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We have numerically investigated the Raman lasing characteristics of a highly nonlinear photonic crystal fiber (HNPCF). HNPCF Raman lasers are designed to deliver outputs at 1.3 µm and 1.48 µm wavelengths through three and six cascades of Raman Stokes cavities when the pumps of 1117 nm and 1064 nm are injected into HNPCF module, respectively. A quantum efficiency of approximately 47% was achieved in a short length of HNPCF for 1.3 µm lasing wavelength. The HNPCF design is modified further to operate in single-mode fashion keeping intact its Raman lasing characteristics. The modified HNPCF design consists of two air-hole rings where the higher-order modes in the central core are suppressed by enhancing their leakage losses drastically, thus ceasing their propagation in the short length of HNPCF. On the other hand, the fundamental mode is well confined to the central core region, unaffecting its lasing performances. Further, the lasing characteristics of HNPCF at 1480 nm are compared with conventional highly nonlinear fiber Raman laser operating at 1480 nm. It is found that one can reduce the fiber length by five times in case of HNPCF with nearly similar conversion efficiency.
©2008 Optical Society of America
1. Introduction
The fiber lasers, both Raman and actively-doped fiber core, are gaining wide interest and promising to be an alternative candidate to the conventional solid-state lasers due to the compatibility with optical fiber communication systems in terms of the reduced losses due to the insertion of non-fiber components. The fiber Raman lasers (FRLs), operating on the principle of stimulated Raman scattering (SRS) process, where the incoming pump photon generates a next Stoke due to SRS thus giving another photon as an output, have generated wide interest [1–6] after the development of high pump lasers. The FRL module constitutes of the gain fiber and the reflectors, which are fiber Bragg gratings (FBGs) in general. The lasing can be achieved at any wavelength by proper choice of pump wavelength and by cascading the pump photon through several Raman Stokes. This mechanism is also referred as the wavelength-conversion and is highly useful for many purposes in optical communications such as remote pumping of pre-installed EDFA systems and the generation of new wavelengths for medical applications.
In recent years, photonic crystal fibers (PCFs) or so called holey fibers (HFs) have been studied extensively because of their superior modal properties in comparison to conventional optical fibers, such as wide single-mode operation for certain geometrical parameters (d/Λ<0.45, where d and Λ are the hole-diameter and air-hole pitch) regardless the operating wavelength [7], strong confinement of light into the core region, scalable modal areas, and controllable dispersion properties [8–10]. The air-holes in the PCF cladding act as index lowering agents producing an average cladding index lower than the pure silica index, guiding the light through total internal reflection. It was profound by Selleri et al. [11, 12] and by us [13–17] that PCFs can be used to amplify the signals from optical fiber link through distributed Raman gain as well as can compensate for the dispersion accumulated over the single mode fiber (SMF) link. The large amount of Raman gain comes from the strong confinement of light into the core without doping it, resulting to the strong overlap between pump (s) and signal (s). To design a FRL, the fiber should have high Raman gain coefficient, small effective area, low threshold, and short length [6]. The small effective mode area in SMFs can be achieved either by raising the germanium concentration or by reducing the core size up to a certain limit. Increasing the germanium concentration may induce other unwanted effects such as material anisotropy, large scattering losses and fiber attenuation. On the other hand in case of PCFs, the small effective mode area can be achieved by controlling its two design parameters; the air-hole diameter d and the pitch-constant Λ. This unprecedented controllability in PCFs makes them attractive for FRLs. Recently Travers et al. [18] and Pei-Guang et al. [19] have demonstrated a continuous-wave holey fiber Raman laser at 1.12 µm and 1.183 µm by using a 1.1 µm and 1.07 µm Ytterbium fiber laser, respectively. Therefore, by employing successive Raman Stokes shifts, one can design a higher-order laser wavelength, such as 1310 nm and 1480 nm.
