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Abstract
We present low-loss tungstate-tellurite fibers doped with Er3+ for laser operation near 2.7 μm. Two “ultra-dry” preforms with cores of TeO2-WO3-La2O3-Bi2O3 glasses doped with 0.4 and 4 mol% of Er2O3 and undoped TeO2-WO3-La2O3 claddings were produced. High-quality multimode fibers were fabricated and characterized. Photoluminescence spectra of about 2.7 μm (4I11/2 → 4I13/2 transition) and about 1.6 μm (4I13/2 → 4I15/2 transition) were measured under excitation by diode pumping at 975 nm (4I15/2 → 4I11/2 transition). The production test and the theoretical investigation of gain-switched laser generation showed potential applicability of the designed samples in the spectral range of interest. Prospective application of single-mode fibers based on the developed glass preforms was also simulated. A feasibility of pulse train generation was demonstrated even for a rough choice of parameters, which is very encouraging for experimental implementation.
© 2017 Optical Society of America
1. Introduction
Mid-IR laser sources have important applications in both basic science and industry, including noninvasive medical diagnostics, laser scalpel, free-space communication, spectroscopy, and remote sensing [1]. The 2.7-3 μm spectral range is characterized by a very high absorption of hydroxyl groups, so lasers operating at these wavelengths are in great demand for medical applications.
Significant progress was demonstrated in recent years for laser systems based on nonlinear optical conversion in chalcogenide, tellurite, fluoride, and germanate fibers, mainly due to the supercontinuum generation (see, for example [2–10],). However, the use of gain fibers doped with rare-earth (RE) ions promises still more progress in creating powerful mid-IR fiber laser sources and simplicity of design. At present, the technologies for creating continuous wave (CW) and pulsed fiber lasers operating at about 3 μm are well developed for fluoride ZBLAN fibers (see [11–14] and the reviews [15,16] with references therein). For pulsed Q-switched lasers, the largest average power achieved is 12 W with pulse energy up to 0.1 mJ [17] and the highest peak power attained so far is 10 kW with pulse energy exceeding 0.5 mJ [18].
However, along with the advantages of high transparency in the mid-IR region and substantial solubility of RE ions, fluoride glasses have pronounced shortcomings. They are mechanically weak, tend to crystallize and react with atmospheric moisture, are characterized by low glass transition temperatures (250-300 °C) and a large coefficient of thermal expansion [5].
An alternative to fluoride glasses as a medium for the laser generation of about 2.7 μm could be tellurium dioxide based glasses. Tellurite glasses have a higher phonon energy, but they are stronger mechanically and possess better chemical stability. Many compositions among the most actively investigated zinc-tellurite and tungstate-tellurite systems are resistant to crystallization. Luminescence in the 2.7-μm region in tellurite glasses was first observed in [19]. The Er-doped 75TeO2-20ZnO-5Na2O-La2O3 glass exhibited strong fluorescence both at 1.5 μm and 2.7 μm. Several research groups produced Er-doped TeO2-based glasses and fibers and studied their properties, including spectroscopic parameters for the 4I11/2 → 4I13/2 energy transition near 2.7 μm [20–25]. Note that the obtained emission characteristics, good thermal stability, and mechanical properties make Er-doped tellurite fibers promising host matrices for 2.7 μm lasing.
