January 15, 2015 / Vol. 40, No. 2 / OPTICS LETTERS
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Influencing supercontinuum generation by phase distorting an ultrashort laser pulse J. A. Dharmadhikari,1 A. K. Dharmadhikari,2,* K. Dota,1 and D. Mathur2 1
Department of Atomic and Molecular Physics, Manipal University, Manipal 576 104, India 2 Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400 005, India *Corresponding author: [email protected] Received November 18, 2014; accepted December 1, 2014; posted December 16, 2014 (Doc. ID 227127); published January 12, 2015
We show that the spectral distribution of the supercontinuum (SC) generated in barium fluoride is amenable to alteration simply by controlling the second- and third-order phase distortion of incident femtosecond-duration pulses. The second- and third-order phase distortions are controlled by an acoustic-optic programmable dispersive filter (AOPDF). The spectral extent on the blue side of the SC is influenced by independently varying the phase distortion of an ultrashort laser pulse. © 2015 Optical Society of America OCIS codes: (320.6629) Supercontinuum generation; (230.1040) Acousto-optical devices; (320.1590) Chirping; (320.5540) Pulse shaping; (190.7110) Ultrafast nonlinear optics. http://dx.doi.org/10.1364/OL.40.000241
Among the many applications of ultrashort laser pulses, supercontinuum (SC) generation [1], filamentation, and material modification [2] continue to attract considerable interest. The physical mechanisms responsible for SC generation are self-phase modulation (SPM), four-wave mixing (FWM), self-steepening, group velocity dispersion, chromatic dispersion, and plasma formation [1]. The spectral properties of the SC depend on both the material characteristics and pump pulse parameters like wavelength, polarization, and pulse duration. SC generation finds several applications in diverse interdisciplinary fields, such as optical frequency metrology and optical coherence tomography. The effect on SC generation of experimental parameters like pulse duration, polarization, incident power, wavelength [3,4], and dual beam pumping [5] has been explored in bulk media [6–10]. In a condensed medium, material dispersion plays a major role in the propagation dynamics of an ultrashort laser pulse. The ultrashort laser pulse is split into subpulses upon propagation; such temporal pulse splitting arrests the self-focusing collapse [11]. Although plasma is generated through multiphoton ionization in condensed media, its effect in stabilizing filament propagation is secondary to that of dispersion, except when the incident peak power is significantly larger than the threshold power for self-focusing [12]. Temporal pulse shaping, a very powerful approach used in various fields of science and technology—such as optical lithography [13], microscopy [14], and chemistry [15]—remains largely unexplored in the context of femtosecond (fs) laser filamentation and SC generation. The effect of pulse chirping on the spectral profile of the SC generated in transparent solids like calcite has been studied [16]. The application of linearly chirped pulses to delay the onset of filamentation in a dispersive medium has been demonstrated [17], but the use of more complex temporal pulse waveforms in filamentation studies is still unexplored. Various techniques are used for shaping fs laser pulses [18]. Liquid crystal displays have been used to achieve phase and amplitude pulse shaping for SC generation in sapphire [19]. An acousto-optic programmable 0146-9592/15/020241-04$15.00/0
