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In photonic crystal fibers with closely spaced zero dispersion wavelengths it is possible to have two pairs of four-wave mixing (FWM) gain peaks. Here, we demonstrate both numerically and experimentally how the outer four-wave mixing gain peaks can be used to produce a strong amplification peak in a picosecond supercontinuum. The method involves feeding back part of the output light of a SC source and time matching it with the pump light. In this way it is possible to produce a gain of over 20 dB near the FWM gain wavelengths.
©2008 Optical Society of America
1. Introduction
The white light generation method known as supercontinuum (SC) generation has been the subject of intense research since the turn of the century and the major effects governing the spectral broadening are now well understood [1]. Research has now moved on to investigate how one can control the stability and distribution of energy in the final spectrum. This would allow it to be optimized for specific applications, such as optical coherence tomography (OCT) [2, 3], optical mammography [4], fluorescence microscopy [5], and wavelength division multiplexing in optical communication [6]. Some of the approaches that have been investigated are the use of a two-color pump [7], inclusion of fiber Bragg gratings (FBGs) [8] or long period gratings (LPGs) [9], the use of cascades of different fibres [10], tapering of the fiber [11–18] and variation of the chirp of the pump pulses [19].
One of the most recent techniques to produce a very high spectral density in a limited section of the spectrum has been the use of a fiber with two closely spaced zero dispersion wavelengths and continuous wave pumping. This has been used to produce very intense light between the two ZDWs [20–23]. Here we present an experimental and numerical investigation of the behavior of such a fiber when pumped with picosecond pulses. This investigation shows that such fibers can has two sets of four-wave mixing (FWM) gain bands and that this can play an important role in generation of the SC. The effect of these bands with picosecond pumping have been predicted numerically but has not previously been verified experimentally. Controlling the amount of energy present in the FWM/Modulation instability (MI) gain band at the input of the fiber has also recently been suggested as a spectral modification technique with great potential [26]. Here we investigate seeding the FWM gain band by reflecting part of the output SC back into the PCF in which it was generated and time matching it with the pump pulses so that it may act as a seed in the gain processes generating the SC. We demonstrate both numerically and experimentally that this can produce a 10-20 dB local gain in the spectrum.
For the demonstration of the seeding it was particularly interesting to use a fiber with two closely spaced zero dispersion wavelengths (ZDWs) because in this type of fiber it is possible to have anomalous dispersion in the pump region while still generating FWM gain bands far from the pump. This will allow the creation of a rather wide SC, which can then be used to seed the FWM gain bands far from the pump. In addition, fibers with two ZDWs have recently been shown to allow the generation of the highest spectral power densities of any SC reported to date [21]. The creation of a local peak in a SC is of particular interest for applications where a high spectral power density is required in part of the spectrum e.g. as pump in pump-probe applications. The local peak would allow higher local power densities to be reached or would require a lower pump power than raising the whole spectrum.
The concept of utilizing feedback in PCFs has been investigated earlier in several contexts. In a linear cavity scheme, a fiber Bragg grating (FBG) has been utilized at the input and output of the nonlinear fiber to produce feedback and amplification of the Raman peak [27]. The result of this approach was that the center of the SC was shifted from the pump wavelength to the Raman gain wavelength. In another case, feedback in a ring cavity including a nonlinear fiber has been used to lower the threshold for FWM peak generation using long ps pulses in the normal dispersion region [28]. Finally, feedback into a SC has also been used with fs pumping in order to achieve broadband tuneable amplification [29].
Here we use ps pumping which means that the pumping system is much simpler than for fs pumping and much higher average power can be used. The ps pumping also means that we are operating in the quasi-CW regime so that the effects identified also should be applicable to ns or CW pumping. Another difference compared to previous seeding investigations is that we are seeding FWM from a pump in the anomalous dispersion region and this makes it possible to generate both a SC and FWM gain peaks simultaneously.