The tungstate-tellurite glass was chosen as a matrix in this study for the following reasons. In comparison with other tellurite glass compositions the TeO2-WO3-La2O3-Bi2O3 (TWLB) system has the benefits of higher glass transition and softening temperatures, higher stability against crystallization, and lower thermal expansion. The optical and thermo-physical properties of tungstate-tellurite glasses can be improved significantly due to application of high-purity starting materials [26]. For producing step-index fibers refractive index can be easily modified by adding bismuth oxide, which significantly increases the refractive index, but practically does not affect the glass transition temperature and crystallization stability at low concentrations [27, 28]. One of the main advantages of tungstate-tellurite glasses is a possibility of creating high concentrations of lanthanides (up to 10 mol% of oxide) [29]. High La2O3 content leads to increased glass transition and softening temperatures and better crystallization stability. Some of La2O3-doped glasses are extremely stable against crystallization inside a wide range of La2O3 concentrations. According to differential scanning calorimetry (DSC) measurements, there was no crystallization in glasses containing 2.5-4 mol% La2O3 at a heating rate of 5 and 10 К/min. Glasses containing less than 2.5 mol% La2O3 are not resistant to crystallization and are not suitable for producing quality fibers [30]. Moreover, the presence of lanthanum oxide in glass composition allows introducing active additives of RE oxides other than La2O3 without significant changes in the physicochemical properties. So, thermal effects of crystallization were not observed within the series of Er-doped TWLB glasses up to 4 mol% Er2O3 at a heating rate of 10 К/min and became apparent at a slow heating rate of 5 К/min for highest Er2O3 concentrations only [31].
Nevertheless, Er-doped tellurite fiber master oscillators at 2.7 μm have not been reported yet, although an Er-doped tellurite fiber master oscillator at 1.56 μm at the 4I13/2 → 4I15/2 transition was first demonstrated 20 years ago [32]. One of the reasons of the absence of tellurite fiber lasers at 2.7 μm is the problem of hydroxyl groups which are strongly absorbing in the range of interest. The second reason is that, under CW pumping, population inversion is hard to achieve in steady-state because the lifetime τ3 of the 4I11/2 energy level is significantly shorter than the lifetime τ2 of the 4I13/2 level. Here we will demonstrate the solution of the first problem by producing high-quality “ultra-dry” TeO2-based samples and will propose to overcome the second challenge by creating on their basis gain-switched lasers with a pulse energy up to 0.1 mJ, a pump pulse duration of about τ3 or shorter, and with a repetition rate smaller than 1/τ2. To the best of our knowledge, the possibilities of obtaining pulse train generation have not been studied for Er-doped tellurite fibers at the 4I11/2 → 4I13/2 energy transition.
Recently, we have successfully developed and studied passive TWLB/TWL step-index multimode fibers with optical loss as low as 0.5 dB/m at 2.7 μm [33], and a low-loss TWL microstructured glass fiber and demonstrated its applicability for nonlinear pulse conversion [33,34]. Here we will present “water-free” TeO2-WO3-La2O3-Bi2O3-Er2O3 (TWLBE) glasses activated by Er3+ and multimode fibers, and report their characterization including spectroscopic measurements. Numerical simulation of laser action in multimode and single-mode active fibers will be performed using experimental data. A home-made computer code has been developed for this purpose. A wide range of parameters will be analyzed, and more preferable ones will be found.
2. Production and characterization of Er-doped TeO2-WO2-La2O3-Bi2O3 glasses and fibers
2.1 Glasses, preforms, and fibers production
72TeO2-24WO3-4La2O3 glasses (cladding composition, TWL) and 71.2TeO2-23.7WO3-(4-x)La2O3-1.1Bi2O3-xEr2O3 glasses where х = 0.4; 4 mol% (core compositions, TWLBE-0.4, Erbium ions concentration is NEr = 1.5⋅1020 cm−3 and TWLBE-4, NEr = 15⋅1020 cm−3) were produced by melting the oxides batch inside a sealed silica chamber at a temperature of 800 °C in the atmosphere of purified oxygen. The TeO2 oxide prepared by an original technique, as well as commercially produced high-purity WO3, La2O3, Bi2O3 and Er2O3 were used for producing the glasses. The total content of the 3d-transition metal impurities in each initial oxide and in glasses did not exceed 0.1-2 ppm wt [35]. The RE oxide was introduced at the stage of charge mixing. The synthesis of the glasses was carried out in platinum crucibles for several hours with recurrent stirring of the melts. Then casts were formed from the melts and annealed at a glass transition temperature (~400 °C). After cooling to room temperature, the casts were mechanically cut, ground and polished. A number of samples of different thicknesses were made for spectroscopic and luminescent studies.
