Supercontinuum generation using photonic crystal fibers is a useful technique to generate light spanning a broad wavelength range, using femtosecond laser pulses. For some applications, one may desire higher power density at specific wavelengths. Increasing the pump power results primarily in further broadening of the output spectrum and is not particularly useful for this purpose. In this paper we demonstrate that by applying a periodic spectral phase modulation to the input pulse using a pulse shaper, the spectral energy density of the output supercontinuum can be enhanced by nearly an order of magnitude at specific wavelengths, which are tunable.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The propagation of laser pulses through photonic crystal fibers (PCFs) leads to spectral broadening resulting from third order optical nonlinearities . When a short laser pulse propagates in an optical fiber that exhibits anomalous dispersion, it evolves into solitons [2, 3]. Solitons shift towards lower frequencies as they propagate in the fiber, due to the Raman Effect. Four wave mixing among the various frequencies generated during this evolution results in the generation of light at frequencies further higher than the pump . PCFs offer high nonlinearity and a dispersion profile that can be tailored by suitably designing the microstructure . With input pulses of sufficiently high power, optical supercontinua are generated, whose spectra can span several hundred nanometers in wavelength.
Supercontinuum light sources are commonly used, together with a monochromator, as a tunable narrowband source. In such an application, it is of much interest to be able to obtain high spectral brightness at the desired wavelength. Increasing the pump pulse energy results in further broadening the output spectrum and is not particularly effective in increasing the spectral energy density at each wavelength. Also, the input pulse energy is limited by the damage threshold of the fiber. In this paper we demonstrate that it is possible to enhance the spectral brightness of the supercontinuum by up to nearly an order of magnitude at desired, tunable wavelengths by tailoring the temporal shape of the input pulse . This approach is likely to be of significant utility in the fields of stimulated Raman spectroscopy and microscopy and photoluminescence excitation spectroscopy [7–11].
Approaches combining pulse shaping and propagation in nonlinear optical media have previously been used in the study of soliton interactions, and have been termed nonlinear pulse shaping [12–14]. In the context of supercontinuum generation, these techniques can be deemed effective whenever the generated supercontinuum is temporally coherent, enabling its temporal control and, as a result, control of its spectrum. Good temporal coherence of the resulting supercontinuum can be ensured using short femtosecond pulses and operating in a regime where the dispersion of the fiber is anomalous, but small in magnitude. We drew our inspiration from experiments in coherent control, and used a train of shaped pulses generated by applying a sinusoidal phase modulation to the input pulse using a pulse shaper . In the following sections, we first describe results of numerical simulations of the propagation of these pulse trains propagating through a highly nonlinear photonic crystal fiber, to show the appearance of intense spectral interference peaks, and then proceed to the experimental demonstration.
The propagation of a pulse in a nonlinear optical fiber is described by the generalized nonlinear Schrödinger equation (GNLSE) . When the spectrum of the pump pulse lies in the anomalous dispersion regime of the PCF, the propagation primarily result from the formation and interaction of solitons. The higher the input pulse energy, the higher the bandwidth resulting from the nonlinear effects. Consider the case of two pulses separated in time by a delay τ. As these pulses propagate, their spectra broaden due to nonlinearity. When the spectral components of the pulse are close to the zero dispersion wavelength of the fiber, the constituent wavelengths are not significantly delayed with respect to each other upon propagation in the fiber. Therefore, we expect coherence to be preserved as they propagate through the fiber and spectrally broaden, resulting in spectral interference patterns that do not vary with time [16,17].
When the energy of an incident pulse is redistributed among two or more pulses, the broadened spectrum corresponding to each pulse is narrower in bandwidth than the original continuum. When one seeks increasing the output energy at a particular wavelength, it is possible to trade bandwidth for increased energy at the wavelength in question, by coherent superposition of the broadened spectra of these pulses. The simple case of two pulses can be conveniently realized experimentally using a pulse shaper to apply linear spectral phase gradients.
