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We demonstrate a method of background component suppression of synthesized pulses for flatly broadened supercontinuum (SC) generation. An adaptive pulse shaping in frequency domain achieved a 26 dB contrast between pulse center and background level in auto-correlation trace by combining two fitness functions during feedback-controlled pulse shaping. The pulse was used as a SC pump, and the spectral peak of the SC at the pump wavelength was suppressed by 5 dB using the combination scheme. Simulation results show that the phase spectra control is required to be within ± π/100 rad to suppress the spectral peak below 3 dB. The results show that adaptive pulse shaping is required to improve SC flatness due to the small mismatch tolerance.
©2013 Optical Society of America
1. Introduction
Broadband supercontinuum (SC) has attracted the attention of researchers in diverse fields. SC has been mainly generated by propagating an intense pump pulse through a highly nonlinear fiber with long nonlinear interaction length. The pump pulses were commonly produced from passively mode-locked lasers with pulse repetition rates in the order of 100 MHz, and the spectral mode spacing of the SC spectra have been in the same order as the repetition rates [1]. Spectral flatness is one of the key characteristics in certain applications. The flatness can be achieved by using highly nonlinear fibers with normal dispersion in the entire SC bandwidth and pump pulses that have low background level [2]. Pulse compression is often employed to achieve high peak power in broadband SC generation, and careful fiber design is needed to suppress the pedestal component and spectral peak at the pump pulse wavelength. In reference [2], a soliton Raman shift was used to generate an intense and clean soliton pulse. The pedestal components, or weak components, remain at the pump pulse wavelength since they contribute less to the spectral broadening due to their low intensities.
Recently, SC with wide mode spacing over 10 GHz were studied for some applications such as multi-carrier sources of wavelength division multiplexing communication [3], optical coherence tomography [4,5], optical spectroscopy [6,7], and calibration of spectrographs [8–10]. The SC with wide mode spacing offers advantages in the high spectral intensity of each modes, which is spectrally resolvable by spectrographs or an optical spectrum analyzer. The generation of flatly broadened SC with wide mode spacing is desired in a plethora of applications, and the use of synthesized pulses as SC pumps has emerged as promising approaches to realize flatly broadened SC.
We have developed an optical pulse synthesizer (OPS), which can generate arbitrary waveforms by manipulating light in the frequency domain [11–14]. Electric fields in the time domain and frequency domain are related by Fourier transform and, consequently, the frequency domain signal processing produces the capability of arbitrary waveform synthesis. When an optical frequency comb (OFC) is used for seed light and each comb line is resolved by a grating, the line-by-line control of the amplitudes and phases of each OFC line can generate repetitive arbitrary waveforms. The waveforms are repetitive and the repetition rates correspond to the spectral mode spacing. We have demonstrated diverse types of pulses, including optical soliton [15], and parabolic pulses [16], and have studied the generation of multi-gigahertz-spacing SC from the synthesized pulses [17].
An approach that uses synthesized pulses as SC pumps been reported from other groups, including an adaptive approach to tailor the spectral profiles [18,19]. The approach is attractive because of its capability to tailor the SC spectral profiles. It can realize unique spectral profiles, which cannot be achieved by pulsed lasers with fixed output pulse shapes, including sech2 and Gaussian shapes. An example of spectrum tailoring is the uniformity enhancement of SC spectrum. Spectrally uniform SC of about 10 nm bandwidth and 10 GHz spacing were generated using the backward propagation calculation and the adaptive approach of pulse shaping [19].
Even though the abovementioned approach is attractive, the accuracy of the generated pulses has not been fully discussed. In particular, the background component of the pulses, due to residual error in the phase spectrum control, should be suppressed for flat SC generation. The SC spectra broaden by a factor of 100 from the initial spectra of the pump pulses, and the spectral density decreases by more than two orders of magnitude relative to the original spectrum. Since the intensity of the background noise is low, the noise remains at the pump wavelength in the SC spectrum, creating sharp peaks. The background component suppression is necessary to generate uniform SC and tailor the SC spectra. In [19], the generated SC experienced small spectral broadening, which was an approximate factor of 10 from the pump pulse, and did not have a spectral peak at the pump wavelength.
In this study, we develop a method for suppressing the background component of the synthesized pulses in flatly broadened SC. We improve fitness function of the genetic algorithm (GA), which was employed for the phase spectrum control of the OFCs, to strongly suppress the background component. The synthesized pulse was used as an SC pump and the proposed method suppressed the peak at the pump wavelength more than the pulse synthesized through the previous fitness function. We also investigate the influence of the phase control accuracy on the SC spectrum in simulation. The simulation showed that strong suppression and feedback control are necessary for precise control while considering the signal crosstalk in the multiple signals to the OPS.
