1. Introduction

Propagation of intense ultra-short laser pulses through transparent media is usually accompanied by a spectrally broad radiation so called white light super-continuum (SC) which extends from the ultraviolet to the infrared range. This spectacular observation was first discovered by Alfano & Shapiro [1] upon focusing nano- and picosecond laser pulses inside condensed media. One of the first observations of spectral super-broadening from ~400 to ~800 nm in gases was performed by Corkum et al. [2], where 70 fs UV pulses and 2 ps dye laser pulses centered at 600 nm were focused in gases with different pressures. A few years later, Braun et al demonstrated the generation of a very long filament (or the order of 10 m) when propagating 100 fs Ti-Sapphire laser pulses in air without using a focusing lens [3]. Subsequently, the filamentation and white light generation resulting from the propagation of intense ultra-short laser pulses in various gases and condensed media were experimentally demonstrated and the underlying physical mechanisms were analyzed through various theoretical models [4–9].

The white light SC generation in transparent materials is known to be mainly resulting from ionization-enhanced self-phase modulation (SPM) with additional contributions from stimulated Raman scattering, temporal self-steepening, instantaneous electronic Kerr nonlinearity, and four-wave parametric processes [5,6,10–15]. The dependence of the spectral broadening of the white light on material band-gap and chromatic dispersion have been also reported [16,17]. In particular, Brodeur et al. have shown that that there is a band-gap threshold above which the spectral width of the continuum tends to increase monotonically and below which there is no continuum generation [16]. The filamentation process, resulting from a dynamic balance between Kerr self-focusing and plasma defocusing effects, is initiated when the peak power of pulse exceeds the critical power for self-focusing in the medium [18]. For peak powers sufficiently higher than the critical power, the beam cross section appears as a collection of randomly distributed spots resulting from small-scale multiple self-focusing of the pulse. Such spots are identified as small-scale filaments acting as sources of the white light. It was demonstrated that each spectral component of the white light can act as a coherent source and thus such white light SC essentially results from the spatial and spectral transformation of the initial pulse during nonlinear propagation inside the medium [5,19].

In this work, we demonstrate remarkably broadband white light SC generation with a high efficiency upon focusing femtosecond pulses from an optical parametric amplifier at 1.5 μm inside silica glass. Stable interference fringes resulting from the superposition of two spatially coherent fields emanating from a pair of filaments were observed for individual spectral components. We show that for the case of focusing very near the input glass surface in air, the interference fringes were observed by excitation at both 800 nm and 1.5 μm, whereas no such fringes were observed with 800 nm irradiation when focusing inside the glass. We attribute this feature to significantly reduced destructive influence of femtosecond breakdown and structural damage on filamentation of pulses at 1.5 μm. Such remarkable resistance of the glass against breakdown and physical damage at 1.5 μm allowed us to realize efficient small-size core optical waveguides in silica based on pure filamentation process within a broader range of writing parameters as compared to the 800 nm case.

2. Experiment

We used a Ti-sapphire chirp pulse amplification laser system (Spectra-Physics) to generate 45 fs transform-limited pulses with 1 kHz repetition rate centered at 800 nm. The system consists of an oscillator (Tsunami) and stretcher followed by a regenerative amplifier and a compressor. The output beam has a diameter of ~5 mm (at 1/e² intensity) and a maximum energy of 2 mJ which can be adjusted by inserting a half-wave plate before the compressor. The pulse width is measured by a single shot autocorrelator. An optical parametric amplifier (OPA) from Spectra-Physics pumped by the 800 nm pulses was used to generate femtosecond signal pulses tuned around 1.5 μm with 1 kHz repetition rate. We obtained a maximum output energy of ~105 μJ by introducing a small negative chirp to the pump beam. The pulse width of the OPA output beam nearly follows that of the chirped pump pulse which was measured to be about 70 fs. The output beam diameter was nearly 5 mm. The sample was a bulk of pure fused silica glass (15 mm × 5 mm × 40 mm) with well polished surfaces. The length of sample along the beam propagation direction was 15 mm. The femtosecond pulses at either 800 nm or 1.5 μm were focused using an achromatic microscope objective (1x, NA: 0.05, f = 73.5 mm, Melles-Griot) very near the input surface in air as well as inside the glass. The input energy was adjusted by inserting neutral density filters before the focusing lens. A white screen was inserted in the far field to observe diverging colorful patterns associated with the white light SC propagating along the beam axis. A digital camera was used to capture these patterns. A microscope objective (10x, f = 16.9 mm) was placed near the output surface of the sample to provide a magnified image of the filaments formed in the focal region. A CCD camera (Hitachi KP-160) equipped with a frame grabber card was employed to capture and digitize the images for data analysis. To avoid saturation of the CCD camera represented by red color pixels, a number of neutral density filters were put before the camera. In order to observe the white light patterns for each spectral component, we used 10 nm wide interference filters at various central wavelengths before the camera. The images of white light patterns induced by single or multi-shot irradiation were recorded using the camera externally triggered by a mechanical shutter inserted before the focusing lens. To analyze the SC spectrum, the white light diverging from the sample was coupled into an optical spectrum analyzer (ANDO-AQ6315A, 350 nm-1750 nm) through a 1 m multi-mode fiber.