dispersive filter (AOPDF) has been shown to alter the spectral shape of the SC by varying the initial chirp in photonic crystal fibers [20]. The effects of spectral shape on two-photon fluorescence excitation have been experimentally investigated using an acousto-optic pulse shaper. By using different spectral window shapes, the two-photon efficiency has been shown to vary by a factor of 2 for differently shaped spectra with the same full width at half-maximum [21]. Experiments and numerical simulations on filamentation using Airy waveforms in water have been recently reported [22]. Kinoform diffractive lenses have been used to demonstrate the control of the spectral extent of the SC [23]. SC generation in water using spatially structured beams has been investigated [24]. We present here a systematic study of the effect of pulse shaping on SC generation in condensed medium— a thin (2 mm) barium fluoride crystal—by controlling the second- and third-order phase distortion of incident pulses using an AOPDF. Figure 1 shows the experimental setup we used. A Ti-Sapphire laser amplifier (0.8 mJ energy, 27 fs, 1 kHz repetition rate) along with an AOPDF (Dazzler, Fastlite) located after 4-pass amplification, was utilized for precise control of the second- and third-order phase distortions. The laser’s output was focused on to the BaF2 sample by a 20-cm lens. The generated SC was collected using a lens, and a spectrometer recorded the SC spectrum. The effect of altering the second- (SOD) and third-order phase distortions (TOD) on the pulse duration was simultaneously monitored using spectral shear interferometry (WIZZLER, Fastlite), which provides information on the pulse duration and spectral phase. To begin with, the pulse is a compressed pulse with zero phase value. By altering the second- and thirdorder phase we measure the SC generated from BaF2 . We carried out two sets of measurements, one in which the incident energy was kept fixed and in the other in which it was the incident power that was kept constant. Figure 2(a) shows typical SC spectra with incident energy kept constant at 0.2 μJ for different values of SOD. For BaF2 , the critical power for self-focusing is 3 MW at 800 nm. With 0.2 μJ energy, the incident power is ∼7 MW. © 2015 Optical Society of America
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Fig. 1. Experimental setup for SC generation in a 2-mm BaF2 crystal. The lower panel depicts the measured duration (27 fs) of the incident 800 nm laser pulse.
This ensures that we do not have multiple filamentation. Such conditions are employed for f − 2f stabilization of carrier envelope phase stabilized lasers or for seeding an optical parametric amplifier. We observe a broad pedestal in the blue side of the SC, and its extent is broadest (up to 375 nm) when the SOD value is set to zero. The broadening due to SPM is symmetric around the central incident wavelength. It has been theoretically shown that space-time focusing and self-steepening form an optical shock wave at the back of the pulse, resulting in a broad pedestal on the blue side [25]. By changing the SOD values toward the positive side (100 fs2 ), the SC spectrum remains unaltered compared to the zero-SOD spectrum. On changing the SOD value toward the negative side (up to −400 fs2 ), the spectrum remains unchanged, but beyond this value the blue side of the spectrum is totally suppressed. We have also measured the corresponding pulse duration and spectral phase. Varying the SOD on the positive side (100 fs2 ) leads to positive chirp and the measured pulse duration is 28 fs, close to the incident pulse duration measured with zero phase. On the negative side (negative chirp), the pulse varies from 30 to 44 fs as the SOD changes from −200 to −700 fs2 . Suppression of the SC on the blue side is a result of the increase of pulse duration from 30 to 44 fs; this decreases the peak incident power on to the sample. Increase in the pulse duration reduces the self-steepening and plasma contribution which, in turn, causes suppression of the blue side of the spectrum. Reduction in the SC width [Fig. 2(a)] at 800 fs2 and −700 fs2 can, thus, be rationalized by considering an increase in pulse duration which, due to the pump pulse energy being constant, results in a reduction of the peak power incident on the BaF2 crystal. In contrast, on keeping the incident power fixed, we observed insignificant variation in the SC spectrum, as shown in Fig. 2(b), which shows data obtained with SOD values varying on both positive and negative sides.
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Fig. 2. SC generation in BaF2 at different SOD values for (a) fixed incident energy (0.2 μJ) and (b) fixed incident power (∼7 MW).