2. Characteristics of the nonlinear fiber
Fig. 1. Characteristics of the 1050-zero-2 fiber. (a) Estimated dispersion profile with ZDWs at 954 nm and 1152 nm. (b) FWM phase matching gain bands as a function of power and pump wavelength. The FWM gain peaks for the 1064 nm pump at 116 W peak power are at 877 nm, 1039 nm, 1091 nm, and 1354 nm, respectively. (c) The phase matching wavelengths for dispersive wave generation from solitons as a function of the solitons central wavelength. This has been marked both without the contribution from the soliton power and for a soliton peak power of 2 kW. Simulations have indicated that the maximum soliton peak power sould be around 1.5 kW. (d) Scanning Electron Microscope (SEM) image of a fiber cross-section, the core diameter is 2.3 μm.
The fiber used in this work is 4 m of 1050-Zero-2 fiber commercially available from Crystal Fibre A/S, Birkerød, Denmark, which is characterized by having two ZDWs, separated by a narrow wavelength interval in which the fiber has anomalous dispersion. In order to determine the dispersion profile of the fiber, its average pitch and holesize were determined from a scanning electron microscope (SEM) image and the dispersion profile calculated using fully-vectorial plane-wave expansions [30]. This method is highly sensitive to variations in the PCF holesize both across the slice inspected, which can be seen in Fig. 1(d), and along the fiber length. In order to find a more precise dispersion profile, the local dispersion at the pump was also determined experimentally. This was done using the relationship between the local dispersion and the frequency shift of the MI gain peaks given by [31],
where Ωmax is the angular frequency shift of the maximum gain from the pump peak, γ is the nonlinearity parameter of the fiber which is stated by the manufacturer to be 37 (Wkm)-1, P0 is the peak power, and β2 is the group velocity dispersion (GVD) parameter with the dispersion D=−β22πc/λ2.
The pump wavelength, the spectral position of the modulation instability (MI) peaks, and the movement of the MI peaks as a function of power were then used with equation (1), to find a local dispersion of 4.5 ps/nm/km. The dispersion curve calculated from the average structural parameters was then shifted to fit this value. A similar method of correcting a SEM image derived dispersion profile using local dispersion measurements was recently used by Cumberland et al. [21]. To simplify the calculation only β2 is included in the dispersion estimation as it is found that the error arising from the simplification is small compared to the measurement error on the pulse length, average power, and peak position. In the case of the 116 W pump the MI peak estimated with equation (1) was 1098 nm, whereas the MI peak calculated using the whole dispersion term derived from the shifted curve was at 1091 nm and the measured was 1093 nm.
The corrected dispersion profile of the fiber can be seen in Fig. 1(a). The two ZDWs means that this fiber has two sets of closely lying FWM phase matching wavelengths. The position of these as a function of pump wavelength and power are shown in Fig. 1(b). Similar fibers with two closely lying ZDWs have been investigated previously both numerically and experimentally using fs pulses, where the focus has been on low noise dual-spectrum generation [32], cross-phase modulation (XPM) SC generation [33], dual wavelength pumping [34], pumping close to the long wavelength ZDW [35], varying the long wavelength ZDW [36], tapering the fiber [14], varying the anomalous dispersion interval [37], the effect of spectral recoil [3, 38], the noise properties of a dispersion-flattened dispersion-decreasing fiber (DF-DDF) [39], and the use of the SC from such a fiber for low-noise OCT [2]. Several studies on the performance of these fibers with CW pumping have also recently been published. Herein the double ZDWs have been used to limit the spectral width of the SC through spectral recoil of solitons [20–23]. However, in the previous CW investigations the contribution from a second pair of FWM gain bands, which is investigated in this work, was not discussed.
3. Experimental investigation
Fig. 2. The setup used to produce the feedback and measure the spectrum. The ”Spectral and Delay Control” (SDC) mirror could be altered in order to produce different seed spectra. The round trip time of the seed, was matched with pump pulse frequency by tuning the distance between the fiber output and the SDC mirror. Meanwhile the output light was monitored on an Optical Spectrum Analyzer. Mirror 6 was removed and substituted with a fiber going to the OSA or a powermeter head when the seed light, was measured. Mirror 12 is used to filter out residual pump power to avoid reflections back to the pomp system.
