We study experimentally the spectral evolution of supercontinua in two different microstructured fibers that are pumped with nanosecond pulses from dual-wavelength sources of either 1064/532 nm or 946/473 nm output. The experimental findings are compared with simulations based on numerically solving the nonlinear Schrödinger equation. The role of cascaded cross-phase modulation processes and the group-delay properties of the fiber are emphasized and demonstrated to determine the extent of the broadening of the continua to the visible wavelengths.
©2006 Optical Society of America
The ultra-bright, broadband, and spatially coherent supercontinuum (SC) light has already found use in applications such as spectroscopy, confocal microscopy, and optical coherence tomography, to name a few [1–4]. The wider use of SC light for present day and future applications depends on the availability of reasonably priced, compact, and easy to operate SC sources that can be tailored to cover the relevant wavelength ranges. At present the simplest and most economical pump laser for a SC source is a diode-pumped passively Q-switched solid-state laser operating close to 1 μm such as a miniature passively Q-switched Nd:YAG laser . Coupled into a highly nonlinear microstructured optical fiber that has its zero dispersion wavelength (ZDW) just below the laser wavelength, it will generate SC light down to 500 nm [6, 7]. Unfortunately this kind of a source does not cover the shortest wavelengths of the visible spectrum down to 400 nm, and the concept is difficult to extend to those wavelengths because of the lack of diode-pumped passively Q-switched lasers that would operate at short enough wavelengths [8, 9]. Frequency-doubled near-infrared lasers produce light with short visible wavelengths (Nd:YAG 532 nm), and they have been used for generation of visible SC in a higher order mode  and in the fundamental mode . However, the submicron fiber waveguides required for generation of fundamental mode SC using a short visible pump wavelength are difficult to manufacture and have a low damage threshold. A frequency-doubled laser operating at 532 nm has also been demonstrated to generate SC in a dispersion-shifted fiber, but the continuum did not cover wavelengths shorter than 500 nm .
The wavelength range that can be achieved by pumping a microstructured optical fiber with a passively Q-switched laser can be greatly extended by pumping the fiber with both the fundamental and second harmonic wavelengths of the laser . The microstructure in the fiber is chosen such that the first ZDW of the fiber is located between the two pump wavelengths. The longer pump wavelength (infrared) experiences anomalous dispersion, whereas the shorter pump wavelength (visible) falls in the region of normal dispersion. The effect of the infrared continuum on the visible pump wavelength leads to the formation of a smooth visible continuum.
Dual-wavelength pumped supercontinuum generation was first demonstrated by Champert at al. and Buchter at al. in 2004 [13–15]. No thorough theoretical explanation was given in these papers as to the process leading to the smooth visible continuum, nor was there any explanation of the limits on the width of the spectrum. The first theoretical studies on dual-wavelength pumped SC generation were done for femtosecond pump pulses by Genty et al. . They found that the spectrum of the visible pump can be widely broadened by a cascaded cross-phase modulation (XPM) process caused by infrared solitons propagating in the anomalous dispersion region . Experimental confirmation of this phenomenon for femtosecond pump pulses was presented by Schreiber et al. . They also gave predictions for the bandwidth of the visible continuum based on the group-delay profile of the fiber, and stated that the predictions should also apply for longer pump pulses.
In this paper we demonstrate experimentally for longer pulses in the nanosecond regime how the continuum evolves and how the extent of the visible part of the continuum depends on the group-delay properties of the fiber. We study two custom made microstructured optical fibers by pumping them with two different passively Q-switched laser sources operating at the wavelengths of 1064/532 nm and 946/473 nm. We also discuss in detail the theory of dual-wavelength pumped SC generation for nanosecond pump pulses and conduct numerical simulations based on the extended nonlinear Schröringer equation in order to to clarify the underlying physical processes. The paper is arranged as follows: In Section 2 we demonstrate experimentally the evolution of the continuum and discuss the results in section 3 based on numerical simulations. The information obtained from the simulations is then applied in Section 4 to show for two different pairs of pump wavelengths how the group-delay properties of the fiber affect the extent of the visible part of the continuum. Section 5 is for conclusions.
