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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 23 — Nov. 10, 2008
  • pp: 18910–18921
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Poor man’s source for sub 7 fs: a simple route to ultrashort laser pulses and their full characterization

Bruno E. Schmidt, Waldemar Unrau, Aldo Mirabal, Shaohui Li, Marcel Krenz, Ludger Wöste, and Torsten Siebert  »View Author Affiliations


Optics Express, Vol. 16, Issue 23, pp. 18910-18921 (2008)
http://dx.doi.org/10.1364/OE.16.018910


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Abstract

A practicable and economic method for the generation and full characterization of laser pulses ranging down to sub 7 fs duration with energies spanning the full µJ domain is presented. The method utilizes a self-induced and self-guiding filamentation of titanium-sapphire based, amplified pulses in air for spectral broadening, a standard chirp mirror compression scheme and transient grating frequency resolved optical gating for determining the spectral phase over the full visible to near infrared range. In this manner, few-cycle laser pulses with a high quality in the spatial beam profile have been generated in an robust arrangement with a minimal amount of standard optical components for their full characterization. The optical scheme demonstrates an uncomplicated, versatile access to this regime of pulsed laser radiation accompanied by a comprehensive analysis.

© 2008 Optical Society of America

1. Introduction

The development of solid-state femtosecond laser technology has provided the basis for the optical nonlinearity fundamental to generating extended coherent bandwidth and ultimately attaining pulsed laser radiation with significantly improved time resolution and enhanced peak power. In recent years, different strategies for improving upon these elementary attributes of ultrashort laser pulses have been pursued. One possible route to these means generally involves propagating pulsed radiation at high field strengths over long optical pathways in a confined volume. This can be realized in several variations, where confinement is generally achieved in micro-structured fibres [1

1. P. St. J. Russell, “Photonic-Crystal Fibers,” J. of Lightwave Technology 24, 4729–4749 (2006). [CrossRef]

], hollow core fibres [2

2. M. Nisoli, S. De Silvestri, and O. Svelto “Generation of high energy 10fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996). [CrossRef]

] or via self-guiding filamentation [3

3. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268 (1986). [CrossRef] [PubMed]

, 4

4. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995). [CrossRef] [PubMed]

, 10

10. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Reports 441, 47–189 (2007). [CrossRef]

, 11

11. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007). [CrossRef]

]. Active processes in the spectral broadening range form self-phase modulation (SPM) [5

5. R. R. Alfano and S. L. Shapiro, “Observation of Self-Phase Modulation and Small-Scale Filaments in Crystals and Glasses,” Phys. Rev. Lett. 24, 592–594 (1970). [CrossRef]

], self-steepening [6

6. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000). [CrossRef] [PubMed]

] and pulse splitting [7

7. M. Trippenbach and Y. B. Band “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

], four-wave-mixing processes (FWM) [8

8. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

] and coherent Raman cascading [9

9. A. M. Burzo, A. V. Chugreev, and A. V. Sokolov, “Stimulated rotational Raman generation controlled by strongly driven vibrational coherence in molecular deuterium,” Phys. Rev. A 75, 022515/1-022515/10 (2007).

] as well as light-plasma interactions [3

3. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268 (1986). [CrossRef] [PubMed]

, 10

10. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Reports 441, 47–189 (2007). [CrossRef]

, 11

11. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007). [CrossRef]

]. Landmarks in the development of this general principle include initial supercontinuum generation in the solid state and liquids [5

5. R. R. Alfano and S. L. Shapiro, “Observation of Self-Phase Modulation and Small-Scale Filaments in Crystals and Glasses,” Phys. Rev. Lett. 24, 592–594 (1970). [CrossRef]

] followed by later work in gaseous media [3

3. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268 (1986). [CrossRef] [PubMed]

]. Building on these developments, interaction lengths were increased through guiding in different forms of nonlinear media. In this framework, solid state micro-structured fibers allow for the generation of pulses with octave spanning spectra in the nano- and recently in the lower mircojoule regime combined with the unique and tunable propagation properties of these materials.[1

1. P. St. J. Russell, “Photonic-Crystal Fibers,” J. of Lightwave Technology 24, 4729–4749 (2006). [CrossRef]

, 12

12. A. M. Zheltikov “ Let there be white light: supercontinuum generation by ultrashort laser pulses,” Physics-Uspekhi 49, 605–628 (2006). [CrossRef]

, 13

13. A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 208, 453–456 (2007). [CrossRef]

, 14

14. L. Di Labio, W. Luthy, V. Romano, F. Sandoz, and T. Feurer “Superbroadband fluorescence fiber fabricated with granulated oxides,” Opt. Lett. 33, 1050–1052 (2008). [CrossRef] [PubMed]