A diagram of the setup used to generate the SC and conduct the back-seeding experiment can be seen in Fig. 2. The pump light was generated using a fiber based modelocked ytterbium fiber laser and amplification system, which generated a 70.2 MHz pulse-train at 1064 nm. It should be noted that the pulse entering the PCF is not transform limited, this is due to the transmission spectrum of the gratings in the pump laser and both self-phase modulation and dispersion in the amplifier system. The spectrum of the pulses can be seen in Fig. 3 (b). The pulse length was measured to be 14.2 ps using autocorrelation.
The elliptical polarization of the output light from the pump system is converted to linear polarization using a λ/4 (2) and a λ/2 (3) waveplate, using a method described by Iizuka [40], before being passed through a free space isolator, OFR IO-5-1064-VHP (4). The transmission loss of the isolator is 1.5 dB. Beyond the isolator, the polarization with respect to the fiber axis is controlled using another λ/2 waveplate (5). Then the light is coupled into the PCF using an achromatic lens (8) with a coupling efficiency of about 50%. The average power through the 4 m PCF (9) was around 115 mW. The loss of the PCF is specified by the manufacturer to be 30 dB/km at 1000-1100nm, and most of the pump power remains in this interval, so fiber losses are assumed to be of little importance. Using a 10% beam splitter (11), a fraction of the collimated output beam of the PCF is split off, coupled into a fiber, and guided to an ANDO 6315A Optical Spectrum Analyzer (OSA) to be analyzed. The main part of the collimated output is terminated in a beam dump when single pass measurements are made. For the feedback measurements, the main part of the output beam is reflected back into the PCF using the Spectral and Delay Control (SDC) mirror(13). The distance between the SDC mirror (13) and the PCF (9) can be varied in order to match the round trip time of the feedback pulse to the period of the pump pulse-train. After the light has been fed back through the PCF, it is collimated by the achromatic lens at the fiber input (8) and passed through the 1064 nm mirror (6) to finally be reflected back by the silver mirror (7), which thus completes the feedback loop.
The feedback system had a loss of at least 8 dB for each round trip of the reflected wavelengths due to coupling and reflection losses and the 10% reflection of the beamsplitter. The spectrum measured with and without the time matched seeding can be seen in Fig. 3 (a) together with the spectrum of the seed. Note that when the seed is being measured in the following, mirror 7 is replaced with a fiber to the OSA. The seed spectrum shown is thus the feedback when it is not interacting with the pump and not the feedback signal present when the entire loop is closed. The experimental setup is described in greater detail elsewhere [41].
3.1. The seeding effect
When inspecting the spectra obtained in the experiment it is important to note that the strongest gain in the seeded spectrum occurs at 919 nm and 1269 nm and that the sum of the energy of photons corresponding to these two wavelengths is just 0.2 % less than the energy of two photons of the pump wavelength. This is a strong indication that the gain is caused by degenerate FWM with the pump. When only inspecting the measurements it is difficult to identify whether other effects are involved as well. When comparing with the FWM gain bands, shown in Fig. 8, it appears that the gain in the region at 890-955 nm is too wide for simple degenerate FWM. In order to better understand which wavelengths play a dominant role in the FWM processes, the feedback system was tested using three different mirrors for the feedback, as can be seen in Fig 4. The mirrors were the 1200-1700 nm mirror, which mainly fed back the long wavelength peak of the SC (Fig. 4 left), a silver mirror, which fed back both sides of the SC (Fig. 4 center) and finally a broad mirror with reflection centered around 780 nm which fed back much less power around 1269 nm (Fig. 4 right). The measurements show that the peaks at 919 nm and 1269 nm are both created as long as the feedback around 1269 nm is strong. However, none of the peaks are created if the feedback around 1269 nm is weak even if the feedback around 919 nm is stronger. This shows that the generation of the peaks is dependent on seeding in the Stokes band but unaffected by seeding in the anti-Stokes band. With a normal FWM process it should be possible to create peaks with seeding in either band. The fact that only the Stokes band can be seeded suggests that there may be other processes such as dispersive wave gain favoring the Stokes band.