We model a Fourier transform spectral pulse shaper employs a spatial light modulator consisting of two independent liquid crystal array windows, A and B, such as the one used for the experimental demonstration. In such a configuration, the output electric field can be described by
The output power is proportional to . To generate a pair of pulses separated by τ, as shown in Fig. 1(a), we use linear spectral phase gradients ϕA = −ϕB = (ω − ω0) τ/2, where ω0 is the carrier frequency of the pulse. We have simulated the effect of propagation of such pulse trains through a nonlinear PCF by numerically solving the generalized nonlinear Schrödinger equation, using the method outlined in ref. . We have used an input pulse of peak power 5 kW and FWHM 200 fs, centered at wavelength 835 nm, which lies in the anomalous dispersion regime of the fiber. We have used PCF dispersion parameters from Table 1 of ref. . The results of these simulations are shown in Figs. 1(b) and 1(c), for three values of τ. From these results it is evident that the energy from the continuum is redistributed into the region closer to the pump wavelength. Also, the presence of high contrast fringes also indicates that coherence is preserved during the propagation of the pulses through the nonlinear PCF. High contrast spectral interference fringes are expected when the time interval is large enough so that there is no temporal overlap between the two pulses [13,16].
When a larger number of pulse copies are generated, their interference leads to sharper and more intense peaks in the output spectrum. Longer trains of pulses can be generated by applying a sinusoidal spectral phase modulation, of amplitude α and periodicity T, across the bandwidth of the pulse. The resulting pulse copies are generated at delays that are multiples of T. The calculated pulse envelope profiles for T = 500 fs and different values of modulation amplitude are shown in Fig. 1(d). The number of pulse copies and the distribution of the energy among them are determined by the sinusoidal modulation amplitude A. Using amplitude α = 0, the pulse is unaltered. With α ≈ 1.4, three copies of approximately equal energy are created, whereas at a modulation level of α ≈ 2.6, four copies of the pulse are generated, forming two pulse pairs which are separated by 2T. The two pulses constituting the pair are separated by T. In each of these cases, satellite pulses of smaller intensity are also be generated. Upon propagation, these lead to significantly less broadened spectra; therefore, they do not contribute to increased intensities away from the pump wavelength. Results from the simulation of the propagation of these pulse trains through the PCF are shown in Figs. 1(e) and 1(f). Together with the enhancement of power density in the form of spectral interference peaks, one also observes that the separation and the width of the peaks decreases with increasing number of pulses in the train.
3.1. Description of the setup
To test results of our simulations, we have used the experimental setup shown in Fig. 2. The output from a Ti-Sapphire laser (Coherent Chameleon Ultra) centered at λ = 780 nm, with a FWHM of approximately 200 fs, emitted at a rate of 80 MHz, is compressed using a prism compressor (Pr1 and Pr2) and is input into a pulse shaper that performs spectral amplitude and phase modulation independently according to Eq. 1. The λ/2 plate followed by the polarizer Pol1, are used to adjust the laser power and set the input polarization to horizontal (x). The pulse shaper is built around a dual window SLM (Jenoptik 320d), in which the phases ϕA(ω) and ϕB(ω) are set using a computer interface. The fast axes of pixels in the two windows are orthogonal to each other, and are aligned at 45° with the input polarization (x). A calibration step is performed to determine the pixel corresponding to each frequency. The x polarized component of the output field, selected by the polarizer Pol2, is of the form given by Eq. 1. The shaped pulses are then coupled into a nonlinear PCF module (Crystal Fiber FemtoWhite 800) that has a zero-dispersion wavelength of approximately 750 nm. The spectrum of the input pulse lies in the anomalous dispersion regime of the fiber. In addition to the pulse compressor, it is essential to perform finer corrections to the pulse dispersion by adding a suitable spectral phase using the pulse shaper that is polynomial in ω − ω0. In the work presented in the current report, we restrict ourselves to correction for the second order dispersion, of the form β(ω − ω0)2 as the pulses are of bandwidth ∼ 7 nm, and higher order dispersion effects are negligible. The value of β is determined at the time of experiment and is usually of the order of 103 fs2 or lower.
