40(11), 1583–1596 (2004).
[Crossref]

V. Varmazyari, P. Parvin, M. Eilchi, N. Shafii Mousavi, H. Habibiyan, and H. Ghafoorifard, “An adjustable EIT-based FBG in Yb: silica master-oscillator fiber power-amplifier system,” IEEE J. Quantum Electron. 54(4), 1–9 (2018).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

S. M. Sadeghi, “Spatial modulation of electromagnetically induced transparency in quantum wells using monolayer growth islands,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1275–1282 (2006).
[Crossref]

X. Yang, M. Yu, D. L. Kwong, and C. W. Wong, “Coupled resonances in multiple silicon photonic crystal cavities in all-optical solid-state analogy to electromagnetically induced transparency,” IEEE J. Sel. Top. Quantum Electron. 16(1), 288–294 (2010).
[Crossref]

IEEE Photonics Technol. Lett. (1)

D. W. Huang, W. F. Liu, and C. C. Yang, “Q-switched all-fiber laser with an acoustically modulated fiber attenuator,” IEEE Photonics Technol. Lett. 12(9), 1153–1155 (2000).
[Crossref]

International Journal of Computer Science Issues (IJCSI) (1)

A. Ikhlef, R. Hedara, and M. Chikh-Bled, “Uniform fiber Bragg grating modeling and simulation used matrix transfer method,” International Journal of Computer Science Issues (IJCSI) 9(1), 368 (2012).

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

Y. He, T. Wang, W. Yan, X. M. Li, C. B. Dong, J. Tang, and B. Liu, “All-optical switching based on the electromagnetically induced transparency effect of an active photonic crystal microcavity,” J. Mod. Opt. 61(5), 403–408 (2014).
[Crossref]

J. Opt. Soc. Am. B (3)

Laser Phys. (1)

N. Shafii Mousavi, P. Parvin, and M. Ilchi-Ghazaani, “Modeling of a Q-switched master oscillator power amplifier fiber laser and gain saturation properties,” Laser Phys. 30(8), 085101 (2020).
[Crossref]

Nature (3)

C. Liu, Z. Dutton, C. H. Behroozi, and L. V. Hau, “Observation of coherent optical information storage in an atomic medium using halted light pulses,” Nature 409(6819), 490–493 (2001).
[Crossref]

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397(6720), 594–598 (1999).
[Crossref]

M. Bajcsy, A. S. Zibrov, and M. D. Lukin, “Stationary pulses of light in an atomic medium,” Nature 426(6967), 638–641 (2003).
[Crossref]

Opt. Commun. (3)

N. A. Russo, R. Duchowicz, J. Mora, J. L. Cruz, and M. V. Andrés, “High-efficiency Q-switched erbium fiber laser using a Bragg grating-based modulator,” Opt. Commun. 210(3-6), 361–366 (2002).
[Crossref]

T. V. Andersen, P. Pérez-Millán, S. R. Keiding, S. Agger, R. Duchowicz, and M. V. Andrés, “All-fiber actively Q-switched Yb-doped laser,” Opt. Commun. 260(1), 251–256 (2006).
[Crossref]

B. S. Ham, P. R. Hemmer, and M. S. Shahriar, “Efficient electromagnetically induced transparency in a rare-earth doped crystal,” Opt. Commun. 144(4-6), 227–230 (1997).
[Crossref]

Opt. Eng. (2)

F. Seguin and T. K. Oleskevich, “Diode-pumped Q-switched fiber laser,” Opt. Eng. 32(9), 2036 (1993).
[Crossref]

A. Chandonnet and G. Larose, “High-power Q-switched erbium fiber laser using an all-fiber intensity modulator,” Opt. Eng. 32(9), 2031 (1993).
[Crossref]

Opt. Express (2)

Opt. Fiber Technol. (2)

R. Poozesh, K. Madanipour, and V. Vatani, “Spectral interference fringes in chirped large-mode-area fiber Bragg gratings,” Opt. Fiber Technol. 31, 134–137 (2016).
[Crossref]

S. Mohammadian, P. Parvin, M. Ilchi-Ghazani, R. Poozesh, and K. Hejaz, “Measurement of gain and saturation parameters of a single-mode Yb: silica fiber amplifier,” Opt. Fiber Technol. 19(5), 446–455 (2013).
[Crossref]

Opt. Laser Technol. (3)

P. Parvin, M. Ilchi-Ghazaani, A. Bananej, and Z. Lali-Dastjerdi, “Small signal gain and saturation intensity of a Yb: Silica fiber MOPA system,” Opt. Laser Technol. 41(7), 885–891 (2009).
[Crossref]

