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We propose an optimised fiber design for obtaining spectrally flat, high power supercontinuum (SC) source covering C+L band of optical communication. The design is based on the principle of controlled expansion of SC bandwidth, in the absence of soliton decay, so that a high output power alongwith smooth spectral profile can be achieved. A detailed optimisation has been carried out with respect to fiber dispersion profile, pulse width and fiber length, and the physical mechanism for each case has been emphasised. Numerical simulations show that single mode output with > 30 dBm (± 0.5 dB) optical power is attainable over 90-nm bandwidth with ~ 16 pJ of input pulse energy.
©2006 Optical Society of America
1. Introduction
Over the last decade, supercontinuum (SC) generation has become a very popular technique to obtain broadband optical sources over any desirable wavelength band. Such broadband sources, covering octaves of bandwidth, find applications in optical coherence tomography, sensing, spectroscopy and DWDM sources for optical communication. Much of the research in the field of SC generation has been focused on extending its bandwidth by dispersion tailoring in various fiber designs including photonic crystal fibers [1], tapered air-clad fibers [2] and highly nonlinear dispersion shifted fibers [3]. For applications involving ultra-wide bandwidths (in excess of 1000 nm), photonic crystal fibers (PCFs) have an edge over conventional fibers because of their small effective areas (~ 3–4 μm 2) and the possibility of shifting the zero dispersion wavelength (ZDW) to wavelengths as short as the visible range. SC spectrum with typical bandwidth of 800–1000 nm having 15–20 dB power variation can be easily generated using high power (kiloWatt) femtosecond pulses in standard PCFs [4].
Dispersion-flattened, conventional highly nonlinear fibers present another class of fibers used for SC generation [5]. Very flat dispersion spectra and effective areas of the order of 10–20 μm 2 can be obtained in these fibers, leading to SC bandwidths in excess of ~ 300 nm. Design simplicity of such fibers alongwith low splice loss (< 0.02 dB) with conventional transmission fibers make them potential candidate for making SC based devices for optical communication systems. One such application is DWDM sources, in which one would prefer to have high power supercontinuum over a narrow bandwidth (~ 100 nm) alongwith good spectral flatness (< 1 dB power variation). Mori et al [6, 7, 8] have shown that a dispersion decreasing, dispersion flattened fiber with a convex dispersion profile can provide SC spectrum with < 1 dB power variation over two wavelength bands (75 nm each) on either side of the pump pulse wavelength (1550 nm). However, the problem with this design is that there is a sharp peak at the pump wavelength in the SC spectrum, and most of the pump pulse energy is stored in this sharp peak. As a result, the spectrally flat region is quite low in power (~ -20 dBm). This sharp peak is typical of most of the supercontinuum spectra, and it is a manifestation of SPM effect during higher order soliton compression. In this paper we propose that a careful choice of dispersion profile, the input pump pulse width and fiber length can prevent this sharp spectral peak and lead to a more even distribution of pump power among the generated wavelengths. We present a design based on conventional dispersion flattened fiber, for obtaining high power, flat supercontinuum in the wavelength bands that are of utmost interest in optical communication systems. Numerical simulations show that single mode output with > 30 dBm (± 0.5 dB) optical power is attainable over 90-nm bandwidth with ~ 16 pJ of input pulse energy.
2. Numerical simulation of nonlinear pulse propagation
Pulse propagation in a single-mode fiber is governed by the following equation [9]:
Here A(z,t) is the slowly varying amplitude of the pulse, α is the background attenuation and γ is the nonlinear parameter of the fiber defined as n 2 is the nonlinear coefficient of the fiber, ω 0 is the center frequency of the pulse, c is the velocity of light in free space and Aeff is the effective area of nonlinear interaction. βm are the coefficients of Taylor series expansion of β(ω) about the carrier frequency ω 0 and R(t) is the Raman response function which includes both the electronic and vibrational contributions. The various terms in the above equation incorporate the effects of dispersion, self phase modulation, self steepening, cross phase modulation, four wave mixing and Raman scattering. Eqn. 1 is valid only under the slowly varying amplitude condition but it is reasonably accurate even for shorter (femtosecond) pulses if sufficient number of higher order dispersive terms are included. We have included dispersion terms upto six orders while solving the above equation using split step Fourier method [9] and we have verified the accuracy of our model by reproducing published experimental results for femtosecond pulses.