In this paper, we present FRLs based on PCFs with several cascades order schemes. We have used a full-vectorial finite element method (V-FEM) [20] to simulate the PCF structure and obtain its modal properties such as effective mode area and Raman gain efficiency (RGE). After calculating its RGE values, we use a set of non-linear differential equations [6] to find the lasing characteristics of PCFs. We have obtained 47% and 29% of conversion efficiencies in 20 m and 10 m lengths of highly nonlinear PCF (HNPCF) lasing at 1.3 µm and 1.48 µm wavelengths, respectively, when input pump powers of 5 W and 8 W are used.
The HNPCF, which we consider in designing 1310 nm and 1480 nm PCF Raman lasers (PCF-RLs), was fabricated by Monteville et al. [21] and its structural parameters were such that it supports well-confined higher-order modes (HOMs). We have further improved the design of HNPCF [21] so that it can operate in effectively single-mode fashion at all wavelengths without tampering its Raman properties. The effectively single-mode operation was achieved by enhancing the leakage losses of the HOMs by decreasing the number of air-hole rings and reducing the size of air-holes in the second air-hole ring. Our modified HNPCF design consists of two rings of air-holes where the first ring air-holes has same air-hole diameter of HNPCF in Ref. [21], while the size of air-holes in the second ring is decreased to 88%. This modified HNPCF structure doesn’t alter the Raman properties such as RGE of the fiber as the fundamental mode remains intact with same propagation constant and hence doesn’t alter the lasing characteristics. The detailed analysis is described in Sec. 3 of this paper. Moreover, the modified HNPCF design may further reduces the scattering losses due to presence of only two air-hole rings, and hence can lower the fiber attenuation. Finally, we have compared the lasing performances of HNPCF to the conventional highly nonlinear fiber (HNF). Numerical simulations have revealed that the fiber length can be reduced almost by a factor of five for nearly similar conversion efficiencies.
2. Modeling of a PCF Raman laser
The FRL module consists of FBGs depending on the number of cascades required to output the desired lasing wavelength with 100% reflectivity of intermediate Stokes and with a certain reflectivity R out (which is the FBG corresponding lasing wavelength) of the output lasing wavelength, the gain fiber, and the pump source. The behavior of FRLs depends on several parameters such as fiber length, output coupler (OC) reflectivity R out, and the insertion losses. Numerical simulations can be used to understand the tradeoff between these parameters. The evolutions of pump and Stokes power inside the FRL module can be described by a set of nonlinear ordinary differential equations [6],
where the superscript ± designates the power P in the forward and backward traveling waves, respectively, γR is the RGE, and ν is the frequency of a given wave. The forward direction is from pump to OC as shown in Fig. 1. The indexes p, i, and n stand for the pump wave, the intermediate Stoke, and the lasing wavelength. The boundary conditions for these nonlinear differential equations are given by,
where R is the reflectivity of forward/backward (+/-) Bragg gratings, L is the length of FRL cavity (i.e. the length of the gain fiber), and R out is the reflectivity of OC. The output power of lasing wavelength can be expressed as
Another two parameters that determine the performance of the fiber laser are the quantum efficiency or the conversion efficiency η and the slope efficiency S, which can be computed by the following equations:
where Pout and Pin are the output lasing power and input pump power.
2.1 Design of a 1310 nm PCF Raman laser
Figure 1(a) shows the cross-section of a HNPCF [21] which has five air-hole rings in the cladding with normalized air-hole size d/Λ=0.80 and lattice constant Λ=2.14 µm, where the background material is pure silica. The HNPCF was designed to give a small effective mode area of 4.1 µm2 and exhibits an attenuation of 5.8 dB/km at 1550 nm wavelength. The wavelength dependence of the refractive index of silica is considered in numerical simulations by Sellemier three term formula [22]. The fabricated HNPCF supports well confined higher-order modes in the core region even at longer wavelengths because of large hole-diameter and short pitch, thus making HNPCF as a multimode fiber. We have modified the design as discussed in Section 3 of this paper, such that only fundamental core mode can propagate. The improvement in HNPCF design is carried in such a manner that its Raman gain characteristics remain unaltered while we filter out the HOMs from the core region by enhancing their leakage losses drastically, keeping fundamental mode as intact into the core.