] Alternatively, the use of gaseous media in hollow core fibres and filamentation allows for high pulse energies to be employed and additionally access light-plasma interactions for spectral broadening and guiding. In this manner, octave spanning bandwidth als well as pulses with compressibility down to a few optical cycles can be obtained with pulse energies ranging to the mJ regime and beyond [15

15. G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006). [CrossRef] [PubMed]

]. This scheme can be extended to the terawatt regime, where white light generation in filaments spanning several hundred meters can be generated with a spectral range extending form approximately 230 nm to 4.5 µm at altitudes beyond 10 km in the framework of atmospheric research with LIDAR. [16

16. J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woeste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003). [CrossRef] [PubMed]

]

Accompanied with their generation, the characterization of extremely short and octave spanning laser pulses is still a issue in current research. Established methods such as interferometric autocorrelation, frequency resolved optical gating (FROG) [17

17. J. N. Sweetser, D. N. Fittinghoff, and R. Trebino, “Transient-grating frequency-resolved optical gating,” Opt. Lett. 22, 519–521 (1997). [CrossRef] [PubMed]

, 18

18. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbgel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997). [CrossRef]

, 19

19. D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of a broadband ultrafast continuum,”J. Opt. Soc. Am. A 25, 34–40 (2008).

] and spectral phase interferometry for direct electric-field reconstruction (SPIDER) [20

20. I. A. Walmsley and V. Wong, “Characterization of the electric field of ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 2453–2463 (1996).

, 21

21. R. Morita, M. Hirasawa, N. Karasawa, S. Kusaka, N. Nakagawa, K. Yamane, L. Li, A. Suguro, and M. Yamashita, “Sub-5 fs optical pulse characterization,” Meas. Sci. Technol. 13, 1710–1720 (2002). [CrossRef]

] with their respective drawbacks and advantages are summarized in Ref [22

22. L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, 67–75 (2008).

]. While nearly single cycle, sub 4 fs pulses have been correlated interferometrically via surface third harmonic generation, access to the spectral phase over the full bandwidth still remains challenging. SPIDER posses the powerful and unique advantage of an analytical approach in obtaining the spectral phase from the respective interferogram, yet the necessity of frequency mixing and pulse shearing can limit the total pulse bandwidth that can be analyzed. FROG techniques substantially vary in the mechanism employed for temporal gating, ranging from second order frequency mixing to third order processes such as self-diffraction, Kerr-based polarization gating and laser induced transient gratings. While FROG intrinsically poses the difficulties associated with an iterative, non-analytical phase retrieval, the variations of this technique that do not rely on bandwidth limited frequency mixing open the noteworthy prospect of a complete phase characterization over octave spanning spectra, as will be demonstrated in this work.

In many cases, the generation, and particularly the characterization, of few cycle laser pulses involve intricate optical schemes that employ non-standard optical components. With the motivation to makes state of the art pulse parameters readily accessible in the framework of commercially available solid-state femtosecond technology, this work describes a means for attaining and fully characterizing octave spanning laser pulses with compressibility in the sub 7 fs regime and energies ranging to upper end of the µJ domain. The strategy described in the following full avoids complex, sensitive optical schemes and relies on an absolute minimal amount of standard optical components. For spectral broadening, self-induced filamentation in air is employed, where the developed setup allows for pulses durations with the highest compression factor attained in a single filamentation process. For the characterization of the obtained pulses, it is demonstrated that transient grating, four-wave mixing based frequency gating permits the full characterization of the spectral phase ranging an octave spanning spectrum, to the best of our knowledge the highest bandwidth so far correlated in a FROG scenario.

2. Methodology

The general scheme for a simple and robust access to high-energy, few-cycle laser pulses in the framework of standard Ti:Sa amplifier technology is depicted in Fig. 1. Beginning with the output of a commercial femtosecond laser system,1 continuum generation is attained through filamentation in air at atmospheric pressure by focusing the laser pulses with a spherical mirror SM1 (f=2 m), as shown in upper part of Fig. 1. Through the spatial confinement and temporal modulation resulting primarily from optical Kerr effect in competition with weak, multi-photon gas ionization and thin plasma formation, this self-initiating and self-guiding process circumvents problems of pointing stability, as well as aperture matching and the optimization of propagation length involved in fiber guiding. Direct filamentation in air make vacuum components as well as entrance and exit windows obsolete and unwanted spectral as well as spatial phase distortions are avoided, vide infra. Assuming 1.0 mJ pulse energy, 7.2×1013 W/cm2 at 1/e2 intensity is achieved assuming a geometric focus of the transversal mode with the corresponding pulse power of 25 GW. This value constitutes approximately eight times the critical power for self-focussing of approximately 3 GW in air [10

10. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Reports 441, 47–189 (2007). [CrossRef]

]. Regardless of hereinafter presented input energies, the transmission after filamentation maintained high values of approximately 95%. An important setting is the adjustment of the beam diameter through iris I1 at 1.5 m ahead of SM1. Reduction of the initial diameter (9.3 mm) from 10% to 30% prevents fluctuation in the filamentation process as well as multi-filamentation in air at atmospheric pressure. In this configuration, the onset of filamentation can be observed through a weak fluorescence roughly 8 cm before the geometrical focus, extending approximately 25 cm. Subsequent to spontaneous termination of the filamentation, the spectrally broadened pulse propagates with a reduced beam diameter and divergence of 2.5 mrad, which is determined by the filamentation process rather than the initial focusing optic SM1. An analysis of spatial, spectral and temporal behavior as well as transmission and conversion efficiency of the initial output of the filament will be given in the following section.

