We propose a new method for generating flat self-phase modulation (SPM)-broadened spectra based on seeding a highly nonlinear fiber (HNLF) with chirp-free parabolic pulses generated using linear pulse shaping in a superstructured fiber Bragg grating (SSFBG). We show that the use of grating reshaped parabolic pulses allows substantially better performance in terms of the extent of SPM-based spectral broadening and flatness relative to conventional hyperbolic secant (sech) pulses. We demonstrate both numerically and experimentally the generation of SPM-broadened pulses centred at 1542nm with 92% of the pulse energy remaining within the 29nm 3dB spectral bandwidth. Applications in spectral slicing and pulse compression are demonstrated.
©2006 Optical Society of America
Recent progress in high quality supercontinuum generation (SCG) techniques in optical fibers has enabled a wide range of applications including optical coherence tomography , frequency metrology  and dense wavelength multiplexed optical communication systems based on spectral slicing . For many applications, optimising the spectral density for a given pump power whilst maintaining a flat spectral profile is critical, whereas for others maintaining a high degree of coherence is a primary concern.
Broad spectra can be generated in both dispersion regimes by launching short pulses in HNLFs. Anomalously dispersive fibers generally provide for the highest broadening factors  resulting from the complex interplay between various non-linear effects e.g. SPM, four wave mixing and soliton self-frequency shift. In normally dispersive fibers, the combination of dispersion and self-phase modulation can allow the generation of flatter spectra . The main limits to spectral pulse quality in this regime is the spectral ripple that arises from SPM of the sech-shaped pulses characteristic of many short pulse lasers, and the effects of wave-breaking which may lead to a significant change in the temporal pulse shape and to a severe transfer of energy into the wings of the spectrum. Such effects can in principle be avoided by using pulses with a parabolic temporal intensity profile . SPM induces a perfectly linear chirp for such a pulse shape meaning that parabolic pulses remain parabolic in shape whilst propagating within a nonlinear fiber, resulting in spectrally-flat, highly-coherent pulses. However, it remains a key issue as to how to reliably generate parabolic pulses in the first instance. To date, it has been shown that parabolic pulses can be generated under certain conditions within normally dispersive optical fiber amplifiers by exploiting the interplay between gain, nonlinearity and dispersion. The use of both rare-earth doped amplifiers [6–7] and Raman amplifiers  for this purpose has been reported. Parabolic pulse generation is also possible by exploiting nonlinear pulse evolution in a normally dispersive dispersion decreasing fiber . Whilst good quality parabolic pulse generation is in principle possible using each of the above approaches they all make for relatively long and complex systems. Recently however we demonstrated a simple compact parabolic pulse source based on reshaping soliton pulses using a SSFBG . The SSFBG applies precise spectral filtering to the amplitude and phase of the incident soliton such that upon reflection the pulses are parabolic in form.
In this paper, we report the results of numerical and experimental studies of SPM-induced spectral broadening of these shaped parabolic pulses in a normally-dispersive, silica-based HNLF. We present results in terms of the extent of spectral broadening, proportion of energy stored within the 3dB bandwidth, and the reduction of spectral ripple relative to the case for conventional sech shaped pulses. Finally, we go on to demonstrate the benefits this simple parabolic pulse reshaping technique can provide for spectral slicing source applications at telecommunications wavelengths, and how the high coherence of the output signal can be exploited for pulse compression.
2. Parabolic pulse generation and experimental set-up
We studied the SPM-induced spectral broadening performance of different pulse-shapes and pulse-widths using the experimental set-up shown in Fig. 1. The transmitter was based on an actively mode-locked erbium fiber ring laser (EFRL) and produced a 5GHz train of 2ps pulses at a wavelength of 1542nm. These pulses were then used as the input to the parabolic pulse shaper formed by a SSFBG. The grating was designed to produce shaped pulses with a parabolic envelope with a full width at half maximum (FWHM) of ~10ps. The grating was apodized using a 5th order super-Gaussian profile which was used to smooth the pulse edges, hence reducing their spectral extent. The quality of the shaped pulses was assessed using simple spectral measurements and either an electro-absorption modulator based frequency-resolved optical gating technique (EAM-FROG) [12–13] for the case of the parabolic shaped pulses, or a commercial SHG-FROG system in the case of the shorter incident laser pulses. Figure 2(a) compares the measured optical spectrum (gray dashed trace) of the pulses reflected off the SSFBG to the designed spectrum of a single parabolic pulse (blue solid trace). As can be seen we can accommodate 11 spectral lobes within the shaped pulse bandwidth with a profile that is in very good agreement with the required spectral form – these results highlight the quality of our grating writing process. Good agreement between the retrieved spectrum (dashed black trace) and the direct spectral measurement is also achieved. However, as can be seen from Fig. 2(a), the agreement is slightly worse at shorter wavelengths due to wavelength dependent insertion loss of this particular sampling EAM. Figure 2(b) shows the temporal profile of the measured shaped pulses (solid blue trace), which is fitted with an ideal parabolic pulse (circles), illustrating excellent agreement between the two. The phase is shown to be nearly constant across the full width of the pulse. We compared the performance of these pulses against that of nearly transform-limited sech pulses with FWHM of 2ps and 10ps, obtained either directly from the laser source or after filtering with a narrowband cavity filter respectively (Fig. 1). The intensity profiles of these pulses together with their corresponding spectra are shown in Fig. 2(c)–(d).
Each of these pulse forms were then amplified and fed into 500m of a HNLF with dispersion -0.87ps/nm/km, dispersion slope -0.0006ps/nm2/km, nonlinear coefficient ~19W-1km-1 and total propagation loss 1dB.