The cascade scheme to obtain 1.3 µm lasing wavelength using HNPCF is shown in Fig. 1(b). The pump of 1117 nm from Yb-doped double clad fiber laser is injected to the HNPCF Raman laser (HNPCF-RL) module. The Raman cavity is comprised of three sets of FBGs whose corresponding Bragg wavelengths (which are the Stokes wavelengths) and attenuation values along with RGEs are given in Table 1. The FBG corresponding to lasing wavelength is defined as the OC with R out reflectivity determined through set of equations (1)–(4). The pump 1117 nm generates a Stoke at 1175 nm, which acts as a pump to generate another Stoke and this process continues till the desired output lasing wavelength is reached. The development of intermediate Stokes starting from pump to final lasing wavelength (1.3 µm) is summarized in Table 1 with their respective attenuation coefficients [21] and the RGE values. The RGE is calculated using V-FEM when the fiber is pumped by a depolarized pump source of 1455 nm [11–14]. The RGE at shorter wavelengths as mentioned in Table 1 are scaled accordingly [23] and becomes larger at shorter wavelength because it scales inversely to the wavelength.
Fig. 1. (a) Transverse cross-section of fabricated HNPCF [21] whose structural parameters are d/Λ=0.80, Λ=2.14 µm, where d is the hole-diameter and Λ is the separation between two consecutive air-holes, (b) cascade scheme to design a 1310 nm HNPCF Raman laser, employing two intermediate Stokes.
Table 1. Parameters for third-order cascades HNPCF Raman laser lasing at 1310 nm.
It can be seen from Table 1 that the HNPCF shows large attenuation coefficients (third column) at the pump and the intermediate Stoke of 1240 nm. These high losses can be compensated by the large gain provided by the HNPCF due to large RGE values. The nonlinear differential equations (1a)–(1c) are solved with boundary conditions (2) in MATLAB [24] to know the evolution of pump and Stokes. Also, note that the genetic algorithm (GA) tool is used in MATLAB to get maximum conversion efficiency. The reflectivity of FBG corresponding to the pump is chosen to 0% so that the pump is propagated once through fiber, while the reflectivity of all intermediate Stokes is 99.9%.
Figures 2(a) and (b) show the variation of output lasing power as a function of output coupler reflectivity R out and fiber length, L, respectively, when an input pump power of 5 W is used. It is evident from the graph that the output lasing power increases up to a certain maximum and then starts to decrease. This maxima point corresponds to the reflectivity of OC to achieve maximum conversion efficiency. From Fig. 2(b), it can be clearly observed that the output power increases as a function of fiber length till a maxima occurs for an input pump power of 5 W and R out=62%. A trade-off is observed between the fiber length and the reflectivity of output coupler.
Figure 3(a) presents the contour color map between the fiber length and the reflectivity of OC with quantum efficiency η as a parameter, when the module is pumped by 5 W of pump power. The curves for threshold power P th as a function of OC reflectivity have also been plotted in the same graph. It can be predicted from the results that the quantum efficiency is maximized for a particular set of R out and fiber length L. As the fiber length increases, the threshold power decreases because the distributed Raman gain increases with increasing fiber length and thus a high value of R out will be required for fiber to lase at desired wavelength.
Fig. 2. Variation of output lasing power as a function of (a) output coupler reflectivity R out and (b) fiber length L when the input pump power was 5 W.
Fig. 3. (a) Variation of fiber length as a function of the reflectivity of OC with η as a parameter for an input pump power of 5 W. The fiber length of 20 m was determined from the color map when the conversion efficiency becomes maximum, (b) output lasing characteristics of a 1310 nm HNPCF-RL module. The HNPCF-RL exhibits slope and conversion efficiencies of 62% and 47%, respectively.