Fig. 1. Experimental setup: The initial laser pulses (40 fs, 0.6-1.5 mJ) are focused with spherical mirror SM1 f=2 m. Dispersion management is achieved by four bounces on a commercial chirped mirror pair CM1 & CM2, (Layertec) with GVD oscillation compensation and average negative GVD of ≈(-)60 fs2 in wavelength range from 680-900 nm. Total reflectivity is ≥ 99.8% from 650-1000 nm at incident angle of 1°. Within the TGFROG, SM2 focuses the three parallel beams in a BK7 glass. k 1 and k 2 are horizontally separated and create a transient grating on which k 3 is scattered. This generates the spectrally dispersed FWM signal (kSb and kSr).

At this point, two geometrical aspects concerning the distortion of the temporal measurement should be discussed. First, movement of mirror TM causes a parallel spatial shift of k3 on surface of SM2. In order to minimize this shift, the incident angle β2 on delay mirror is only 1° which cause a parallel shift of 2 µm for a scan range of 200 fs. Since parallel shift does not change focus position in first approximation, the shift of 2 µm is negligible. More important is an analysis of the temporal resolution for a non-collinear interaction of three beams. The intersection angle θ inside the medium between two k-vectors introduces a geometrical time smearing Δτ. Therefore, angle θ is kept small (0.6°) by use of relatively long focal length f combined with a small beam separation, di. Assuming Gaussian beams, the temporal smear can thus be calculated according to ref. [25

25. R. Trebino, “Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses” (Kluwer Academic Publishers, 2000).

] by Δτ=(fθλ)/(diπc) where c is speed of light and λ denotes laser wavelength. For the present TG-FROG setup, Δτ possess a maximum value of 0.63 fs when long wavelength of 900 nm is assumed as upper limit. Δτ blurs the physical value τ 0 and gives a measured value τmeas=τ02+ξΔτ2 with a scaling constant x which depends on beam geometry. For three intersecting beams, ξ ≈ 5/3 in a forward box configuration. Based on above equations, the blurring of a 6 fs pulse results in pulse lengthening of less than 6% through the measurement in this beam geometry. The determination of pulse duration was therefore carried out by evaluating the raw data obtained directly from FROG trace. The Wigner representation was projected onto the horizontal time axis and fit assuming a Gaussian temporal profile. Circles in Fig. 4 correspond to measured data points whereas unbroken lines display the Gaussian fit. Different than the case of two beam correlations, the deconvolution factor for Gaussian functions is 32 for a three beam [25

25. R. Trebino, “Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses” (Kluwer Academic Publishers, 2000).

] geometry in a χ (3) process. Retrieval of spectral phase from the FROG data was accomplished utilizing the generalized projection method [18

18. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbgel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997). [CrossRef]

, 26

26. D. J. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B 25, A120–A132 (2008).

]. As a further advantage of employing FWM based correlation, it should be noted that in standard correlation techniques involving frequency conversion, the common method for increasing phase matched bandwidth involves reducing the propagation length through the nonlinear medium, currently down to a crystal thickness of 5-10 µm. Thus, χ (2)nonlinear processes, i.e. three wave mixing, reach physical limitation in their dimensions as well as transparency when octave spanning spectra are gated. In contrast to this, FWM can easily be carried out in a spectral range extending into the deep UV as will as into the IR domain, with the only requirement being the transparency of the medium. As shown here, phase-matching of broadband spectra extending over an octave is automatically realized in this process through the dispersion of the signal direction. From this, FWM mixing can be viewed as one of the most flexible nonlinear processes with respect to the spectral range and bandwidth in the correlation of pulsed laser radiation. For the experiments carried out here, standard BK7 microscope objectives where employed and provided that the focus was placed at front face of the medium, a crosscheck for varying thickness and different composition of the medium showed no significant change of the pulse duration when correlating few cycle laser pulses.

3. Results and discussion

In the following, an analysis of the initial filament output will be given for varying input pulse parameters with regards to the spatial beam profile as well as the efficiency and mechanism in spectral broadening. Following this, the capability to characterize the spectral phase of femtosecond laser pulses with bandwidths of up to 500 nm, spanning the visible to NIR range will be discussed. From this, the optimal filamentation conditions for obtaining few cycle laser pulses will be analyzed in view of the spectral phase retrieved form the supercontinuum pulse. Within this analysis, different filamentation conditions will be presented that allow for obtaining an output with a spectral phase suitable for compression of selected spectral regions to the sub 7 fs regime. Furthermore, different pulse energies in the filament output, obtained from the radial selection of the transversal mode, are compared with respect to their compressibility.