3. Fiber design and modeling
Figure 1 shows the refractive index profile of the dispersion-flattened W-fiber. Here Δ is defined as ( - )/2 where n 3 corresponds to pure silica refractive index (calculated using Sellemeier’s equation [10]) and i = 1,2 refer to core and depressed cladding respectively. To calculate the effective refractive indices and the normalised modal fields of the guided fundamental mode in the proposed fiber, we obtain the eigenvalue equation using Matrix method [11] and solve it by bisection method. The effective refractive index of the mode is calculated upto fifteenth decimal place so as to accurately determine the dispersion coefficients (βm ). The fiber refractive indices and dimensions are so chosen that the fiber is single moded in the entire wavelength range of operation and the fundamental mode field is tightly confined to the core to enhance nonlinearity. It is also ensured that the fiber has a flat spectral variation of dispersion coefficient D around the pump wavelength, which is chosen to be at 1555 nm.
4. Optimisation for high power, flat bandwidth supercontinuum
4.1. Effect of dispersion slope
The process of supercontinuum generation is an interplay between various nonlinear and dispersive effects. One of the important steps in spectral broadening is the higher order soliton fission caused primarily due to the perturbation by third order dispersion (TOD) or self steepening effect or spontaneous Raman scattering (SRS) [9]. In short lengths of fibers, SRS is usually not dominant and soliton decay is primarily caused by the presence of finite third order dispersion if the pump pulse is close to the zero dispersion wavelength. Soliton decay due to TOD splits the input pulse into a solitonic pulse in the anomalous dispersion regime and a dispersive wave (DW) in the normal dispersion regime [12]. As a result the spectral as well as the temporal spectrum gets divided into distinct parts and the spectral flatness gets deteriorated. Thus for applications involving narrow but flat bandwidths, one would like to avoid soliton decay so that the spectrum broadens itself uniformly under the sole effects of SPM and GVD, and the pump pulse power gets evenly distributed among the neighbouring wavelengths. Such soliton decay can be suppressed if the magnitude of β 3 is kept low (i.e dispersion slope is small). So the first requirement for designing a flat bandwidth DWDM source is to use a fiber with minimum, positive dispersion slope (e.g. at the peak of convex dispersion profile). Figures 2 and 3 show the evolution of SC spectrum in a single fiber for two different values of β 3. All the other parameters are kept the same-pump wavelength-1555 nm, input peak power-200 W and pulse width-80 fs. The fiber parameters are Δ1 = 1.2%, Δ2 = -0.5% and b/a = 3. We may note here that for higher value of β 3 the soliton decay takes place much before any significant spectral broadening takes place, and hence such a case is undesirable for high power, flat bandwidth applications. Figure 4 shows the dispersion profile of the designed fiber for different scaling ratios (pulling speeds while fiber drawing). The solid blue line (Dpeak ~0.5 ps/km.nm) shows the profile used for generating Figs. 2 and 3.
Fig. 4. Dispersion profiles of the designed dispersion-flattened W-fiber for different scaling ratios
4.2. Effect of input pulse width
Pulse width is another important parameter which decides the bandwidth as well as spectral flatness of the supercontinuum spectrum. We observe that even when the soliton decay due to DW generation is avoided, the supercontinuum spectrum is usually characterised by a sharp spiked structure around the pump wavelength in spectral domain. Such a spiked structure is caused by the phenomenon of higher order soliton compression. When a higher order solitonic pulse is injected in a fiber with high anomalous dispersion, then the interplay between SPM and positive dispersion causes the pulse to compress [9]. This process is known as higher order pulse compression and is very instrumental in broadening the pulse spectrum. During this process the wings of the pulse are not as well compressed as the central part and as a result the compressed output pulse attains the shape of a narrow spike over a broad pedestal of energy in the temporal domain. The corresponding pulse spectrum is characterised by sharp peak in the center of the pulse spectrum, which traps most of the pulse energy in it and two low power side lobes on either side of the central peak. As the pulse propagates in the fiber, the spectral side lobes broaden spectrally but remain low in power [7]. Thus for high power, spectrally flat SC, higher order soliton compression should be avoided by using femtosecond pulses in fibers operating near zero dispersion regime.
