Birefringent photonic-crystal fibers provide efficient polarization-sensitive anti-Stokes frequency conversion of unamplified 35-fs Ti: sapphire laser pulses, giving rise to a doublet of intense blue-shifted emission spectral lines centered at 490 and 510 nm. We show that this anti-Stokes doublet can be wavelength-demultiplexed by a polarization-separating prism. Generation of the 510-nm signal is decoupled from frequency conversion to 490 nm by accurately polarizing the pump field along one of the principal axes of the elliptically deformed fiber core.
©2005 Optical Society of America
Photonic-crystal fibers (PCFs)  radically enhance nonlinear-optical spectral transformations of ultrashort pulses, allowing creation of novel fiber-optic broadband light sources  and efficient frequency shifters . Such PCF components are extensively used in many areas of ultrafast science, giving an excess to the carrier--envelope phase , allowing the generation of stabilized frequency combs for optical metrology and femtosecond clockwork , permitting creation of novel optical coherence tomographs  and generators of correlated photons , improving the performance of nonlinear spectrographs  and microscopes  based on coherent anti-Stokes Raman scattering, and expanding the applicability range of femtosecond laser sources to photochemistry and photobiology .
The remarkable structure flexibility of PCFs suggests interesting strategies for the design of fibers with a high modal birefringence [11–13]. Birefringent PCFs allow efficient polarization control of nonlinear phenomena, including supercontinuum generation [14, 15], four-wave mixing , and emission of frequency-shifting solitons , suggesting the ways of creating polarization-controlled frequency converters of ultrashort laser pulses  and sources of amplitude-squeezed light [19, 20].
In this work, we show that birefringent PCFs provide efficient polarization-sensitive anti-Stokes frequency conversion of unamplified femtosecond Ti: sapphire laser pulses, giving rise to a doublet of intense blue-shifted signals whose spectra are centered at 490 and 510 nm. Methods of polarization optics will be used for the wavelength-demultiplexing this two-color anti-Stokes PCF output. We will show that the generation of the 510-nm signal can be decoupled from frequency conversion to 490 nm by accurately polarizing the pump field along one of the principal axes of the elliptically deformed fiber core.
2. Birefringent PCFs and the laser system
Photonic-crystal fibers were fabricated of fused silica with the use of the standard technology, described in detail elsewhere . An SEM image of the fiber cut is shown in the inset to Fig. 1(a). An elliptically deformed core of this MS fiber with semiaxis sizes ρx ≈ 2.0 μm and ρy ≈ 1.6 μm, measured along its long (x) and short (y) axes, gives rise to form birefringence, removing the degeneracy from the doublet of fundamental fiber modes. The modes of this doublet polarized along the x- and y-axes of the PCF core have different propagation constants, βx = β 0 + δβx and βy = β 0 + δβy, where β 0 is the propagation constant of the doublet of degenerate fundamental modes in the unperturbed fiber with an ideally circular core and δβx and δβy are the birefringence-induced corrections to the propagation constant for the modes polarized along the long and short axes of the ellipse approximating the fiber core, respectively.
Because of form anisotropy of the fiber, the group-velocity dispersion (GVD) for the doublet of fundamental PCF modes passes through zero at different wavelengths (Fig. 1(a)), offering the way to control nonlinear-optical interactions of ultrashort laser pulses. In particular, as shown in earlier work , birefringent PCFs can serve as efficient frequency converters, providing a two-color anti-Stokes-shifted output with central frequencies of blue-shifted radiation controlled by dispersion profiles of the doublet of fundamental modes. Here we show that this two-color output of a birefringent PCF (Fig. 1(b)) can be conveniently demultiplexed by means of polarization optics.
The femtosecond laser system used in our experiments (Fig. 2) was based on an Ar-laser-pumped Ti: sapphire laser, which generated 30-fs pulses of radiation with a central wavelength of 810 nm and an energy up to approximately 10 nJ at a pulse repetition rate of 100 MHz. An optical isolator served to protect the laser oscillator from radiation backreflected from the focusing optics and the fiber. A 40x lens was used to couple laser radiation into a PCF with a length of 30 cm, placed on a three-dimensional translation stage. Radiation coming out of the fiber was collimated with an identical lens. Ando spectrum analyzers were used to measure the spectra of radiation at the input and at the output of the PCF. To spatially separate radiation components with orthogonal polarizations, a Glan--Taylor prism polarization analyzer was inserted in the output beam (Fig. 2), enabling polarization-selective spectral and intensity-profile measurements on the blue-shifted output of the PCF.
3. Results and discussion
We start with polarization-nonsensitive measurements, performed with no polarization-selective prism in the output beam and with no polarization control of the input field. Figure 1(b) presents a typical polarization-nonselective spectrum of PCF output generated by 810-nm Ti: sapphire laser pulses with an initial pulse width of 35 fs and an input energy of about 5 nJ. The central wavelength of input laser radiation, as can be seen from Fig. 1(a), falls within the range of anomalous dispersion for the doublet of fundamental PCF modes. The pump field therefore tends to form solitons, which become red-shifted as they propagate through the fiber due to the Raman effect . Spectral features representing these red-shifted solitary waves are clearly seen in the output spectrum presented in Fig. 1(b).