Fig. 3. (a) Output of the PCF. Gray: spectrum without seeding. Black: spectrum with seeding. Black dashed: the seed which was fed back through the system. (b) Spectrum of the pump at the input of the PCF
Fig. 4. SC spectra generated using various feedback spectra. The three columns correspond to the spectra produced using a 1200-1700 nm mirror (left), an Ag mirror (center), and a broad spectrum mirror centered at 780 nm (right) as the SDC mirror. The top row shows the output spectrum from the PCF with (black) and without (gray) feedback, while the bottom row shows the spectrum which is fed back through the system, measured at mirror 6 in the setup. Note that all these spectra are plotted on a linear scale.
3.2. The feedback delay
In order to investigate the effect of the temporal overlap between the pump pulse and feedback pulse, which resulted in an amplification, the length of the delay arm was altered slightly while the spectrum was monitored. In this fashion the effect of the seeding as a function of temporal delay between the pump pulse and the feedback pulse could be measured. This is shown in Fig. 5, where the difference in dB between the seeded and the unseeded spectrum has been plotted as a function of the delay. The spectrum at a few sample delays can be seen in Fig. 6.
Fig. 5. Experimental measurement of the difference in dB between the spectra with and without feedback as a function of delay of the seed. The Y-axis shows the delay between the feedback pulse and the pump pulse measured at the output
Fig. 6. Spectra measured in the experiment with different feedback delays corresponding to slices in the plot in Fig. 5. Black lines show the spectrum with feedback, gray lines without feedback.
The most noticeable characteristic of the temporal gain interval is that the strongest effect occurs around 0 ps delay. The 0 ps delay point was set to be the delay distance at which the fast diode measurements showed that the feedback pulse and the pump pulse were exactly overlapping at the beam splitter at the output of the PCF. One would expect that the greatest effect of the feedback would occur when the feedback pulse was temporally matched with the pump at the input of the PCF. The fact that the strongest effect of feedback coincides with the temporal overlap at the output indicates that the temporal overlap at the output occurs with the same delay as the temporal overlap at the input and thus that the group velocity of the feedback pulse must closely match the velocity of the pump pulse. A close matching of group velocities is a requirement for efficient FWM in a pulsed setup, and as the gain occurs at the point when the pulses overlap at the output the gain could be caused by a FWM process. It is also evident that the interval of -0.6 ps to 0.6 ps in which a strong gain is produced is very narrow, when considering that the pump pulse has a FWHM of 14.2 ps. Compared to this the roundtrip of the feedback pulses is 42.7 ns, while the period of the spectral modulations induced by the MI is approximately 135 fs. The short peak generation interval indicates that many round trips are necessary to build up the gain, so that the length of the roundtrip time must be very close to a multiple of the pump pulse separation period in order for the seed to overlap with the pump pulse through many roundtrips.
It may be noted that the presented seeding of the SC generation is somewhat similar to effects generated by modulation instability in ring laser cavities. Most relevant is the work by Nakazawa et al. [42] where a time matched cavity length was used to generate amplification of the MI bands when pumping with ps pulses at the ZDW. The result was the generation of a train of soliton pulses. Here we seed far from the pump wavelength, in the normal dispersion regime, where there is no temporal compression and pulses in the amplified peak therefore must be expected to become temporally broad. If one wanted to use the method presented here to generate solitons at a wavelength far from the pump it is possible that this could be achieved by feeding the seed back though a fiber with anomalous dispersion in a ring cavity setup instead of using the Fabry-Perot cavity presented here. The temporal compression to solitons might then occur in an average soliton regime as presented by Matos et al. [43]
4. Numerical results
We model the propagation of the pulses using the generalized nonlinear Schrödinger equation (NLSE) [1, 31]
where A(z,T) is the field envelope in a retarded time frame T = t - β1 z moving with the group velocity 1/β1 of the pump, along the fiber axis z. ℱ {A} = Ã denotes Fourier transform. ω0 is the center angular frequency of the computational frequency window. γ(ω) =n 2ω0/[cA eff(ω)] is the nonlinear parameter, where n 2 = 2.6 × 10-20 m2/W is the nonlinear-index coefficient for silica, c is the speed of light in vacuum, and A eff(ω) is the effective core area [31]. The dispersion profile was obtained as explained in section 2 and the dispersion parameters βm are obtained from a polynomial fit to the dispersion profile [14].