3. Results and discussion

Typical far-field pictures of the SC corresponding to approximately 5000 shots generated by focusing 1.5 μm and 800 nm pulses at 1.3 μJ in silica glass are shown in Figs. 1(a) and 1(b), respectively. They both exhibit a pattern consisting of a single colored disk, however their different colors suggests that the spectral contents of the white lights generated at these wavelengths are not the same. For higher input powers as high as a few times the critical power, the patterns evolved to a more complicated form of the colorful distinct ring(s) surrounding the central disk. This is a typical signature of the white light generated by ultrashort laser pulses in condensed media and in gases which is caused by the conical emission [20–22]. The measured critical power for self-focusing in silica glass was reported as ~4.4 MW at 800 nm [6]. Since the critical power scales as λ², at 1.5 μm it is evaluated as ~15.4 MW. This corresponds to an input pulse energy of ~1.1 μJ for our 70 fs pulses as compared to ~0.2 μJ for the 45 fs pulses used in our earlier experiments with 800 nm pulses [23].

 

Fig. 1. Digital photograph of the white light SC induced by focusing (a) 1.5 μm and (b) 800 nm pulses at 1.3 μJ using the 1x objective lens.

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Consistently, we noted that no visible white light was generated at 1.5 μm for input energies lower than approximately 1 μJ. A typical white light spectrum induced by focusing 1.5 μm pulses at 11 μJ inside the silica glass is shown in Fig. 2(a), as compared to the input pulse spectrum (without sample) shown in Fig. 2(b). Note that the small peaks near 800 nm and 520 nm in Fig. 2(b) are associated with the residual pump beam and an additional co-propagating beam created by third harmonic generation or by other nonlinear optical parametric processes, respectively. As seen, a remarkably broad SC ranging from 1750 nm (upper limit of the optical spectrum analyzer) down to 400 nm has been generated as compared to that obtained in the earlier experiments using 800 nm pulses [6,23]. Accordingly, it is interesting to outline the special features of the SC spectrum generated at 1.5 μm:

Clearly, the basic mechanism responsible for the SC generation at 800 nm, that is the free-electron enhanced SPM process [24] occurring in the intensity clamped filament zone, can generally explain the basic features of the spectra observed at 1.5 μm. This standard model or scenario can also account for the increased band-width of the SC spectrum based on its band-gap dependence previously reported [16]. In fact, according to a recent report by Nagura et al. it is actually the ratio of the band-gap energy to the photon energy that would determine the amount of broadening, independently of the pump wavelength and the medium’s band-gap [25]. Note that for a given material band-gap, a higher maximum or clamped intensity (I_MAX) is expected at a longer pump wavelength and this is causing, in turn, a larger nonlinear phase, ϕ_NL and thus a larger broadening. In addition, it is worth mentioning that we have observed considerably (i.e., 4–5 times) longer filaments at 1.5 μm (as compared to 800 nm) which is also likely to contribute to a larger nonlinear phase accumulation, since ϕ_NL is also

 

Fig. 2. (a) Measured white light SC spectrum induced by focusing 1.5 μm pulses in the silica, (b) spectrum of the input pulse beam (without sample).

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proportional to the nonlinear interaction length, i.e., filament length. The scenario mentioned above has been supported recently by a numerical simulation showing that, in addition to intensity clamping, chromatic dispersion is also playing a major role in establishing the extent of the SC spectra [17]. This is especially relevant to our case since the 1.5 μm pump that we used is lying in the anomalous dispersion regime, as opposed to the 800 nm case. For instance, it is likely that the balance between the anomalous dispersion and the SPM would contribute to the stability of the filament and to its observed longer length. A thorough numerical analysis would be required in order to assess to what extent dispersion is altering the SC generation. However, based on our observations, it is rather obvious that dispersive effects should be taken into account in trying to analyze the spectra.

By further increasing the input power, two and more filaments were formed near the beam propagation axis. A digital picture of the stable interference fringes resulting from the coherent superposition of white light fields emanating from a pair of filament upon focusing 1.5 μm pulses at 4 μJ under irradiation with ~5000 shots in silica is shown in Fig. 3(a). We never observed such a stable fringe pattern by focusing pulses in the glass at 800 nm neither at 4 μJ nor at any other pulse energy (Fig. 3(b)). We believe that optical breakdown and damage occurring around the geometrical focus at rather low pulse energies and co-existing with filamentation at 800 nm [23] significantly disturb the formation of filaments in the focal zone. As a result, the spatial distribution of the filaments, i.e. their mutual position in the longitudinal and transverse planes constantly varies. Consequently, the resultant white light pattern would be highly unstable thus preventing the formation of Young fringes in the far field. To further analyze the role of optical breakdown (and structural damage) in these results, we focused both beams in air very near the glass input surface. The CCD images of the fringes (500 nm center frequency) produced in single and multi-shot (5000 pulses) irradiation regimes using 1.5 μm and 800 nm pulses at 7 μJ are shown in Figs. 4 and 5 respectively.