3.1. General attributes of the filament output

The transversal mode obtain from the filamentation of standard amplified pulses (1.3 mJ, 40 fs @ 807 nm) is illustrated by means of a CCD camera image of the supercontinuum output in Fig. 2b. The high radial symmetry of the intensity profile in the spatial mode generally obtained from plasma filamentation in gaseous media can clearly be seen from the horizontal and vertical cross section in Fig. 2a. Important to consider in the framework of filamentation is the transversal homogeneity of spectral broadening reflected in the output mode. In order to characterize this quality of the filamentation, the spectral behavior is recorded at different positions by scanning a small diaphragm transversely across the mode, as shown in Fig. 2c. Within a radius of 80% of peak intensity, all general characteristic spectral signatures remain virtually constant except the high frequency cut off. Particulary noteworthy in Fig. 2c is the conformity of the amplitude modulations in the spectral signature form approximately 500 to 950 nm within 25% of peak intensity of the transversal mode. An estimate of conversion efficiency toward visible wavelengths region ranging from 450–720 nm was carried out by numerically integrating the corresponding area in plot of Fig. 2c. Under the given conditions, typically 15%-20% of overall intensity are transferred to the visible range. Contrary to the center of the mode, the peripheral region at 10% of maximum intensity clearly exhibits narrower bandwidth with a different spectral signatures and a slight red-shift.

3.2. Temporal gating of octave spanning white light

Figure 3 shows the acquired FROG trace as well as the spectral phase retrieval when the full bandwidth obtained form filamentation is directly coupled into the TG-FROG described above. Settings of the input pulse for filamentation are chosen to demonstrate the capability of generating octave exceeding spectra within single filamentation in atmospheric air as well as capability to characterize the spectral phase spanning this spectrum via TG-FROG. This demonstrates a simple means for the full characterization of pulsed radiation in this regime and establishes the tools for gaining new experimental insight to the fundamental mechanisms underlying filamen- tation via spectral phase analysis. Widest spectra were generated when iris I1 was nearly fully open, providing a pulse energy of 1.3 mJ and a prechirp of roughly 500 fs2. These settings denote limiting values for air at atmospheric pressure before intensity fluctuations and spatial distortion of beam profile occur. When aiming for broadest spectra, two different sections in the FROG trace become distinguishable. The leading part of the pulse is temporally and spectrally significantly modulated, whereas the spectrum from 650 down to 380 nm shows a predominately smooth spectral profile as well as a smooth phase profile down to 600 nm. For a simple and qualitative interpretation of these to distinct pulse regions, a briefly summary of the current understanding of spectral broadening through filamentation is necessary. In gas phase filamentation, it is primarily the competition between Kerr effect and plasma generation that cause the pulse to experience spatio-temporal modulations with the corresponding spectral modifications. Propagation is influenced by self-focusing [27

27. J. H. Marburger, “Self-focusing: Theory,” Prog. Quantum Electron. 4, 35–110 (1975). [CrossRef]

] and multi photon ionization [28

28. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62–64 (1996). [CrossRef] [PubMed]

], where the latter acts to arrest the collapse of beam. The balancing of both effects results in extended self-guiding [4

4. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995). [CrossRef] [PubMed]

]. On the spectral side, Kerr induced SPM [8

8. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

] accompanied by a minor red shift [30

30. T. Lehner and N. Auby, “Stabilization of the Kerr effect by self induced ionization: Formation of optical light spatially localized structures,” Phys. Rev. E 61, 1996–2005 (2000).

] leads initially to symmetric broadening accompanied by the respective phase distortions. Onset of plasma generation and thus lowering of the refractive index forces asymmetry of the temporal phase and spectral envelop [8

8. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

, 6

6. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000). [CrossRef] [PubMed]

], respectively. This general plasma blue-shift together with the shock dynamics [29

29. N. Akzbek, M. Scalora, C. M. Bowden, and S. L. Chin, “White light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353 (2001). [CrossRef]

] resulting form the trailing pulse flank, give rise to asymmetric blue shift of the spectrum. Further spectral asymmetry may also be attributed to non-resonant FWM [8

8. G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

]. Providing sufficient intensity in nonlinear evolution, the pulse undergoes temporal splitting [3

3. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268 (1986). [CrossRef] [PubMed]

, 31

31. A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999). [CrossRef]

, 7

7. M. Trippenbach and Y. B. Band “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

].

