1. Introduction

Nowadays, the techniques of frequency conversion of femtosecond laser pulses have been well developed for their wide range of applications in physics, photochemistry, and photobiology. In the past decade, cascaded four-wave mixing (CFWM) has been demonstrated as a powerful method for generating frequency converted femtosecond laser pulses, and it has been widely used in four-wave parametric amplification [1], high-power ultrashort pulses generation [2–4], and femtosecond stimulated Raman spectroscopy [5]. Because of the non-requirement of symmetry, various transparent isotropic materials have been used as working media in CFWM, such as BK7 glass [6], sapphire plate [7], and fused silica [8, 9].

In actual situation, CFWM may be impeded by competing with other nonlinear effects, such as self-focusing, self- and cross-phase modulation, and stimulated Raman scattering. The low threshold power density for generating CFWM has been demonstrated in our previous work [10], where a glass with high optical nonlinearity was used [11, 12]. However, when the materials with high third-order nonlinear refractive index were used as working media, a concurrent disadvantage may be predictable. That is the lowing of power density for generating other nonlinear optical effects. For instance, the critical power $P_{cr}=3.77{\lambda }^2/(8\pi n{n}_2)$ (λ is the laser wavelength, n and n₂ represent the linear and nonlinear refractive index of the medium at the relevant wavelength) for self-focusing in tellurite glass (Te glass) is about one magnitude lower than that in fused silica [13]. In recent CFWM experiments, beam breakup, which could be treated as another competing effect, was observed due to spatial asymmetric distribution of input beams [14, 15]. Though two-dimensional multicolored arrays could be induced by beam breakup, the arrays were not very regular, which were not suitable for the practical applications.

In this investigation, regular two-dimensional multicolored arrays were obtained through CFWM processes together with prefabricated grating structure in a Te glass. The grating structure consisted of Te crystalline lines was inscribed by high-repetition rate femtosecond laser pulses. The grating-assisted generating two-dimensional CFWM sidebands are much more regular than those induced by beam breakup.

2. Experiments

Glass sample with a composition of 75TeO₂-20ZnO-5Na₂O (mol.%) was prepared by conventional melt-quenching technique. Reagent grade TeO₂, ZnO and Na₂CO₃ were used as starting materials. The raw materials were mixed and melted in an alumina crucible at 800 °C for 40 minutes in air. Then the melt was poured onto a stainless-steel plate at room temperature. Transparent glass was annealed at 250°C for 2 h. After that, the Te glass was cut and polished to a sample with thickness of 1.5 mm. A commercial femtosecond Yb-fiber laser system (FLCPA-02USCT11, Calmar Laser, Inc.) emitting 370 fs, 1030 nm laser pulses at a repetition rate of 500 kHz was employed for the fabrication of grating structure in Te glass. The laser pulses were focused at 100 μm beneath the glass surface via a microscope objective (50 × , NA = 0.8). The grating structure with a size of 3 × 3 mm² was inscribed by direct-writing with laser power of 100 mW and scanning speed of 60 μm/s.

A femtosecond pump-probe arrangement was employed for the generation of CFWM sidebands, as described in our previous works [10]. A commercial Ti: sapphire regenerative amplifier (RegA900, Coherent Inc.) system, which emitted pulses with central wavelength of 800 nm, pulses duration of 50 fs, and repetition rate of 1 kHz, was used as the laser source. The output beam was splitted into two relatively delayed parts (beam_1 and beam_2). These two beams were focused onto the Te glass sample by a single lens with the focal length of 400 mm at a small angle of 3.0°. The beam diameter of beam_1 and beam_2 on the sample were about 630 and 700 μm, respectively. Beam_1 advanced beam_2 a time delay of 130 fs by adjusting a time-delay device. Due to the up-chirped femtosecond laser pulses [16], the shorter wavelength components of beam_1 overlapped with the longer wavelength components of beam_2 at this time delay. According to the phase-matching of CFWM processes, the CFWM sideband signals appeared on beam_1 side [17].