3.2. A pair of pulses
To generate two pulses separated in time by τ, the following spectral phase gradients were applied across the bandwidth of the pulse.Fig. 3, for a single excitation pulse (zero delay) the blue end of the output spectrum consists of a smooth continuum of frequencies that lie in the visible region. For delays longer than about 250 fs, spectral interference fringes are clearly visible, with a periodicity which increases as the delay between the two pulses increases. Notably, the spectral envelope of the supercontinuum varies with delay, likely due to some artifacts introduced into the pulse shape by the shaping apparatus. For small values of the delay, the two pulse copies still overlap and interference is not pronounced. In the presence of such pulse overlap, or close proximity of pulses, nonlinear effects can appear in the output spectrum due to the interactions between the solitons that evolve from the two pulses . The minima of spectral interference fringes observed in the supercontinuum do not reach zero energy density, indicating that there exists an incoherent component, that may arise due to temporal fluctuations in the input pulses .
3.3. Multiple pulses
In order to increase the spectral brightness of the supercontinuum at the constructive interference peaks, it is desirable to generate not two but rather multiple temporally equidistant pulses, preferably using phase-only modulation so as to reduce losses. To this end, we apply the following spectral phase across the bandwidth of the spectrum .Fig. 4(a). In general the variation is complex, owing to interference between supercontinua generated by pulses of various intensities. Figure 4(b) shows the spectra for modulations α = 1.42 and α = 2.58 in which most of the input pulse energy is distributed among a train of pulses of equal energy, as shown in Fig. 1(d). For α = 1.42, the coherent superposition of continua generated by the pulses results in an interference pattern consisting of a series of peaks with every alternate peak suppressed, which is characteristic of three interfering waves. At the maxima, the intensity is higher than that of the continuum generated by the undivided pulse by a factor of more than 3, despite the fact that the energy of each of the pulses is significantly reduced. This is due to the spectral focusing induced by constructive interference at particular frequencies. Note that the exact value of A for which the best contrast is obtained may vary between measurements due to the discrete nature of the liquid crystal array in SLM and small alignment changes. Even higher peak intensities are obtained by superposing a larger number of pulse copies, as seen for the case α = 2.58. The spectra of these pulses are not as strongly broadened in comparison with the pulses containing higher energy, since the initial pulse energy is being divided into the replicas generated. However, the energy in some of the supercontinuum frequencies is higher by nearly an order of magnitude than that obtained from a single high energy pulse. Moreover, the enhanced peaks are narrower (in this case by a factor of five) due to the longer train of pulses leading to their generation . For practical applications, tunability of the supercontinuum generated frequencies is necessary. Such control of the position of the spectral maxima can be performed by weakly varying the periodicity of the modulation i.e. T, as shown in Fig. 4(c), for a modulation amplitude of 1.4. As can be seen, the variation of the peak positions with changes in T is approximately linear. The lower bound on the value of T is set by the condition that there should not be significant pulse overlap, as in the two pulse case. This, however, does not set a significant limitation since the duty cycle of the generated supercontinuum peaks is relatively small. Notably, more copies can be generated with more elaborate pulse shapes , although these require that the discretization of the SLM be finer. There is potential to further improve the energy density redistribution using adaptive pulse shaping techniques . The energy density at the desired wavelength in the supercontinuum spectrum could be used as a feedback signal for the optimization.
The above observations lead us to conclude that coherent superposition of optical supercontinua generated by pulse trains can be used to generate narrow-band high intensity peaks in the output spectrum. Using a train of four pulses of approximately equal energy, we have demonstrated an increase in spectral brightness of nearly an order of magnitude at specific tunable wavelengths. Since the central wavelength of the pulses (780 nm) is close to the zero dispersion wavelength of the pulse (≈750 nm), the spectral components of the pulse are not delayed significantly with respect to each other upon propagation in the PCF. The exchange of energy among the frequency components of the supercontinuum would therefore be dominated by coherent processes such as four wave mixing. This phenomenon can be used as a means of achieving higher intensities at selected wavelengths. This is more effective in increasing spectral brightness at a particular wavelength than increasing the pump power, which primarily results in further broadening of the supercontinuum spectrum. Moreover, it enables to increase the overall pump energy coupled into the supercontinuum generation since the damage threshold for multiple pulse trains occurs at a higher total energy. Also, this concentration of energy can be achieved purely by phase modulation. The nonlinear pulse shaping scheme is not limited to the particular goals described here. In particular, it can be utilized to generate more complex spectral intensity profiles which may be beneficial for applications such as two-dimensional spectroscopy or multiplexed imaging. There is also scope for further optimization of the output spectrum using adaptive pulse shaping techniques.