Fig. 2. Transversal mode characterization of the filament output with an input of 1.3 mJ pulse energy. (a) Horizontal (light green) and vertical (black) cross section of corresponding image in (b). (c) Spectra taken at different transverse intensities: maximum (light orange), 50% (black), 25% (light green), 11% (blue) of the maximum in the transversal profile.
Fig. 3. (a) TG FROG traces and associated projection on time axis of the uncompressed bandwidth from 370-950 nm after filamentation with 1.3 mJ pulse energy. Temporally split and spectrally strongly modulated NIR part experiences complicated phase distortions whereas the VIS spectral components obey quadratic phase. (b) Phase retrieval of white light spectrum from the FROG trace in (a) with the original pulse spectrum (grey line), retrieved spectral phase (green dotted line) and spectrum (black line).

The acquired FROG trace of the filament output in Fig. 3 together with the retrieved spectral phase distinctly reflect the different mechanism involved in the spectral broadening. The strong modulations in the FROG trace around the laser fundamental arise when nonlinear propagation through the entire filament extend beyond a symmetric SPM to complex phase distortions manifesting themselves in the apparent temporal splitting. The corresponding spectral phase in the inlet of Fig. 3b retrieved form the FROG trace for this region further reflects phase distortions beyond SPM and its highly irregular contour clearly shows that under these filamentation conditions, compressibility with conventional methods is unpracticable. A very different picture is seen in the visible part of the obtained FROG trace and the spectral phase in Fig. 3. Spectral phase retrieval for this the unmodulated part of continuum primarily obeys a smooth quadratic behavior. Here, truncation of the spectral phase function at 560 nm is caused by numerical unwrapping when dealing with very steep slopes as well as termination of the retrieved spectral amplitude. However, the total hight stroking over 300 radian was obtained by the retrieval. This phase function corresponds to a GVD of approximately 900 fs2 assuming a purely linear chirp. Considering the propagation in air amounting to 150 fs2, the remaining positive chirp is attributed to the spectral broadening mechanism in the filament. This is supported by the observation that the phase function remains constant for a different prechirp of the input pulse. The distinct and manageable phase function in this region clearly reveals straight forward compressibility. This is in contrast to the band ranging the red to NIR spectral domain under filamentation conditions set for maximal spectral broadening.

3.3. Compression to few cycle pulses

Fig. 4. Pulse compression using chirped mirror pair with (-)60 fs2/bounce and an input pulse energy of (a) 1.0 mJ (b) 650 µJ and (c) 760 µJ for filamentation. The obtained filament out is radially selected, attenuating the output in (a) from 950 to 30 µJ with a transversal mode radius of 500 µm, (b) from 620 to 20 µJ with a transversal mode radius of 500 µm and (c) from 720 to 25 µJ full radius of the transversal mode (see Fig. 2). Circles correspond to measured data points whereas straight line displays a Gaussian fit. Highest input pulse energy in (a) causes modulation at NIR wavelengths and successive reduction of input pulse energy leads to clean temporal pulse compression in (b) and (c). 1 mJ denotes threshold energy before increased temporal satellites arise. Measurements (b) and (c) compare the compressibility of the filament output for different radial selection of the transversal mode output of the filament.
Fig. 5. Spectral phase retrieval of few cycle pulses generated in atmospheric air and subsequent compression by chirped mirrors. (a) Modulated spectral and temporal structures appear for shortest FWHM of 6.3 fs in Fig. 4a. (b) Filamentation with 0.65 mJ results in smooth spectral broadening with linear spectral phase and clean temporal profile corresponding to Fig. 4b.

4. Conclusion

The strategy employed for the generation as well as full characterization of few cycle pulses and octave exceeding supercontinua described above is distinguished in both cases by the ease of realization and the high economy in optical components. The white light generation via filamentation in atmospheric air under conventional laboratory laser conditions (0.6-1.5 mJ) and a characterization by a FWM based FROG scheme can be easily realized. The noteworthy capability to frequency gate the full coherent bandwidth emitted from the filament allows for a general insight to the mechanism of filamentation as well as the optimal conditions for pulse compression of different spectral regions with varying input energies and radial output selection. The work presented above opens a variety of aspects for future investigations. The utilization of a more complex phase correction provided by liquid crystal base pulse shapers opens the prospect of compressing the full bandwidth of the filament output as well as the generation of complex pulse forms for spectroscopic applications [34

34. A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B: 90, 427–430 (2008).

]. Furthermore, the high quality in the spatial beam profile allows for a second filament to be ignited with the given output, bringing a higher conversion into the visible components of the spectrum and eventually compression to shorter pulse durations. While the qualitative spectral phase retrieval presented here has provided insight to the mechanism of spectral broadening and compressibility of filament output, a truly quantitative retrieval remains challenging for high bandwidths with intricate phase structure. This will be approached by employing slicing techniques as well as incorporating genetic algorithms in the iterative optimization of a quantitative spectral phase assignment. Further work will also focus on a better understanding of spectral broadening via filamentation through spectral phase analysis under varying filament conditions. The presented achievements and outlook given here aspire to establish few cycle laser pulses as a readily achievable standard for implementation in a wide spectrum of spectroscopic applications.