3. System results
Prior to performing experiments we simulated the propagation of the different waveforms in the HNLF using the standard split-step Fourier method in order to examine the dependence of the spectral broadening on the initial pulse properties (shape and energy). The different cases are compared for the same initial pulse energy in terms of the 3dB spectral bandwidth and the ratio between the energy within the 3 dB bandwidth and the total energy of the pulses. This last parameter allowed us to quantify the optical wave breaking phenomenon, characterized by the appearance of side lobes at the edges of the pulse spectrum. The results we obtained for the three different pulse forms are summarized in Fig. 3(a)–(b). The initial 2 ps sech pulses undergo the greatest spectral broadening (~33 nm for the highest energy level of 100 pJ). However, as soon as the energy levels increase, wave-breaking effects become severe with only half of the energy remaining in the central part of the spectrum. The 10ps sech pulses do not exhibit such an energy transfer to the spectral wings with more than 90% of the energy remaining within the 3dB bandwidth. Their spectra broaden almost linearly with increasing pulse energy, reaching ~17nm for the highest pulse energy considered (100pJ). By contrast the 10ps parabolic pulses broaden up to ~29nm for 100pJ pulse energy (similar to the 2ps sech case). However, in this case most of the energy (~92%) is confined within the central 3dB bandwidth of the spectrum, as in the case of 10ps sech pulses.
In order to confirm our numerical analysis we performed spectral broadening experiments. The results of this comparison are presented in Figs. 3(a)–(b) where it is seen that very good agreement between theory and experiment is obtained, albeit a slight difference originating from non ideal experimental pulse shapes. This confirms that the SSFBG shaped parabolic pulses give excellent performance in terms of providing higher more uniform spectral densities across extended wavelength ranges relative to soliton pulses. This can offer significant benefits in terms of maximising the total throughput in spectral slicing applications as we shall show below. Fig. 3(c) shows the experimental spectra measured after the HNLF, for the three cases, for a pulse energy level of ~100pJ. The spectral traces are normalized with respect to total energy and plotted on a linear scale. The spectral shapes of the sech pulses both show high relative ripple, which could compromise the quality of the processed signal, for example in terms of unequal WDM channel amplitudes after slicing of the SC spectrum. The spectral shape of the parabolic pulses is smoother and flatter compared to the other two cases providing more optimal conditions for further applications of the signal, as discussed above. (Note that the slight peak at the central wavelength in the power spectrum of the output signal is simply an artefact of the current transmitter and should be ignored). Figure 3(d) shows the good agreement between the spectrum of the measured and ideal parabolic, plotted on a logarithmic scale. The flat top spectrum and the rapidly falling edges of the experimental trace are characteristic of the parabolic pulse form with a linear chirp.
The flat spectrum and optimised spectral density are attractive for spectrally sliced source applications since we can tailor the shape of the flat generated spectrum to match the full bandwidth of the arrayed waveguide grating (AWG) filter minimising the overall loss and thereby maximising the spectral density per channel. To show this we filter out the broadband spectrum using an AWG with 100 GHz channel spacing. Fig. 4(a) shows a superposition of the spectra of all 38 channels after the AWG. The channels are generated in the 1528-1558nm-wavelength range. The optical signal-to-noise ratio (SNR) for each channel was better than 30dB. The pulse width of each individual channel together with the time bandwidth were also characterized as a function of wavelength demonstrating the homogeneous pulse quality across the full wavelength operating range (Fig. 4(b)). The pulse duration and time bandwidth product are almost constant at ~7.2ps and 0.58 respectively, across all channels, as determined mainly by the AWG filter characteristics. An example of the pulse shape and chirp associated with a filtered channel, (channel 6), measured using SHG-FROG is shown in Fig.4(c). Oscilloscope traces of three randomly chosen channels are shown in Fig. 4(d) and confirm the good noise performance of the system.
Pulses of such a broad spectral bandwidth are potentially useful for other applications such as pulse compression, provided of course that they have a smooth chirp profile. To test this we launched the spectrally broadened parabolic pulses into ~30m of SMF. An attenuator was placed before the SMF to allow us to set the power levels so as to avoid nonlinear effects in the compression fiber. The broad spectrum of the compressed pulse meant that it was not possible to use either of our FROG techniques to assess the signal directly within the time domain so we performed simple autocorrelation measurements. The inset in Fig. 5 shows the numerically compressed pulse intensity profile using the ideal apodized parabolic pulses of Fig. 2(b) as the starting waveform, which exhibits a predicted FWHM of ~190fs. Figure 5 shows the corresponding calculated autocorrelation trace, which has a predicted FWHM of ~260fs. In the same graph we also plot the measured autocorrelation trace. If we assume the same conversion factor from autocorrelation to real pulse duration as derived from the simulations (1.365), the autocorrelation width corresponds to a de-convolved pulse width of 310fs (i.e. ~50% more than the theoretical minimum). This represents a compression factor of more than 30 relative to the initial 10ps parabolic pulses highlighting the quality of the linear chirp generated in the HNLF. We believe that this difference between numerical and experimental predictions can be attributed to deviations from an ideal parabolic pulse shape.
In conclusion, we have numerically and experimentally demonstrated the application of SSFBG-based linear pulse shaping into parabolic pulses for the generation of ultra-flat broadened spectra in a normal dispersion HNLF. These parabolic pulses provide optimum performance in terms of spectral broadening, flatness and density as compared to sech pulses of various pulse widths. We have also demonstrated potential applications including spectrally sliced pulse source generation and efficient pulse compression.
Chrisophe Finot gratefully acknowledges the financial support through the European Union Marie-Curie Fellowship scheme. Morten Ibsen acknowledges the Royal Society of London for the support through a University Research Fellowship.
References and links
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