From numerical simulations, the length of HNPCF, R out and η are obtained as, 20 m, 62%, and 47%, respectively. Next, we evaluate the lasing characteristics for 20 m long HNPCF module lasing at 1310 nm. The variation of output lasing power is demonstrated in Fig. 3(b). We can clearly see that up to 2 W of input pump power no lasing occurs, but the lasing starts as the pump power increases beyond 2 W. This determines the threshold power of the HNPCF-RL that is calculated as 1.96 W. After this threshold, the output lasing power varies linearly with the input pump power. The slope of the curve tells about the slope efficiency of the fiber laser. Using Eq. (5), the slope efficiency of a 1310 nm HNPCF-RL is obtained as 62%, while the conversion efficiency is 47%.
2.2 Design of a 1480 nm PCF Raman laser
In this section, we design a 1480 nm PCF Raman laser. Figure 4 describes the cascade scheme to achieve a 1480 nm as an output lasing wavelength with the help of FBGs. A total of six Raman Stokes are needed to convert the pump wavelength of 1064 nm into 1480 nm. The attenuation coefficients at different Stokes and pump are summarized in Table 2. The RGE can be scaled [23] at pump and Stokes as RGE varies inversely with the wavelength and is shown in Table 2. The incident pump source is injected at z=0. The pump generates a cascade of n Stokes waves (n=6 for 1480 nm output) in the cavity through SRS process.
Fig. 4. Cascade scheme to obtain 1480 nm lasing wavelength by converting 1064 nm input wavelength through SRS process.
A 1064 nm pump is injected into a HNPCF-RL module where the sixth Stokes FBG has reflectivity R out while other FBGs have reflectivity of 99.9%, and the reflectivity of the FBG corresponding to the pump is taken as ~0% (i.e. the pump propagate once through optical fiber). In Fig. 5(a), a contour map between fiber length L and output FBG reflectivity R out is plotted as a function of conversion efficiency η that is computed using Eq. (4) for an input pump power of 8 W. The dark red region in Fig. 5(a) illustrates the maximum conversion efficiency. Therefore, for maximum conversion efficiency (which is 29.4% in present case), we can obtain corresponding fiber length and the reflectivity of OC as 10 m and 25%, respectively. After determining the fiber length and the reflectivity of output FBG, we evaluate the lasing performance of the proposed HNPCF-RL. The threshold power for HNPCF-RL was calculated as 2.48 W. The output lasing power for a 10 m long HNPCF-RL is depicted in Fig. 5(b) as a function of input pump power. The output power varies linearly as a function of the input pump power after the threshold power. The slope efficiency of the curve is 42.3 %. In Table 3, the lasing performances of the HNPCF-RL are summarized. It can be seen that as the input pump power P in increases, the fiber length decreases in contrary to the conversion efficiency. The 9 m long HNPCF-RL exhibits conversion and slope efficiency of 32.2% and 43.8%, respectively when the input pump power is set 10 W.
Fig. 5. (a) Contour plot between fiber length and reflectivity of output FBG as a function of conversion efficiency for an input pump power of 8 W, (b) variation of output lasing power P out as a function of input pump power P in. The HNPCF Raman laser demonstrates a slope efficiency of 42.3 % in a 10 m long HNPCF.
Table 2. Parameters for sixth-order cascades HNPCF Raman laser lasing at 1480 nm
Table 3. Lasing performances of sixth-order cascades HNPCF Raman laser at 1480 nm
Table 4. Leakage loss characteristics of HE21 mode confined in the HNPCF core for different number of air-hole rings at 1064 nm, 1310 nm, and 1480 nm wavelengths
3. Modification in HNPCF design: towards single-mode operation
The HNPCF fabricated by Monteville et al. [21] has large air-hole diameter (d/Λ=0.80) and confines the HOMs (i.e. LP11-like modes) into the core region. The fabricated HNPCF structure was composed of five air-hole rings in the cladding as mentioned before in Section 2 that strongly confine both fundamental and the HOMs. The best way to suppress the HOMs from the core region is enhancing their leakage losses. The leakage losses can be raised either by reducing the number of air-hole rings in the case where the air-hole diameter is large enough to confine the fundamental mode (such as in the HNPCF case) or by decreasing the diameter of air-holes [25]. However, decreasing the air-hole diameter in the first ring may affect its modal properties thus Raman lasing characteristics. Therefore, we decrease the number of air-hole rings one-by-one and computes the leakage loss or confinement loss in the wavelength range from 1064 nm to 1480 nm. Table 4 summarizes the leakage loss values of the HOM (HE21 mode) at 1064 nm, 1310 nm, and 1480 nm wavelengths for five, four, three, two and one air-hole rings in the cladding.