Laboratoire international associe Imaginano; Israeli Center of Research Excellence “Circle of Light”; Crown Photonics Centre; European Research Council consolidator grant ColloQuantO (no. 712408).
References and links
1. J. M. Dudley and J. R. Taylor, “Ten years of nonlinear optics in photonic crystal fibre,” Nat. Photonics 3(2), 85–90 (2009). [CrossRef]
2. A. M. Weiner, Ultrafast Optics (Wiley, 2009). [CrossRef]
3. G. P. Agrawal, Nonlinear Fiber Optics (Elsevier Science, 2013).
4. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006). [CrossRef]
6. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000). [CrossRef]
7. K. Tada and N. Karasawa, “Broadband coherent anti-Stokes Raman scattering spectroscopy using pulse-phaper-controlled variable-vavelength soliton pulses from a photonic crystal fiber,” Jpn. J. Appl. Phys. 47(12R), 8825–8828 (2008). [CrossRef]
8. K. Tada and N. Karasawa, “Broadband coherent anti-Stokes Raman scattering spectroscopy using soliton pulse trains from a photonic crystal fiber,” Opt. Commun. 282(19), 3948–3952 (2009). [CrossRef]
9. K. Tada and N. Karasawa, “Single-beam coherent anti-Stokes Raman scattering spectroscopy using both pump and soliton Stokes pulses from a photonic crystal fiber,” Appl. Phys. Express 4(9), 092701 (2011). [CrossRef]
10. X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, “Highly anisotropic and robust excitons in monolayer black phosphorus,” Nat. Nanotechnol. 10(6), 517–521 (2015). [CrossRef] [PubMed]
11. J. Suh, T. L. Tan, W. Zhao, J. Park, D.-Y. Lin, T.-E. Park, J. Kim, C. Jin, N. Saigal, S. Ghosh, Z. M. Wong, Y. Chen, F. Wang, W. Walukiewicz, G. Eda, and J. Wu, “Reconfiguring crystal and electronic structures of MoS2 by substitutional doping,” Nat. Commun. 9(1), 199 (2018). [CrossRef] [PubMed]
13. E. R. Andresen, J. M. Dudley, D. Oron, C. Finot, and H. Rigneault, “Nonlinear pulse shaping by coherent addition of multiple redshifted solitons,” J. Opt. Soc. Am. B 28(7), 1716–1723 (2011). [CrossRef]
14. E. R. Andresen, J. M. Dudley, D. Oron, C. Finot, and H. Rigneault, “Transform-limited spectral compression by self-phase modulation of amplitude-shaped pulses with negative chirp,” Opt. Lett. 36(5), 707–709 (2011). [CrossRef] [PubMed]
16. I. Zeylikovich, V. Kartazaev, and R. R. Alfano, “Spectral, temporal, and coherence properties of supercontinuum generation in microstructure fiber,” J. Opt. Soc. Am. B 22(7), 1453–1460 (2005). [CrossRef]
17. C. Corsi, A. Tortora, and M. Bellini, “Mutual coherence of supercontinuum pulses collinearly generated in bulk media,” Appl. Phys. B 77(2–3), 285–290 (2003). [CrossRef]
18. J. M. Dudley and J. R. Taylor, eds., Supercontinuum Generation in Optical Fibers (Cambridge University, 2010). [CrossRef]
19. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27(13), 1180–1182 (2002). [CrossRef]
20. A. Tortora, C. Corsi, and M. Bellini, “Comb-like supercontinuum generation in bulk media,” Appl. Phys. Lett. 85(7), 1113–1115 (2004). [CrossRef]
21. D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15(5), 1615–1619 (1998). [CrossRef]