1. Introduction

Propagation of intense ultrashort laser pulses in transparent condensed media or optical fibers can induce ultrabroadening of the original spectrum, which is called supercontinuum (SC) or white light generation. This broadband source of SC raises much interest for its wide applications such as characterization of optical components, interferometry or optical coherence tomography, and the generation of few-cycle pulses [1–4]. Bandwidth is a critical issue in some applications. For instance, in optical coherence tomography a large bandwidth of SC is equivalent to a good spatial resolution. Besides, as a broadband light source, practical applications usually favor a flatter spectrum. Thus far, efforts have been devoted to generating wider and flatter SC spectra. Since the SC spectrum usually broadens asymmetrically, with a larger frequency shift towards the anti-Stokes side, the effective approach is to use longwavelength pulse pumping or photonic crystal fibers (PCFs) [5, 6]. Bulk materials may favor high power of SC while PCFs favor flat spectra [7]. In addition, the duration of pump pulse plays a vital role in SC generation. It has been observed that in bulk media, shorter pump pulses generate broader SC spectra with higher conversion efficiency [8]. As decreasing the duration of pump pulses in PCFs, higher pump power is required to maintain the bandwidth of SC due to the broadening mechanism of soliton fission. On the other hand, SC induced by short pump pulses (e.g., ~10-fs) contains less noise [9]. Unfortunately, short pulses down to ~10 fs are not always available particularly in the region of long wavelength. Here we focus on generating broadband SC with flat spectra in bulk materials, which may facilitate wide practical uses. We study and demonstrate an effective pumping scheme using dualwavelength femtosecond pulses with moderate durations of ~100 fs to generate broad and flat SC spectrum in a bulk material. The pump condition of short pulse or large bandwidth is alternatively accomplished by the wavelength separation between the two pump lasers; while flatter spectra may be obtained by adjusting the relative power of two pump lasers. Dualwavelength pumping was previously adopted to generate SC in PCFs, which favors the generation of SC in the blue region and leads to complex behaviors of the resultant SC spectrum that depend on the parameters of the fibers [10–12].

In this paper, SC generation by dual-wavelength pumping is first analyzed theoretically. We show that the wavelength separation between two pump lasers is qualitatively equivalent to a large bandwidth of single pump laser. Dual-wavelength pumping is studied experimentally by using two femtosecond lasers at wavelengths of 800 nm and 1054 nm. Femtosecond laser at 1054 nm is obtained from an optical parametric amplifier (OPA) pumped by a regenerative amplifier of Ti: sapphire laser at wavelength of 800 nm. The result shows that the generated SC in the visible and infrared regions can be greatly increased by using dual-wavelength pumping. Through adjusting the power of pump laser at 800 nm, flatter SC spectra can be obtained. Finally, the experimental results are discussed.

2. Theoretical analysis

Following Yang and Shen [13], the formulae describing the propagation and spectrum broadening of two femtosecond lasers of different wavelengths are:

ε_m (z,t) is the electric field envelope defined as E_m (z,t)=ε_m (z,t)exp(ik_mz-iω_mt) with m=0, 1 denoting λ=800 nm and λ=1054 nm, respectively. For ε_m |ε_m (z,t) exp(iφ_m ), we assume the phase evolution of the two lasers are identical, i.e., φ ₀(z,t)≈φ ₁(z,t). The equations describing the evolution of amplitudes and phases of both lasers (m=0, 1) can be written as:

In accordance with the assumptions of Ref. [13] and supposing the boundary conditions ${\mid {\epsilon }_m\mid }^2=A_m^2⁄\cosh [(t-\frac{n_{0}z}{c})⁄\tau ]$ and φ_m (0,t)=0, the maximum anti-Stokes and Stokes shifts, Δω ₊ and Δω₋ are obtained:

where Q_m =n ₂ $A_m^2$z/cτ. In a simple case where the two lasers are of equal amplitude (i.e., A ₀(z,t)≈A ₁(z,t), hence Q ₀≈Q ₁), the dual-wavelength pumping may be equivalent to singlewavelength pumping with modified ω and Q :