2. Suppression method and experimental setup
In this section, we describe the background component suppression method of the synthesized pulse. The synthesized pulses were used as pump pulses for SC generation. The experimental setup for SC generation using an optical pulse synthesizer is shown in Fig. 1 . We produced a seed OFC by modulating single-frequency light from a tunable laser diode by two cascaded phase modulators driven by 12.5 and 25.0 GHz signals. The laser output power and wavelength were 5.5 dBm and 1560.7 nm, respectively. The seed OFC had 31 lines and approximately 400 GHz bandwidth within 20 dB [14]. It was amplified by an erbium doped fiber amplifier (EDFA) and was input to OPS. The OPS was fabricated by a silica-based planar lightwave circuit technology and consisted of an arrayed waveguide grating (AWG), which had 30 output channels with 12.5 GHz spacing, and thermo-optic intensity and phase modulators in each channels. The components were integrated on a single silica-based chip. The AWG divided the individual lines to different output waveguides and the modulators controlled the power and phase. The frequency-domain modulation produced time-domain arbitrary waveforms. The modulation signals of the intensity modulators were determined from the spectrum of the OPS output measured by an optical spectrum analyzer (OSA). Those of the phase modulators were determined through a feedback control monitoring the auto-correlation traces. The feedback control procedure is described in detail subsequently in this section.
Fig. 1 Experimental setup for optical pulse synthesis and generation of supercontinuum with wide mode spacing. TLD: tunable laser diode, LN: lithium niobate, AWG: arrayed waveguide grating, EDFA: erbium-doped fiber amplifier, DFF:dispersion flattened fiber, DSP:digital signal processor.
After the pulse synthesis, the pulse was amplified up to a 30.5 dBm average power by a high power EDFA and transmitted through a 1-km-long dispersion flattened fiber (DFF) for spectral broadening. The dispersion and dispersion slope of the DFF were −0.17 ps/nm/km and 0.003 ps/nm2/km at 1550 nm, respectively. The dispersion profile was almost convexly parabolic and symmetric about the wavelength axis centering at 1560 nm. The nonlinear coefficient and loss were 7 /W/km and 0.25 dB/km, respectively. The spectra of the DFF output were measured by the OSA.
The control procedure of the power and phase spectra is described as follows. In this work, the target waveform was a transform-limited 3.2-ps-wide Gaussian pulse which was the shortest pulse we can generate using the synthesizer. The target power spectrum was calculated by Fourier transform of the waveform. The power spectrum of the comb was directly measured by the OSA and the intensity modulation was performed to target the spectrum to be the Gaussian profile. Direct measurement and precise control of the phase spectrum are difficult, and we introduced the genetic algorithm (GA) to generate target pulse shapes by feedback control.
We used the auto-correlation waveforms for the feedback control of the phase spectra. A computer-based digital signal processor obtained the auto-correlation waveforms, calculated the fitness values, and fed the signal back to the controller of the synthesizer. We introduced two fitness functions to calculate the feedback signals. One fitness function was the peak intensity of the auto-correlation waveform (hereafter “Fitness 1”). The other was difference between the target waveform and the measured waveform in logarithm scale of vertical axis (hereafter “Fitness 2”).
The feedback control using Fitness 1 cannot suppress the weak background noise originating from the small phase mismatch because the background component is not considered in the fitting (Fig. 2(a) ). The feedback control using Fitness 2 can evaluate the small background noise, and consequently suppress the background components (Fig. 2(b)). Fitting the linear scale difference does not distinguish between the pulse center and the background component and cannot sufficiently suppress the background components. Fitness 2 was calculated with the following equation.
Fig. 2 Illustrations of difference of the two fitness functions (a) peak power fitness function (Fitness 1), (b) Fitness function is calculated from the difference between target waveform and measured waveform (Fitness 2)
However, Fitness 2 is less-sensitive to the shape distortion at the pulse center, and cannot be introduced from the first generation of the GA. Thus, we first introduced Fitness 1 and subsequently Fitness 2.
3. Experimental results
Figure 3 shows the evolution of the fitness value during the feedback control of the phase spectrum. The triangles and circles express average and best fitness values in each generation, respectively. We employed Fitness 1 until the 100th generation. After the 50th generation, we readjusted the polarization state of the generated pulse and EDFA output power before the auto-correlator, and there was a discontinuity in the fitness series. During the generations, the fitness values gradually increased and the pulse became clearer.