The transverse field distribution E(x,y,ω) of the fundamental mode was calculated with fully-vectorial plane-wave expansions. From this A eff(ω) was calculated using the more general definition suitable for fibers, where some of the field energy may reside in the air-holes [44]. R(t) is the Raman response function [31,45]
where f R = 0.18 is the fractional contribution of the delayed Raman response, τ1 = 12.2 fs, and τ2 = 32 fs. Θ(t) is the Heaviside step function.
The propagation Eq. (2) is solved using the split-step Fourier method [31], with an implementation of the adaptive step-size method [46] using a local goal error of 10-6. The relative change in photon number (a measure of the numerical error that is ideally zero in the absence of loss [45]) was on the order of 10-6% for each propagation along the length of the fiber.
To realistically model the finite linewidth of the pump laser, we used the same phase noise model as in Ref. [47], since the underlying phase-diffusion model is physically well-founded [48, 49]. The linewidth in the simulations was set to 32 GHz (∼ 0.1 nm).
4.1. Unseeded supercontinuum
The simulation of the unseeded spectrum was made using a sech-shaped pulse with 116 W peak power, 14.2 ps FWHM (corresponding to an average power of 131 mW for a repetition rate of 70.2 MHz), center wavelength 1064 nm, and a fiber length of 4 m. The temporal resolution was 0.95 fs and 217 points were used.
Fig. 7. Comparison between simulated and measured spectra. Black: Measured spectrum. Grey dashed: Simulated spectrum.
The numerical simulations predict a spectrum which is similar to what has been found in experiments as shown in Fig. 7. However, there are some significant differences, most notably that the simulations predict much less power in the short wavelengths than found through measurement. The differences are thought mainly to be due to errors in determination of the exact dispersion profile of the fiber. The dispersion of this fiber is very close to zero in a wide area around the pump and the simulations are therefore very sensitive to variations in the dispersion. It is difficult to determine the exact value of the dispersion and as the holesize of this fiber may vary up to 2% along the fiber [50, 51] the dispersion will also vary. The differences between the simulated and measured output spectra of the fiber are therefore not larger than could be expected. Based on the differences between the simulated and measured spectrum it is expected that the actual ZDW wavelengths in the fiber of the experiment are located considerably closer to the pump wavelength than was simulated. This would explain why there appears to be little red-shifting of the solitons [23].
The processes behind the SC generation in the numerical simulations can be explained when one examines the development of the spectrum along the fiber as shown in Fig. 8 and Fig. 9 and compares this to the plots of the fiber dispersion, FWM phasematching wavelengths, and dispersive wave phasematching wavelengths in Fig. 1(a), 1(b), and 1(c), respectively. After 0.8 m four peaks start to grow at around 880, 1040, 1090, and 1355 nm. This FWM amplification of certain wavelengths is the spectral sign of the creation of temporal modulations on the pulse known as modulation instability (MI). The MI eventually leads to the breakup of the initial pulse into solitons. The solitons subsequently generate dispersive waves, which should grow at the phasematched wavelengths [14, 52] located around 820 nm and 1300 nm if one assumes the wavelength of the solitons to be around 1064 nm (see Fig. 1 (c). These can be seen in the spectrum (Fig. 8) from 1.6 m and beyond. Subsequently the solitons will start to red shift due to Raman scattering until they approach the ZDW at 1152. This will lead to a gradual shift in the dispersive waves toward the wavelengths 790 nm and 1160 nm as shown in Fig. 1 (c). As can be seen at 1.6-4.0 m the shift of the dispersive wave peaks stop at around 800 nm and 1230 nm. This may be due to the red shift of the solitons being limited by spectral recoil from their dispersive waves [3, 20–23, 35, 38]. In addition to the dispersive waves and degenerate FWM there may also be some contribution to the spectral broadening from cascaded FWM processes.