The monolithic double-layer preforms for fiber production with core of TWLBE-0.4 (Preform-0.4) and TWLBE-4 (Preform-4) glasses and cladding of TWL glass were fabricated by the technique of simultaneous melt extrusion. Preforms for producing tellurite fibers with a step profile of refractive index were obtained in the form of double-layered castings in which the “dry” core is protected from external impact by the cladding at all stages of optical fiber fabrication. Note that a similar technique for preform production was used in the earlier works [36,37]. Typical sizes of our monolithic preforms are the following: outer diameter 16 mm, core diameter 5-7 mm, and length 50-60 mm (see Fig. 1(a)). The difference in the core diameter along the preform is explained by faster cooling of the lower part of the melt of the cladding glass during preform molding. After cutting and polishing the preforms had the following dimensions: 16 mm outside diameter, 51 and 60 mm length, and 4-6 mm core diameter (see Fig. 1(b,c)). The physical properties of the preforms are presented in Table 1.
Fig. 1 (a) Scheme of preforms for producing tellurite fibers. (b) Photo of Preform-0.4 with diameter of 16 mm and length of 51 mm. (c) Photo of Preform-4 with diameter of 16 mm and length of 60 mm
Table 1. Physical properties of the produced preforms
By stretching Preform-4, that is most suitable for generation at 2.7 μm from the point of view of highest erbium concentration, a multimode fiber was successfully manufactured in an atmosphere of purified oxygen using a protective polymer coating. The strength of the obtained fiber (core diameter 50 μm, cladding diameter 130 μm, numerical aperture 0.12) is sufficient for research and applications.
2.2 DSC measurements
The NETZSCH STA - 409 PC Luxx instrument was used for DSC studies. Measurements were performed in an argon flow with a flow rate of 60 ml/min, at the heating rate of 10 К/min within the temperature range of 200-700 °C. Glass samples of TWLBE-0.4 and TWLBE-4 core compositions were disc-shaped and had a diameter of several mm and mass of about 30-50 mg. The measurement accuracy was estimated to be ± 3 °C.
The addition of erbium oxide had almost no impact on the glass transition temperature and on the resistance to crystallization for TWL and TWLB glasses [30] (see Fig. 2). The thermograms of the DSC obtained at a heating rate of 10 K/min do not feature clear thermal effects of crystallization and melting of the crystalline phase. The glass transition temperature remained unchanged with increasing concentration of erbium oxide. This allowed doping of the fiber core with erbium ions without changing the other properties.
However, it should be noted that at slower heating rates, for example at a heating rate of 5 K/min, glasses with a high erbium oxide content tended to crystallize [31]. Therefore, samples were formed and fibers were drawn under the condition of minimum exposure within the temperature range of possible crystallization.
2.3 Transmission spectra, absorption of hydroxyl groups, and optical loss
The visible spectra were recorded by the spectrophotometer Lambda 900 and the IR spectrum was recorded by the IR Nicolet 6700 Fourier spectrometer. The transmission spectra of TWL, TWLBE-0.4, and TWLBE-4 glass samples of different thicknesses are shown in Fig. 3.
Fig. 3 (a) Visible and near IR transmission spectra of TWL, TWLBE-0.4, TWLBE-4 glass samples 0.2 cm thick. (b) IR transmission spectra of pieces of Preform 0.4 (TWL, TWLBE-0.4 glasses) and Preform 4 (TWL, TWLBE-4 glasses)
The TWL glass containing lanthanum oxide is highly transparent in the visible and near-IR regions, the absence of characteristic absorption bands of 3d-transition metals and RE elements in the presented wavelength region confirms the low content of the impurities. The spectra of TWLBE-0.4 and TWLBE-4 glass samples are abundant with characteristic erbium ion absorption bands. The short-wave transparency edge for all studied glass compositions is located at about 450 nm (see Fig. 3(a)). In the studies of luminescent characteristics of glasses and fibers, the absorption band corresponding to the 4I15/2-4I11/2 transition with a maximum of about 0.97 µm was chosen for pumping (see Fig. 3(a)). The absorption coefficient in this band is directly proportional to the concentration of Er2O3.