In earlier measurements carried out in photonic crystal fibers [4], it was shown that the SC spectrum is altered on changing the SOD value. However, these measurements were carried out only at fixed incident energy. Figure 3 shows SC spectra at different TOD values. By keeping the incident energy fixed at 0.2 μJ, the variation in SC spectra with TOD value is shown in Fig. 3(a). As is seen, when the TOD value is 3000 fs3 , the SC spectrum is unaltered and is similar to that at zero TOD. Note here that on changing TOD, the pulse duration changes as it splits into many sub-pulses, leading to overall broadening. On increasing TOD values toward the positive side (5000 to 10000 fs3 ), we observe suppression of the SC spectrum, particularly in the blue side; the spectrum also becomes symmetric around the center wavelength. On changing the TOD value to 5000 fs3 , the pulse duration changes to 31 fs, with sub-pulses on the trailing part of the pulse. For changes in TOD toward the negative side (up to −5000 fs3 ), we observe that the spectrum remains similar to that at zero TOD. Even with TOD values as high as −20000 fs3 , we observe only a slight reduction in the SC width. We now discuss our result when the incident power was kept fixed (7 MW). Here we observe suppression of the SC width on the blue side of the spectrum when the TOD value is positive. The SC spectra in this case are symmetric around the center wavelength, indicating that the broadening in the SC in this case is purely because of SPM. On the negative side, we observe no suppression of the SC width, even at TOD value as high as −20000 fs3 . Our observations on SC widths at different values of SOD and TOD can be rationalized as follows. In case of second-order distortion, the increase in pulse duration
January 15, 2015 / Vol. 40, No. 2 / OPTICS LETTERS
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Fig. 3. SC generation in BaF2 at different TOD values for (a) fixed incident energy (0.2 μJ) and (b) fixed incident power (7 MW).
is symmetric without any reshaping of the pulse; this results in almost identical SC spectra even when the SOD values are varied at constant values of incident power. At fixed incident laser energy, the variation in SC spectra is due to the increase (or decrease) of pulse duration that results in different incident power. SC generation is driven by the instantaneous intensity, and changing the pulse duration will result in change in the instantaneous intensity, leading to alteration in the SC spectra. In case of TOD, there is reshaping of the pulse that drives the dynamics of SC generation. Both positive and negative TOD split the laser pulse in the time domain, generating sub-pulses which are separated by a few tens of femtoseconds. A typical pulse with TOD is shown in Fig. 4. In earlier measurements carried out in BK7 glass, it was shown that the transmitted pulse from a 1 in. BK7 sample shows pulse splitting. Moreover, the transmitted spectrum shows modulation at moderate powers. With increase in power, secondary splitting was observed in BK7 glass [11]. Such pulse splitting is also known to 1.0
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Fig. 4. Left panel: laser pulse with TOD of 5000 fs3 . Right panel: laser pulse with TOD value −10000 fs3 .
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arrest the self-focusing. More recent experiments in water have monitored complete pulse dynamics in space and time during filamentation of 400-nm, 10-fs pulses under different focusing conditions [26]. They observed spectral modulations in both experiments and numerical simulations that were attributed to pulse splitting events. In another report, periodic modulation in the SC spectra has been observed in sapphire, a result of secondary pulse splitting causing interference between the first and subsequent pulses with overlapping spectra [27]. In Fig. 3, we observe modulation in the SC spectrum around the incident wavelength, where SPM is the dominant broadening mechanism. Even though our sample length is an order of magnitude smaller compared to experiments in [11], we observe modulation in the spectrum due to pulse splitting that is present in pulses with TOD. In our measurement at positive TOD values, we observe reduction in the SC width that is a signature of pulse splitting arresting the continuum generation. This reduction in SC is observed at both fixed energy and fixed power for positive TOD values. At negative TOD values, the SC width is similar to that observed for a chirp-free pulse. In summary, we have carried out a systematic study of the effect of pulse shaping on SC generation in barium fluoride by controlling the second- and third-order phase distortion of incident pulses using an acousto-optic programmable dispersive filter (AOPDF). Our measurements show that the spectral extent on the blue side of the SC can be influenced by independently varying the SOD and TOD of an ultrashort laser pulse. Financial support from the Department of Science and Technology is acknowledged by JAD (Women Scientists Scheme) and by DM (J C Bose National Fellowship). References 1. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007). 2. J. A. Dharmadhikari, R. Bernard, A. K. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, Opt. Lett. 38, 172 (2013). 3. F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, Nat. Commun. 3, 807 (2012). 4. J. Darginavicius, D. Majus, V. Jukna, N. Garejev, G. Valiulis, A. Couairon, and A. Dubietis, Opt. Express 21, 25210 (2013). 5. K. Wang, L. Qian, H. Luo, P. Yuan, and H. Zhu, Opt. Express 14, 6366 (2006). 6. A. K. Dharmadhikari, F. Rajgara, and D. Mathur, Appl. Phys. B 80, 61 (2005). 7. A. K. Dharmadhikari, F. A. Rajgara, and D. Mathur, Appl. Phys. B 82, 575 (2006). 8. A. K. Dharmadhikari, K. Alti, J. A. Dharmadhikari, and D. Mathur, Phys. Rev. A 76, 033811 (2007). 9. A. K. Dharmadhikari, J. A. Dharmadhikari, and D. Mathur, App. Phys. B 94, 259 (2009). 10. P. J. M. Johnson, V. I. Prokhorenko, and R. J. D. Miller, Opt. Express 17, 21488 (2009). 11. J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996). 12. A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006). 13. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000). 14. J. P. Ogilvie, D. Debarre, X. Solinas, J.-L. Martin, E. Beaurepaire, and M. Joffre, Opt. Express 14, 759 (2006).