2. Experimental results: Evolution of the continuum
Two triangular-lattice microstructured optical fibers, PCF-I and PCF-II, were fabricated to study the spectral evolution of a weaker visible pump propagating together with a stronger infrared pump that generates infrared continuum. Both fibers have a relative hole size of d/Λ = 0.7, but a different pitch (1.55 μm for PCF-I and 1.35 μm for PCF-II). The group-delay curves of the fibers shown in Fig. 1(a) were calculated from the design parameters using a commercial beam propagation code . The group-delay matching curves for the visible and infrared wavelengths are shown in Fig. 1(b). The parameters of the fibers were chosen such that the group velocities at the two wavelengths 532 nm and 1064 nm would be nearly the same. We expected that this would cause asymmetric broadening of the 532 nm pump towards the blue wavelengths, which will be seen in the next sections.
A 2-meters long piece of PCF-I was used to study the spectral evolution of the SC as a function of the input power. We used as the pump source a diode-pumped passively Q-switched Nd:YAG laser that produces 3 ns pulses with a peak power of 2 kW at the wavelength of 1064 nm. The repetition rate is 20 KHz. 15 percent of the output pulse energy was frequency doubled to 532 nm using an external KTP crystal. A low conversion efficiency was chosen purposely so that the visible pump would not affect the infrared continuum. The power of the visible pump was also low enough to avoid any stimulated Raman scattering processes that could cause additional redshift to the spectra. Both pump wavelengths were coupled into the microstructured fiber using a 7.5 mm focal length achromatic lens. The coupling efficiency was approximately 20 % giving peak powers of 50 W and 350 W for 532 nm and 1064 nm, respectively, at the input to the fiber.
Experimental spectra of the visible and infrared continua for increasing peak power are shown in Fig. 2. The infrared pump at 1064 nm propagating in the anomalous dispersion region evolves into an asymmetric continuum towards longer wavelengths as the input power is increased. Simultaneously, the visible part of the continuum is first redshifted a few tens of nanometers, and then blueshifted about hundred nanometers giving as a result a smooth continuum of blue light. The evolution of the visible part of the continuum only is displayed in Fig 3. It can be seen that as a function of the input power the visible pump first exhibits modulation sidebands (see red curve in Fig. 3(a)), is redshifted some tens of nanometers , and finally generates a smooth blueshifted wing. If only the 532 nm light is launched into the fiber no spectral broadening is observed.
We also recorded the evolution of the continuum as a function of the propagation length keeping the pump power in the fiber constant. The results are shown in Fig. 4. Qualitatively, the results are similar to those obtained by varying the input power, which is explained by the fact that the strength of the nonlinear interactions causing SC generation are approximately proportional to the product of the power and the interaction length .
3. Simulation results
To gain insight into the experimental observations, the propagation of broad pulses along the fibers employed in the experiments was simulated by solving the nonlinear Schrödinger equation with a split-step Fourier method (SSFM) and second-order Runge-Kutta algorithms [19,20]. A set of coupled differential equations were used to describe the evolution of the pump (infrared) and the probe (visible) pulses, A 1 and A 2, respectively. The coupling is introduced in the equations as the cross-phase modulation term on the right-hand side of Eqs. (1) and (2):
In these equations, R(T) represents both the instantaneous and delayed response of the fiber  and are the coefficients of the Taylor-series expansion of the propagation constant around the pump and probe frequencies ω 1 and ω 2, respectively. In the SSFM the dispersion term of the equations is solved in the frequency domain so that the full simulated propagation constant of the fiber is included instead of the Taylor-series expansion . The losses are neglected in the model. Furthermore, in order to keep the computation time within reasonable limits, the duration of the input pulse was restricted to 125 ps (both for the pump and probe). The peak power of the pump and probe pulses were set to 350 W and 50 W, respectively. We made test runs also for longer pulse durations but over a shorter propagation distance and found out that the development of the continuum was nearly identical to that observed for the 125 ps pulses. Therefore, we expect that the essentials of the continuum formation are revealed already for the 125 ps pulse duration. In the simulations, initial noise was included because noise is present experimentally, and allows for efficient seeding of MI processes . If the noise is not included in the simulations, the formation of a continuum is not observed, thus showing evidence of the crucial role played by noise in the initial broadening.
Figure 5 illustrates the simulated evolution of the continuum spectrum in the visible and the infrared at different stages of propagation along PCF-I. To allow for comparison with the experiments, the simulated spectra are displayed with the same resolution as that employed in the measurements. The general trends of the evolution are similar to those observed experimentally and, in particular, the simulations reproduce qualitatively well the continuum spectrum at the visible wavelengths. The quantitative discrepancies are attributed to the uncertainty on the exact values of the group-delay of the fiber and the input pulse parameters. One should also note that the simulated spectra only represent continua generated by one input pulse, whereas the experimental results are averages of the spectra produced by a large number of input pulses that have slightly varying amplitudes .