For evaluation of the hydroxyl groups content, the thicker sections of two-layer preforms for step-index tellurite fiber production were studied by the IR spectroscopy. The transmission spectra of the cores doped with 0.4 and 4 mol% Er2O3 and the claddings of the preforms are presented in Fig. 3(b). The high transparency range of the glasses is up to the wavelength of ~5 µm. A sharp fall of transparency becomes apparent after the wavelength of 4.5 µm and is attributed to multiphonon absorption.
It can be seen from the spectra that the samples have a low content of hydroxyl groups, OH absorption bands with maxima at about 1.5, 2.3, and 4.6 μm are not detected. The main absorption band of OH with a maximum at about 3 μm is very weak. The Er3+ absorption band in the core spectra is observed at 1.55 μm, its intensity depends on erbium oxide concentration and sample thickness. It can be noted that the samples are highly transparent; there are no characteristic absorption bands of other impurities.
For all the samples studied, the spectral dependences of the hydroxyl groups absorption at the maximum of the main band were calculated using the Beer–Lambert–Bouguer law ln(I0/I) (see Fig. 4), where I is the intensity of light that has passed through the sample and I0 is the initial light intensity (with the Fresnel reflection loss taken into account). For the glasses obtained by melting the batch in crucibles inside a sealed silica glass chamber in the atmosphere of purified oxygen, values of the absorption coefficient are very low. In addition, they are very close between the core and the cladding glasses of the same preform due to the same melting conditions for every pair. This means that significant concentrations of erbium do not impair the effectiveness of our drying technique. For the considered core compositions, the absorption amounts to 0.004 and 0.009 for the TWLBE-0.4 (0.4 cm thick) and TWLBE-4 (0.6 cm thick) samples, respectively.
Fig. 4 Absorption spectra within hydroxyl groups band of Preform-0.4 (TWL, TWLBE-0.4 glasses, 0.4 cm thick) and Preform-4 (TWL, TWLBE-4 glasses, 0.6 cm thick)
It should be noted that, when calculating volume absorption coefficient in insufficiently long samples, one must take into account the absorption by hydroxyl groups adsorbed at the ends. (Hydroxyl groups may be adsorbed from air or from polishing liquid.) Towards this end, a special methodology was proposed in [38]. The total absorption is ln(I0/I) = 2β + αL, where 2β is the absorption by surface hydroxyl groups and α is volume absorption coefficient. Attenuation by the surfaces is approximately equal to 0.0035-0.004 for a wide number of tungstate-tellurite glasses. Therefore, volume absorption coefficients for the studied glasses are found as follows: α ≈0.001 cm−1 for TWLBE-0.4 and α ≈0.009 cm−1 for TWLBE-4, respectively.
Further, we estimated the concentration of hydroxyl groups as C = α/ε, where ε is the OH- groups molar absorptivity at the band near ~3000 cm−1. As the molar absorptivity (molar extinction coefficient) ε is unknown for the given glass compositions, we had to use the available data corresponding to other tungstate-tellurite glasses [39]. Molar absorptivity of “water” in a number of TeO2-based glasses was found using vacuum dehydration [39]. An averaged value of ε(H2O) for tungstate-tellurite glasses from [39] amounts to ε ≈95·ln(10) l/(mol⋅cm), then the molar concentration of water in TWLBE-0.4 is CTWLBE 0.4(H2O) = 4.57 ⋅ 10−6 mol/l but OH-groups molar concentration is twice as high. So, the content of OH-groups is NTWLBE-0.4(OH) = 2 CTWLBE-0.4(H2O)·NAvogadro = 5.5⋅1015 cm−3. Analogously, the content of OH-groups in TWLBE-4 is NTWLBE-4(OH) ≈5⋅1016 cm−3.
So, the content of OH- groups in the TWLBE-0.4 glass is 2.7·104 times less than Er3+ concentration and the content of OH- groups in the TWLBE-4 glass is 3·104 times less than erbium ion concentration (see Table 1). These facts guarantee minimum influence of the OH impurity on the luminescent properties of Er3+-doped TWLBE glasses.