It can be deduced from Table 4 that as the number of air-hole rings decreases, the leakage loss of HE21 mode increases, but the leakage loss stays below than 0.1 dB/m at 1064 nm for two air-hole rings structure and sharply increases for one ring HNPCF structure. In addition, the leakage loss of the fundamental mode is also quite large (more than 20 dB/m) for 1-ring HNPCF. Therefore, we can conclude from this analysis that in 1-ring HNPCF, both fundamental and HOMs are very leaky and hence it can’t be considered as a proper HNPCF design with suppressed HOMs with effectively single-mode operation. Consequently, we continue with two ring structure and to further enlarge the leakage loss level of HE21-mode, we decrease the diameter of air-holes in the second air-hole ring. We checked the leakage loss value of HE21 mode by decreasing the hole-diameter gradually in the second air-hole ring and we arrived at final step that the diameter of air-holes in the second ring, referred as d′, is approximately 88% of the diameter of air-holes in the first ring i.e. d′/Λ=88% d/Λ. As a conclusion, the modified HNPCF as shown in Fig. 6(a), has structural parameters as d/Λ=0.80 (first air-hole ring), d′/Λ=0.70 (second air-hole ring), and Λ=2.14 µm. The leakage loss of the fundamental mode in this modified HNPCF is 0.09 dB/m at 1480 nm wavelength that is below than the acceptable leakage loss level.
Figure 6(b) explains the leakage loss characteristics of the fundamental mode and HE21-mode in the modified HNPCF structure (shown in Fig. 6(a)). The solid blue curve corresponds to the fundamental mode whereas the solid red curve stands for HE21-mode. It can be clearly observed from the results that the leakage loss of HOM (HE21) increases drastically and is more than 1 dB/m at 1064 nm wavelength and 200 dB/m at 1480 nm wavelength, thus inhibiting HOM propagation, while keeping the single-mode operation with unaltered Raman lasing characteristics.
Fig. 6. (a) The modified design of effectively single-mode HNPCF whose parameters are d/Λ=0.80, d′/Λ=0.70, and Λ=2.14 µm. The HOMs are suppressed by enhancing their leakage losses, (b) leakage loss characteristics of the fundamental and HOM (HE21) in the modified HNPCF structure as shown to the left (Fig. 6(a)). Numerical simulations show that the modified HNPCF exhibits the same lasing characteristics as by HNPCF with five air-hole rings.
4. Comparison with conventional highly nonlinear fiber Raman laser
To compare the lasing performances of HNPCF Raman laser at 1480 nm, we have evaluated the lasing characteristics of the conventional HNF [26] from Sumitomo Elec. Ind., which has a small effective mode area of ~10 µm2 at 1550 nm and exhibits the peak RGE of 3.84 W-1.km-1 at a frequency shift of 13.2 THz when pumped with a depolarized pump of 1455 nm. The conventional HNF shows attenuations of 2.32 dB/km and 0.98 dB/km at 1064 nm and 1480 nm wavelengths, respectively. Note that, the GA in MATLAB is used to attain the length of HNF and reflectivity of the OC for maximum conversion efficiency as tabulated in Table 5. Figure 7 demonstrates the comparison between the output lasing characteristics of conventional HNF (solid blue curve) and HNPCF (solid red curve). The reflectivity’s of Bragg gratings corresponding to 1480 nm output coupler for both 50 m long conventional HNF-RL and 9 m long HNPCF-RL are 11% and 22%, respectively. It can be seen that the fiber length is reduced almost by a factor of five when HNPCF is used to lase at 1480 nm in compare to HNF-RL. It is also noticed that the conversion efficiency is nearly constant for an input pump power of 10 W (see Tables 4 and 5). We have further tabulated the lasing performances of conventional HNF-RL in Table 5. It shows the conversion and slope efficiency of 34.1 % and 37.5%, respectively, for a 50 m long HNF at an input pump power of 10 W.