We note that in the absence of the infrared pump, no continuum is generated around the visible pump wavelength. Therefore, we first examine the formation of the infrared continuum alone as it drastically influences the continuum generated at the visible wavelengths. After a short distance of propagation in the fiber the pump spectrum develops symmetrical side-bands typical of modulation instability (MI) effects (see Fig. 5). With further propagation, multiple side-bands grow from noise. In the time domain the MI spectral side-bands correspond to a modulation of the pulse envelope. This modulation effectively breaks the original pump pulse into multiple ultra-short pulses with widths on the order of tens of femtoseconds as can be seen from Fig. 6. Since the dispersion is anomalous at the infrared pump wavelength, these pulses rapidly evolve into solitons. The spectra of the solitons overlap with the Raman gain bandwidth and therefore the pulses experience the soliton self-frequency shift (SSFS). This results in the expansion of the infrared continuum solely towards longer wavelengths [23,24].
We next consider the situation when both the infrared and visible pump pulses are launched simultaneously into the fiber. The infrared pulse evolves into a continuum as described previously. The onset of the continuum formation at the visible wavelengths can be divided into two stages. The infrared spectral components impose a nonlinear phase-shift on the visible pump which leads to XPM-induced modulation instability around the visible pump wavelength. After a short distance of propagation, the modulation instability manifests itself in the spectra as two symmetrical sidebands located around the probe (see Fig. 5). With further propagation, the nonlinear phase-shift grows and multiple side-bands are generated corresponding to the breaking up of the visible pulse into sub-pulses (see Fig. 6(b)). The second phase of the broadening is asymmetric. It occurs first on the red wavelength side and then with further propagation shifts towards the blue wavelengths due to multiple XPM interactions. The temporal width of the solitons emerging from the infrared pump pulse is short and, correspondingly, their peak power is high. Consequently, the nonlinear phase-shift imposed by the multiple solitons onto the visible sub-pulses is large, which substantially affects the visible spectrum. As the solitons shift towards longer wavelengths due to the SSFS they are continuously delayed and interact through XPM with the MI-induced spectral components generated around the visible pump. In absence of dispersion the solitons would cause no net frequency-shift on the visible sub-pulses . However, far away from the ZDWs, the group-velocity dispersion is nonzero inducing walk-off between the visible sub-pulses and the infrared solitons. Thus, the XPM frequency-shifted components of the visible sub-pulses escape the temporal interaction region with the solitons, which leads to a net frequency-shift of the visible sub-pulses. The sign of the group-velocity difference between the visible sub-pulses and the solitons determines the direction of the spectral broadening. When the solitons travel at a faster (slower) velocity than the visible pulses, they induce a net red-shift (blue-shift) on the spectrum of the visible pulses. As can be seen from Fig. 1, the solitons travel faster than the visible pulses until their center wavelength is shifted beyond ~1150 nm. Further wavelength-shift reverses the sign of the group-velocity difference. This explains why the spectral broadening occurs first towards the red wavelengths and later towards the blue. It should be noted that there is no energy transfer between the infrared and visible components, but the energy of the visible components is only redistributed .
The physical mechanism responsible for the generation of the visible continuum is in fact quite similar to that described previously in the context of femtosecond pulses [16, 17, 25]. However, in the case of initially broad pulses, the number of sub-pulses emerging from the original pump pulse is increased considerably, resulting in multiple XPM interactions with the visible pulse and yielding a smooth continuum at the visible wavelengths. Another effect contributing to the apparent smoothness of the visible continuum lies in the noise seeding of the modulation instability which leads to the formation of the infrared continuum. The random character of the MI processes is responsible for the smooth structure of the infrared continuum [22, 26] and this smoothness is transposed to the visible continuum through XPM. The extent of the visible continuum on both the red and blue sides depends on the maximum group-delay compensation leading to cascaded XPM processes. More specifically, the visible spectral components frequency-shifted through XPM get separated from their corresponding infrared frequency components due to dispersion. Further frequency-shift of the infrared components due to intra-pulse Raman scattering allows to compensate for the delay induced by dispersion. Therefore, the infrared solitons catch up with the XPM-generated frequency components, which leads to further cascaded XPM interactions. This means that the maximum width of the visible continuum is mostly determined by the properties of the group-delay curve of the fiber and the values of the pump wavelengths. Based on these conclusions we performed an additional set of experiments to demonstrate the effect of the fiber group-delay properties on the width of the visible continuum.