M. Ilchi-Ghazaani and P. Parvin, “Impact of cavity loss on the performance of a single-mode Yb: silica MOFPA array,” Opt. Laser Technol. 65, 94–105 (2015).
[Crossref]

A. González-García, B. Ibarra-Escamilla, O. Pottiez, E. A. Kuzin, F. Maya-Ordoñez, M. Duran-Sánchez, C. Deng, J. W. Haus, and P. E. Powers, “High efficiency, actively Q-switched Er/Yb fiber laser,” Opt. Laser Technol. 48, 182–186 (2013).
[Crossref]

Opt. Lett. (2)

Optics Communications (1)

L. Luo and P.L. Chu, “Passive Q-switched erbium-doped fibre laser with saturable absorber,” Optics Communications 161(4-6), 257–263 (1999).
[Crossref]

Photonics and Nanostructures-Fundamentals and Applications. (1)

G. Rostami, M. Shahabadi, A. Afzali-Kusha, and A. Rostami, “EIT based tunable metal composite spherical nanoparticles,” Photonics and Nanostructures-Fundamentals and Applications. 10(1), 102–111 (2012).
[Crossref]

Phys. A (1)

Q. Liang, H. Jiang, H. Wang, and Z. Jiang, “The manipulating of electromagnetically induced transparency in Pr3+: Y2SiO5 crystal by a rf-driving field,” Phys. A 387(1), 108–114 (2008).
[Crossref]

Phys. B (2)

A. Fang, H. Xu, Z. Dai, and Z. Jiang, “Theoretical study of electromagnetically induced transparency in Er3+: YAlO3 crystal,” Phys. B 328(3-4), 204–210 (2003).
[Crossref]

J. Jayarubi, A. J. Peter, and C. W. Lee, “Electromagnetically induced transparency in a GaAs/InAs/GaAs quantum well,” Phys. B 550, 184–188 (2018).
[Crossref]

Phys. Lett. A (1)

H. Xu, Z. Dai, and Z. Jiang, “Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+: YAG crystal,” Phys. Lett. A 294(1), 19–25 (2002).
[Crossref]

Phys. Rev. A (1)

T. Y. Abi-Salloum, “Electromagnetically induced transparency and Autler-Townes splitting: Two similar but distinct phenomena in two categories of three-level atomic systems,” Phys. Rev. A 81(5), 053836 (2010).
[Crossref]

Phys. Rev. B (1)

R. M. Shelby, R. M. Macfarlane, and C. S. Yannoni, “Optical measurement of spin-lattice relaxation of dilute nuclei: La F 3: Pr 3+,” Phys. Rev. B 21(11), 5004–5011 (1980).
[Crossref]

Phys. Rev. Lett. (3)

A. Kasapi, M. Jain, G. Y. Yin, and S. E. Harris, “Electromagnetically induced transparency: propagation dynamics,” Phys. Rev. Lett. 74(13), 2447–2450 (1995).
[Crossref]

K. J. Boller, A. Imamoğlu, and S. E. Harris, “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66(20), 2593–2596 (1991).
[Crossref]

S. E. Harris, J. Field, and A. Imamoğlu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64(10), 1107–1110 (1990).
[Crossref]

Phys. Status Solidi (c) (1)

L. Silvestri and G. Czajkowski, “Electromagnetically induced transparency in asymmetric double quantum wells in the transient regime,” Phys. Status Solidi (c) 5(7), 2412–2415 (2008).
[Crossref]

Physical review letters. (1)

S. Harris and Y. Yamamoto, “Photon switching by quantum interference,” Physical review letters. 81(17), 3611–3614 (1998).
[Crossref]

Physics Today (1)

K. Kowalski, V. Cao Long, K. Dinh Xuan, M. Głódź, B. Nguyen, and J. Szonert, “Electromagnetically induced transparency,” Physics Today 50(7), 36–42 (1997).
[Crossref]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77(2), 633–673 (2005).
[Crossref]

Other (11)

M. O. Scully and M.S. Zubairy, “Quantum optics,” 1999, American Association of Physics Teachers.

P. W. Milonni, Fast light, slow light and left-handed light, (CRC Press, 2004).

https://www.rp-photonics.com/fiber_bragg_gratings.html .

L. Zhang, J. Wang, X. Feng, L. Yang, X. Li, and M. Zhao, “Optical switching property of electromagnetically induced transparency in a lambda system,” In Eighth International Symposium on Optical Storage and 2008 International Workshop on Information Data Storage, vol. 7125, p. 712514. International Society for Optics and Photonics (2009).

