1. Introduction

It is known that a high-peak-power ultrashort laser pulse propagating through transparent bulk media is usually accompanied by many interesting phenomena, such as strong modifications in the temporal, spatial and spectral properties of the laser pulse [1–3]. The primary process responsible for these changes is self-focusing which causes the laser beam to be compressed in space, resulting in a corresponding catastrophic collapse [4]. This behavior is then balanced by the defocusing effect from the creation of a plasma, leading to the formation of a so-called filament [5,6]. Because of this complexity, several scenarios have been elaborated to explain the nature of the filamentation process, such as the self-channeling model, the moving focus picture, and the spatial replenishment model [7–9]. Recently, the filament process has been observed in both near IR and UV wavelength regions [10–12]. In dielectric solids this filament process has been adopted as an attractive way to develop waveguides, three-dimensional optical storage, and for microfabrication [13,14].

On the other hand, extensive studies have shown that the interaction of intense ultrashort light pulses with matter can result in the generation of optical radiation over an extremely broad spectral range, which is termed supercontinuum or white-light generation [15,16]. This phenomenon has been observed in a great variety of transparent materials including gases, liquids and solids since the first discovery by Alfano in 1970 [17]. Although self-phase modulation (SPM) is considered to be the dominant and triggering mechanism that leads to spectral broadening, it cannot explain the complicated spectral characteristics completely. Ionization-induced SPM, four-wave mixing and self-steepening are believed to play roles as well [2,15,18].

The connection between white-light generation and self-focusing was firstly pointed out by Corkum, et al [19]. In this case a white-light continuum is emitted from a single filament. When more intense laser pulses are focused, a group of various filaments are usually observed because of beam splittings. Recently, multiple foci processes have been investigated when a single femtosecond laser pulse was focused into different media [6,20–24]. Although some spatial information associated with self-focusing can be obtained from these experiments, the complex physics of pulse temporal and spectral evolution during filamentation inside nonlinear dispersive materials are still not well understood. As demonstrated by some studies, for pulses in the femtosecond regime, group-velocity dispersion (GVD) of the material is expected to dramatically alter the dynamics of the self-focusing process [2,22,25,26]. Using the nonlinear Schrodinger equation in the positive GVD regime, it is found that above a certain threshold power the laser pulse undergoes temporal splitting which can arrest catastrophic self-focusing. However, A. Zozulya pointed out that the physical processes responsible for the initial splitting of the input pulse did not necessarily result in multiple splitting [27]. Therefore, the dynamics of filamentation and white-light generation in nonlinear dispersive media have become an active topic of the research.

Based on new experimental results, in this paper we offer spatiotemporal and spectral dynamics of filament generation in bulk media with normal GVD. When femtosecond laser pulses are focused into a ZK7 glass, the production of up to 5 multiple refocusing filaments is visualized through microscopic imaging of the spatial plasma luminescence and characterization of far-field emission patterns. At higher laser powers spatially distinct refocusing filaments are observed to fuse together into a single relatively long plasma channel. Measured white-light spectra with the creation of multiple refocusing filaments suggest that ultrashort laser pulses undergo the single splitting, then multiple splittings and finally coalesce in the temporal domain. Furthermore, our observation of stable interference structures on the far-field emission patterns demonstrate that multiple transverse filaments generated from a single laser beam are mutually spatial coherent.

2. Experiment

The schematic experimental configuration is depicted in Fig. 1. The laser pulses are generated by a commercial Ti:sapphire laser system, which was composed of a femtosecond oscillator (Spectra Physics, Tusnami 3960) and a compound chirped pulse amplifier (Spectra Physics, HP-Spitfire) operated at a 1 kHz repetition rate. The entire laser system is able to provide 2 mJ pulses centered around 800 nm. The pulse width of 50 fs was continuously monitored using a single shot autocorrelator (Positive Light, SSA). The output beam from the laser amplifier is linearly polarized in parallel direction and the pulse-to-pulse energy stability is normally less than 3% in the amplitude.

A thin circular adjustable diaphragm was placed into the light path to cut down the beam size properly. The transmission through this aperture was measured about 83%. After propagating through free space, the pulses were reduced in power or energy by passing through a neutral density (ND) wheel, whose attenuation could be changed continuously through its rotation. Then these pulses were focused into a block of ZK7 glass by a concave reflective gold-mirror with a radius of 1 m. The size of the glass block is 2.5 cm × 1.5 cm × 0.7 cm and its surfaces are polished. The distance between the diaphragm and the glass sample is about 1.2 m. The beam diameter on the focal position was estimated to be 190 μm. By using a CCD camera, we measured the transverse beam profile at the focal point as shown by the inset picture in Fig.1. Because of Fresnel diffraction from the diaphragm [28], interference pattern was seen clearly on the transverse beam profile.