4. Experimental results: Effect of the fiber group-delay
The effect of the fiber group-delay properties on the width of the continuum was studied by pumping the two sample fibers using two distinct pairs of pump wavelengths 1064/532 nm and 946/473 nm. The length of both fibers was chosen to be approximately 20 meters in order to be able to observe the fully evolved continuum. For the 1064/532 nm pumping we used the same laser as in Section 2, but with a lower conversion efficiency to the second harmonic in order to avoid stimulated Raman scattering in the long fiber. For the 946/473 nm pumping a diode pumped passively Q-switched Nd:YAG-laser operating on the quasi-three-level 946 nm transition was built. The laser produces 4 ns pulses with a peak power of 3 kW. A small fraction of the 946 nm output was frequency doubled to 473 nm using an external BiBO crystal. Coupling of the pump pulses into the fiber was achieved using the same achromat as for the 1064/532 nm case.
The measured output spectra are shown in Fig. 7. The 1064/532 nm pumping is seen to produce highly asymmetric spectra with mainly blueshifted wavelengths, while the 946/473 nm pumping creates more symmetrical spectra. The difference is explained by the relative position of the pump wavelength pairs on the group-delay curves of the fibers. For the 1064/532 nm pumping, the visible and infrared pumps are nearly group-delay matched, and therefore the infrared continuum contains mainly components with group-delays larger than that of the visible pump thus causing a large blueshift on it. For the 946/473 nm pumping the infrared continuum contains components with group-delays both smaller and larger than that of the visible pump thus causing both red- and blueshift on the visible pump through XPM.
When comparing the output spectra of the two fibers, the short wavelength cutoff is found to be independent of the choice of the pump wavelength pair but specific to the fiber. The cutoff is in fact set by the visible wavelength corresponding in group-delay to the wavelength of the maximum infrared group-delay, i.e. at the second zero dispersion wavelength of the fiber. This delay is larger for PCF-I than for PCF-II leading to a shorter cutoff wavelength for PCF-I. It was observed that the short wavelength cutoff saturates at a fiber specific value for sufficient infrared power, and that a further increase in the laser power only increases the intensity of the blue part of the visible spectrum. The properties of the visible spectra for wavelengths longer than the visible pump can also be explained from the group-delay properties. For the 946/473 nm pumping the shape of the redshifted spectra are almost identical for the two fibers. This is partly accounted for by the fact that the group-delay profiles of the fibers are almost identical in the wavelength range of 946–1350 nm. One would also expect that the group-delay in the visible wavelength range plays a role. In particular, the limit on the red side of the visible spectrum is set by the group-delay matching wavelength corresponding to the infrared pump at 946 nm. This is indeed what is observed for PCF-II but it does not apply to PCF-I. We believe that this discrepancy is due to the uncertainty on the calculated group-delay curve and the actual group-delay of PCF-I is likely to be closer to that of PCF-II in the region 500–600 nm. We believe that the same discrepancy causes the difference in the position of the redshifted peak in the measured (see Fig. 4) and the calculated (see Fig. 5) spectra for the 1064/532 nm pumping of PCF-I. In the case of the 1064/532 nm pumping the shapes of the red sides of the spectra of the two fibers are markedly different. The difference is caused by the relative group-delay difference of the pump wavelengths. For PCF-II, the visible and infrared pump wavelengths are group-delay matched, which results in the absence of redshift because of the lack of infrared continuum components with low enough group-delay values. For PCF-I the group-delay of the 1064 nm pump is smaller than that of the 532 nm pump, and a redshifted peak is observed. In this case the redshift is limited by the fact that at approximately 1150 nm the infrared group-delay becomes larger than that of the 532 nm pump.
We have demonstrated experimentally how for nanosecond dual-wavelength pumped super-continua generation the spectrum in the visible wavelengths evolves, and how the width of the continuum and the type of the broadening, i.e., red- or blueshift, depends on the group-delay properties of the fiber. Numerical simulations based on the nonlinear Schrödinger equation were carried out to gain insight into the evolution of the visible continuum. The main effect causing spectral broadening of the visible pump was found to be a cascaded XPM-process induced by the infrared continuum. For sufficient infrared pump power, the extent of the visible continuum was found to be limited by the group-delay properties of the fiber such that the visible continuum covers the wavelengths that are group-delay matched with the infrared continuum. Thus, by adjusting the group-delay properties or the structure of the fiber one can design a dual-wavelength pumped SC source such that the extent of the visible continuum is optimized for the application at hand.
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