J. T. Verdeyen, “Laser electronics,” laser electronics (1989).

R. Loudon, “The quantum theory of light,” OUP Oxford (2000).

S.E. Harris, G. Y. Yin, A. Kasapi, M. Jain, and Z. F. Luo, “Electromagnetically induced transparency,” in Coherence and Quantum Optics VII. SpringerC p. 295–304 (1996).

M. Soljacic, J.D. Joannopoulos, and L.V. Hau, “Using electro-magnetically induced transparency in photonic crystal cavities to obtain large non-linear effects,” Google Patents, (2006).

V.N. Philippov, J.K. Sahu, C.A. Codemard, W.A. Clarkson, J.N. Jang, J. Nilsson, and G.N. Pesrson,“All-fiber 1.15-mJ pulsed eye-safe optical source. in Fiber lasers: technology, systems, and applications,” International Society for Optics and Photonics. (2004).

R.I. Álvarez-Tamayo, M. Durán-Sánchez, O. Pottiez, B. ibarra-Escamilla, E.A. Kuzin, and M. Espinosa-Martínez, “Active Q-switched fiber lasers with single and dual-wavelength operation,” InTech (2016).

S. Kivistö, T. Hakulinen, M. Guina, K. Rößner, A. Forchel, and O. Okhotnikov, “2 watt 2 µm Tm/Ho fiber laser system passively Q-switched by antimonide semiconductor saturable absorber,” in Solid State Lasers and Amplifiers III International Society for Optics and Photonics (2008).

Supplementary Material (1)

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Figures (8)

Fig. 1.
Fig. 1. Typical Λ-type EIT system with Rabi frequencies Ωp and Ωc driven by probe and control fields respectively. Note that the spontaneous decay rates ${\mathrm{\gamma }_{\textrm{ij}}}$ labels the transition $|\textrm{i}\rangle $ and $|\textrm{j}\rangle $ states and Δp and Δc ascertain the detuning of the probe and control fields [49]
Fig. 2.
Fig. 2. a) Energy diagram of a three-level Λ-type EIT nanocrystal b) EIT material incorporated in FBG as a number of periodic (nL, nH) layers. Note that nL/nH stand for the layers alongside FBG for low / high refraction indices in FBG and Λ denotes to be the grating period. The control field in terms of successive ultra-short pulses irradiate whole FBG length (L) to attain the adequate laser intensity required for EIT process. Typical values of the parameters are given as below: nL=1.4415, nH=1.4589, Λ = 375 nm, L=75 µm.
Fig. 3.
Fig. 3. a) absorption and b) phase shift versus probe pulse detuning under two distinct cases, i.e., Ωc=0 (no control field) and at the attendance of control field Ωc=1 THz (typical)
Fig. 4.
Fig. 4. Spectral transmission in terms of detuning versus, a) Rabi frequency of control field (N=1×1021 m−3, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), b) dopant concentration of EIT nanocrystals (Ωc=1 THz, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), c) FBG length (Ωc = 1 THz, N=1×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.24$ THz) and d) spontaneous decay rate (Ωc = 1 THz, N=1×1021 m−3, L=187.5 µm) in steady-state mode.
Fig. 5.
Fig. 5. Time-dependent transmission versus (a) Rabi frequency of control at (N=1×1021 m−3, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), (b) nanocrystal concentration at (Ωc=1 THz, L=187.5 µm, ${\mathrm{\gamma }_{31}} = 0.24$ THz), (c) FBG length at (Ωc = 1 THz, N=1×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.24$ THz) and (d) spontaneous decay rate at (Ωc = 1 THz, N=1×1021 m−3, L=187.5 µm). The insets display the variation of rise time in terms of four varying parameters of interest, respectively.
Fig. 6.
Fig. 6. Typical transmission and rise time in terms of, a) Rabi frequency of control (case I: N=6×1021 m−3, L=262.5 µm, ${\mathrm{\gamma }_{31}} = 0.3$ THz; case II: N=1×1021 m−3, L=37.5 µm, ${\mathrm{\gamma }_{31}} = 0.05$ THz), b) EIT concentration (case I: Ωc = 1 THz, L=262.5 µm, ${\mathrm{\gamma }_{31}} = 0.3$ THz; case II: Ωc = 3 THz, L=37.5 µm, ${\mathrm{\gamma }_{31}} = 0.05$ THz), c) FBG length (case I: Ωc = 1 THz, N=6×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.3$ THz; case II: Ωc = 3 THz, N=1×1021 m−3, ${\mathrm{\gamma }_{31}} = 0.05$ THz) and d) decay rate in Si nanocrystals (case I: Ωc = 1 THz, N=6×1021 m−3, L=262.5 µm; case II: Ωc = 3 THz, N=1×1021 m−3, L=37.5 µm). Note that case II values are determined at large Ωc, low N, short L where as ${\mathrm{\gamma }_{31}}$ is not very sensitive to trise.
Fig. 7.
Fig. 7. a) Probe wavelength (and ωp) versus decay rate ${\mathrm{\gamma }_{31}}$ (Eq. (6)), b) Low index (nL) and FBG reflectance (Eq. (1)1 and 13) in terms of Rabi frequency of control, inset: nL versus under whole range of Ωc, a portion of nL is highlighted in the interval of 0.7–1.2 THz, c) corresponding EIT absorbance versus Ωc, d) probe wavelength of FBG versus Ωc. Note that nL increases to equate nH in terms of Ωc at point Q where FBG reflectance entirely vanishes. Simultaneously, the probe wavelength slightly shifts from 1.08 to 1.09 µm at Q.
Fig. 8.
Fig. 8. a) Time-dependent transmission of probe field, b) Temporal transmittance of FBG-EIT by applying a short pulse of control field to model the fast switching performance. Note that trise, tcp and tfall denote to be rise time, duration of control pulse and fall time, respectively.

