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In this paper, we report, for the first time, an inherently gain-flattened discrete highly nonlinear photonic crystal fiber (HNPCF) Raman amplifier (HNPCF-RA) design which shows 13.7 dB of net gain (with ±0.85-dB gain ripple) over 28-nm bandwidth. The wavelength dependent leakage loss property of HNPCF is used to flatten the Raman gain of the amplifier module. The PCF structural design is based on W-shaped refractive index profile where the fiber parameters are well optimized by homely developed genetic algorithm optimization tool integrated with an efficient vectorial finite element method (V-FEM). The proposed fiber design has a high Raman gain efficiency of 4.88 W-1· km-1 at a frequency shift of 13.1 THz, which is precisely evaluated through V-FEM. Additionally, the designed module, which shows ultra-wide single mode operation, has a slowly varying negative dispersion coefficient (-107.5 ps/nm/km at 1550 nm) over the operating range of wavelengths. Therefore, our proposed HNPCF-RA module acts as a composite amplifier with dispersion compensator functionality in a single component using a single pump.
©2005 Optical Society of America
1. Introduction
Photonic crystal fibers (PCFs), one of the novel innovations in fiber optic industry, have been the subject of intensive research since last few years [1] due to their intriguing and remarkable properties such as ultra-wide band single mode operation [2], small and large effective area and overall controlled dispersion properties like ultra-flattened dispersion [3] and high-negative dispersion [4–7]. The presence of air-holes in their cladding makes them versatile for many applications as well the control over the structural parameters at fabrication stage provides freedom to optimize the PCF structure for a new set of applications. By manipulating the air-hole diameter and lattice period of the PCF, small effective area can be realized easily whereas in conventional optical fiber, the core has to be doped heavily to get a small effective area with high nonlinearity which in turn increases the optical losses. However, PCFs are made from pure silica where small effective area is achieved by varying its geometrical parameters which lead further to large Raman gain. Therefore, PCFs are the most viable candidate for gain medium applications.
Fiber Raman amplifiers (FRAs) are becoming more relevant and practical now a days due to their critical merits over EDFAs [8, 9]. However, to design a discrete or distributed flat gain FRAs, several pumps are used [8–10]. This makes complex and tedious design procedure as well the number of components increases thereby increases the cost of the system. In recent past, efforts have been put [11, 12] to design broadband gain-flattened FRAs using a single pump where the conventional fiber structure is perturbed either to dual core shaped or W-shaped profile. Due to small effective area and high nonlinearity [13] offered by PCFs and freedom to design the fiber structure, PCFs have also attracted attention to act as a promising Raman gain medium. Previously, Raman amplification properties of PCFs have been investigated [14–16], where the studied PCF shows positive dispersion and no effort has been made to flatten the gain response. To deploy PCF in existing fiber links it must have the negative dispersion so that it can compensate the dispersion accumulated during conventional fiber link and as well provide large Raman gain. Recently, such integrated device is proposed by the authors [17], which was based on dual core PCF design and where the wavelength dependent effective area of the fiber was used to flatten the gain curve using a single pump in C-band. Designing an optimized PCF structure for a particular application is an important concern now days. Several optimization tools like genetic algorithm (GA) [18, 19] are being used. Consequently, we have developed an optimization tool based on GA integrated with vectorial finite element method (V-FEM) [20, 21]. We have used this homely developed tool to optimize the PCF design parameters.
In this paper, we present an inherently gain flattened, high gain of 13.7 dB (with ±0.85-dB gain flatness) highly nonlinear PCF (HNPCF) design, which is based on W-shaped refractive index profile and has slowly varying negative dispersion coefficient (-107.5 ps/nm/km at 1550 nm) over the operating range of wavelengths using a single pump in C-band. The wavelength dependent leakage loss property of PCF is utilized to flatten the gain. Therefore, our PCF design integrates two key functionalities (gain and dispersion compensation) in a single component. To the best of author’s knowledge, it is the first report of such inherently gain-flattened PCF design employing leakage loss property of the PCF. Here, we would like to emphasis that an entirely different approach is adopted to control the gain-flatness of proposed HNPCF Raman amplifier (HNPCF-RA) unit in contrary to the previously reported by authors [17].