Fig. 8. Development of the spectrum along the fiber according to numerical simulations. Vertical dotted black lines mark the ZDWs at 954 nm and 1152 nm. The FWM gain, shown in the lower part of the figure, is calculated for the pump power of 116 mW. The FWM gain peaks are at 877 nm, 1039 nm, 1091 nm, and 1354 nm.
Fig. 9. Spectrogram showing the calculated temporal distribution of the spectral energy at the output of the fiber. The white horizontal lines mark the position of the ZDWs. The evolution of the spectrogram along the fiber can be downloaded as a movie (2.2MB). [Media 1]
4.2. Feeding back part of the SC spectrum
It has been shown in the previous section that the 1050-zero-2 fiber allowed the generation of light in a rather wide spectrum. The light is generated by a combination of dispersive wave generation and FWM. It was therefore natural to continue the investigation of this fiber by exploring the effect of providing a seed for FWM gain by recycling part of the light generated near the FWM phase matching wavelengths and time matching it with the input pump pulses. In order to simulate the feedback, the output from the first simulation (termed ‘unseeded’) was numerically filtered through two super-Gaussian transmission filters to simulate that the Ag mirror reflects light in a broad spectrum while the light around the pump is removed by the 1064 nm mirrors. One transmission filter has a center wavelength of 1300 nm and a bandwidth of 200 nm; the other filter has a center wavelength of 900 nm and a bandwidth of 160 nm. The power of the filtered pulse is then scaled down to 40 % to represent coupling losses of 60 % (∼ 4 dB). The filtered pulse is then propagated in 4 m of fiber to simulate the back propagation. It is assumed that there is no interactions with the counter propagating pump pulses on the way back though the fiber since the interaction length with these is extremely short. Finally, the output of this simulation is scaled to 40% to again represent a coupling loss of 60%, added to a new pump pulse, whose noise is identical to the first one, and propagated in 4 m of fiber to simulate the first back-seeded pulse. This procedure is repeated for simulating multiple back-seeds.
4.3. Effect of feedback
Fig. 10. Numerical simulation result of a seeding with one, two and three roundtrips in the cavity. Dashed black lines mark the FWM gain areas. Vertical black dotted lines mark the outer ZDWs.
When the pump pulses were propagated through the fiber together with a time matched seed from the output light it was found that the seeded output spectrum grew significantly different from the unseeded one, as can be seen in Fig. 10. The regions in which the unseeded spectral power is increased by seeding are similar to those found in experiments. However, the increase in power in the numerical simulations is much smaller than in the experiment this is thought to have two causes. First, only a few round trips of the seed are simulated whereas the gain in the experiment may build up as the steady-state produced by the contribution from many round trips. Second, as has been shown in section 3.2, the gain was highly dependent on the delay between the seed and the pump pulse. The spectra shown for the experiment were measured when the delay between the seed pulse and the pump had been optimized to produce the largest gain. In contrast it has not been possible to find the optimal delay point in the simulations as the number of simulations has been limited by long computation times. The gain observed in the simulations is therefore much smaller.