Tables (1)

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Table 1. Typical EIT parameters used in the FBG modeling [42,55]

Equations (17)

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$$_{{\Delta _p} = {\omega _{31}} - {\omega _p}}$$
$$_{{\Delta _c} = {\omega _{32}} - {\omega _c}}$$
$${\Omega _c} = \frac{{{\mu _{23}}{E_c}}}{{2\hbar }}$$
$${\Omega _p} = \frac{{{\mu _{13}}{E_p}}}{{2\hbar }}$$
$${N_3}(t) = {N_3}(0)\textrm{exp} ( - 2{\gamma _{31}}t)$$
$${\gamma _{31}} = \frac{{\omega _p^3{e^2}\mu _{13}^2}}{{3\pi {\varepsilon _0}\hbar {c^3}}}$$
$$\chi = \frac{{N\mu _{31}^22{\rho _{31}}}}{{{\varepsilon _0}\hbar {\Omega _p}}} = \frac{{N\mu _{31}^2}}{{{\varepsilon _0}\hbar }}\frac{{ - ({\Delta _p} - {\Delta _c}) + i{\gamma _{21}}}}{{\Omega _c^2 + ({\gamma _{31}} - i{\Delta _p})({\gamma _{21}} + i({\Delta _p} - {\Delta _c}))}}$$
$$\chi = \frac{{N\mu _{31}^22{\rho _{31}}}}{{{\varepsilon _0}\hbar {\Omega _p}}} = \frac{{N\mu _{31}^2}}{{{\varepsilon _0}\hbar }} \times \left[ {\frac{{i{\Omega _p}{e^{i{\Delta _p}t}}(({\gamma_{21}} + i({\Delta _p} - {\Delta _c}))}}{{\Omega _c^2{e^{i2{\Delta _c}t}} + ({\gamma_{31}} + i2{\Delta _p})({\gamma_{21}} + i({\Delta _p} - {\Delta _c}))}}} \right]$$
$$\alpha = {\mathop{\rm Im}\nolimits} (\chi ) \times L$$
$$T = \textrm{exp} ( - {\mathop{\rm Im}\nolimits} (\chi ) \times L) = \textrm{exp} ( - \alpha )$$
$$n = \sqrt {\frac{{n_0^2 + {\textrm{Re}} \chi + \sqrt {{{(n_0^2 + {\textrm{Re}} (\chi ))}^2} + {\mathop{\rm Im}\nolimits} {{(\chi )}^2}} }}{2}} $$
$$\lambda = 2{n_{eff}}\Lambda $$
$${I_c} = \frac{1}{2}c{n_L}{\varepsilon _0}E_c^2$$
$$R(L,\lambda ) = {\tanh ^2}(\gamma L)$$
$$\gamma = \sqrt {{\kappa ^2} - \Delta {\beta ^2}} $$
$$\kappa = \frac{{\pi \Delta {n_{eff}}}}{\lambda }$$
$$\Delta \beta = \beta - \frac{\pi }{\Lambda }$$