In order to ensure each data measurement on a fresh area of the glass, the sample was mounted on translation stages, being capable of moving in three-dimensional space. Each time the laser spot on the glass surface was moved 500 μm away from the pervious location. The resolution and total translation available in each dimension are 10 μm and 25 mm, respectively. The position and the number of generated filaments were controlled based on the location of the focal point, the spatial distribution of input pulses and the incident laser energy.

The spatial distribution of white-light filaments generated inside the glass was imaged from the plasma luminescence by a commercial microscope, which was suspended over the glass surface in the direction perpendicular to the beam propagation. The magnified images from the microscope were then detected using a charge-coupled device (CCD) image sensor and processed on a computer. The transmission spectrum of white-light filaments out of the glass sample was collimated through a 10× objective lens into a fiber- pigtailed spectrometer (Ocean-Optics, SD2000) with a spectral resolution of 5 nm. Before the collection lens, a high reflection dielectric mirror for 800 nm was inserted as a spectral filter to block the transmitted fundamental beam. To void further complications in the spectral measurement, an iris was placed close to the back surface of the sample to eliminate the outer conical emissions from white-light filaments. However, when the far-field distribution of white-light filaments is observed, the iris after the sample was removed. Thus white-light emissions could be projected directly onto a screen and then they were recorded by a digital camera.

 

Fig. 1. Schematic of the experimental setup for measuring the evolution of white-light filaments in ZK7 glass. 1: Microscope; 2: Iris; 3: 800nm filter; 4: 10 × objective lens; 5: optical fiber detector; Inset image: the transverse beam profile at the focal position.

Download Full Size | PDF

3. Results and discussion

The experiment was first performed as follows to investigate the production of refocusing filaments during the nonlinear propagation of femtosecond laser pulses through the ZK7 glass sample. When the power of femtosecond laser pulses was set low enough, white-light filaments can not be found inside the glass if there is no any light blocking from the input diaphragm. However, when the input diaphragm was reduced properly to the diameter of 6 mm, a diffraction pattern with the axial maximum intensity was observed in the transverse beam profile at the focal position. As a result, a single short white-light filament appeared inside the glass. As shown by the photograph in Fig. 2(a), the length of this filament is about 800 ¼m. At this moment, the power of femtosecond laser pulses transmitted through the incident diaphragm was measured to be 4 mW. Correspondingly, a typical snapshot of the far-field emission pattern from this single short filament is shown in the picture of Fig. 3(a). As can be seen clearly, the whole pattern consists of two separated parts: one is a central spot with colorful light distributions, while the other is an annular conical ring of red light. The colorful portions around the central spot are likely due to Rayleigh scattering in the ZK7 glass.

In our experiment, since the filtering effect of the high reflectivity mirror after the glass, the spectral intensity distribution from white-light filaments can be obtained by calibration of the measured spectrum to the transmission of the filter. The blue curve in Fig. 4(a) illustrates the output spectrum from a single short filament inside the ZK7 glass at a laser power of 4 mW, and the black curve in this figure is the incident light spectrum. As can be seen, the white-light spectrum is broadened almost symmetrically towards the shorter and longer wavelength regions, but with a slight appearance of a blue tail (note that the observations on the red side of wavelength are limited by the spectrometer). In addition, a pair of Stokes and anti-Stokes components (at 12300 and 12600 cm^-1) can also be seen near the central part of the white-light spectrum. According to the theoretical analyses, this kind of broadening of the on-axis spectrum measured in our experiment would suggest that ultrashort laser pulses undergo a slight temporal splitting in the case of the incident laser power just above the threshold of filamentation [25]. It should be noted that when the laser intensity is so low that nonlinear effects during the laser propagation through the sample can be ignored, the beam size on the screen was measure about only 1.5 mm in the diameter.