Fig. 7. Comparison between lasing performances of a conventional HNF (solid blue curve) and a HNPCF (solid red curve) Raman lasers operating at 1480 nm wavelength. It can be deduced from the numerical results that the length of fiber can be reduced drastically almost by a factor of five in case of HNPCF Raman laser.
Table 5. Lasing characteristics of a conventional HNF Raman laser lasing at 1480 nm.
5. Discussion and concluding remarks
To summarize our work, we have numerically investigated 1310 nm and 1480 nm fiber Raman lasers based on HNPCF by designing third and sixth order cascade Raman cavities, respectively. The modal properties of HNPCF were numerically investigated through V-FEM and the laser rate equations have been solved to evaluate the lasing characteristics of the HNPCF. The attenuation of HNPCF was taken into account while solving the laser equations. Numerical simulations revealed that a 20 m and a 10 m long piece of HNPCF is required to attain conversion efficiencies of 47% and 29.4% with slope efficiencies of 62% and 42.3% when the reflectivity of output FBG was set to 62% and 25%, respectively. To the best of authors’ knowledge on the literature survey, this is the first numerical demonstration of a 1.3 µm and 1.48 µm fiber Raman lasers based on HNPCF.
Additionally, we have modified the HNPCF design fabricated by Monteville et al. [21], which was multimode in nature. Both fundamental and HOMs were well-confined within the core region. We have proposed the design strategy to make HNPCF effectively single-mode over the desired wavelength by suppressing the HOMs from the core. The suppression of HOMs (LP11-like modes) was done by enhancing their leakage losses, which was achieved by decreasing the number of air-hole rings to two and reducing the diameter of air-holes of the second air-hole ring. The modified HNPCF design ensures its single-mode operation without altering its Raman lasing characteristics. Finally, we have shown the comparison between lasing performances of conventional HNF and HNPCF. It has been found that the length of fiber can be decreased almost by a factor of five for nearly similar conversion efficiencies. Therefore, one can predict that benefits of utilizing the HNPCF structures in designing FRLs are their small effective mode area, high RGE, and reduced fiber length in comparison to FRLs based on conventional HNFs. The fiber Bragg gratings can be written into the core of pure silica HNPCF by an ArF laser with a 193-nm pulse width of 15 ns operating at a repetition rate of 40Hz as described by Groothoff et al. in Ref. [27].
Also, note that the modified design has two air-hole rings, which may reduce the scattering losses caused due to large number of air-holes in the cladding. Therefore, the improved HNPCF may lower the fiber attenuation smaller than 5.8 dB/km at 1550 nm as reported by Monteville et al. [21]. It was also yielded from simulations that the HNPCF doesn’t show any birefringence and hence we didn’t see any polarization mode dispersion issues that can affect its lasing performances. We haven’t considered the splice issues between the HNPCF and the pump (a conventional ytterbium-doped fiber laser emitting at 1064 nm or 1117 nm) in designing the HNPCF-RL, and it is now actively under consideration. However, one can expect low splice losses using an intermediate buffer or ferrule technique as demonstrated by Saval et al. [28], where the splice losses between the conventional fiber and the HNPCF can be reduced below 0.6 dB.
Acknowledgements
S.K. Varshney kindly acknowledges to Japan Society for Promotion of Science (JSPS) for their support in carrying out this work. Authors acknowledge to Indo-Japan collaboration project on: Infrastructural Technology for Advanced Use of Photonic Crystal Fibers in Optical Communication Systems.
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