1. Introduction

Birefringence in optical fibers helps to maintain polarization of guided modes [1], allowing the creation of optical gyroscopes and laser interferometers [2], as well as the demonstration of quantum-optical phenomena [3] and photon entanglement generation [4]. The degeneracy of guided modes in such fibers is removed by breaking the cylindrical symmetry of the fiber. Standard methods to fabricate a birefringent fiber include [2] using the form birefringence of a fiber where the core or the cladding is elliptical in shape and inserting rods of borosilicate glass on the opposite sides of the fiber core [5] (PANDA, or bow-tie fibers). As demonstrated recently by experimental studies and numerical simulations, silica╍air microstructure (MS) fibers [6, 7] offer the ways to achieve very high degrees of modal birefringence [8 – 10] due to the remarkably rich diversity of core╍cladding configurations that can be implemented by means of MS-fiber technologies. Ortigosa-Blanch et al. [8] have demonstrated the modal birefringence as high as Δn = Δβ/k ≈ 3.7 10^-3 (Δβ is the difference of propagation constants for the guided modes whose degeneracy was removed by birefringence and k= ω/c, ω is the radiation frequency and c is the speed of light) for MS fibers with a noncircular core. Important insights into the principles and design aspects of highly birefringent MS fibers have been provided by Steel and Osgood [9] and Hansen et al. [10]. Birefringent MS fibers have been shown to allow polarization control of supercontinuum generation [11, 12] and have been employed for the generation of amplitude-squeezed light [13, 14].

In this work, we will show that birefringent MS fibers allow a highly efficient generation of frequency-tunable anti-Stokes line emission as a result of nonlinear-optical spectral transformation of unamplified femtosecond Ti: sapphire laser pulses. We will use femtosecond pulses of 820-nm pump radiation polarized along the fast and slow axes of the elliptical core of a fused silica MS fiber to generate intense blue-shifted lines centered at 490 and 510 nm, respectively, observed as bright blue and green emission at the output of a 10-cm microstructure fiber.

2. Birefringent microstructure fibers

Microstructure fibers were fabricated of fused silica with the use of the standard technology, described in detail elsewhere [15]. An elliptically deformed core of these MS fibers (Fig. 1(a)) with semiaxis sizes ρ_x ≈ 1.0 μm and ρ_y ≈ 0.8 μm gives rise to form birefringence, removing the degeneracy from the doublet of fundamental fiber modes. The modes of this doublet polarized along the large (x) and small (y) axes of the elliptical core of the fiber are referred to as the fast and slow modes, respectively. These modes have different propagation constants, β_x = ρ ₀ + δβ_x and ρ_y = ρ₀ + δβ_y , where β ₀ is the propagation constant of the doublet of degenerate fundamental modes in the unperturbed fiber with an ideally circular core and δβ_x and δβ_y are the birefringence-induced corrections to the propagation constant for the modes polarized along the large and small axes of the ellipse approximating the fiber core, respectively. The group-velocity dispersion (GVD) for these modes passes through zero at different wavelengths, offering the way to control nonlinear-optical interactions of ultrashort laser pulses.

 

Fig. 1. (a) An SEM cross-section image of the microstructure fiber. (b) Group-velocity dispersion calculated for (1) the fundamental mode of the MS fiber with an unperturbed, circular core with the radius ρ = (ρ_x ρ_y )^1/2 ≈ 0.89 μm, (2) the slow and (3, open circles) the fast Gaussian fundamental modes [Eq. (1)] in a birefringent fiber with a refractive index profile given by Eq. (2), and (4, crosses) the fast mode in an elliptical-core fiber with a stepwise refractive-index profile [Eq. (4)].

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The generic idea of our experiments is to design the birefringence of MS fibers in such a way as to be able to switch the frequency of anti-Stokes lines emitted as dispersive waves [16, 17] by coupling the pump pulses into the orthogonal-polarized modes of the birefringent MS fiber. To accomplish this plan, we should provide an anomalous dispersion for the pump pulse, to allow the pump pulse to form solitons, and switch the zero-GVD point between the pump and the blue-shifted signal, in order to tune the wavelength of the anti-Stokes line.