Since to achieve similar levels of spectral width, picosecond pulses have to undergo greater amount of compression as compared to femtosecond pulses, the spectrum corresponding to compressed picosecond pulses is much more deteriorated in terms of spectral flatness. Therefore, it is more advantageous to use femtosecond pulses at the input. Another important point to keep in mind is that operating with ultrashort pulses close to the zero dispersion regime again increases the chances of soliton decay by dispersive wave generation, which could degrade the SC flatness. Thus one has to choose the pulse width and the dispersion profile iteratively for maximum flatness and high power density. Figure 5 shows the normalised output supercontinuum spectra obtained with different input pulse widths. The input pulse energy is the same in all the cases and the length is optimised for best flatness. The rest of the parameters are the same as in Fig. 6. The 40 fs pulse undergoes soliton decay just after the shown length and generates a broad but highly non-flat spectrum. The 120 fs pulse has a narrower bandwidth and the ripple due to peaks and valleys is sharper as compared to the 80 fs case. It has been observed that maximum flatness is achieved if the fiber consists of two sections, the first half with peak dispersion Dpeak =-0.05 ps/km.nm (orange curve in Fig. 4) and the second half with Dpeak =0.5 ps/km.nm (blue curve in Fig. 4). The total length of the fiber is 3.7 m. By having the first half of the fiber with peak dispersion on slightly negative side, we are further delaying the process of solitonic compression. Thus in the first half of the fiber, the pulse broadens smoothly under the sole effect of SPM and in the second half, pulse compression starts to take place and the spectrum broadens further. Figure 6 shows the optimised supercontinuum spectrum in the designed fiber with input pulse width is 80 fs and the peak power is 200 W. We may note from Fig. 6 that high power (> 30 dBm) output power with ± 0.5 dB ripple is achievable over 90 nm bandwidth (1512 nm – 1602 nm) over C+L band of optical communication systems.
4.3. Fiber length
Fiber length is an obvious parameter affecting the power density and flatness of supercontinuum spectrum. As the fiber length increases, the SC spectrum lowers down in intensity and spreads out in bandwidth alongwith creation of finer spectral features. Thus there is always an optimum fiber length for which the flatness is maximised.
5. Optimisation of bandwidth and power output
In this section, we show that the SC spectrum can be further tailored according to the requirements of the system by choosing different operating conditions. For example by a choice of different dispersion profiles and fiber lengths one can achieve a lower bandwidth-higher output power spectrum or vice-versa. Figure 7 shows the different spectra achieved by changing the peak dispersion coefficient (Dpeak in ps/km.nm) of the fiber and optimising the total fiber length (L). The corresponding dispersion plots are shown in Fig. 4 and the input pulse parameters are the same as in Fig. 6. L 1 and L 2 for the red curve in Fig. 7 refer to lengths of the first and second sections of the fiber respectively. We may note that very high power with flat but narrower bandwidth can be achieved by operating in slightly higher anomalous dispersion regime (black curve).
One of the important advantage of the proposed design is that the output power level of the SC spectrum can be tuned by varying the input pulse power, without degrading the spectral flatness. This gives a dynamic range of power levels available for the DWDM source based on this design. Figure 8 shows the SC spectra under three input power levels. For input peak power (Pp ) lower than 150 mW, the SC is not efficiently generated because the nonlinear effects are substantially reduced.
6. Conclusions
A comprehensive analysis for spectral shaping of high power supercontinuum over 90-nm bandwidth has been presented. The physical mechanisms responsible for affecting the spectral flatness of supercontinuum have been discussed and an optimised design for flat-top (< ± 0.5 dB ripple), high power supercontinuum source covering C+L band of optical communication window has been presented. The spectral flatness is shown to be tolerant with respect to the input pump power and possibilities of higher output power spectra over narrow wavelength range have also been discussed.
References and links
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