It is believed that the gain is created mainly by seeding of FWM gain. The seeding of the outer FWM gain band leads to a significantly stronger peaks at these wavelengths. This will lead to a depletion of the pump, which may hamper the soliton creation through modulation instability and thereby the dispersive wave generation. On the other hand the increased transfer of energy from the pump to the FWM gain band should increase the modulation imposed on the pump pulse and could in that way increase modulation instability. In order to find which process is dominant one may inspect the spectral distribution when seeding. It appears that the seeding gives a decrease in the peak at 820 nm, which was identified earlier as the short wavelength dispersive wave. At the same time the interval from 830 nm to 950 nm, whose center is close to the lowest FWM gain peak, experiences a gain. There appears to be little change in the area of 950-1200 nm but the long wavelength dispersive wave peak at around 1280 nm appears to be slightly red-shifted. Finally the FWM gain peak at 1355 is considerably amplified. It appears that the two areas where the energy is increased are centered around the outer FWM gain bands. Meanwhile the long wavelength dispersive wave is red-shifted as can be seen when the seeded spectrum fills the ”valley” in the unseeded spectrum at 1275 nm on Fig. 10. This would occur if the solitons produced by the MI had a lower intensity and their red-shift therefore does not bring them as close to the 1152 nm ZDW (see Fig. 1 (c)). A reduced intensity of the solitons would also make the short wavelength dispersive wave generation less efficient and explain the reduction of the 820 nm peak, which is observed. It would thus appear that the seeding of the FWM band in this case primarily leads to a depletion of the pump without significantly increasing the modulation instability. In this fiber, and with this pump, the effect of seeding the FWM bands is thus different from what was recently found with noise seeding of the FWM band in a fiber with a single ZDW. [26, 53]. There the seeding of the modulation instability band lead to an increase in the frequency of solitons with very high peak power and thereby an increase in the maximum soliton red-shift. The difference in results may be due to the FWM region seeded here being in a normal dispersion region, but it may also be an effect of the soliton dynamics here being modified by soliton repulsion.
4.4. Numerical investigation of the feedback delay
The variation of the delay, which was investigated experimentally in section 3.2, was also tested numerically. This was done by temporally shifting the seed -2 or -4 ps before it was added to the pump pulse and otherwise running the simulation as described in section 4. The result can be seen in Fig 11. As can be seen, both the peak at 1354 and the short wavelength interval at 830-950 grows significantly stronger when the seed is delayed. The optimal delay has not been found, but the plots shown here are enough to show that the strong dependence on delay, which was found in the experiment, is also present in the numerical simulations. It is believed that the strong dependence on delay is due to the FWM gain being much stronger when the seed is temporally exactly matched with the peak of the pump pulse.
5. Conclusion
In this work we have demonstrated both numerically and experimentally how a SC spectrum is generated when one pumps with picosecond pulses in the anomalous dispersion region between two closely spaced ZDWs. As has been shown earlier with CW pumping [20–23], the long wavelength ZDW limited the SC by stopping the Raman shift of the solitons. However, the dispersive wave generation above the ZDW was more prominent than for CW pumping, as one should expect from the higher peak power. It has also been shown that a double pair of FWM gain bands contributed very significantly to the SC generation in this case. To the best of our knowledge this is the first time that pumping of the second pair of FWM gain bands has been experimentally verified with picosecond pulses. Since these pulses are in the quasi-CW regime it is expected that these effects may also be found with nanosecond and CW pumping.
Fig. 11. Numerically simulated effect of varying the feedback delay. Dashed black lines mark the FWM gain areas. Black dotted lines mark the outer ZDWs.
We have also investigated the effect of feeding part of the SC output back into the PCF and time matching it with the pump pulses so that it could act as seed in the FWM gain band. Through this method it has been shown that strong local amplification peaks can be created. In an experiment it has been shown that the local increase in the spectrum can reach over 20 dB and it is thus a promising spectral modification technique.
The generation of a peak in the SC could also be useful for a number of pump-probe applications, such as Coherent Anti-Stokes Raman Scattering (CARS), where a strong pump peak is needed for excitation with a weaker continuum for probe wavelengths [54].
It is important to be aware of the possible effect of a feedback loop, which is demonstrated here, even if one does not wish to use it to modify the SC spectrum, because it can appear accidentally. This may occur if the facets of the PCF are not angle cleaved and its length accidentally gives it a round trip time which is close to a whole number of pulse periods. The effect will also be important if one uses long ns pulses with short PCFs or CW light, where the pulse is longer than the round-trip time for the light in the fiber, and the pulse thus can overlap temporally with its own reflections.
Acknowledgments
This work was funded by Photonics Academy Denmark. We thank Crystal Fiber A/S for a fruitful dialog on determining fiber dispersion and for providing the 1050-zero-2 fiber used. Finally the authors would like to thank Lars Hagedorn Frandsen, DTU Fotonik, for providing the scanning electron microscope image of the fiber.
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