1. Introduction

Photonic-crystal fibers (PCFs) [1–3] open new horizons in ultrafast laser technologies, providing unprecedented efficiencies of spectral transformation of unamplified femtosecond laser pulses [4]. Fibers of this type can serve as efficient sources of broadband radiation [5, 6], frequency-comb expanders [7, 8], and frequency shifters [9], finding numerous applications in optical frequency metrology [10], coherent spectroscopy [11], nonlinear microscopy [12], carrier--envelope phase stabilization [13, 14], optical parametric amplification of few-cycle laser pulses [15], and biomedical optics [16].

PCFs with a high air-filling fraction of the cladding provide a large difference in refractive indices of the core and the cladding (high delta), leading to a strong confinement of the laser field in a micron-diameter fiber core [17]. Such high-delta PCFs dramatically enhance optical nonlinearities [18], serving as efficient supercontinuum generators and frequency up- and down-converters for short-pulse laser sources. Birefringence, induced in such PCFs by the form anisotropy of the core [19, 20] or the cladding [21], allows polarization control of supercontinuum generation [22, 23] and frequency shifting [24, 25], as well as polarization demultiplexing of the multicolor frequency-shifted output of the PCF [26].

In this work, we show that a high-delta PCF with a more complex, comma-shaped core offers interesting new options for tunable supercontinuum generation. We demonstrate that such PCFs can support two different types of guided modes, efficiently transforming unamplified 30-fs Ti: sapphire laser pulses into supercontinuum emission through two different physical mechanisms. The two regimes of supercontinuum generation, leading to two different types of output spectra, are switched by displacing the input end of the fiber with respect to the laser beam in the transverse direction.

2. Experimental technique and photonic-crystal fibers

Experiments were performed with the use of a Ti: sapphire oscillator with an X-folded cavity, pumped with a 4-W second-harmonic output of a diode-pumped Nd: YVO₄ laser (Millennia VS, Spectra-Physics). A Brewster-cut Ti: sapphire crystal with a length of 2.3 mm was placed at the center of the laser cavity between two focusing mirrors (Newport) with a focal length of 50 mm. Chirped mirrors and a prism pair were used for dispersion compensation. The separation of the prisms in the pair is 240 mm. Each of the chirped mirrors (Layertec, Germany) provides an average group-dispersion delay (GDD) of about 60 fs² per bounce at 800 nm. Chirped mirrors in our laser cavity provide a flat GDD profile over a broad spectral band. The level of GDD is controlled by the prism separation and can be tuned from negative to positive values. Such a laser oscillator can deliver pulses with a typical temporal width of about 30 fs, an energy up to 5 nJ at a pulse repetition rate of 100 MHz and a central wavelength of 800 nm.

Photonic-crystal fibers employed for supercontinuum generation in this study were fabricated of fused silica using a standard stack-and-draw technique [1, 2]. The cross-section view of the PCF is presented in inset 1 to Fig. 1. The fiber cladding, as can be seen from Fig. 1, is characterized by a high air-filling fraction, strongly confining laser radiation to the fiber core. The comma-like shape of the fiber core allows the existence of two types of well-localized guided modes with bell-shaped field intensity profiles reaching their peak values at the center of the mode (insets 2 and 3 in Fig. 1). Images of beam patterns typical of the first-type modes from this family are presented in Figs. 2(a)–2(c). Field intensity profiles for this type of modes have a shape of distorted circles (inset 2 in Fig. 1), with transverse mode sizes measured along two orthogonal directions in the cross section of the fiber being very close to each other. The group-velocity dispersion (GVD) calculated for this type of modes as a function of the radiation wavelength using the finite-element method (FEM) is shown by curve 1 in Fig. 1. The zero GVD wavelength is 783 nm in this case, lying close to the central wavelength of Ti: sapphire laser pulses used in our experiments.

The modes of the second type have elliptical field intensity profiles (inset 3 in [1 and Figs. 2(d) – 2(f)], with the long axis of the elliptical beam pattern oriented along the tail of the comma-shaped fiber core. The zero-GVD wavelength for this type of modes is 630 nm (curve 2 in Fig. 1), providing anomalous dispersion for Ti: sapphire laser pulses. The two types of modes considered here could be easily discriminated one against another (see Figs. 2(a)–2(f)) by displacing the input end of the fiber with respect to the laser beam in the transverse plane. To facilitate selective excitation of these modes, the PCF was placed on a three-dimensional translation stage. A 40x lens was used to couple laser radiation into the PCF. The PCF output was collimated with an identical lens and was studied with an Ando spectrum analyzer.