Further, we measured optical loss by the cut-back method using immersion with an indium-gallium alloy in the fiber manufactured from Preform-4. One can see in Fig. 5 that the optical loss is less than 2 dB/m up to a wavelength of 2.85 μm. The lowest optical loss at the level of 0.5 dB/m is observed in the range of 2-2.3 μm, and at a wavelength of 2.75 μm the loss is 1.2 dB/m. A possible way for further reducing the optical loss is fabrication of a preform with erbium content as high as in Preform-4 and with a content of hydroxyl groups as low as in Preform-0.4.
Fig. 5 Total optical loss of multimode fiber made of Preform-4. Core doped with Er3+/undoped cladding diameters are 50/130 μm.
2.4 Luminescent properties of glasses and fibers
The luminescence spectra were recorded by an MDR-2 monochromator; a laser diode at 975 nm was used as a pump, and a photovoltaic InSb detector P5968 was used as a receiver. First of all, we measured luminescence spectra near 2.7 μm in the bulk TWLBE-0.4 and TWLBE-4 samples (see Fig. 6(a)). The intensity was higher for the sample with a higher erbium concentration, but not proportional to it under the same pump.
Fig. 6 (a) Luminescence spectra of TWLBE-0.4 and TWLBE-4 glasses for 4I11/2 → 4I13/2 transition under excitation at 975 nm with 0.5W power. (b) Measured luminescence decay at 0.98 μm after 5-ns pump pulse.
Next, the lifetimes of the 4I11/2 → 4I13/2 transition were measured using 976 nm optical parametric oscillator excitation with a pulse duration of ~5 ns by recording the 0.98 µm emission by an infrared PMT with a photocathode having time response ~20 ns. Figure 6(b) shows the emission decay characteristics at 0.98 μm. The exponential decay component was estimated to be 113 µs and 99 µs for TWLBE-0.4 and TWLBE-4, respectively. We also measured lifetimes of the 4I13/2 level for the TWLBE-0.4 and TWLBE-4 samples to be 7.2 and 6.4 ms, respectively.
Luminescent characteristics of the multimode gain fiber made of Preform-4 were also studied. Figure 7(a) demonstrates the recorded emission spectra of the fibers of different lengths near 2.7 μm (4I11/2 → 4I13/2 transition) and near 1.6 μm (4I13/2 → 4I15/2 transition). The spectra were not corrected for the diffraction grating reflectivity and photodetector sensitivity. Sophisticated behavior of the dependences different for the two bands probably due to the complicated energy transfer processes was observed [25]. The intensity maxima for both emission bands were observed for the fiber length of 10 cm. Further, we took a 10-cm piece of fiber and measured spectra at different pump powers (see Fig. 7(b)). The higher the pump power, the higher the emission intensity was; the dependence was monotone.
Fig. 7 Photoluminescence spectra of multimode fiber with 50/130 μm core/cladding diameters made of Preform-4 under excitation at 975 nm: for pump power of 88 mW for different gain fiber lengths (a); for different pump powers for fiber length of 10 cm (b).
3. Modeling gain-switched fiber lasers
The conducted tests and the obtained data indicate that the manufactured samples are of high quality and can, in principle, be used to create a laser. Moreover, we are planning to produce single-mode fibers based on the developed high-purity low-loss TWLBE/TWL glasses, which may have additional advantages over existing multimode fibers. Therefore, here we present numerical simulation of gain-switched laser operation for both types of active fibers based on the experimental results.