Fig. 2. Spectral variation of effective index of the fundamental core mode (
2. Fiber design and principle
Figure 1 shows the transverse cross-section of designed HNPCF and its schematic refractive index profile. The proposed fiber is based on W-shaped refractive index profile, and has N (filled with light blue color) and N′ number of air-holes rings in inner and outer cladding, embedded in silica glass matrix (denoted by red color). The hole-diameter of outer cladding is reduced to d′ in order to control the leakage loss of the fiber, d and Λ are the hole-diameter of inner clad and lattice period of designed fiber, respectively. The values of Λ, d, and d′ are optimized by using GA to obtain highly negative dispersion profile. In the GA analysis, the following fitness function is maximized:
with
where w 1 is the scaling parameter and is taken as 0.001 and D is the chromatic dispersion coefficient in [ps/nm/km].
Clearly, the maximum value of fitness function F is zero when w 1 f 1 is -∞. Therefore, maximizing F is equivalent to obtaining highly negative dispersion profile in the wavelength range of interest. From our preliminary investigation, it is expected that the dispersion profile is almost linearly varied between 1.4 to 1.55 μm, having negative dispersion slope (as shown in Fig. 6 later), with a “cut-off” (around 1520-nm) between the effective index of the fundamental core mode and the effective index of the outer clad. The wavelength range used in GA analysis is 1.44 μm to 1.47 μm (as shown by Eq. (2)) to save computational time and making the problem simple. If the “cut-off” is included in the wavelength range of interest, the complex eigenvalue problem, which usually require special numerical treatment, has to be solved. The searching areas for each parameter to be optimized are Λ = 1.4~1.6 μm, d=0.40Λ~0.60Λ, and d′=0.30Λ~0.50Λ. However, by lowering the pitch less than 1.4 μm, one can achieve highly negative dispersion. But, this may impose the limit of fabrication as well as such small pitch design may find difficulty in splicing with conventional fibers. Therefore, keeping such facts in mind, we have constrained our searching areas as defined above. Firstly, we optimize the negative dispersion profile of the PCF structure through GA under above-mentioned constraints and then we manually adjust the outer clad air-hole diameter to match the “cut-off”.
The fiber’s parameters obtained by GA as discussed above are, d=0.596 μm, d′= 0.54 μm, Λ=1.4 μm, with N=11 and N′=3. The geometrical parameters of HNPCF are optimized in such a way that there is a “cut-off” between the effective index of the fundamental core mode and the effective index of the outer clad at 1526 nm wavelength. After this “cut-off” (λc), the leakage loss increases rapidly, which in turn compensates for the high Raman gain efficiency. The designed HNPCF shows an effective area of 7.47 μm2 at 1550-nm wavelength.
The spectral variation of effective indices of the fundamental core mode and the outer clad is depicted in Fig. 2. The solid red (
Generally, PCFs are leaky structures and the control of leakage loss is one of the important concerns. It can either be controlled by using large air-hole size or by increasing the number of air-hole rings. There is a trade-off between the number of air-hole rings, air-hole diameter, and the leakage loss of PCF [22, 23]. Increasing the hole-diameter, the leakage loss can be reduced thereby decreasing the number of air-hole rings. With large hole-size, PCF shows positive dispersion for a fixed value of pitch [5, 6]. Therefore, to maintain the leakage loss with large negative dispersion, and suitable “cut-off”, large number of air-hole rings is required with moderate air-hole size. The selection of fourteen (14) number of air-hole rings for our proposed HNPCF design is not a random selection. Leakage loss for different total number of air-hole rings viz. 12, 13, 14, and 15 has been evaluated and finally we reached to value of 14. After fixing this total number of air-hole rings, we proceed with selection of air-hole rings in inner and outer clad, which has impact on gain-flatness and net gain spectra (later shown in Fig. 13). Therefore, by varying the number of inner and outer cladding airhole rings, one can have different spectral variations of leakage loss (later shown in Fig. 12) for wavelength range λ>λc. Consequently, the increase in leakage loss can be tuned to compensate for higher gain efficiency at higher wavelength, thus leading to inherently flattened gain. Moreover, our proposed HNPCF is effectively single moded over the range of operating wavelengths. In addition, the HNPCF remains effectively single-moded for range of operating wavelengths as the normalized air-hole size d/Λ is less than 0.43 [24, 25]. The splice loss between HNPCF-RA module and conventional SMF due to mode field diameter mismatch is theoretically evaluated according to the definition [26] and its spectral variation is exhibited in Fig. 3. The splice loss, which is calculated at both ends of the HNPCF module, is larger than what we consider in the present paper (as discussed later in sec. 4).