We use two models to analyze the dispersion of the birefringent MS fiber with an elliptical core (Fig. 1(a)) used in our experiments. The first model involves a Gaussian approximation

for the fundamental modes of a fiber with a cross section of an arbitrary shape f(x/ρ_x , y/ρ_y ) and the refractive index profile

where a_x and a_y are the effective mode sizes along the x- and y-axes, respectively, ρ_x and ρ_y are the characteristic sizes of the fiber core, n _core is the refractive index of the fiber core, Δ = ($n_{\mathit{\text{core}}}^2$ - $n_{\text{clad}}^2$)/($n_{\mathit{\text{core}}}^2$), n _clad is the refractive index of the cladding.

Polarization corrections to the unperturbed propagation constant β ₀ in such a fiber are given by [1]

The second model is an elliptical-core fiber with a stepwise refractive-index profile where the boundary has a form of an ellipse (x/ρ_x )² + (y/ρ_y )² = 1 with a small ellipticity e = (1 - ${\rho }_y^2$/${\rho }_x^2$)^1/2. The difference of propagation constants β_x and ρ_y in such a fiber is written as [1]

where ρ = (ρ_x ρ_x )^1/2 and V = kρn _core(2Δ)^1/2.

In Fig. 1(b), we plot the GVD for the fundamental mode of the MS fiber with an unperturbed, circular core with the radius ρ = (ρ_x ρ_x )^1/2 ≈ 0.89 μm (curve 1) along with the GVD for the slow (curve 2) and fast (curves 3, 4) modes in a birefringent fiber calculated with the use of Eqs. (3) and (4) as a function of the radiation wavelength λ around the zero-GVD point. The zero-GVD point for the guided mode polarized along the fast axis, as can be seen from the results presented in Fig. 1(b), is blue-shifted with respect to the zero-GVD point for the mode polarized along the slow axis. Both models of modal birefringence used in our calculations predict the shift of the zero-GVD point of approximately 8 nm (cf. curves 3 and 4 in Fig. 1(b)) as we switch from one of the MS-fiber eigenmodes to the other. This GVD shift, as will be shown in the next section, is sufficient to switch the frequency of the anti-Stokes signal, generated by unamplified 820-nm femtosecond pump pulses, by 20 - 30 nm, showing that birefringent MS fibers are ideally suited as sources of tunable radiation in the visible range.

3. Experimental

The femtosecond laser system used in our experiments was based on an Ar-laser-pumped self-starting femtosecond laser with a SESAM. This laser generated 35-fs pulses of radiation with a central wavelength of 820 nm and an energy up to approximately 10 nJ at a pulse repetition rate of 100 MHz. These laser pulses were transmitted through an optical isolator and were coupled by a micro-objective into the core of an MS fiber sample (Fig. 1(a)) with a length of 5 - 50 cm, placed on a three-dimensional translation stage. Radiation coming out of the fiber was collimated with an identical micro-objective and was split into two beams. One of these beams was delivered to a spectrograph, while the other one was used to visualize the transverse intensity distribution in the emission coming out of the microstructure fiber by imaging the output end of the fiber onto a CCD camera.

Propagation of unamplified Ti: sapphire-laser pulses through the MS fiber was accompanied by nonlinear-optical effects, leading to the spectral broadening of the pump and generation of new spectral components (Figs. 2, 3). Spectra of radiation measured at the output of the MS fiber with different energies of input pump pulses (Fig. 2(a)) indicate spectral transformation features characteristic of soliton effects [16 - 19]. In particular, signatures of self-frequency-shifted solitons are observed in the spectra of radiation measured at the output of a 30-cm MS fiber (see Fig. 2(a)). These solitons are produced by pump pulses propagating through the fiber in the regime of anomalous dispersion and are red-shifted apparently due to the predominant Raman amplification of the long-wavelength part of their spectrum. These solitons can lose some of their energy as they become coupled to wavenumber-matched dispersive waves [16], giving rise to frequency-shifted radiation [17, 19]. Starting with the average power of input pulses of about 320 mW, these solitonic effects along with wave-mixing processes resulted in the generation of broadband emission at the output of the fiber with a spectrum spanning from 400 up to 1200 nm (Fig. 2(b)). This scenario of supercontinuum generation has been studied in detail in earlier work and has been described in the extensive literature [17, 19].