Acknowledgments

The financial support provided by the Deutsche Forschungsgemeinschaft within the Sonderforschungsbereich 450 “Analysis and Control of Ultrafast Photoinduced Reactions” and the Sonderforschungsbereich 546 “Structure, Dynamics and Reactivity of Aggregates of Transition Metal Oxides” as well as the Leibniz Graduate School for Molecular Biophysics is gratefully acknowledged by the authors. The authors greatly appreciate the support form Dr. Daniel J. Kane for generously providing the algorithm used for the spectral phase retrieval. fruitful discussion with Dr. Kamil Stelmaszczyk, Philipp Rohwetter and Dr. Estelle Salmon are gratefully acknowledged.

Footnotes

1The Laser system consists of cw (Verdi V5, Coherent) pumped oscillator (Femtosource, Femtolasers; 80 MHz, 6 nJ/pulse) which is coupled into multi-pass amplifier system (Odin C, Quantronix; 1 kHz, 0.6-1.5 mJ/pulse, 40 fs (FWHM) centered at 807 nm, Δλ=35 nm (FWHM).

References and links

1.

P. St. J. Russell, “Photonic-Crystal Fibers,” J. of Lightwave Technology 24, 4729–4749 (2006). [CrossRef]

2.

M. Nisoli, S. De Silvestri, and O. Svelto “Generation of high energy 10fs pulses by a new pulse compression technique,” Appl. Phys. Lett. 68, 2793–2795 (1996). [CrossRef]

3.

P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, “Supercontinuum generation in gases,” Phys. Rev. Lett. 57, 2268 (1986). [CrossRef] [PubMed]

4.

A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, “Self-channeling of high-peak-power femtosecond laser pulses in air,” Opt. Lett. 20, 73–75 (1995). [CrossRef] [PubMed]

5.

R. R. Alfano and S. L. Shapiro, “Observation of Self-Phase Modulation and Small-Scale Filaments in Crystals and Glasses,” Phys. Rev. Lett. 24, 592–594 (1970). [CrossRef]

6.

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582–3585 (2000). [CrossRef] [PubMed]

7.

M. Trippenbach and Y. B. Band “Dynamics of short pulse splitting in dispersive nonlinear media,” Phys. Rev. A 56, 4242–4253 (1997).

8.

G. Yang and Y. R. Shen, “Spectral broadening of ultrashort pulses in a nonlinear medium,” Opt. Lett. 9, 510–512 (1984). [CrossRef] [PubMed]

9.

A. M. Burzo, A. V. Chugreev, and A. V. Sokolov, “Stimulated rotational Raman generation controlled by strongly driven vibrational coherence in molecular deuterium,” Phys. Rev. A 75, 022515/1-022515/10 (2007).

10.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Reports 441, 47–189 (2007). [CrossRef]

11.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly-ionized, optically-transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007). [CrossRef]

12.

A. M. Zheltikov “ Let there be white light: supercontinuum generation by ultrashort laser pulses,” Physics-Uspekhi 49, 605–628 (2006). [CrossRef]

13.

A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov “Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber,” Opt. Commun. 208, 453–456 (2007). [CrossRef]

14.

L. Di Labio, W. Luthy, V. Romano, F. Sandoz, and T. Feurer “Superbroadband fluorescence fiber fabricated with granulated oxides,” Opt. Lett. 33, 1050–1052 (2008). [CrossRef] [PubMed]

15.

G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, “Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament,” Opt. Lett. 31, 274–276 (2006). [CrossRef] [PubMed]

16.

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woeste, “White-Light Filaments for Atmospheric Analysis,” Science 301, 61–64 (2003). [CrossRef] [PubMed]

17.

J. N. Sweetser, D. N. Fittinghoff, and R. Trebino, “Transient-grating frequency-resolved optical gating,” Opt. Lett. 22, 519–521 (1997). [CrossRef] [PubMed]

18.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbgel, and B. A. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997). [CrossRef]

19.

D. Lee, P. Gabolde, and R. Trebino, “Toward single-shot measurement of a broadband ultrafast continuum,”J. Opt. Soc. Am. A 25, 34–40 (2008).

20.

I. A. Walmsley and V. Wong, “Characterization of the electric field of ultrashort optical pulses,” J. Opt. Soc. Am. B 13, 2453–2463 (1996).

21.

R. Morita, M. Hirasawa, N. Karasawa, S. Kusaka, N. Nakagawa, K. Yamane, L. Li, A. Suguro, and M. Yamashita, “Sub-5 fs optical pulse characterization,” Meas. Sci. Technol. 13, 1710–1720 (2002). [CrossRef]

22.