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15. I. Pastirk, E. J. Brown, Q. Zhang, and M. Dantus, J. Chem. Phys. 108, 4375 (1998). 16. V. Kartazaev and R. R. Alfano, Opt. Lett. 32, 3293 (2007). 17. G. Mechain, C. D’Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, and R. Sauerbrey, Opt. Commun. 247, 171 (2005). 18. A. Monmayrant, S. Weber, and B. Chatel, J. Phys. B 43, 103001 (2010). 19. D. Schumacher, Opt. Lett. 27, 451 (2002). 20. Y. Jiang, Y. Leng, X. Chen, X. Li, and Z. Xu, Opt. Commun. 281, 2449 (2008). 21. C. J. Bardeen, V. V. Yakovlev, J. A. Squier, K. R. Wilson, S. D. Carpenter, and P. M. Weber, J. Biomed. Opt. 4, 362 (1999).
22. C. Ament, M. Kolesik, J. V. Moloney, and P. Polynkin, Phys. Rev. A 86, 043842 (2012). 23. C. Romero, R. B. Varillas, A. Camino, G. M. Vega, O. M. Yero, J. H. Toro, and J. R. Vázquez deAldana, Opt. Express 19, 4977 (2011). 24. N. Kaya, J. Strohaber, A. A. Kolomenskii, G. Kaya, H. Schroeder, and H. A. Schuessler, Opt. Express 20, 13337 (2012). 25. A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000). 26. A. Jarnac, G. Tamosauskas, D. Majus, A. Houard, A. Mysyrowicz, A. Couairon, and A. Dubietis, Phys. Rev. A 89, 033809 (2014). 27. V. Jukna, J. Galinis, G. Tamosauskas, D. Majus, and A. Dubietis, Appl. Phys. B 116, 477 (2014).
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Influencing supercontinuum generation by phase distorting an ultrashort laser pulse J. A. Dharmadhikari,1 A. K. Dharmadhikari,2,* K. Dota,1 and D. Mathur2 1
Department of Atomic and Molecular Physics, Manipal University, Manipal 576 104, India 2 Tata Institute of Fundamental Research, 1 Homi Bhabha Road, Mumbai 400 005, India *Corresponding author: [email protected] Received November 18, 2014; accepted December 1, 2014; posted December 16, 2014 (Doc. ID 227127); published January 12, 2015
We show that the spectral distribution of the supercontinuum (SC) generated in barium fluoride is amenable to alteration simply by controlling the second- and third-order phase distortion of incident femtosecond-duration pulses. The second- and third-order phase distortions are controlled by an acoustic-optic programmable dispersive filter (AOPDF). The spectral extent on the blue side of the SC is influenced by independently varying the phase distortion of an ultrashort laser pulse. © 2015 Optical Society of America OCIS codes: (320.6629) Supercontinuum generation; (230.1040) Acousto-optical devices; (320.1590) Chirping; (320.5540) Pulse shaping; (190.7110) Ultrafast nonlinear optics. http://dx.doi.org/10.1364/OL.40.000241
Among the many applications of ultrashort laser pulses, supercontinuum (SC) generation [1], filamentation, and material modification [2] continue to attract considerable interest. The physical mechanisms responsible for SC generation are self-phase modulation (SPM), four-wave mixing (FWM), self-steepening, group velocity dispersion, chromatic dispersion, and plasma formation [1]. The spectral properties of the SC depend on both the material characteristics and pump pulse parameters like wavelength, polarization, and pulse duration. SC generation finds several applications in diverse interdisciplinary fields, such as optical frequency metrology and optical coherence tomography. The effect on SC generation of experimental parameters like pulse duration, polarization, incident power, wavelength [3,4], and dual beam pumping [5] has been explored in bulk media [6–10]. In a condensed medium, material dispersion plays a major role in the propagation dynamics of an ultrashort laser pulse. The ultrashort laser pulse is split into subpulses upon propagation; such temporal pulse splitting arrests the