 

Fig. 2. (a) The spectra of radiation at the output of the microstructure fiber with a length of 30 cm measured for different input powers of 35-fs 820-nm pump pulses: (1) 30 mW, (2) 50 mW, (3) 70 mW, and (4) 100 mW. (b) The spectrum of supercontinuum emission produced by 820-nm pump pulses with an initial duration of 35 fs and an input power of 320 mW in a microstructure fiber with a length of 30 cm and the cross-section structure shown in Fig. 1(a).

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Fig. 3. Generation of anti-Stokes line emission in a 10-cm MS fiber by 820-nm pump pulses with an initial duration of 35 fs polarized along (1) the fast and (2) the slow axes of the fiber core. The average power of pump radiation is (a) 100 mW and (b) 200 mW.

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We focus here on the possibility to use the birefringence of MS fibers to tune the intense anti-Stokes line generated in the frequency range of 480 - 520 nm as a part of the above-described spectral transformation of femtosecond pulses. This blue-shifted signal, observed also in earlier experiments with MS fibers [20, 21], has been previously employed for photochemical [22] and spectroscopic [23] applications. Our experiments show (Figs. 3(a), 3(b)) that the frequency of this anti-Stoke signal can be switched by coupling the linearly polarized pump pulse into orthogonal-polarized modes of a birefringent MS fiber. Unamplified Ti: sapphire laser pulses with an initial pulse duration of about 35 fs polarized along the fast axis of the elliptical fiber core efficiently generate an anti-Stokes signal centered at 490 nm (curves 1 in Figs. 3(a), 3(b)). When linearly polarized pump pulses with identical parameters are coupled into the slow mode of our MS fiber, we observe the generation of an anti-Stokes signal centered at 510╍520 nm (curves 2 in Figs. 3(a), 3(b)). This switching of the central frequency of the anti-Stokes signal is correlated with the change in the zero-GVD wavelength, which gets blue-shifted by 8 nm as the polarization of the pump field is rotated by 90° with respect to the slow axis and is coupled to the fast mode of the MS fiber. The frequency switching of the anti-Stokes signal is easily observed on a white screen as a change in the color of bright emission coming out of the fiber (Figs. 4(a), 4(b)). Femtosecond pump pulses with field polarization set to excite a combination of modes in the birefringent MS fiber allow the generation of a set of anti-Stokes lines, with the amplitude ratios of these lines controlled by the angle between the pump field and the slow axis of the fiber core. With the input pump field coupled into the fundamental mode of the MS fiber and polarized along its slow and fast axes, it was possible to achieve respectively 15% and 12% efficiency of pump energy conversion to the anti-Stokes component predominantly (no less than 90%) emitted in the fundamental mode. Frequency conversion efficiency up to 20% was achieved for the anti-Stokes signal emitted into a mixture of the fundamental and higher order (TE₀₁- and HE₂₁-like) guided modes.

 

Fig. 4. Anti-Stokes emission produced in the MS fiber by 820-nm pump pulses with an initial duration of 35 fs polarized along (a) the fast and (b) the slow axes of the fiber core.

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4. Conclusion

Experiments presented in this paper demonstrate that MS fibers with a specially designed birefringence offer the ways to create efficient frequency-tunable sources of short pulses in the visible range. We have shown that birefringent MS fibers allow a highly efficient generation of frequency-tunable anti-Stokes line emission as a result of nonlinear-optical spectral transformation of unamplified femtosecond Ti: sapphire laser pulses. We used femtosecond pulses of 820-nm pump radiation polarized along the fast and slow axes of the elliptical core of a fused silica MS fiber to generate intense blue-shifted lines centered at 490 and 510 nm, respectively, observed as bright blue and green emission at the output of a 10-cm microstructure fiber. The proposed method of frequency conversion of ultrashort pulses using birefringent MS fibers can enhance the capabilities of unamplified femtosecond laser pulses, extending their applicability range to ultrafast spectroscopy, time-resolved measurements, photochemistry, and photobiology.