3. Raman amplification model
The Raman gain efficiency (RGE) γR, related to the frequency separation Δν between the interacting signals, is calculated according to [15, 27]
where is , ip are the normalized signal and pump intensities which are calculated through V-FEM by incorporating Poynting vector definition [15], S is the PCF cross-section, and C SiSi(Δν) is the Raman spectra relative to Si-O-Si bounds when the pump wavelength is λ ref =1455-nm [27]. The peak value of Raman gain coefficient for PCF (at Δν=13.2 THz), for unpolarized pump and signal, at 1455-nm pump wavelength is 3.34×10-14 m/W [15]. The double Rayleigh backscattering (DRB), which causes a delayed replica of the signal with the same propagation direction as the signal that interferes with the signal and generates noise, becomes more pronounced in FRAs than for EDFAs [8, 9]. This DRB induced noise is termed as multi-path interference (MPI). To evaluate the DRB-induced MPI, the Rayleigh backscattering coefficient is the key parameter to be known. Due to the complex topology in the PCF cladding in comparison to conventional optical fiber, PCFs may suffer from the DRB induced noise. The Rayleigh backscattering coefficient is evaluated through [16]
where n Si = 1.45 is the refractive index of silica, CR is the Rayleigh scattering coefficient which is assumed to be 1 dB/km/μm4 and i(x,y) is the normalized field intensity of a signal. The variation of RGE of the optimized HNPCF is shown in Fig. 4 as a function of frequency shift. The RGE spectrum is obtained at 1455-nm depolarized pump. The RGE peak for the proposed HNPCF structure is 4.88 W-1 · km-1 at a frequency shift of 13.1 THz. Figure 5 represents the spectral variation of Rayleigh backscattering coefficient for the optimized HNPCF.
Fig. 4. Variation of Raman gain efficiency as a function of frequency shift for the designed HNPCF pumped at 1455 nm depolarized pump.
The analysis of the FRA performances is based on a set of propagation equations, which describe the forward and backward power evolutions of pumps, signals, and noise along the fiber. The HNPCF-RA is modeled through Eq. (5)–(8) [16, 28], where interactions between pump-to-pump, pump-to-signal, and signal-to-signal are considered. Raman rate equations consider the effect of amplified spontaneous emission (ASE) noise and its thermal dependence as represented by Eq. (8). Despite the benefits, FRAs exhibit DRB which may induce the cross talk between the signals. DRB is an important concern due to long interaction length of fiber. In PCFs, DRB may appear due to its complex design. Therefore, to know the impact of DRB, separate set of equations is written as expressed by Eq. (7).
with
where +/- sign indicates the forward/backward direction, , , and are the forward/backward power of kth pump or signal, ASE noise, and single Rayleigh backscattering (SRB) at frequency νk at the distance z along the fiber, respectively, νref is the reference frequency where RGE spectrum is measured and it scales RGE coefficient if the pump frequency is different than νref, kp is polarization factor which is equal to 2, h is the Planck’s constant, kB is the Boltzman’s constant, T is the absolute temperature of the fiber which is fixed to 300°K for present analysis, and αk and εk are, respectively, the fiber attenuation and the Rayleigh backscattering coefficient at frequency νk , both are expressed in km-1. The usage of pumps in backward direction makes the problem as two-point boundary-value which is solved by Dormand-prince method that considers Runge-Kutta’s (RKs) algorithm. The boundary conditions are applied at PCF input and output ends as Psignal |z=0 = Pso and Ppump |z=L = Ppo , respectively, where L is the length of PCF, Pso and Ppo are the input powers of signal and pump, respectively. After solving Eq. (5)–(8) with RKs algorithm, the Raman gain, optical signal-to-noise ratio (OSNR) due to both ASE and Rayleigh backscattering component, DRB [16], and noise figure (NF) [29] are calculated as
where Ps stands for the signal power at fiber end, Δμ is the OSNR bandwidth which is 0.1 nm (i.e. 12.5 GHz) for present analysis.