3. Experimental results and discussion

3.1 Grating structure preparation

The optical microscope photograph of the grating pattern inscribed in Te glass is shown in the inset of Fig. 1 together with the diffraction pattern when a He-Ne laser (632.8 nm) was used as light source. The first-order diffraction efficiency η was measured to be about 20%. According to the expression $\eta ={(\pi \Delta nd/\lambda \cos \theta )}^2$ [18] (the d, λ and θ are the thickness of the grating, the wavelength of the irradiated light, and the angle between the surface normal and the diffracted laser beam, respectively), the corresponding refractive index change of the femtosecond laser irradiated region was calculated to be about 0.05. This value was about one magnitude larger than that induced in fused silica [19]. Figure 1 shows the micro-Raman spectrum measured at the region irradiated by the femtosecond laser with high-repetition rate. Comparing with the unirradiated region, two typical peaks at 120 cm⁻¹ and 140 cm⁻¹ can be observed, which can be assigned to the vibration of A1 and E modes of Te crystals, respectively. Further, all the Raman peaks located at ~440 cm⁻¹, ~666 cm⁻¹ and ~740 cm⁻¹ ascribed to the vibration of Te-O bond are vanished [20]. During the irradiation of the femtosecond laser, nonlinear multi-photon absorption and ionization occur in the sample, resulting in the formation of free electrons, and breaking of chemical bonds e.g. Te-O and formation of Te atom. In the case of using the repetition rate (500 kHz) femtosecond laser, local temperature will increase due to heat accumulation effect. When the temperature around the focal point reaches suitable temperature for nucleation and crystal growth, Te atoms migrate and aggregate to form Te crystals. Therefore, we confirmed that the Te crystals were precipitated after the irradiation with high-repetition rate femtosecond laser pulses, which resulted in the enhancement of refractive index. The damage threshold of the Te glass was estimated about 20 GW/cm², and it was slightly enhanced for the glass with grating structure.

 

Fig. 1 Micro-Raman spectra measured at the femtosecond laser irradiated region and unirradiated region, respectively. The inset shows the microscope image of grating structure and diffraction pattern of a He-Ne laser at 632.8 nm.

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3.2 One-dimensional multicolored sidebands generation

Firstly, the CFWM experiment was performed in the Te glass without grating structure. The CFWM sideband signals could be easily obtained when the power densities of two input beams were at relative low levels due to the large optical nonlinearity of the Te glass [21]. Frequency up-converted CFWM signals (AS1-AS4) appeared on beam_1 side when the power densities of beam_1 and beam_2 were set at 28.5 × 10⁹ and 15.5 × 10⁹ W/cm², respectively, as shown in Fig. 2(a).The S1 denoted in Fig. 2(a) was a frequency down-converted CFWM signal, which was generated by two photons in beam_2 and one photon in beam_1. At this condition, the profiles of beam_1, beam_2 and the generated CFWM sideband signals were distinct, and no noise was observed.

 

Fig. 2 One- and two-dimensional multicolored patterns generated in Te glass without grating structure. The input power densities of beam_1 and beam_2 were (a) 28.5 × 10⁹ and 15.5 × 10⁹ W/cm², (b) 55 × 10⁹ and 35 × 10⁹ W/cm², and (c) 90 × 10⁹ and 70 × 10⁹ W/cm², respectively.

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When the power densities of the two incident beams were increased to 55 × 10⁹ (beam_1) and 35 × 10⁹ W/cm² (beam_2), respectively, two-dimensional multicolored pattern was observed. This multicolored pattern could be separated into two parts. One was around the incident pump beams, and the other showed multicolored was distributed around the CFWM sideband signals. For the high peak power, which was more than 100 times larger than the critical threshold of self-focusing in the Te glass, various transverse instabilities could occur [22, 23]. We considered that the pump beam breakup occurred at this power density condition, which led to the degradations of pump beams. Simultaneously, one dimensional CFWM signals turned to two-dimensional multicolored pattern. When the power densities of beam_1 and beam_2 increased to 90 × 10⁹ and 70 × 10⁹ W/cm², respectively, the two-dimensional multicolored pattern became more bright, and blue pattern appeared on the boundary, as shown in Fig. 2(c). However, the boundaries among each CFWM signal in two-dimensional multicolored pattern were indistinct. For the purpose of applications, the two-dimensional multicolored CFWM signals induced by beam breakup were not suitable.