self-focusing collapse [11]. Although plasma is generated through multiphoton ionization in condensed media, its effect in stabilizing filament propagation is secondary to that of dispersion, except when the incident peak power is significantly larger than the threshold power for self-focusing [12]. Temporal pulse shaping, a very powerful approach used in various fields of science and technology—such as optical lithography [13], microscopy [14], and chemistry [15]—remains largely unexplored in the context of femtosecond (fs) laser filamentation and SC generation. The effect of pulse chirping on the spectral profile of the SC generated in transparent solids like calcite has been studied [16]. The application of linearly chirped pulses to delay the onset of filamentation in a dispersive medium has been demonstrated [17], but the use of more complex temporal pulse waveforms in filamentation studies is still unexplored. Various techniques are used for shaping fs laser pulses [18]. Liquid crystal displays have been used to achieve phase and amplitude pulse shaping for SC generation in sapphire [19]. An acousto-optic programmable 0146-9592/15/020241-04$15.00/0
dispersive filter (AOPDF) has been shown to alter the spectral shape of the SC by varying the initial chirp in photonic crystal fibers [20]. The effects of spectral shape on two-photon fluorescence excitation have been experimentally investigated using an acousto-optic pulse shaper. By using different spectral window shapes, the two-photon efficiency has been shown to vary by a factor of 2 for differently shaped spectra with the same full width at half-maximum [21]. Experiments and numerical simulations on filamentation using Airy waveforms in water have been recently reported [22]. Kinoform diffractive lenses have been used to demonstrate the control of the spectral extent of the SC [23]. SC generation in water using spatially structured beams has been investigated [24]. We present here a systematic study of the effect of pulse shaping on SC generation in condensed medium— a thin (2 mm) barium fluoride crystal—by controlling the second- and third-order phase distortion of incident pulses using an AOPDF. Figure 1 shows the experimental setup we used. A Ti-Sapphire laser amplifier (0.8 mJ energy, 27 fs, 1 kHz repetition rate) along with an AOPDF (Dazzler, Fastlite) located after 4-pass amplification, was utilized for precise control of the second- and third-order phase distortions. The laser’s output was focused on to the BaF2 sample by a 20-cm lens. The generated SC was collected using a lens, and a spectrometer recorded the SC spectrum. The effect of altering the second- (SOD) and third-order phase distortions (TOD) on the pulse duration was simultaneously monitored using spectral shear interferometry (WIZZLER, Fastlite), which provides information on the pulse duration and spectral phase. To begin with, the pulse is a compressed pulse with zero phase value. By altering the second- and thirdorder phase we measure the SC generated from BaF2 . We carried out two sets of measurements, one in which the incident energy was kept fixed and in the other in which it was the incident power that was kept constant. Figure 2(a) shows typical SC spectra with incident energy kept constant at 0.2 μJ for different values of SOD. For BaF2 , the critical power for self-focusing is 3 MW at 800 nm. With 0.2 μJ energy, the incident power is ∼7 MW. © 2015 Optical Society of America
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Fig. 1. Experimental setup for SC generation in a 2-mm BaF2 crystal. The lower panel depicts the measured duration (27 fs) of the incident 800 nm laser pulse.