4. Numerical results and discussion
Figure 6 interprets the spectral variation of leakage loss and dispersion for the optimized HNPCF design. The leakage loss varies from 0.74 dB/km to 1.79 dB/km. The optimized HNPCF has a slowly varying negative dispersion coefficient (-102 ps/nm/km to -110 ps/nm/km) over the C-band wavelengths. The HNPCF has a dispersion slope of -0.26 ps/nm2/km, resulting relative dispersion slope of 0.0024 nm-1. Figure 7 corresponds to the residual dispersion of 2-km long optimized HNPCF in the link of 12.5-km long conventional single mode fiber (SMF). The residual dispersion varies from -1.98 ps/nm to 2.44 ps/nm for wavelength of interest, which is suitable for 40-Gbps transmission systems [30].
Further, nineteen signals (1530–1558 nm) spaced at 200 GHz are launched to the optimized HNPCF-RA module of length 2-km with an input power of -10 dBm/ch. Numerical simulations show that 13.7 dB net gain with ±0.85-dB gain ripple (GR) is achievable over 28-nm bandwidth, pumped at 1450-nm with 520 mW of power. Note that several pumps are used to flatten the gain in discrete type FRAs [10]. Recently, Kakkar et al [12] have designed a flat gain discrete fiber Raman amplifier based W-shaped highly nonlinear fiber (HNLF). HNLF Raman amplifier module of 13.6-km length shows ±1.4-dB GR. In contrary to the gain flatness reported in the literature [12], our optimized HNPCF-RA module of length 2-km provides high gain of 13.7 dB with ±0.85-dB GR over 28-nm bandwidth as shown in Fig. 8.
Figure 9 presents the DRB spectra for the optimized HNPCF. The DRB varies from -44.8 dB to -41.9 dB, keeping low DRB induced noise in HNPCF-RA. However, Figs. 10 and 11 stand for the noise figure and OSNR for 2-km long optimized HNPCF. NF varies from 8.03 dB to 7.42 dB, providing NF tilt of 0.61 dB, while OSNR changes from 39.56 dB to 40.75 dB with 0.59-dB OSNR ripple. The effect of wavelength dependent fiber attenuation is included in the calculation of Raman performances of the HNPCF. A typical value of attenuation coefficient for a conventional high delta fiber (0.55 dB/km at 1550 nm) is considered [12, 31] for the present analysis. But, in general, such small cored PCFs may possess high loss values upto few tens dB/km. With successive progress on fabrication technology of PCFs, these losses can be reduced further to the level of conventional fibers.
In lumping the designed HNPCF-RA module to the conventional SMF link, large splice loss values can be expected due to mode-field diameter mismatch (as shown in Fig. 3). Since our HNPCF-RA is a single stage amplifier. Therefore, the feedback of partial gain into the HNPCF gain medium is not considered in the present analysis. The large splice loss can be reduced by splicing the HNPCF-RA to conventional SMF in a specially constructed manner [32]. The splice-free interface of PCFs with SMFs technique is versatile enough to interface any type of index guiding silica PCF [32]. Therefore, in our simulations we have considered the splice loss of 0.6 dB between highly nonlinear PCF to conventional SMF [32]. The actual splice loss as evaluated theoretically (shown in Fig. 3) is large at short signal wavelengths. This may deteriorate the overall gain performances. An effect of actual splice loss on overall Raman performances of PCFs is now under investigation.