High-order dispersion induces wave-matching resonances between solitons and dispersive waves, giving rise to intense blue-shifted emission in the PCF output spectra [22, 23]. For low pump field powers, the generic wave-matching condition for such soliton--dispersive wave resonances is written as [22, 23] Ω = 1/2ε, where Ω is the frequency difference between the soliton and the resonant dispersive wave and ε is the parameter controlling the smallness of perturbation of the nonlinear Schrödinger equation, which can be represented as  ε = |β 3/6β 2| for PCFs with second-order dispersion β 2 = ∂ 2 β/∂ω 2 and third-order dispersion β 3 = ∂ 3 β/∂ω 3. We now use the above arguments to estimate typical frequency shifts Ω for birefringent PCFs used in our experiments. With β 2 ≈ 420 fs2/cm and β 3 ≈ 1370 fs3/cm at 810 nm for the x-polarized mode, we arrive at the wavelength shift |δλ| = (λ 2Ω)/(2πc) ≈ 320 nm. Similarly, for the y-polarized mode, we have β 2 ≈; 380 fs2/cm and β 3 ≈ 1320 fs3/cm, yielding |δλ| = (λ 2Ω)/(2πc) ≈ 300 nm. Starting with the average power of input pulses of about 320 mW, dispersive waves along with red-shifted solitons, complemented by 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. This scenario of supercontinuum generation has been studied in detail in earlier work and has been described in the extensive literature [25, 26]. We focus here on the intense anti-Stokes line generated in the frequency range of 480 – 520 nm (Fig. 1(b)) as a part of the above-described nonlinear-optical spectral transformation of femtosecond pulses in the PCF. This blue-shifted signal, observed also in earlier experiments with PCFs , has been previously employed for photochemical  and spectroscopic  applications. Our earlier experiments have shown  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 PCF.
With a Glan--Taylor prism inserted into the output beam, we can spatially separate two orthogonal-polarized components in the PCF output and analyze their spectra as functions of the polarization of the input field. The results of these measurements are presented in Figs. 3(a) – 3(f). In Figs. 3(a) and 3(b), the pump field is polarized along the short axis of the PCF core. Two polarization components in the PCF output, spatially separated with the Glan--Taylor polarization analyzer, are observed as two green spots of different brightness on a screen (the inset in Fig. 3(b)). The beam corresponding to the y-polarized component of the PCF output is much brighter than the radiation with the orthogonal polarization. The anti-Stokes part of the spectrum is dominated by a peak centered at 510 nm. For the y-polarized component (Fig. 3(a)), the amplitude of this peak is approximately 5 times higher than for the orthogonal polarization (Fig. 3(b)).
Similar tendencies are observed when the pump field is oriented along the long axis of the PCF core. In this case, the anti-Stokes part of PCF output is dominated by the 490-nm spectral peak (Figs. 3(c), 3(d)). The polarization-selective prism gives two differently colored spots on a screen in this case. The beam corresponding to x-polarized radiation is observed as a bright blue spot, while the spot corresponding to the orthogonal polarization has no blue color at all (the inset to Fig. 3(d)). Spectral analysis of these two polarization components of the PCF output shows that the amplitude of the 490-nm line in x- polarized radiation (Fig. 3(d)) is at least three orders of magnitude higher than the amplitude of this line for the orthogonal polarization (Fig. 3(c)). This result shows that the generation of the 510-nm signal can be efficiently decoupled from frequency conversion to 490 nm by accurately polarizing the pump field along the principal axis of the PCF core.
Orienting the input field at an angle of 45° with respect to the principal axes of the PCF core, we couple the pump into both modes of the fundamental doublet. Both 490- and 510-nm emission lines are then generated in the fiber, in agreement with our expectations based on the qualitative analysis of resonant frequencies of soliton instabilities. The Glan--Taylor prism then efficiently separates the blue (490-nm) and green (510-nm) beams, as can be seen from the inset to Fig. 3(f) and from the spectra presented in Figs. 3(e) and 3(f), showing that the 490- and 510-nm signals are predominantly polarized along the y- and x-axes. These signals are thus demultiplexed with a polarization-separating prism as orthogonal polarizations in PCF output. This polarization arrangement demonstrates two-color frequency conversion in eigenmodes of a birefringent PCF with a high-contrast polarization demultiplexing.
We have demonstrated that birefringent PCFs can provide efficient polarization-sensitive anti-Stokes frequency conversion of unamplified femtosecond laser pulses, giving rise to doublets of intense blue-shifted emission lines. These anti-Stokes doublets can be wavelength-demultiplexed by polarization-separating prisms, giving rise to two spatially separated single-color beams. Such polarization-demultiplexed two-color frequency conversion has been demonstrated in our experiments for 35-fs pulses of a Ti: sapphire laser, generating a doublet of blue-shifted spectral lines centered at 490 and 510 nm through nonlinear-optical spectral transformation in eigenmodes of a birefringent PCF.
We are grateful to E.E. Serebryannikov for useful discussions and Yu.N. Kondrat’ev, V.S. Shevandin, K.V. Dukel’skii, and A.V. Khokhlov for the fabrication of fiber samples. This study was supported in part by the President of Russian Federation Grant MD-42.2003.02, the Russian Foundation for Basic Research (projects nos. 03-02-16929, 03-02-20002-BNTS, 04-02-39002-GFEN2004, and 04-02-81036-Bel2004), INTAS (projects nos. 03-51-5037 and 03-51-5288), the US Civilian Research and Development Foundation for the Independent States of the Former Soviet Union (award no. RP2-2558), National Key Basic Research Special Foundation (project no. 2003CB314904), National Nature Science Foundation of China (project no. 60278003), and National High-Technology Program of China (project no. 2003AA311010).
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