A highly birefringent silicate glass photonic-crystal fiber (PCF) is employed for polarization-controlled nonlinear-optical frequency conversion of femtosecond Cr: forsterite laser pulses with a central wavelength of 1.24 μm to the 530╍720-nm wavelength range through soliton dispersion-wave emission. The fiber exhibits a modal birefringence of 1.2·10-3 at the wavelength of 1.24 μm due to a strong form anisotropy of its core, allowing polarization switching of the central wavelength of its blue-shifted output by 75 nm. Polarization properties and the beam quality of the blue-shifted PCF output are shown to be ideally suited for polarization-sensitive nonlinear Raman microspectroscopy.
©2006 Optical Society of America
Birefringence in optical fibers helps to maintain polarization of guided modes , allowing the creation of optical gyroscopes, laser interferometers, and other practical fiber-optic devices and components . Fiber birefringence is often used to phase-match nonlinear-optical interactions of fiber modes for the efficient frequency conversion of laser radiation , realization of quantum-optic protocols , and photon entanglement generation . The degeneracy of guided modes in birefringent fibers is removed by breaking the cylindrical symmetry of the fiber structure. Standard technologies of birefringent fiber fabrication  are based on the form anisotropy, which can be induced by making the fiber core or cladding elliptical in shape and/or inserting rods of another material (often borosilicate glass) on the opposite sides of the fiber core  (PANDA, or bow-tie fibers).
Photonic-crystal fiber (PCF) technologies [6, 7] offer a remarkably rich diversity of core–cladding configurations, suggesting new interesting possibilities for mode birefringence engineering [8 – 10]. In nonlinear optics, birefringent PCFs allow efficient polarization control of supercontinuum generation [11–13], four-wave mixing , and soliton wavelength conversion . The vectorial nature of nonlinear-optical interactions in birefringent PCFs allows the creation of PCF-based polarization-demultiplexed supercontinuum sources and frequency converters [16, 17]. Birefringent PCFs have been recently employed to create interesting new types of fiber lasers , polarization splitters , and sources of amplitude-squeezed light [20, 21]. PCFs with subwavelength noncircular cores and a high core╍cladding refractive-index steps have been shown  to provide limiting values of form birefringence in fiber structures at the level defined by the trade-off between diffraction and step-index field confinement.
In this work, we use a highly birefringent silicate glass PCF with a birefringence of 1.2·10-3 for nonlinear-optical frequency conversion of femtosecond Cr: forsterite laser pulses with a central wavelength of 1.24 μm to the visible range through soliton dispersion-wave emission. These experiments show that polarization-controlled vectorial soliton dynamics in the silicate glass birefringent PCF allows a 75-nm shift in the central wavelength of dispersive-wave PCF output to be achieved by launching linearly polarized Cr: forsterite laser pulses into orthogonal polarization fiber modes.
2. Birefringent silicate glass photonic-crystal fiber
Birefringent PCFs used in our experiments (Fig. 1) were fabricated of sodium-calcium silicate SK222 glass, which was made at the Institute of Electronic Materials Technology in Warsaw and which includes 68.4% of SiO2, 2.4% of Al2O3, 2% of B2O3, 12.3% of Na2O, 0.7% of K2O, 7.1% of CaO, and 7.1% of ZnO. Glasses with such a composition tend to exhibit a higher nonlinearity (up to a factor of 2) than fused silica. Figure 2(a) presents the wavelength dependence of the refractive index for this glass, defined by fitting the available experimental data (dots) with the Sellmeier equation (the solid line) .
PCFs were fabricated using a standard stack-and-draw technique [6, 7]. In the first stage of this procedure , glass capillaries (rods) are stacked together into a desired structure. This array is then drawn down to a subpreform. In the second stage, the subpreform produced in the first stage of the process is inserted into a larger-inner-diameter glass tube, and the whole structure is drawn to produce the PCF. The resulting fiber had a noncircular core with two well-defined nearly orthogonal principal axes, whose lengths were equal to 2 and 8 μm (Fig. 1). Dispersion and birefringence properties of silicate glass PCFs were calculated using both the finite-element method (FEM)  and biorthonormal basis method . A noncircular core of PCFs used in our experiments gives rise to form birefringence, removing the degeneracy from the doublet of orthogonal-polarized fundamental fiber modes. As a result, the mode indices nx,y = βx,y /k 0 (βx,y are the propagation constants of the orthogonal-polarized modes and k 0 = 2π/λ is the wave number of radiation with a wavelength λ) for these modes differ by B = |nx - ny| ≈ 1.2·10-3 at λ = 1.24 μm. The fiber loss at this wavelength was estimated as 15 dB/m and was largely due to the loss in glass (12 dB/m). The effective mode area of 8.5 μm2 at λ = 1.24 μm corresponded to the nonlinear coefficient γ ≈ 25 W-1km-1, which is a factor of 1.3-1.9 higher than the nonlinearity of a silica fiber structure with the same mode area. The fiber remained multimode at λ = 1.24 μm; however, both the pump laser radiation and the blue-shifted field were robustly guided in the fundamental mode. The group-velocity dispersion (GVD) for the orthogonal-polarized fundamental modes passes through zero at different wavelengths (1035 and 1075 nm, Fig. 2(b). We show in the following sections of this paper that vectorial nonlinear-optical processes can map this zero-GVD-wavelength shift onto the shift in the central wavelength of the frequency-upconverted PCF output, allowing the wavelength switching by 75 nm by rotating polarization of the input laser field.
