We demonstrate highly efficient white light generation by focusing 45 fs long pulses of 800 nm laser radiation with 1 mJ energy onto a 10 cm long barium fluoride crystal. The entire wavelength band from 400–1000 nm was generated with efficiency greater than 40%. We also observe multiphoton absorption induced fluorescence in the crystal. By employing line focusing geometry at low intensity, we show that white light fringes are formed with a single laser beam, indicative of the coherent property of the white light that is produced.
©2004 Optical Society of America
The propagation of an ultrashort pulse through a medium can lead to considerable broadening of its spectrum. This effect, known as supercontinuum (SC) or white-light generation, has been observed in various media . The continuum that is generated using femtosecond pulses is distinct from that obtained with longer (picosecond) pulses. In the former, the anti-Stokes frequency components temporally lag the Stokes components, and the continuum exhibits a smaller divergence; in both cases, the spectral width depends on the medium in which the SC is generated [1–4]. The femtosecond continuum beam appears as a white disk that is surrounded by a distinct, concentric, rainbow-like pattern (conical emission). The term “white-light continuum” is usually reserved for the low-divergence, central part of the beam and excludes the conical emission.
Self-phase modulation (SPM) [2,5], ionization-enhanced SPM [2–3], and four-wave mixing  are some of the mechanisms that have been invoked to explain the white-light continuum, and the extent of its spectral width. But it is fair to state that the physics is not properly understood. However, self-focusing is known to play an important role in generation of white light continuum [3,7–9]. Experiments have shown that the power threshold for continuum generation coincides with the calculated critical power for self-focusing, in line with the proposal made by Bloembergen  to explain the picosecond continuum. For the femtosecond continuum in condensed media, an important mechanism of free-electron generation is multiphoton excitation (MPE) [11–12]. Experiments conducted by Brodeur and Chin [13–14] have confirmed that continuum generation is triggered by self-focusing; furthermore, a strong dependence of continuum generation and self-focusing on the medium’s band gap has been observed. There appears to exist a band gap threshold of 4.7 eV below which the medium does not generate a continuum, and above which the spectral width of the continuum increases with band gap. The enhancement of SPM by free electrons generated by MPE has been proposed as the primary mechanism of continuum generation [13,14]. Self-focusing cannot proceed indefinitely. Hence, a mechanism that arrests its collapse is needed, and in condensed media multiphoton ionization (MPI) may be such a process . MPI first reduces the incident energy of the collapsing field and then produces a plasma that absorbs, defocuses, and spectrally blue-shifts the intense laser field. The combined effects of MPI and plasma defocusing limits further collapse of self-focusing and clamps the maximum intensity reached by the collapsing pulse. Thus, limiting of the maximum intensity is believed to be one of the dominant factors that determine the spectral extent of SC generation . Recently, chromatic dispersion  has also been shown to be a major contributor to limiting the spectral extent of SC generation apart (from band gap dependence) in both gases as well as condensed media.
The efficiency of white light generation appears not to have been quantified in previous work, and relatively little effort seems to have been expended to remedy this situation. We demonstrate here that by using very short (45 fs) pulses, highly efficient white light generation is achieved in an inorganic material, barium fluoride, which has large band gap and low dispersion. Furthermore, our experiments confirm that multiphoton excitation occurs during continuum generation. We also show that, at low incident intensity, the white light continuum is spatially coherent.
The laser system used in the current experiments is a chirped pulse amplification system. Briefly, the system comprises an oscillator delivering a 88 MHz pulse train with an average mode-lock output power of 500 mW. The full width half maximum bandwidth of the oscillator pulses, as measured with a spectrometer, is ~55 nm. The pulse train from the oscillator is sent into an amplifier system comprising a pulse stretcher, a pulse picker, which slices the input pulse train to 1 kHz, an amplifier, comprising a Ti:sapphire crystal, which is pumped by a 1 kHz Q-switched Nd:YLF laser, followed by a pulse compressor. The pulse makes 9 passes in the multipass amplifier in a ring configuration. After compression we obtain pulses of 45 fs with output energy of up to 1mJ at 1 kHz repetition rate.
The laser beam was focused on a 10 cm long barium fluoride crystal using a 30 cm focal length lens. The spectrum of the white light was recorded using a fiber optic coupled spectrometer. To study two-photon absorption, the induced fluorescence was measured using the fourth harmonic of a picosecond Nd:YAG laser operating at 10 Hz. For observing the coherence property of the white light continuum, a cylindrical lens of 20 cm was used to line focus a fraction of the incident femtosecond laser energy (~60 µJ) onto a 8 mm long glass (BK-7) window.
3. Results and discussion
The linear transmittance of BaF2 cuts off at ~135 nm, corresponding to an optical gap of 9.2 eV. Its refractive index varies from 1.50 to 1.47 over the spectral region 355–1064 nm. Pure barium fluoride is a well-known scintillator, its high efficiency being due to high density and the two luminescence bands centered at 330 nm and ~200 nm . Figure 2 shows the spectrum that we measured of the white light that is shown in the right panel of Fig. 1. The spectrum covers the range 400–1000 nm. Fig. 2 also shows the spectrum of the incident fs laser beam, appropriately attenuated so that it could be displayed in the same plot.
For a typical laser energy of 900 µJ incident on the crystal, the energy of the entire white light continuum (Fig. 2) was measured to be ~400 µJ using an energy meter with a nearly flat and wide response that covered the range 400–1100 nm. Over many measurements, the minimum value of efficiency was measured to be ~40% over the entire band. The efficiency of white light in the visible region was measured to be more than 20% when color glass filter (BG 39) was used to stop radiation beyond 700 nm wavelength.