Our FEM analysis shows that the PCF used in our experiments can also support other guided modes with more complicated field intensity profiles. However, with the fiber axis aligned with the input beam, the efficiency of radiation coupling into those modes was at least a factor of 9 lower than that for the first- and second-type modes shown in Fig. 2. Within the entire visible and near-IR spectral ranges, we did not observe any significant deviations of spatial beam profiles measured at PCF output from the field intensity patterns predicted for the modes of the first and second type. Finally, the most intense spectral components dominating the output PCF spectra in our experiments were adequately explained by numerical simulations including only the modes of the first and second types. All these results suggest that the influence of higher order modes in our experiments was very weak.

3. Results and discussion

In experiments, both types of PCF modes considered in Section 2 above provided a high efficiency of spectral transformation of unamplified femtosecond Ti: sapphire laser pulses (Figs. 3(a) – 3(f)). With a fiber length of 2 m, 30-fs Ti: sapphire laser pulses with an initial energy of a few nanojoules and an initial central wavelength of 800 nm were transformed into a supercontinuum emission with a spectrum spanning over the entire visible and partially covering the near-infrared spectral range [Figs. 4(a), 4(b)]. The whole supercontinuum emission was observed in either the first- or the second-type PCF mode (Fig. 2). Within the entire visible and near-IR spectral ranges, radiation generated in higher order modes were at least an order of magnitude less intense than the emission produced in the two considered bell-shaped PCF modes. Supercontinua generated by the modes of the first and second type, however, noticeably differed both visually [cf. Figs. 3(a)–3(c) and Figs. 3(d)–3(f)] and in their significant spectral properties. While the modes of the first type generated a broadly spanning supercontinuum emission with a smooth spectrum stretching from 450 to 1400 nm [Fig. 4(a)], supercontinuum emitted by the modes of the second type featured an enhanced short-wavelength wing, dominated by intense spectral lines centered at 400–450 nm [Fig. 4(b)]. To understand the physics behind this difference, we performed experiments with a shorter, 20-cm segment of the same PCF. These measurements have demonstrated that the two types of PCF modes considered here generate supercontinuum through two different physical mechanisms.

 

Fig. 1. Group-velocity dispersion for the modes of the first (1) and second (2) type for the photonic-crystal fiber with a comma-shaped core shown in inset 1. Field intensity profiles in the first- and second-type modes are shown in insets 2 and 3.

Download Full Size | PDF

For the first-type modes, the central wavelength of laser radiation lies close to the zero-GVD wavelength. In this regime, frequency components ω ₁ and ω ₂ belonging to the spectrum of the laser field experience, as discussed in Ref. [27], an efficient parametric decay through FWM ω ₁ + ω ₂ = ω _s + ω _a, resulting in the generation of the Stokes and anti-Stokes sidebands with central frequencies ω _s and ω _a. Phase matching for such a process is automatically satisfied for pump frequencies ω ₁ and ω ₂ lying close to the zero-GVD point [27], as in the case of the first-type mode of the considered PCF, leading to a depletion of this region in the spectrum of the laser field. As a result, the spectrum of the laser pulse splits into two parts [Fig. 5(a)]. The short-wavelength part of the spectrum senses normal dispersion, spreading out in the time domain. The long-wavelength part of the spectrum falls within the region of anomalous dispersion and can form solitons. These solitons undergo a continuous frequency down-shift due to the Raman effect-phoneomenon known as soliton self-frequency shift (SSFS) [27]. Such solitonic features are also observed in the output spectra of 2-m PCFs (line 2 in Fig. 4(a)]. Higher order dispersion induces wave-matching resonances between solitons and dispersive waves [28, 29], leading to intense emission in the visible [30]. For higher input powers and longer fiber lengths, the spectral components related to dispersive waves merge together with solitonic spectral features, giving rise to broad and smooth output spectra spanning over a spectral range from 450 to 1400 nm [line 3 in Fig. 4(a)].

 

Fig. 2. Beam patterns of the first (a, b, c) and second (d, e, f) type modes at the output of the photonic-crystal fiber with a comma-shaped core with a peak power of the input field of (a, d) 8 kW, (b, e) 11 kW, and (c, f) 14 kW.