3. The laser setup
The laser system used in our experiments consisted of a Cr4+:forsterite master oscillator, a stretcher, an optical isolator, a regenerative amplifier, and a compressor . The master oscillator, pumped with a fiber ytterbium laser, generated 30 - 50-fs light pulses of radiation with a wavelength of 1.23-1.25 μm at a repetition rate of 120 MHz. These pulses were then transmitted through a stretcher and an isolator to be amplified in a Nd: YLF-laser-pumped amplifier and recompressed to the 100-fs pulse duration with the maximum laser pulse energy up to 40 μJ at 1 kHz. These pulses were coupled into the fundamental mode of the silicate glass birefringent PCF with the use of standard micro-objectives.
4. Results and discussion
The central wavelength of the amplified 1.24-μm Cr: forsterite laser output falls within the range of anomalous dispersion for the both modes of the fundamental mode doublet in the high-B PCF used in our experiments. The laser pulses therefore tend to form solitons as they propagate through the fiber. Such solitons were clearly observed in PCF output spectra as isolated features in the range of wavelengths from 1.24 to 1.40 μm. In accordance with the standard scenario of nonlinear-optical transformation of short pulses in PCFs [28, 29], solitons generated by the input field undergo a continuous frequency down shift due to the Raman effect  and experience instabilities related to the third and higher order dispersion . For the dispersion profiles of guided modes in the PCF used in our experiments, these perturbations force solitons to emit radiation energy in the form of dispersive waves in the anti-Stokes region. The central wavelength of this blue-shifted emission is controlled by the soliton-dispersive wave, Cherenkov-type phase matching . The frequency of the blue-shifted PCF output can thus be switched by modifying the dispersion profile of the fiber.
With birefringent PCFs, this switching operation can be performed by varying polarization of the input laser field. A high birefringence of PCFs translates the difference in dispersion profiles of orthogonal-polarized PCF modes into large wavelength shifts of the anti-Stokes PCF output. In our experiments, by rotating polarization of the linearly polarized 100-fs 7-nJ Cr: forsterite laser pulses at the input of the PCF, we observed a shift in the central wavelength of the dispersive-wave emission at the output of the fiber from 575 to 650 nm (curves 1 and 2 in Fig. 3). In the upper panel of Fig. 3, we plot the mismatch δβ = βs (λ 0) - β(λd) of the propagation constant β(λd) of dispersive-wave emission at the wavelength λ d in one of the orthogonal-polarized modes of the fundamental PCF mode doublet and the propagation constant of the soliton βs (λ 0) centered at the pump wavelength λ 0= 1.24 μm. As can be seen from the comparison of the upper and lower panels of Fig. 3, the central wavelengths of blue-shifted emission bands observed at the output of the PCF correlate well with the wavelengths where dispersive waves guided in the orthogonal-polarized modes of the fundamental PCF mode doublet are phase-matched with the soliton produced by Cr: forsterite laser pulses. For an 8-cm-long piece of PCF, the maximum energy of the 575- and 650-nm PCF output was estimated as 70 and 90 pJ, corresponding to the energy conversion efficiencies of 1.0 and 1.3%, respectively. The energies of both spectral components at the output of the fiber display a monotonic growth as functions of the fiber length, saturating for a fiber length of about 10 cm. With special precautions made to stabilize the laser pulse parameters, the drift of the output energy of the blue-shifted PCF output within 2 hours of operation did not exceed 10%.
By orienting the input laser field at an angle of 45° with respect to the principal axes of the PCF core, we were able to couple the laser field into a combination of orthogonal-polarized PCF modes. With such a polarization arrangement, spectral peaks corresponding to dispersive-wave emission in both PCF modes were observed in the fiber output. As the energy of 100-fs laser pulses was increased up to 16 nJ, the spectral components corresponding to the orthogonal-polarized PCF modes merged together, leading to the generation of broadband radiation at the output of the fiber (curve 3 in Fig. 3).