The results of our measurements enable the following deductions to be made: i) highly efficient conversion of infrared radiation into white light is observed, and ii) there is no apparent damage to the crystal, even at relatively high intensities. We have not attempted to optimize the length of the crystal for efficient white light generation. The pulse duration of the continuum is, of course, an important parameter and we believe that an extremely short white light pulse may be achievable after compression.
In our experiments we also observed blue emission from the region around the beam waist inside the BaF2 crystal. The left panel of Fig. 3 shows an example of such emission when an 800 nm incident beam was used. This type of emission has not been reported in earlier experiments on generation of white light continua. As already noted, BaF2 has two luminescence bands, centered at 330 nm and ~200 nm. Thus, for emission in this spectral range to occur, either the crystal has to absorb at least 6 photons of 800 nm or it has to be postulated that energetic electrons from field-induced ionization are responsible for the excitation.
We tested the hypothesis that multiphoton excitation might be initiated by light intensity that is enhanced by self-focusing within the crystal by making measurements at a different wavelength of incident laser radiation. Since the band gap of BaF2 is 9.2 eV, it should exhibit two-photon absorption for photon energies between 4.6<hν<9.2 eV. This corresponds to wavelengths <270 nm. We utilized the fourth harmonic of a Nd:YAG laser to provide 266 nm radiation. Barium fluoride is known to have a large two-photon absorption coefficient at 266 nm (0.06 cm/GW) . Blue emission was, indeed, observed in our measurements, indicating that emission was due to multi-photon absorption. An illustrative result with incident 266 nm light is shown in the right panel of Fig. 3.
We were also able to confirm that emission in this case was due to a two-photon process by measuring the upconverted emission at various values of incident laser intensity and confirming that a square dependence on incident intensity is observed. We also conducted experiments at other wavelengths of incident laser light, such as 355 nm radiation obtained from the third harmonic of our Nd:YAG laser. No evidence was found for upconverted emission in such cases.
We now discuss the coherence property of our white light source. As already discussed, white light generation is likely to be the result of many competing processes and, consequently, the characteristics of the output beam are difficult to predict. Intuitively, it is difficult to expect that phase relations would remain intact when white light pulses are produced using mode-locked lasers. In principle, it is possible to use a Young’s double slit geometry to determine, in fairly simple fashion, the spatial coherence of the white light that is generated in these experiments. We have done this by placing two pinholes along the direction of propagation of white light, and by measuring the fringe visibility of the interference pattern that is obtained in the far field. For fringes to be formed, it would be necessary for the existence of two or more secondary sources of white light within the crystal.
Is it possible to create two, or more than two, white light sources within the medium? It is known that above a certain threshold power the input beam decomposes into small filaments inside the medium . Each filament can then generate white light continua [19–20]. Investigation of spatial coherence in such cases has shown that each filament preserves the coherence of the incident laser pulse . Thus, the supercontinuum that is generated from a single filament is known to possess a high degree of spatial coherence . It has recently been shown that white light generated from multiple filaments also exhibits a high degree of spatial coherence . In these experiments a stable interference is obtained in the far field that indicates that for white light generated in these filaments, each spectral component has the same coherence as the initial pump pulse. This coherence has been observed using both spherical and cylindrical lens focusing. The advantage of using a cylindrical lens is that one can generate a horizontal array of stable white light sources. Stable interference has been observed in water using line focusing and results have been shown to be in agreement with theoretical predictions made using the analogy with Young’s classic double slit experiment .
Self-focusing depends on the material parameter n2. On the other hand, fringe formation is indicative of the coherence of the white light that is generated and not a specific property of the BaF2 crystal that we have used for white light generation. Indeed, fringes have been observed in lower-intensity, long-pulse experiments on sapphire . We have conducted a number of experiments to observe white light interference from self focused filaments at an even lower intensity than in earlier experiments . Using materials like sapphire and BK-7 glass, we were able to observe a stable fringe pattern well below the threshold of breakdown of glass. In our experiments the fringes, examples of some of which are shown in Fig. 4 (using a green filter), were perpendicular to the line focus plane. Upon changing the orientation of the line focus by 90° we observed that the fringes became horizontal. As noted above, these fringes are not specific to BK-7 glass, and are expected to appear in experiments with any high-bandgap material that produces white light.
We made measurements of fringe stability as a function of incident intensity, expecting that at higher intensities many more filaments might form, giving rise to a more complex interference pattern. We found that increasing the laser intensity did result in smearing of the fringe pattern such that the resulting fringe images were not as distinct as those that are depicted in Fig. 4.
4. Concluding remarks
Highly efficient white light generation has been demonstrated in a 10 cm long barium fluoride crystal that is irradiated by 45 fs long pulses of 800 nm laser radiation with incident energy up to 1 mJ. The entire visible band along with the near-infrared region of the spectrum was generated, spanning the wavelength region from 400 nm to 1000 nm. A minimum efficiency of ~40%, an unexpectedly high value, was measured across the entire band for this process. A novel facet of the present measurements was the observation that, along with white light generation, multi-photon absorption induced fluorescence is also observed within the crystal. The highly coherent nature of the white light was demonstrated by the formation of interference fringes that arise from multiple filaments that are created within 8 mm thick BK-7 glass upon its irradiation by a single, low-intensity laser beam employing line focusing geometry.
We would like to acknowledge V. Nanal and M. K. Sharan for providing us with the unusually large barium fluoride crystal. Useful discussions with M. Krishnamurthy are gratefully acknowledged.
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