Further, we show the affect of varying the number of inner and outer clad air-hole rings on the net gain spectra of HNPCF. The leakage loss varies by varying the number of inner and outer clad air-hole rings, as examined in Fig. 12. When N=14 (i.e. there is no perturbed airhole rings, and all fourteen air-hole rings are build from hole-diameter d), the leakage loss is very small and as the number of perturbed air-hole rings (i.e. outer clad rings) increases, keeping intact the total number of air-hole rings, e.g. N=12, 11, 10; and N′=2, 3, 4, respectively, the leakage loss rises rapidly. Figure 13 stands for the variation of net gain spectra for different set of inner and outer clad air-hole rings. It can be clearly seen from Fig. 13 that GR becomes minimum for a particular set of inner and outer clad air-hole rings. Therefore, it can be concluded from Figs. 12 and 13 that GR minimizes for an optimum selection of inner and outer clad air-hole rings (which is N=11, and N′=3), that corresponds to optimum leakage loss spectra (represented by solid blue color line).
Fig. 12. Spectral variation of leakage loss for different set of air-hole rings in inner and outer clad of the HNPCF.
Fig. 13. Effect of leakage loss on net gain spectra for different set of air-hole rings in inner and outer clad of HNPCF.
Table 1 summarizes and compares the Raman performances of our optimized HNPCF-RA module to the HNLF-RA module reported in the literature [12]. Our optimized HNPCF-RA module shows the best overall Raman performances reported till far in case of PCF and as well conventional fiber type using a single pump with additional benefit of high negative dispersion. Further, such gain flattening can be achieved in any desired wavelength band by appropriately selecting the pump wavelength and fiber structural parameters to have suitable “cut-off”. Therefore, our proposed fiber module can serve as an integrated device with two key functionalities embedded in a single component.
Table 1. Comparison of Raman performances of our optimized HNPCF-RA module and conventional HNLF-RA module [12]
5. Sensitivity analysis of HNPCF-RA module
We performed the sensitivity analysis of structural parameter variation on Raman performances of 2-km long optimized HNPCF-RA module. We did the analysis for three different cases; (i) ±1% variation in the lattice period, (ii) ±1% variation in the hole-diameter of inner cladding and (iii) ±1% variation in the hole-diameter of outer cladding. It is observed that ±1% variation in the hole-diameter of outer cladding doesn’t affect the OSNR, NF, and DRB performances of optimized HNPCF-RA module; however, it affects only the magnitude of net gain and the gain ripples. Further, changing the hole-diameter of inner cladding airholes has the impact on its OSNR, DRB, NF and gain characteristics. The OSNR, DRB, NF and net gain varies by ±1%, ±1.3%, ±0.13%, and ±6% to its optimized values, respectively. Next, by varying the lattice period of HNPCF to ±1%, net gain changes to ±3% (i.e. ±0.5 dB) value and DRB is reduced by ±1.4 %. Figure 14 represents the affect of structural parameter fluctuation on net gain spectrum of the proposed HNPCF-RA module. Additionally, by decreasing the pitch to 1% from its optimum value, the dispersion decreases to -112 ps/nm/km from -107.5 ps/nm/km.
Fig. 14. Spectral variation of net gain spectra for (i) optimized HNPCF-RA and ±1% variation in the (ii)-(iii) lattice period, (iv)-(v) hole diameter of inner cladding air-holes and (vi)-(vii) hole-diameter of outer cladding air-holes, of the optimized HNPCF-RA module.
6. Conclusion
We have demonstrated a novel inherently gain-flattened HNPCF design based on W-shaped refractive index profile. The HNPCF structural parameters are well optimized by homely developed GA optimization tool. The wavelength dependent leakage loss is optimized by varying the number of inner and outer clad air-hole rings to achieve the optimized net gain spectrum with ± 0.85-dB gain ripple and net gain of 13.7 dB over 28-nm bandwidth by usage of single pump. The additional advantage of the proposed fiber is that it has slowly varying negative dispersion in operating range of wavelengths. The Raman performances of our designed HNPCF are also compared with the conventional HNLF design based fiber amplifier. It is examined that our optimized HNPCF shows the overall better Raman performances. The fiber tolerance analysis is performed for the optimized HNPCF design to realize its practicality. The fabrication of such device is now under consideration.
Acknowledgments
Authors acknowledges to 21st Century COE (Center of Excellence) program: Meme-Media Technology Approach to the R&D of the Next Generation Information Technologies.
References and Links
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) and outer clad (
) of the designed HNPCF.