With gradual increase of laser power, the single short filament brightens and its far-field emission pattern seems to be enhanced as well. However, the length of this single filament was observed to remain almost constant. When the input laser power increased up to 5 mW, we observed the formation of a second short filament closer to the input face, which is in accord with numerical simulations of a simple self-focusing model [8]. As reproduced by Fig. 2(b), the lengths of the two distinct longitudinal filaments are in fact identical and they are the same as that at the lower laser power. This observation suggests that the higher laser power would make the beam undergo refocusing events instead of a simple extending of the original filament length. Fig. 3(b) presents the far-field emission pattern from these two refocusing filaments, in which both the central white-light spot and the conical emission become more evident. Moreover, it is clear that the conical emission consists of more annular rings and begins to be colorful. Fig. 4(b) displays the transmission white-light spectrum under the circumstance of the two refocusing filaments. It is very interesting that in this case the white-light continuum is characterized by a dramatic spectral broadening towards the shorter wavelengths with clear evidence of oscillatory structure, or it can be described by a long blue-shifted pedestal with a sharp cut-off frequency. A presence of an inverse Raman dip at ~ 700 nm is also found in Fig. 4(b).

Since the ZK7 glass in our experiment serves as the nonlinear dispersive medium, the characteristic frequency modulation in the measured white-light spectrum can be understood as the result of temporal splitting of the single pulse. With the help of recent studies, above a certain threshold power the presence of a small amount of positive GVD causes the splitting of the original input pulse into two temporally separated pulses away from the pulse center [25,26]. The two generated similar continua sources are separated in time, then they interfere with each other to form the spectral modulation, and the period of this modulation is inversely related to the temporal separation of the pulses. In Fig. 4(b), the measured spectral interfringe space of about 10 nm implies that the two split ultrashort pulses are separated by 75 fs in the temporal domain. Because the split pulses are shorter in time, the inclusion of high-order dispersion terms becomes necessary and may also signal a breakdown of the slowly varying envelope approximation [26]. In this regime optical shock formation is also undoubtedly significant and gives rise to asymmetry in the generated spectra [29].

As the incident laser power stepped up to 6 mW, an additional refocusing short filament could be found inside the glass. The spatial intensity distribution of the plasma luminescence and the corresponding far-field emission pattern are illustrated in Fig. 2(c) and Fig. 3(c), respectively. As shown, the length of these three longitudinal filaments is still identical to the original one at the lower laser power, but the spatial interval between filaments reduces greatly. For its far-field emission pattern, it is found that the number of the annular ring continues to increase and green light begins to appear in the outside layer of the conical emission. Fig. 4(c) demonstrates the measured transmission supercontinuum, which is seen to have a slightly continuous broadening towards the blue light region. The evidence of the reduced oscillatory structure with wider spectral space suggests that the two newly split pulses may in turn undergo a secondary temporal splitting. Actually, when the filament is propagate-ing further inside the glass at higher laser power, the amplitude balance of split pulses begin to diminish due to the intensity competition and material dispersions. Therefore, the contrast of spectral interference becomes reduced, just like what we observed in the experiment.

The production of multiple refocusing filaments can be visualized with progressively increased laser powers, which are demonstrated by the photographs in Figs. 2(d)–2(f). It is clear that when the laser power is higher, more refocusing filaments are created and the spacing between refocusing filaments becomes shorter. In our experiment, the maximum number of distinct refocusing filaments inside the glass sample has been observed up to 5 at an input laser power of 8 mW. In particular, when the laser power is as high as 9 mW, separated longitudinal filaments are no longer observed, even when they are magnified by 50 times. Instead, we found a spatial fusion of multiple refocusing filaments takes place. Consequently, a single relatively long plasma channel is formed at this moment, as shown by the photograph in Fig. 2(f). Different from other previous studies [6,20–24], this phenomenon provides a new aspect for the long filament generation and control in the condensed media. It should be noted that this single long plasma channel can keep clean and grow up to about 1cm long when the input laser power increases continuously up to100 mW. In the experiment, further increase of incident laser power was found to result in some split filaments in the transverse plane. The evolution of far-field emission pattern from multiple refocusing filaments is shown by Figs. 3(d)–3(f). Here we can find that the central white-light spot becomes bigger and more intense with increasing laser power, and the blue light due to Rayleigh scattering is clearly visible to the eye. In addition, the conical emission displays more colorful rings (red-green-blue) especially at the laser power of 8 mW.

 

Fig. 2. Micro-visualized multiple refocusing filaments inside ZK7 glass at progressively higher femtosecond laser powers. The above photographs (from left to right) show 1, 2, 3, 4, 5 refocusing filaments and a single relatively long plasma channel due to the spatial fusion, successively. The corresponding input power is 4, 5, 6, 7, 8 and 9 mW, respectively.