Δω ₊ and Δω₋ are given by Eq. (4) and Eq. (5), respectively. The defined frequency ω and pump parameter Q can be easily obtained, assuming a moderate Q ₀~1:

As shown by Eq. (9), the pump parameter Q hence the frequency shift or spectrum broadening increases with the frequency difference between the pump lasers. In Ref. [13], the anti-Stokes and Stokes shifts were given as Δω _±=ω ₀{[($Q_0^2$+4)^1/2±Q ₀]/2-1 with Q ₀=n ₂ A ² z/τc∝Δω (Δω is the bandwidth of pump pulse), which indicates that the spectrum broadens with the increase of pump pulse bandwidth. In analogy, our theoretical deduction suggests that dual-wavelength pumping is equivalent to single-wavelength pumping with the frequency ω=(ω ₀+ω ₁)/2 lying between the two pump frequencies, while the effective bandwidth is Δω_eff =ω ₀-ω ₁. As a consequence, broad SC can be generated with dual-wavelength pumping.

3. Experimental results and discussions

The femtosecond pulses at 1054 nm were generated in a homemade OPA pumped by the regenerative Ti: sapphire amplifier at wavelength of 800 nm [14]. The pulse durations of two pump lasers at 800 nm and 1054 nm were measured to be ~100 fs and ~120 fs, respectively. The two lasers were focused by an achromatic lens (f=50 mm) and incident onto a 2 mm sapphire plate. The temporal overlap of two pump pulses was guaranteed by detecting their sum frequency generation in a 0.5-mm thick BBO crystal. In order to avoid optical damage, the sapphire plate was placed at 5-mm after the focus. The beam diameters (at 1/e intensity) before the lens for the 800 nm pulse and the 1054 nm pulse were ~0.8 cm and ~0.4 cm, respectively. A white screen was inserted in the far field to observe the diverging colorful patterns associated with SC generation. In the case of dual-wavelength pumping, a variable neutral density filter was inserted in the optical path to adjust the power of pump laser at 800 nm. To analyze the spectrum, the generated SC was coupled into an optical spectrum analyzer (ANDO-AQ6315A, 350 nm-1750 nm). The resolution was set to be 5 nm and the measurement was averaged over 100 times.

 

Fig. 1. Measured spectra of SC and the corresponding pump pulse (inset). (a) The pump laser at 800 nm, and (b) the pump laser at 1054 nm.

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We first study SC generation with single-wavelength pumping. Minimum pulse energy required to excite SC was measured, which was ~10 µJ and ~5 µJ for pump lasers at 800 nm and 1054 nm, respectively. The beam radii in the sapphire plate were estimated to be ~0.4 mm and ~0.2 mm for the pump lasers at 800 nm and 1054 nm, respectively, assuming Gaussian beam profiles. With above measured minimum pulse energies, the required intensities to excite SC were about 20 GW/cm² and 30 GW/cm² for the two pump pulses, respectively. Therefore, the required minimum intensities to excite SC are quite the same for slightly different pump wavelengths. In the regime of single-wavelength pumping, pulse energy was fixed at 22 µJ for each pump laser. SC in the near field was a white spot surrounded by blue rings in visual appearance, which was the same for both pumping wavelengths.

The generated SC spectra are studied for the case pumped by single femtosecond laser (Fig. 1). The typical SC spectrum generated by the pump laser at 800 nm is shown in Fig. 1 (a), which is quite similar to that obtained by other authors [15]. It can be seen that the SC generated by the laser at 1054 nm covers a whole octave, i.e., from 1400 nm down to ~350 nm. In particular, the SC spectrum features a broad peak in the visible region (500 nm to 600 nm), which is quite different from that pumped by the laser at 800 nm. Since self-phasemodulation (SPM) only accounts for the symmetric spectrum broadening around the pump spectrum, while self-steepening, shock formation and ionization-enhanced SPM for the asymmetric broadening towards the anti-Stokes side, we postulate that four-wave parametric process contributes to this peak. In addition, the small peak near 1450 nm appears in the SC spectrum is the residual light accompanied with the pump laser at 1054 nm, which exists even without the sapphire plate and is due to the parametric process in the OPA crystal.