This ensures that we do not have multiple filamentation. Such conditions are employed for f − 2f stabilization of carrier envelope phase stabilized lasers or for seeding an optical parametric amplifier. We observe a broad pedestal in the blue side of the SC, and its extent is broadest (up to 375 nm) when the SOD value is set to zero. The broadening due to SPM is symmetric around the central incident wavelength. It has been theoretically shown that space-time focusing and self-steepening form an optical shock wave at the back of the pulse, resulting in a broad pedestal on the blue side [25]. By changing the SOD values toward the positive side (100 fs2 ), the SC spectrum remains unaltered compared to the zero-SOD spectrum. On changing the SOD value toward the negative side (up to −400 fs2 ), the spectrum remains unchanged, but beyond this value the blue side of the spectrum is totally suppressed. We have also measured the corresponding pulse duration and spectral phase. Varying the SOD on the positive side (100 fs2 ) leads to positive chirp and the measured pulse duration is 28 fs, close to the incident pulse duration measured with zero phase. On the negative side (negative chirp), the pulse varies from 30 to 44 fs as the SOD changes from −200 to −700 fs2 . Suppression of the SC on the blue side is a result of the increase of pulse duration from 30 to 44 fs; this decreases the peak incident power on to the sample. Increase in the pulse duration reduces the self-steepening and plasma contribution which, in turn, causes suppression of the blue side of the spectrum. Reduction in the SC width [Fig. 2(a)] at 800 fs2 and −700 fs2 can, thus, be rationalized by considering an increase in pulse duration which, due to the pump pulse energy being constant, results in a reduction of the peak power incident on the BaF2 crystal. In contrast, on keeping the incident power fixed, we observed insignificant variation in the SC spectrum, as shown in Fig. 2(b), which shows data obtained with SOD values varying on both positive and negative sides.
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500 600 700 800 Wavelength (nm)
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Fig. 2. SC generation in BaF2 at different SOD values for (a) fixed incident energy (0.2 μJ) and (b) fixed incident power (∼7 MW).
In earlier measurements carried out in photonic crystal fibers [4], it was shown that the SC spectrum is altered on changing the SOD value. However, these measurements were carried out only at fixed incident energy. Figure 3 shows SC spectra at different TOD values. By keeping the incident energy fixed at 0.2 μJ, the variation in SC spectra with TOD value is shown in Fig. 3(a). As is seen, when the TOD value is 3000 fs3 , the SC spectrum is unaltered and is similar to that at zero TOD. Note here that on changing TOD, the pulse duration changes as it splits into many sub-pulses, leading to overall broadening. On increasing TOD values toward the positive side (5000 to 10000 fs3 ), we observe suppression of the SC spectrum, particularly in the blue side; the spectrum also becomes symmetric around the center wavelength. On changing the TOD value to 5000 fs3 , the pulse duration changes to 31 fs, with sub-pulses on the trailing part of the pulse. For changes in TOD toward the negative side (up to −5000 fs3 ), we observe that the spectrum remains similar to that at zero TOD. Even with TOD values as high as −20000 fs3 , we observe only a slight reduction in the SC width. We now discuss our result when the incident power was kept fixed (7 MW). Here we observe suppression of the SC width on the blue side of the spectrum when the TOD value is positive. The SC spectra in this case are symmetric around the center wavelength, indicating that the broadening in the SC in this case is purely because of SPM. On the negative side, we observe no suppression of the SC width, even at TOD value as high as −20000 fs3 . Our observations on SC widths at different values of SOD and TOD can be rationalized as follows. In case of second-order distortion, the increase in pulse duration
January 15, 2015 / Vol. 40, No. 2 / OPTICS LETTERS
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Fig. 3. SC generation in BaF2 at different TOD values for (a) fixed incident energy (0.2 μJ) and (b) fixed incident power (7 MW).