L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, “Techniques for the characterization of sub-10-fs optical pulses: a comparison,” Appl. Phys. B 70, 67–75 (2008).

23.

I. Z. Kozma, P. Baum, U. Schmidhammer, S. Lochbrunner, and E. Riedle, “Compact autocorrelator for the online measurement of tunable 10 femtosecond pulses,” Rev. Sci. Instrum. 75, 2323–2327 (2005). [CrossRef]

24.

M. Li, J. P. Nibarger, C. Guo, and G. N. Gibson, “Dispersion-free transient-grating frequency-resolved optical gating,” Appl. Opt. 38, 5250–5253 (1999). [CrossRef]

25.

R. Trebino, “Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses” (Kluwer Academic Publishers, 2000).

26.

D. J. Kane, “Principal components generalized projections: a review,” J. Opt. Soc. Am. B 25, A120–A132 (2008).

27.

J. H. Marburger, “Self-focusing: Theory,” Prog. Quantum Electron. 4, 35–110 (1975). [CrossRef]

28.

E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, “Conical emission from self-guided femtosecond pulses in air,” Opt. Lett. 21, 62–64 (1996). [CrossRef] [PubMed]

29.

N. Akzbek, M. Scalora, C. M. Bowden, and S. L. Chin, “White light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353 (2001). [CrossRef]

30.

T. Lehner and N. Auby, “Stabilization of the Kerr effect by self induced ionization: Formation of optical light spatially localized structures,” Phys. Rev. E 61, 1996–2005 (2000).

31.

A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, “Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation,” Phys. Rev. Lett. 82, 1430–1433 (1999). [CrossRef]

32.

L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, “Spectral reshaping and pulse compression via sequential filamentation in gases,” Opt. Express 16, 390–401 (2008). [CrossRef] [PubMed]

33.

C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, “Generation of intense few-cycle laser pulses through filamentation parameter dependence,” Opt. Express 13, 7541–7547 (2005). [CrossRef] [PubMed]

34.

A. Galler and T. Feurer, “Pulse shaper assisted short laser pulse characterization,” Appl. Phys. B: 90, 427–430 (2008).

OCIS Codes
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(320.5520) Ultrafast optics : Pulse compression
(320.7100) Ultrafast optics : Ultrafast measurements
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Optics

History
Original Manuscript: June 30, 2008
Revised Manuscript: August 18, 2008
Manuscript Accepted: September 1, 2008
Published: November 3, 2008

Citation
Bruno E. Schmidt, Waldemar Unrau, Aldo Mirabal, Shaohui Li, Marcel Krenz, Ludger Wöste, and Torsten Siebert, "Poor man’s source for sub 7 fs: a simple route to ultrashort laser pulses and their full characterization," Opt. Express 16, 18910-18921 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-23-18910