After the 100th generation, we changed the fitness function from Fitness 1 to Fitness 2. The fitness values became smaller after the 100th generation, and it saturated around the 170th. At the 180th generation, we stopped the feedback control and the overall process took about 4 hours. The generated pulse was controlled to be closer to the target Gaussian waveform with the suppressed background level. At the 129th generation, there was a jump in the best fitness series. The series was smoothly changed after the generation, and we assume that the measurement error occurred at the specific data point. The OPS generated the stable pulse at least over 6 hours. The system had high repeatability so that it was able to generate the almost same pulses after 8 days [14].
Figure 4(a) and 4(b) show the auto-correlation traces of the generated pulses in linear and logarithmic scale in the vertical axis, respectively. The black curves show the waveform generated only using the Fitness 1 (Pulse 1). The red curves show the waveform using Fitness 1 and subsequently Fitness 2 (Pulse 2). The auto-correlation width of the Pulse 1 and 2 was 4.50 and 4.39 ps which corresponded to the inferred pulse width of 3.20 and 3.11 ps, respectively.
Fig. 4 Auto-correlation waveforms of the generated Gaussian pulses (a) linear scale, vertical axis, and (b) logarithmic scale, vertical axis. (black curve: the phase spectrum controlled only by Fitness 1 (Pulse 1); red curve: the phase spectrum controlled by combining Fitness 1 and 2 (Pulse 2)).
Although the two curves have only a small difference at the pulse center, the background component is high in the Pulse 1 trace. In contrast, the background component of Pulse 2 cannot be seen in the linear horizontal scale (Fig. 4(a)). The background noise is clearly shown in Fig. 4(b). The ratios between the pulse peak intensity and background noise of Pulse 1 and Pulse 2 were 17 dB and 26 dB, respectively. The 26 dB contrast of the trace is the measurement limit of the auto-correlator used in the experiment. The fitness function combination scheme realized a background noise suppression of 9 dB.
Figure 5 shows the SC spectra generated by the pulses shown in Fig. 4. The lower and upper spectra were generated by Pulse 1 and Pulse 2, respectively. We show the simulated SC spectrum, which was calculated from the transform-limited 3.2-ps-wide Gaussian pulse. The detailed simulation is described in the next section. The simulation and the experimental results are in good agreement and indicate that the pulses had Gaussian shape. The 20 dB bandwidths were 108 and 118 nm, respectively.
Fig. 5 Spectra generated from the pump pulses with simulation result without phase mismatch (blue curve): Pulse 1 (black curve), Pulse 2 (red curve).
The two pulses had very similar waveforms and generated similar spectra. Pulse 2 had better background noise suppression ratio than Pulse 1, and the sharp peak at the pump wavelength was consequently suppressed as shown in Fig. 5. The lower and upper spectra had 8 dB and 3 dB spectral peaks, respectively. The results show that the combination of the two fitness functions improved the accuracy of the phase spectrum control and strengthened the background suppression. Further suppression of the center peak is expected by optimizing the feedback control parameters through GA. Spectral peak suppression can be realized by direct optimization of the spectrum. However, the method takes considerably long time because of the measurement time of the SC spectrum. To suppress the spectral peak at the pump wavelength, the background component suppression was a sufficient and effective method.
4. Simulation results and discussions
In this section, we discuss the influence of the phase mismatch on the SC spectra based on the calculation results. The pump pulse was a 3.2-ps-wide Gaussian pulse at the center wavelength of 1560.6 nm and peak power of 28 W, which corresponds to an average power of 30.5 dBm at 12.5 GHz repetition rate. The pulse parameters were set according to the experimental conditions described in the previous section. To include control error of the phase spectra, the pump pulses were calculated using the following procedure. A transform-limited 3.2-ps-wide Gaussian pulse was Fourier transformed and each spectral component was randomly phase-shifted. The random phase shift had zero mean and normal distribution. The phase-shifted electric field spectra were inverse Fourier transformed to pump pulses. Note that only the phase of the spectra was shifted; the average power of the pulse was not changed but the peak power of the pulse changed due to the phase shift.
The phase shift distribution ranged within ± π/N, N = 10–2000. The pulse evolution and spectral broadening along a 1-km-long DFF was calculated by the split-step Fourier method. The dispersion and dispersion slope of the DFF was −0.17 ps/nm/km and 0.003 ps/nm2/km at 1550 nm, respectively, and the propagation loss and the nonlinear coefficient was 0.25 dB/km and 7 /W/km, respectively. The fiber parameters were the same as those in the experimental setup. We calculated 100 types of the pump pulses with different phase shift patterns in each distribution range and analyzed the heights of the spectral peaks of the generated SC spectra. We defined the heights of the spectral peaks as the largest difference within ± 5 THz from the center frequency between the SC spectra generated from the transform limited Gaussian pulse and the Gaussian pulse with a phase mismatch.