Download Full Size | PDF

 

Fig. 3. Side images of the photonic-crystal fiber with a comma-shaped core generating supercontinuum in the first (a, b, c) and second (d, e, f) type modes with a peak power of the input field of (a, d) 8 kW, (b, e) 11 kW, and (c, f) 14 kW.

Download Full Size | PDF

For the mode of the second type, the spectrum of the input field lies in the region of anomalous dispersion. High-order dispersion effects induce efficient blue-shifted emission in the visible already at the initial stage of spectral transformation of the laser field in the PCF [(Fig. 5(b)]. The central wavelength of dispersive-wave emission, which takes place in the regime of Cherenkov radiation [29], is controlled by phase matching between the parent soliton and the emitted dispersive wave. The phase-matching condition providing a resonant energy exchange between a soliton with a propagation constant β_s and a central wavelength λ₀ and a dispersive wave with a propagation constant β and a central wavelength λ_d is written as [29] δ_s = β_s (λ₀) - β(λ_d) = 0. In the inset to Fig. 5(b), we plot the propagation-constant mismatch δ_s calculated as a function of radiation wavelength for the second-type PCF mode. The time duration of a soliton in these calculations was chosen on the basis of numerical simulations using the generalized nonlinear SchrÖdinger equation [27] and was taken equal to 50 fs. It can be seen from the results presented in the inset to Fig. 5(b) that solitons with a central wavelength around 800 nm can emit phase-matched dispersive waves with a central wavelength of about 420 nm. This prediction agrees well with the experimental PCF output spectrum, shown in Fig. 5(b). Because of the form birefringence of the PCF core, the intensities of individual spectral components in the PCF output spectrum were sensitive to the polarization of the input field, suggesting the way to switch the wavelength of the frequency-shifted PCF output [26]. For any polarization state of the input field, the central frequencies of the most intense spectral components at the output of the fiber, identified as dispersive-wave emission of solitons in the PCF, were determined by the condition of wave matching between the soliton and the dispersive wave.

 

Fig. 4. Spectra of the PCF output measured with 30-fs Ti: sapphire laser pulses coupled into the first (a) and second (b) type mode of the fiber. The fiber length is 2 m. The initial peak power of laser pulses is (1) 0.8 kW, (2) 5 kW, and (3) 15 kW.

Download Full Size | PDF

Red-shifted solitons are also clearly seen for the second-type PCF mode. The wavelength dependence of dispersion and effective mode area eventually arrest the Raman-induced frequency shift of solitons. For second-type modes, as can be seen from Fig. 5(b), the lower amplitude and, therefore, a larger pulse width of red-shifting solitons leads to a lower frequency shift rate, preventing formation of a powerful long-wavelength wing of the output spectrum, similar to that observed for the first-type modes. As the fiber length and the input power increase, blue-shifted emission related to dispersive waves merges together with the solitonic part of the spectrum, forming a supercontinuum with an enhanced short-wavelength wing [curve 3 in Fig. 4(b)]. This wing is dominated by intense spectral lines centered at 400–450 nm, emitted by powerful solitons at the initial stage of nonlinear-optical pulse transformation in the fiber.

 

Fig. 5. Spectra of the PCF output measured with 30-fs 12-kW Ti: sapphire laser pulses coupled into the first (a) and second (b) type mode of the fiber. The fiber length is 20 cm. The inset in Fig. 5(b) shows the propagation-constant mismatch δ _s = β _s (λ₀) – β(λ_d) between a soliton with a central wavelength λ₀ and a dispersive wave with a central wavelength λ_d calculated as a function of the wavelength λ_d for the second-type PCF mode.

Download Full Size | PDF

4. Conclusion

We have demonstrated in this work that a fused silica high-index-step photonic-crystal fiber with a comma-shaped core can support two different types of guided modes with bell-shaped intensity profiles. These modes are shown to efficiently transform unamplified 30-fs Ti: sapphire laser pulses into supercontinuum emission through two different physical mechanisms. The modes of the first type provide broadly spanning supercontinuum emission with a smooth spectrum stretching from 450 to 1400 nm. The initial stage of supercontinuum generation in these modes involves four-wave mixing around the wavelength of zero group-velocity dispersion, leading to the depletion of the pump field. The modes of the second type generate supercontinuum with an enhanced short-wavelength wing, dominated by intense spectral lines centered at 400–450 nm. The two regimes of supercontinuum generation and the two types of output spectra are switched by displacing the input end of the fiber with respect to the laser beam in the transverse direction.