3.1 Numerical model
For the cases considered here, the population densities of the 4I11/2 and 4I13/2 levels are much smaller than the population density of the ground state 4I15/2. So, up-conversion, excited-state absorption, and cross-relaxation processes [23, 25] can be neglected, and according to the three-level energy scheme shown in Fig. 8(a), the rate equations for the population densities n1, n2, n3 (normalized to NEr) are defined by [40]:
where t is the time; Wpa and Wpe are the absorption and emission stimulated rates of the pump, respectively; Wsa and Wse are the absorption and emission stimulated rates of the signal, respectively; τ3 is the total lifetime of the level 4I11/2; τ2 is the total lifetime of the level 4I13/2; τ32 is the lifetime of the 4I11/2 → 4I13/2 transition. The rates of stimulated transitions are defined aswhere h is the Planck constant; c is the speed of light; σpa and σpe are the absorption and emission cross sections, respectively, at the pump wavelength λp; σse and σsa are the emission and absorption cross sections, respectively, at the signal wavelength λs; Γp and Γs are the overlap factors of the pump and signal intensity distribution, respectively, with the Er-doped core having an effective cross section area Aeff;. Pp is the pump power; Ps+ and Ps– are the powers of signal waves propagating in the forward and backward z – direction along the fiber.Fig. 8 Simplified scheme of Er energy levels (a). Variant of experimental laser scheme (b). Pump pulses at the input end (blue) and generated output pulses (black) (c). Temporal evolution of output signal power in periodic regime (d). Averaged population defined by Eq. (10) for different time scales (e, f). RL = 0.85, αs = 2 dB/m, Ppump = 10 W.
To describe propagation of the pump and signal waves in the simple laser scheme shown in Fig. 8(b), we use partial differential equations with the boundary conditions at the input (z = 0) and output (z = L) fiber ends for signal waves and initial condition for the pump wave at the input:
where Vgr is the group velocity; αp is the linear loss at λp; αs is the linear loss at λs; R0 and RL are the reflection coefficients for the signal at the input and output fiber ends, respectively; Pp(0, t) is the launched pump pulse with peak power Ppump, the characteristic pump pulse duration Tp, and the characteristic time of its on and off t1. We also initially set a small seed power for signal waves (for t ≤ L/Vgr) to simulate non-stationary generation. The output signal power isThe system of equations is solved numerically in the finite-difference approximation with an explicit scheme using a constant step Δt = Δz/Vgr for stability. A home-made computer code has been developed for this purpose. We analyze the possibilities of obtaining laser generation in the produced multimode fibers, and also investigate and optimize the design of the system based on single-mode fibers. The values of the parameters used in the simulation are listed in Table 2.Table 2. Parameters for fiber laser modeling
3.2 Multimode fibers
In this section, we consider the simplest possibility of creating a laser at 2.7 μm based on the multimode fibers described in Section 2. The duration of the pump pulses at 0.98 μm is assumed to be about 100 μs, the duration of the leading and trailing edges is about 10 μs, which can be easily obtained from CW laser diodes using cheap electro-optic modulators. The pump intensity is supposed to be distributed uniformly over the cladding. The overlap integral Γp is estimated as the ratio of the cross-section areas of the core and the cladding. It is expected that the signal will be generated in many transverse modes and its intensity will be approximately constant over the core cross-section. The interaction between the modes is neglected, therefore Eqs. (1) - (9) remain relevant. The pump absorption coefficient is estimated as ΓpNErσpe + αp ≈0.245 cm−1, so on the optimized length L = 8 cm, 86% of pump power is absorbed.
Figure 8(c-f) shows the temporal dynamics of a laser system with specific parameters for qualitative understanding of the occurring processes. When the pump is switched on, the upper laser level 4I11/2 starts to be populated. The initial population of the 4I13/2 level is zero. Laser oscillating starts to develop when the threshold is reached. It is determined from the condition that the signal gain for a cavity round trip is comparable to the total losses involving the linear fiber loss and the loss of radiation output from the cavity. Before switching on the pump, all Er3+ ions are in the ground state (n1(z, 0) = 1, n2 (z, 0) = 0, n3(z, 0) = 0). When the first pump pulse is applied, n3 starts to increase linearly with time. One can see in Fig. 8(d, e) the populations averaged over the fiber length that are defined as
At the moment of spike generation, n3 decreases, and n2 increases by the corresponding value. When the duration of the pump pulse is comparable to τ3, the depopulation of the upper level 4I11/2 due to spontaneous nonradiative transitions becomes significant. But the population of the 4I13/2 level with a lifetime of several ms continues to increase. The efficiency of generation decreases until complete disappearance. Therefore, the pump duration should be chosen around τ3 or shorter. After this, the residual population relaxes from the 4I11/2 level to the 4I13/2 level with a characteristic lifetime τ3. Relaxation from the 4I13/2 level to the ground state 4I15/2 occurs with a characteristic time τ2 >> τ3. Therefore, the repetition rate of the pump pulses should be low enough for the vast majority of the excited ions to have sufficient time to transit from the 4I13/2 level to the ground state by the time of the second pump pulse arrival.