 

Fig. 3. (a) Digital photograph of a typical white light interference fringe produced by focusing 4 μJ pulses at 1.5 μm inside the glass, (b) white light pattern created at 4 μJ with 800 nm pulses.

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It appears that in the case of focusing outside the sample (i.e. when no optical breakdown occurs in the glass), the white light fringes could be observed under excitation with 800 nm pulses as well. Furthermore, a comparison of the fringe images for the single and multi-shot irradiation regimes clearly suggests a good shot-to-shot stability and reproducibility of the spatial profiles of the laser beams (see the two-dimensional line scans).

The formation of such fringes evidently suggests that the white light emitted from a laser-induced filamentary source is essentially coherent and that this property is prevailing for each spectral component of the white light. In order to have a qualitative analysis and comparison of such interference fringes with those produced in the two-slit Young experiment, first we evaluated the filament size and separation by analyzing the observed fringes and afterwards compared the obtained data values with those measured directly [26]. By analogy with the classic Young’s experiment with hard rectangular slits, the filament separation can be estimated as: a ~dλ/Λ where d = 410 mm is the distance between the filaments and the white screen, λ = 500 nm denotes the filter’s wavelength, and Λ = 10 mm represents the fringe period. This approximation yields a filament separation of ~20.5 μm. The filament diameter could be readily estimated based on the Gaussian beam theory as: b = 4a/πm where m is the number of fringes counted on the screen for a specific wavelength. Thus, for m = 12 the filament diameter was evaluated to be ~2.2 μm.

 

Fig. 4. CCD images of the white light fringes (500 nm component) produced by a pair of filament for (a) single shot, (b) multi-shot irradiation (5000 pulses) of the silica with 7 μJ pulses at 1.5 μm, (c) two-dimensional line scans corresponding to the single and multi-shot irradiation images. The beam was focused in air very close to the input surface.

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Fig. 5. White light fringe images corresponding to those illustrated in Fig. 4 but now obtained with 800 nm pulses. The beam was focused in air very close to the input surface.

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On the other hand, we imaged the cross sections of the filaments formed near the end of the glass output surface onto the CCD camera in order to directly measure the filament diameter and separation. Fig. 6(a) shows an image of a pair of filament (500 nm component) generated by 7 μJ femtosecond pulses at 1.5 μm. From these images, the filaments diameters and separation were deduced to be ~2.5 μm and 21 μm, respectively.

 

Fig. 6. (a) Image of a pair of filament (500 nm component) formed by 7 μJ pulses at 1.5 μm, (b) image of a bunch of filaments produced at 34 μJ.

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We notice a quite good agreement between the estimated values and those measured directly. The slightly higher value of the filament size is suspected to be due to our failure to exactly place the CCD camera at focal plane of the imaging lens. As mentioned above, for higher pulse energies more filaments were formed and their interference pattern became too complicated so that no pronounced and clear fringes were observed in the far field. A typical image of a bunch of filaments created in the silica at 34 μJ is shown in Fig. 6(b). Note that due to intrinsic spatial offsets among the heads of the filaments along the beam propagation direction, the images of those slightly out of focus have appeared relatively larger and less intense.

We were able to realize efficient waveguides with small-size core and index change in excess of 6 × 10^-3 in silica glass using femtosecond pulses at 1.5 μm by moving the sample through the focal point along the beam propagation direction [27]. This result demonstrates the possibility of modifying the refractive index of silica (band-gap ~9 eV) at 1.5 μm through transferring of energy of the generated plasma to the glass structure. In the femtosecond regime, such plasma is created in the focal volume mainly through nonlinear ionization processes such as tunneling and/or multi-photon excitation of at least 11 photons from the valence to the conduction bands as opposed to 6 photons required for excitation with 800 nm pulses. A major advantage of the waveguides produced at 1.5 μm as compared to those already realized at 800 nm is the possibility of micro-machining at considerably higher pulse energies or lower translation speeds without creating structural damage accompanied by void like morphology inside the glass. That is, no void-like damage was observed for a pulse energy as high as 23 μJ, while by using the 800 nm pulses such damage occurred at a pulse energy higher than ~2 μJ. It is just mentioned here that by using scanning electron microscopy together with chemical etching techniques we have measured core (i.e. filament) sizes of approximately 2 μm which reasonably agree with the filament size deduced from analysis of the interference fringes. Details of the experiment and results on waveguide writing with 1.5 μm pulses will be published elsewhere.

4. Conclusions

Strong and coherent white light SC was generated with spectral broadening ranging from 400 nm to at least 1750 nm by focusing femtosecond pulses at 1.5 μm inside the silica glass. The coherence property for each spectral component of the white light emanating from a pair of filament was demonstrated by the formation of stable interference fringes at 1.5 μm. The size and separation of the filaments deduced from analysis of the observed fringe patterns were consistent with those directly measured through the CCD images. Unlike excitation with 800 nm pulses and owing to remarkably higher resistance of silica glass against laser-induced breakdown and structural damage at 1.5 μm, we fabricated small-size core waveguides within a broader micro-machining window based on pure filamentation process.