3.3 Grating-assisted generating two-dimensional multicolored arrays

When the two pump beams with power densities of 10 × 10⁹ (beam_1) and 8 × 10⁹ W/cm² (beam_2) were focused to the grating structure in Te glass, only two columns of spots were observed, as shown in Fig. 3(a).These spots were linearly diffracted from the input beams, and no CFWM processes occurred simultaneously. Therefore, the diffraction of grating structure appeared even the input power densities were very low, and the CFWM processes needed certain critical power densities to occur. When the input power densities increased, regular two-dimensional light arrays could be observed, as shown in Fig. 3(b). Though the power densities of pump beams were kept the same as those used in Fig. 2(b), the CFWM signals in the two-dimensional arrays were well separated from each other in space. Figure 3(d) shows the defined frame for describing sidebands conveniently. The two large spots denoted as b1(0, 0) and b2(−1, 0) referred to beam_1 and beam_2, respectively. The sideband (m, n) was referred to the one located at the mth column and the nth row. The generation of two-dimensional multicolored arrays was considered as the results of diffraction by the grating structure. Therefore, the sidebands at row_n ($\left|n\right|\ge 1$) inherited the profiles of sidebands on row_0. When the power densities of beam_1 and beam_2 increased to 90 × 10⁹ and 70 × 10⁹ W/cm², respectively, both of the numbers and strength of sidebands were increased, as shown in Fig. 3(d). Because the spectra of CFWM sidebands only depended on the phase-matching conditions, but not the input power densities, there were no any spectral differences between the same orders in Figs. 3(b) and 3(d). The normalized spectra of the sidebands (m, 0) ($\left|m\right|\ge 1$) were shown in Fig. 3(e). A spectral region from 480 to 730 nm was covered by the spectra of frequency up-converted CFWM signals. The average central wavelength blue-shift interval of neighboring sidebands was about 15 nm. There was no supercontinuum detected at each CFWM sideband. After the experiment, we checked the glass sample with grating structure. No additional Te crystals were precipitated, because the light intensities were too low to precipitate Te crystals under present experimental condition. The central wavelength of each sideband could be turned by changing either the crossing angle or the relative time delay between two input pump beams.

 

Fig. 3 (a) Diffracted pattern of two input femtosecond laser beams. The input power densities of beam_1 and beam_2 were 10 × 10⁹ and 8 × 10⁹ W/cm², respectively. Regular two-dimensional multicolored arrays generated in Te glass with grating structure. The input power densities of beam_1 and beam_2 were (b) 55 × 10⁹ and 35 × 10⁹ W/cm², and (c) 90 × 10⁹ and 70 × 10⁹ W/cm², respectively. (c) Definition of two-dimensional multicolored arrays. (e) Spectra of sidebands (m, 0) ($13\ge \left|m\right|\ge 1$).

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In order to analyze the spectral characteristics of the diffracted sidebands, we typically measured the spectra of sidebands (4, n) ($\left|n\right|\ge 1$), as shown in Fig. 4.Figures 4(a) and 4(b) show the normalized spectral profiles of sidebands above and below (4, 0). Comparing with the spectral profile of (4, 0), the spectra of (4, n) ($\left|n\right|\ge 1$) were much narrower, and the whole spectral regions were all located within it, which confirmed us that the sidebands (4, n) ($\left|n\right|\ge 1$) were linearly diffracted from (4, 0). The spectra of high diffracted orders were narrower than those of low orders. This was because the emission angles of higher diffracted orders were larger [24], which introduced larger phase-mismatching in CFWM processes, resulting in the phenomenon of spectral narrowing.

 

Fig. 4 Spectral profiles of sidebands (a) (4, n) ($n\ge 0$), and (b) (4, n) ($n\le 0$).

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Since the large diffraction efficiency of the grating structure, the beam breakup was not observed when the input power densities were sufficiently high. The grating-assisted generation of two-dimensional multicolored arrays exhibit a very superior way for avoiding other nonlinear effects, such as beam breakup. Meanwhile, the two-dimensional multicolored arrays were much more regular than those induced by beam breakup. It could be expected that the spectra of two-dimensional multicolored CFWM sidebands will be extended to ultraviolet region by further increasing pump power if a grating structure of higher diffraction efficiency is employed. In this condition, the beam breakup, which disturbs the two-dimensional arrays, may still be avoided. In order to enhance the diffraction efficiency, we could increase the power of high-repetition rate laser to precipitate much more Te crystals when we write the grating structure in Te glass. Therefore, the refractive index change at the laser modified region will be increased, which enhances the diffraction efficiency of the grating structure.

4. Conclusion

In summary, regular two-dimensional multicolored arrays were generated through CFWM processes together with prefabricated grating structure in a Te glass. The grating structure consisted of Te crystalline lines was inscribed by irradiating femtosecond laser pulses of high-repetition rate. The beam breakup was sufficiently suppressed when the input power densities were sufficiently high. The regular two-dimensional multicolored arrays with broad bandwidth could be applied in very wide fields, such as two-dimensional spectroscopy, and two-dimensional all-optical switching.