The case Δν = 100 Hz is illustrated in Fig. 8(c-f). For the second pump pulse, the generation threshold becomes slightly higher due to the residual population of the 4I13/2 level. In this case, the energy generated in the second pulse train is smaller than in the first one (see Fig. 8(c)). After a few pump pulses, the system enters a periodic regime, signals are generated with constant energy and constant time structure (see Fig. 8(b)). Figures 8(e, f) show the dependence of populations on time.
Next, the laser operation is simulated for different values of peak power, reflection coefficients at the output, and fiber optical losses (see Fig. 9). Clearly, for efficient generation, the output reflection coefficient should be sufficiently high, which may be realized by a dichroic mirror or a Bragg grating. As one can see in Fig. 9, tolerance to optical loss and reflection coefficient is allowed. For a laser diode with a maximum peak power of about 2 W, the reflection coefficient should be higher than 90% and the optical loss should be lower than 3 dB/m. It is worthy of note that our fibers have a lower loss level. For a power of 5 W, the range of values is broader: RL down to ~75% and αS up to 5 dB/m. For Ppump ≥ 5 W and αS ≤ 3 dB/m, the optimal RL is about 80-85%. The calculated output energies are about tens of μJ for a pump power of 5-15 W and may reach 100 μJ and higher for Ppump ≥20 W. Therefore, as shown by numerical simulation, the multimode fiber can be used as an active element of a gain-switched laser at a wavelength of 2.7 μm. In this case, the system parameters may be matched roughly enough.
Fig. 9 Laser signal energy as a function of reflection coefficient at the multimode fiber output for different pump peak powers Ppump and fiber losses.
3.3 Single-mode fiber
To obtain a high-quality laser beam, single-mode fibers are preferable. Here we consider double-clad fibers with effective core/cladding diameters of 10/100 μm. It is assumed that the pumping is uniformly distributed over the first cladding. For the signal, the field of the fundamental mode LP01 is calculated and the overlap integral is estimated. The pump absorption coefficient is estimated to be 0.02 cm−1, so the fiber length should be about 100 cm. First, we consider laser operation under 100 μs pump pulse. The simulated dependence of the output energy on the reflection coefficient at the output end for different loss levels is shown in Fig. 10.
Fig. 10 Laser signal energy at 2.7 µm as a function of reflection coefficient at single-mode fiber output for different pump peak powers Ppump and fiber loss.
It is assumed that reflection at the output can be implemented using a dichroic mirror or a Bragg grating, or even a fiber cleavage. A minimum reflection coefficient is chosen to be 10%, which roughly corresponds to the Fresnel reflection coefficient from the cleavage normally to the fiber. For a single-mode fiber, it is efficient to use relatively small reflection coefficients, which was realized experimentally for Er: ZBLAN mid-IR fiber laser [11]. Fiber cleavage is also advantageous, since it allows avoiding use of additional reflective elements and also reducing peak laser intensity in the cavity. For single-mode fibers, the output pulse energies and requirements for loss are similar to the case of multimode fibers. For a pump power of about 2 W, loss should be lower than 3 dB/m, but for Ppump ≥ 5W it may be a little higher. The calculated output energies are also about tens of μJ for a pump power of 5-15 W and may reach 100 μJ for Ppump ≥20 W.