In Fig. 6 and Fig. 7 , we show examples of the simulation results with phase shift distribution ranges of ± π/2000 and ± π/20, respectively. We show the examples with the tallest peaks among the 100 spectra in each case. Each Figs. shows (a) the pump pulse waveform, (b) generated SC spectrum with and without phase mismatch, and (c) the spectrogram of the SC spectrum with phase mismatch. The temporal resolution of the spectrogram was 1 ps.
Fig. 6 Simulation of the SC generation with and without random phase shift ranging within ± π/2000: (a) pulse waveforms, (b) generated SC spectra, and (c) spectrograph of the SC generated from the pulse shown in (a) by the red curve.
Fig. 7 Simulation of SC generation with and without random phase shift ranging within ± π/20: (a) pulse waveforms, (b) generated SC spectra, and (c) spectrograph of the SC generated from the pulse shown in (a) by the red curve.
In Fig. 6(a), the contrast between the pulse peak and the background level was over 60 dB because of the small phase mismatch within ± π/2000. The background component was sufficiently small so that the pulse could generate a flat SC with a spectral peak as small as 0.14 dB (Fig. 6(b)). The spectrograph (Fig. 6(c)) shows that the background component was well suppressed by the precise phase control. On the contrary, the larger phase shift distribution of ± π/20 raised the contrast up to 30 dB as shown in Fig. 7(a). The SC had a sharp peak of 7.9 dB at the pump wavelength (Fig. 7(b)). Figure 7(c) shows that the background component had the comparable spectral density to the broadened spectrum and formed a spectral peak.
The spectral bandwidth of the transform-limited pulse was 140 GHz and the generated SC had an approximately 100 times broader bandwidth. The spectral broadening decreased the spectral density by a factor of 100 (20 dB) around the pump wavelength. The background component generated by the phase mismatch contributes less to the spectral broadening and forms a sharp peak at the pump pulse wavelength. The lower the pump pulse contrast, the higher the peak in the SC spectrum. When the spectral broadening factor is low, peaks cannot be observed in the SC spectrum. Only a strong control of the pulse spectrum can realize a broadband SC with spectral tailoring capability.
Figure 8(a) and 8(b) show the heights of the spectral peaks and the highest sub peak in auto-correlation trace against phase mismatch range, respectively. The points represent the mean peak height among the 100 cases and the error bars show the highest and the lowest peaks. For example, to suppress spectral peaks less than 3 dB, the phase mismatch should be restricted to around ± π/100 rad. Such small phase change is difficult to measure, and adaptive and feedback control of the pump pulse synthesis is required to generate such precisely controlled pulses. According to the 3 dB spectral peak in Fig. 5, the phase mismatch of Pulse 2 synthesis was assumed to be in the range of ± π/20– ± π/100. In our experiment, the 26-dB contrast of the auto-correlation trace was limited by the sensitivity of the auto-correlator. Figure 8(b) indicates that the highest sub peak or the contrast of the trace was approximately 30–40 dB.
Fig. 8 (a)Spectral peak height and (b) highest sub peak in auto-correlation trace against random phase shift range.
5. Conclusion
We investigated the background component suppression of the synthesized pulse using the OPS and applied the pulse as a SC pump. First, we demonstrated the highly precise optical pulse synthesis by a combination of two fitness functions in the GA feedback control. A 26 dB contrast between pulse center and background level was realized in the auto-correlation trace. The pulse was introduced into the DFF, and the SC spectrum with a 20 dB bandwidth of 118 nm and with a peak less than 3dB at the pump wavelength was generated. The combination suppressed the background component by 9 dB and the spectral peak at the pump wavelength by 5 dB. Second, we calculated the impact of the phase mismatch in the phase spectrum on the uniform SC generation. The mismatch forms the background component in the synthesized pulse. When the pulse was used as the SC pump, the component formed the spectral peak because it does not contribute to spectral broadening. The simulation results showed that precise phase control within ± π/100 is required to suppress the spectral peak below 3 dB.
The above results show that adaptive and feedback control with an appropriate evaluation method is required to generate a background-free clean pulse by frequency domain pulse shaping and smooth SC spectrum. The adaptive pulse shaping is also beneficial in other nonlinear applications including broader SC generation [18] and pulse compression [20]. Although complicated interaction between nonlinear phenomena and linear dispersion make us difficult to predict the output characteristics, the method should be effective to get the desired output even in unidentified fibers.
Acknowledgments
This work was financially supported by a Grant-in-Aid for Young Scientists (B) #23760326 from Japan Society for the Promotion of Science (JSPS) and R&D through Fostering Young ICT Researchers as part of the Strategic Information and Communications R&D Promotion Programme (SCOPE) from the Ministry of Internal Affairs and Communications (MIC), Japan.
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