 

Fig. 2. The measured SC spectra with dual-wavelength pumping for different pump conditions: The two pump pulses are completely separated, and the pump pulse energy at 800 nm is 8 µJ in this case (black line); the two pump pulses are temporally overlapped and the pump pulse energy at 800 nm is 3 µJ (green line) or 8 µJ (red line). Pump pulse energy at 1054 nm is fixed at 22 µJ. All the spectra are normalized to the maximum peak of the SC spectrum generated by the two temporally separated pulses.

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The generation of SC with dual-wavelength pumping is studied (Fig. 2). During the experiment, the pulse energy of the pump laser at 1054 nm was fixed at 22 µJ that was well above the critical power for SC generation; while the pump pulse energy at 800 nm was varied from 3 µJ to 8 µJ that was below the critical power. When the two pump pulses were completely separated, only the laser at 1054 nm could induce SC generation. The SC spectrum is similar to that shown in Fig. 1(b) except a pump pulse component at 800 nm. When the two pump pulses were overlapped, however, the colorful SC pattern was observed with a sharp increase in its brightness. Due to the contribution of pump at 800 nm, the frequency component in the visible region from 550 nm to 750 nm is greatly enhanced, which makes the SC spectrum rather flat. In the region around 700 nm, the conversion efficiency is almost an order of magnitude higher than that pumped by a single laser at 1054 nm. The SC is also generated more efficiently in the long wavelength regions around 900 nm and 1380 nm.

Moreover, the SC spectrum is extended in the long wavelength region up to 1600 nm. On the other hand, in the short wavelength region there is no significant change caused by dual-wavelength pumping.

Dual-wavelength pumping may provide an effective means to obtain a flat SC spectrum by adjusting the pump energy at 800 nm. As clearly shown in Fig. 2, increasing the pulse energy at 800 nm can indeed make the resultant SC spectrum flatter in the wavelength regions of 550 nm to 750 nm and 1300 nm to 1400 nm. The effect of a flatter SC spectrum caused by the dual-wavelength pumping is most significant when the pulse energy at 800 nm is ~8 µJ.

It is important to discuss the SC generation by dual-wavelength pumping. When the two pulses are completely separated, only the 1054 nm pulse exceeds the critical power for self-focusing and thus collapses, accompanied by broadening of the spectrum. In contrast, the power of the 800 nm pulse is below the critical power and thus will not generate SC alone. However, when the two pump pulses overlap spatially and temporally, the pump laser at 800 nm will also undergo catastrophic collapse and induce strong SC generation due to cross-phase-modulation (XPM). This may account for the dramatic increase of efficiency in the visible region. The existence of the 800 nm pulse induces a larger nonlinear phase shift through XPM experienced by the 1054 nm pulse, which leads to the red shift towards the Stokes side. Due to the existence of the 800 nm pulse and the enhanced SC in the visible region, intensified four-wave parametric process also contributes to the generation of SC in the near infrared.

4. Conclusion

In conclusion, we have studied and demonstrated that dual-wavelength pumping is an effective means to acquiring ultrabroad SC with flatter spectra in a bulk sapphire. By pumping with two femtosecond lasers at 800 nm and 1054 nm, a flatter SC spectrum from 350 nm to 1600 nm is obtained. The conversion efficiencies in the visible and near infrared regions are significantly enhanced due to the dual-wavelength pumping. Relative intensity ratio between the two pump lasers is a degree of freedom to adjust the shape of SC spectrum. We have obtained SC with a flatter spectrum in the wavelength regions of 550 nm to 750 nm and 1300 nm to 1400 nm.