Further, the temporal structure of the pulse train is examined in more detail. Figure 11 demonstrates the dependence of the output peak power and energy on time for different reflection coefficients. The time profile of the leading edge of the pump is also shown. The lower the reflection coefficient, the higher the signal peak power of the first spike is. But the higher the reflection coefficient, the earlier the generation threshold is achieved in time.
Fig. 11 (Upper row) Temporal evolution of output signal power for different reflection coefficients. Green curves correspond to the time profile of the leading edge of the pump (right axes). (Lower row) Temporal evolution of output signal energy. Each subplot is calculated for the indicated thereon pump peak power and fiber loss of 2 dB/m.
For some applications, high-quality single pulses should be generated. With the use of fast feedback systems, it is possible to adjust the duration of the pump pulses, turning the pump off after generating the first spike at a wavelength of 2.7 μm. Note that a similar case was experimentally demonstrated for an Er-doped ZBLAN fiber [41]. Here the simulation is performed for the pump on/off time t1 = 100 ns. As a result, pulses with a duration of order 100 ns and an energy of order 1 μJ can be obtained. The curves for energy and duration as a function of reflection coefficient in the first spike for different peak pump powers are plotted in Fig. 12(a,b), respectively. The signal energy increases with increasing pump peak power.
Fig. 12 Energy of the first spike (a), spike duration (b), and optimal pump pulse duration for generating only one spike (c) as functions of reflection coefficients for different pump peak powers Ppump. The inset demonstrates typical temporal structure of pump and signal pulses. Fiber loss is 2 dB/m for (a), (b), (c). Energy of the first spike (d), its duration (e), and optimal pump pulse duration for generating only one spike (f) as functions of fiber loss (for RL = 0.1). t1 = 100 ns for all subplots.
The higher the peak power, the shorter the spike is. The optimal pump pulse duration is shown in Fig. 12(c). The corresponding temporal structure of the pump and signal pulses is presented in the inset. The output energy and duration of the first spike dependence on fiber loss is shown in Fig. 12(d,e), respectively, for RL = 0.1. The loss dependence of optimal pump pulse duration is shown in Fig. 12(c). For this mode, fiber loss should be ≤ 2 dB for Ppump = 2 W. For higher pump power, fibers with larger loss may be used. So, this mode may also be implemented in experiment.
4. Conclusions
In this paper, a possibility of realizing a diode-pumped gain-switched laser at 2.7 μm based on specially developed Er-doped tellurite glass fibers was investigated. Low-loss multimode fibers made of “ultra-dry”, crystallization resistant TeO2-WO3-La2O3-Bi2O3-(Er2O3) glasses were fabricated and characterized experimentally. The lowest optical loss at the level of 0.5 dB/m was observed in the range of 2-2.3 μm, and at a wavelength of 2.75 μm the loss was equal to 1.2 dB/m. The estimated content of hydroxyl groups in the core was 3·104 times less than erbium ions concentration, which guarantees a negligible impact on the optical properties of Er3+. The emission spectra of the fibers near 2.7 μm (4I11/2 → 4I13/2 transition) and near 1.6 μm (4I13/2 → 4I15/2 transition) were measured for different pump powers at 975 nm and different fiber lengths. Numerical simulation of laser action in multimode as well as in single-mode fibers (planned for manufacturing as prospective ones) was performed using data of the experiments. A home-made computer code was used. The pump pulse duration should be comparable or smaller than the lifetime of the upper laser level. It is shown that for multimode active fibers, the reflection coefficient at the output should be about 80-90%. For single-mode fibers, it is optimal to use cleavage normal to the axis of the fiber with Fresnel reflection coefficient of about 10% at the output. For optical loss of about 3 dB/m and smaller under pumping with a pulse duration of about 100 μs and peak power of several W the output energy is tens of μJ, but for the peak power of about 20 W the output energy may exceed 100 μJ.
Funding
Russian Science Foundation (No. 17-12-01324).
Acknowledgments
We are grateful to Dr. Alexander D. Plekhovich for DSC-measurements and to Dr. Boris I. Galagan and Dr. Sergey I. Sverchkov for fruitful discussions.
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