is symmetric without any reshaping of the pulse; this results in almost identical SC spectra even when the SOD values are varied at constant values of incident power. At fixed incident laser energy, the variation in SC spectra is due to the increase (or decrease) of pulse duration that results in different incident power. SC generation is driven by the instantaneous intensity, and changing the pulse duration will result in change in the instantaneous intensity, leading to alteration in the SC spectra. In case of TOD, there is reshaping of the pulse that drives the dynamics of SC generation. Both positive and negative TOD split the laser pulse in the time domain, generating sub-pulses which are separated by a few tens of femtoseconds. A typical pulse with TOD is shown in Fig. 4. In earlier measurements carried out in BK7 glass, it was shown that the transmitted pulse from a 1 in. BK7 sample shows pulse splitting. Moreover, the transmitted spectrum shows modulation at moderate powers. With increase in power, secondary splitting was observed in BK7 glass [11]. Such pulse splitting is also known to 1.0
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Fig. 4. Left panel: laser pulse with TOD of 5000 fs3 . Right panel: laser pulse with TOD value −10000 fs3 .
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arrest the self-focusing. More recent experiments in water have monitored complete pulse dynamics in space and time during filamentation of 400-nm, 10-fs pulses under different focusing conditions [26]. They observed spectral modulations in both experiments and numerical simulations that were attributed to pulse splitting events. In another report, periodic modulation in the SC spectra has been observed in sapphire, a result of secondary pulse splitting causing interference between the first and subsequent pulses with overlapping spectra [27]. In Fig. 3, we observe modulation in the SC spectrum around the incident wavelength, where SPM is the dominant broadening mechanism. Even though our sample length is an order of magnitude smaller compared to experiments in [11], we observe modulation in the spectrum due to pulse splitting that is present in pulses with TOD. In our measurement at positive TOD values, we observe reduction in the SC width that is a signature of pulse splitting arresting the continuum generation. This reduction in SC is observed at both fixed energy and fixed power for positive TOD values. At negative TOD values, the SC width is similar to that observed for a chirp-free pulse. In summary, we have carried out a systematic study of the effect of pulse shaping on SC generation in barium fluoride by controlling the second- and third-order phase distortion of incident pulses using an acousto-optic programmable dispersive filter (AOPDF). Our measurements show that the spectral extent on the blue side of the SC can be influenced by independently varying the SOD and TOD of an ultrashort laser pulse. Financial support from the Department of Science and Technology is acknowledged by JAD (Women Scientists Scheme) and by DM (J C Bose National Fellowship). References 1. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007). 2. J. A. Dharmadhikari, R. Bernard, A. K. Bhatnagar, D. Mathur, and A. K. Dharmadhikari, Opt. Lett. 38, 172 (2013). 3. F. Silva, D. R. Austin, A. Thai, M. Baudisch, M. Hemmer, D. Faccio, A. Couairon, and J. Biegert, Nat. Commun. 3, 807 (2012). 4. J. Darginavicius, D. Majus, V. Jukna, N. Garejev, G. Valiulis, A. Couairon, and A. Dubietis, Opt. Express 21, 25210 (2013). 5. K. Wang, L. Qian, H. Luo, P. Yuan, and H. Zhu, Opt. Express 14, 6366 (2006). 6. A. K. Dharmadhikari, F. Rajgara, and D. Mathur, Appl. Phys. B 80, 61 (2005). 7. A. K. Dharmadhikari, F. A. Rajgara, and D. Mathur, Appl. Phys. B 82, 575 (2006). 8. A. K. Dharmadhikari, K. Alti, J. A. Dharmadhikari, and D. Mathur, Phys. Rev. A 76, 033811 (2007). 9. A. K. Dharmadhikari, J. A. Dharmadhikari, and D. Mathur, App. Phys. B 94, 259 (2009). 10. P. J. M. Johnson, V. I. Prokhorenko, and R. J. D. Miller, Opt. Express 17, 21488 (2009). 11. J. K. Ranka, R. W. Schirmer, and A. L. Gaeta, Phys. Rev. Lett. 77, 3783 (1996). 12. A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. Di Trapani, Phys. Rev. E 73, 016608 (2006). 13. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000). 14. J. P. Ogilvie, D. Debarre, X. Solinas, J.-L. Martin, E. Beaurepaire, and M. Joffre, Opt. Express 14, 759 (2006).
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