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References

  1. P. St. J. Russell, "Photonic-Crystal Fibers," J Lightwave Technol. 24, 4729-4749 (2006). [CrossRef]
  2. M. Nisoli, S. De Silvestri, and O. Svelto "Generation of high energy 10fs pulses by a new pulse compression technique," Appl. Phys. Lett. 68, 2793-2795 (1996). [CrossRef]
  3. P. B. Corkum, C. Rolland, and T. Srinivasan-Rao, "Supercontinuum generation in gases," Phys. Rev. Lett. 57, 2268 (1986). [CrossRef] [PubMed]
  4. A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, "Self-channeling of high-peak-power femtosecond laser pulses in air," Opt. Lett. 20, 73-75 (1995). [CrossRef] [PubMed]
  5. R. R. Alfano and S. L. Shapiro, "Observation of Self-Phase Modulation and Small-Scale Filaments in Crystals and Glasses," Phys. Rev. Lett. 24, 592-594 (1970). [CrossRef]
  6. A. L. Gaeta, "Catastrophic collapse of ultrashort pulses," Phys. Rev. Lett. 84, 3582-3585 (2000). [CrossRef] [PubMed]
  7. M. Trippenbach and Y. B. Band "Dynamics of short pulse splitting in dispersive nonlinear media," Phys. Rev. A 56, 4242-4253 (1997).
  8. G. Yang and Y. R. Shen, "Spectral broadening of ultrashort pulses in a nonlinear medium," Opt. Lett. 9, 510-512 (1984). [CrossRef] [PubMed]
  9. A. M. Burzo, A. V. Chugreev, and A. V. Sokolov, "Stimulated rotational Raman generation controlled by strongly driven vibrational coherence in molecular deuterium," Phys. Rev. A 75, 022515/1-022515/10 (2007).
  10. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Reports 441, 47-189 (2007). [CrossRef]
  11. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, "Ultrashort filaments of light in weakly-ionized, optically-transparent media," Rep. Prog. Phys. 70, 1633-1713 (2007). [CrossRef]
  12. A. M. Zheltikov " Let there be white light: supercontinuum generation by ultrashort laser pulses," Physics-Uspekhi 49, 605-628 (2006). [CrossRef]
  13. A. V. Mitrofanov, A. A. Ivanov, M. V. Alfimov, A. A. Podshivalov, and A. M. Zheltikov "Microjoule supercontinuum generation by stretched megawatt femtosecond laser pulses in a large-mode-area photonic-crystal fiber," Opt. Commun. 208, 453-456 (2007). [CrossRef]
  14. L. Di Labio, W. Luthy, V. Romano, and F. SandozT. Feurer "Superbroadband fluorescence fiber fabricated with granulated oxides," Opt. Lett. 33, 1050-1052 (2008). [CrossRef] [PubMed]
  15. G. Stibenz, N. Zhavoronkov, and G. Steinmeyer, "Self-compression of millijoule pulses to 7.8 fs duration in a white-light filament," Opt. Lett. 31, 274-276 (2006). [CrossRef] [PubMed]
  16. J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Woeste, "White-Light Filaments for Atmospheric Analysis," Science 301, 61-64 (2003). [CrossRef] [PubMed]
  17. J. N. Sweetser, D. N. Fittinghoff, and R. Trebino, "Transient-grating frequency-resolved optical gating," Opt. Lett. 22, 519-521 (1997). [CrossRef] [PubMed]
  18. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbgel, and B. A. Richman, "Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating," Rev. Sci. Instrum. 68, 3277-3295 (1997). [CrossRef]
  19. D. Lee, P. Gabolde, and R. Trebino, "Toward single-shot measurement of a broadband ultrafast continuum,"J. Opt. Soc. Am. A 25, 34-40 (2008).
  20. I. A. Walmsley and V. Wong, "Characterization of the electric field of ultrashort optical pulses," J. Opt. Soc. Am. B 13, 2453-2463 (1996).
  21. R. Morita and M. Hirasawa and N. Karasawa and S. Kusaka and N. Nakagawa and K. Yamane and L. Li and A. Suguro and M. Yamashita, "Sub-5 fs optical pulse characterization," Meas. Sci. Technol. 13, 1710-1720 (2002). [CrossRef]
  22. L. Gallmann, D. H. Sutter, N. Matuschek, G. Steinmeyer, and U. Keller, "Techniques for the characterization of sub-10-fs optical pulses: a comparison," Appl. Phys. B 70, 67-75 (2008).
  23. I. Z. Kozma, P. Baum, U. Schmidhammer, S. Lochbrunner, and E. Riedle, "Compact autocorrelator for the online measurement of tunable 10 femtosecond pulses," Rev. Sci. Instrum. 75, 2323-2327 (2005). [CrossRef]
  24. M. Li, J. P. Nibarger, C. Guo, and G. N. Gibson, "Dispersion-free transient-grating frequency-resolved optical gating," Appl. Opt. 38, 5250-5253 (1999). [CrossRef]
  25. R. Trebino, Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, 2000).
  26. D. J. Kane, "Principal components generalized projections: a review," J. Opt. Soc. Am. B 25, A120-A132 (2008).
  27. J. H. Marburger, "Self-focusing: Theory," Prog. Quantum Electron. 4, 35-110 (1975). [CrossRef]
  28. E. T. J. Nibbering, P. F. Curley, G. Grillon, B. S. Prade, M. A. Franco, F. Salin, and A. Mysyrowicz, "Conical emission from self-guided femtosecond pulses in air," Opt. Lett. 21, 62-64 (1996). [CrossRef] [PubMed]
  29. N. Akzbek, M. Scalora, C. M. Bowden, and S. L. Chin, "White light continuum generation and filamentation during the propagation of ultra-short laser pulses in air," Opt. Commun. 191, 353 (2001). [CrossRef]
  30. T. Lehner and N. Auby, "Stabilization of the Kerr effect by self induced ionization: Formation of optical light spatially localized structures," Phys. Rev. E 61, 1996-2005 (2000).
  31. A. A. Zozulya, S. A. Diddams, A. G. Van Engen, and T. S. Clement, "Propagation dynamics of intense femtosecond pulses: multiple splittings, coalescence, and continuum generation," Phys. Rev. Lett. 82, 1430-1433 (1999). [CrossRef]
  32. L. T. Vuong, R. B. Lopez-Martens, C. P. Hauri, and A. L. Gaeta, "Spectral reshaping and pulse compression via sequential filamentation in gases," Opt. Express 16, 390-401 (2008). [CrossRef] [PubMed]
  33. C. P. Hauri, A. Guandalini, P. Eckle, W. Kornelis, J. Biegert, and U. Keller, "Generation of intense few-cycle laser pulses through filamentation parameter dependence," Opt. Express 13, 7541-7547 (2005). [CrossRef] [PubMed]
  34. A. Galler and T. Feurer, "Pulse shaper assisted short laser pulse characterization," Appl. Phys. B:  90, 427-430 (2008).

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