Download Full Size | PDF

 

Fig. 3. Recorded far-field emission patterns from multiple refocusing filaments inside ZK7 glass at different laser powers. The above pictures from (a) to (f) represent the situation of 1, 2, 3, 4, 5 refocusing filaments and a single long fused plasma channel, respectively.

Download Full Size | PDF

 

Fig. 4. Measured evolution of output spectra with variation of refocusing filaments formed inside ZK7 glass. The above curves from (a) to (f) represent the situations from 1, 2, 3, 4, 5 refocusing filaments and a single long fused plasma channel, respectively. The black curve in (a) is the spectrum of the incident femtosecond laser pulses.

Download Full Size | PDF

Figures 4(d)–4(f) demonstrate the evolution of white-light spectrum from the quantitative increment of refocusing filaments. It is shown that the spectral periodic modulations become progressively weaker and the interference fringe spacing widens. This would suggest that the temporal interval between the split pulses gets shortened and the imbalance between their intensity amplitudes becomes significant. Therefore, the process of multiple temporal splittings of the pulse can be deduced to occur. However, at a laser power of 9 mW there is no spectral periodic modulation to be observed, as shown in Fig. 4(f). According to the theoretical analysis, for multiple temporal split pulses, with increasing power the central peak would grow and finally merged with the leading and trailing peaks [21]. Therefore, the observed behavior with a disappearance of spectral interference fringes could represent a coalesce of split pulses into a single broad one in the temporal domain. It should be noted that in our experiment the input laser power for the temporal pulse coalesce coincides with that for the spatial filament fusion. Furthermore, when we continued to increase the incident laser power, similar transmission spectra without visible periodic modulations from filaments were detected, and they were also seen to be cut off at the particular wavelength.

Next we investigated the spatial coherence properties of white-light filaments that are generated in a transversal plane perpendicular to the beam propagation. In the experiment, when the incident laser power is reduced much below the breakdown threshold of glass sample through reducing the diameter of the diaphragm, a pair of parallel filaments was observed to form inside the glass. Fig. 5(a) demonstrates the microscopic image of transverse positions for two generated filaments. From this figure, it is found that the two transverse filaments have an identical length of 1mm and their spatial separation is about 100 μm. When their transmission beams are projected directly onto the white screen, a typical set of double-slit interference fringes is observed to show on the far-field emission pattern. As shown clearly by Fig. 5(c), the optical fringe pattern appears not only on the central white-light spot and the related light scattering portion but also on the conical red ring. These phenomena suggest the spatial coherence among these multiple filaments is much higher in the comparison with some previous reports [30,31]. In addition, as the input laser power was increased greatly many more white-light filaments were created in both longitudinal and transverse directions, as shown in Fig. 5(b). Under this condition, much more complex interference patterns appear on their far-field emission, which is shown by Fig. 5(d). The optical interference patterns in the far-field strongly suggest that these multiple transverse filaments that were produced from a single laser beam are mutually spatial coherent.

 

Fig. 5. Observed spatial coherence among filaments generated inside ZK7 glass. (a) and (b) are imaged transversal positions of two or multiple filaments, respectively; (c) and (d) are the corresponding far-field emission patterns with typical interference fringes resulting from two and multiple transverse filaments, respectively.

Download Full Size | PDF

4. Conclusion

The experimental observations in this paper illustrated a new scenario of complex dynamics involved in white-light filamentation by focusing femtosecond laser pulses into ZK7 glass. With increasing laser power, up to 5 refocusing filaments have been visualized through microscopic imaging of their spatial distributions. At higher laser power, the more refocusing filaments are produced, but each short distinct filament length remains almost constant. However, further increase of the laser power makes multiple refocusing filaments undergo the spatial fusion, leading to a single long clean plasma channel inside the glass. On the other hand, the evolution of far-field emission patterns from the production of multiple refocusing filaments has been also investigated in detail. The measured white-light spectra from multiple refocusing filaments suggest that ultrashort laser pulses propagating through the dispersive media suffer subsequent temporal changes of single splitting, multiple splittings and coalescence. Finally, the observed stable interference far-field patterns confirmed that a high degree of spatial coherence is preserved between transverse multiple filaments. All of these above understandings would make it possible to tailor the characteristics of generated light for a particular application.