With this work largely motivated by the idea of creating compact PCF sources for nonlinear Raman microspectroscopy [31–33], of special value is the demonstrated wavelength tunability of the PCF output around the central wavelength of the second harmonic of Cr: forsterite laser radiation (λ SH ≈ 620 nm, shown by a vertical dashed line in Fig. 3). Our experimental results presented in Fig. 4 demonstrate that the highly birefringent silicate glass PCF pumped with femtosecond pulses of 1.24-μm Cr: forsterite laser radiation can generate blue-shifted radiation, providing an access to the 700-1500-cm-1 fingerprint region of Raman transitions in molecules of biological significance. Moreover, this PCF can serve as a source of either Stokes or pump radiation in nonlinear Raman microspectroscopy as its output can be either blue- or red-shifted with respect to λ SH (see Fig. 3), depending on the polarization of the input laser field. Since the blue-shifted PCF output is intended for the use in CARS microspectroscopy along with a much more powerful fixed-frequency second-harmonic field of a Cr: forsterite laser, the energy level of the frequency-shifted radiation achieved in our experiments should be sufficient for this application.
To demonstrate the suitability of the polarization-controlled blue-shifted output of the high-B silicate glass PCF for high-spatial-resolution, high-spectral-contrast nonlinear Raman microspectroscopy, we measured the transverse field-intensity profile and examined polarization properties of the 650-nm emission band in the fiber output. The far-field beam pattern of the 650-nm PCF output (see the inset in Fig. 3) indicates that nonlinear-optical frequency conversion is well-localized in the fiber core, giving rise to a smooth, high-quality output beam. Using a high-numerical-aperture micro-objective, we could easily focus this beam into a spot with a diameter of 0.9 μm. Polarization measurements performed with the use of a polarization analyzer placed behind the output end of the PCF show that the 650-nm emission band in the PCF output is predominantly linearly polarized. To measure the depolarization ratio for this band, we first adjusted the polarization analyzer in such a way as to provide minimum transmission for the PCF output, I min. We then rotated the analyzer to achieve maximum transmission, I max. The ratio I min/I max was estimated as 0.08 in these experiments, suggesting that the PCF output is ideally suited for polarization-sensitive nonlinear Raman spectroscopy and microscopy.
We have demonstrated that a highly birefringent PCF pumped with near-infrared femtosecond laser pulses can serve as a radiation source in the visible with polarization-controlled output spectrum. For a silicate glass PCFs used in our experiments, a strong form anisotropy of the fiber core gives rise to a modal birefringence of 1.2·10-3. The zero-GVD wavelengths for the fundamental doublet of orthogonal-polarized modes in this PCF are separated by nearly 40 nm. Vectorial nonlinear-optical processes interactions in the birefringent PCF translate this zero-GVD-wavelength difference into the shift of the central wavelengths of dispersive-wave radiation emitted by orthogonal-polarized solitons. This effect allows the blue-shifted PCF output to be switched by approximately 75 nm by rotating polarization of the input laser field. The suitability of this polarization-controlled blue-shifted PCF output for high-spatial-resolution, high-spectral-contrast nonlinear Raman microspectroscopy has been demonstrated.
We thank Przemyslaw Szarniak (Institute of Electronic Materials Technology, Poland) for his contribution to the development of the fibers used in the experiment. This study was performed as a part of the European Science Foundation COST P11 action. AVM, YML, AAI, AAB, and AMZ acknowledge a partial support of their research by the Russian Foundation for Basic Research (projects 06-02-16880, 04-02-39002-GFEN2004, and 05-02-90566-NNS), the Russian Federal Research and Technology Program (contract no. 02.434.11.2010), INTAS (projects nos. 03-51-5037 and 03-51-5288), and CRDF (Award no. RUP2-2695). RB and DP acknowledge the support by research grant 3 T11B 053 28 of the Polish Committee of Scientific Research. IB and DL acknowledge the support by research grant VEGA1/2018/05.
References and links
1. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, New York, 1983).
2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989).
3. S. Schmitt, J. Ficker, M. Wolff, F. König, A. Sizmann, and G. Leuchs, “Photon-number squeezed solitons from an asymmetric fiber-optic Sagnac interferometer,” Phys. Rev. Lett. 81, 2446–1449 (1998). [CrossRef]
4. Ch. Silberhorn, P. K. Lam, O. Wei., F. König, N. Korolkova, and G. Leuchs, “Generation of continuous variable Einstein-Podolsky-Rosen entanglement via the Kerr nonlinearity in an optical fiber,” Phys. Rev. Lett. 86, 4267–4270 (2001). [CrossRef] [PubMed]
5. K.-H. Tsai, K.-S. Kim, and T. F. Morse, “General solution for stress-induced polarization in optical fibers,” J. Lightwave Technol. 9, 7–17 (1991). [CrossRef]
8. A. Ortigosa-Blanch, J. C. Knight, W. J. Wadsworth, J. Arriaga, B. J. Mangan, T. A. Birks, and P. St. J. Russell, “Highly birefringent photonic crystal fibers,” Opt. Lett. 25, 1325–1327 (2000). [CrossRef]
9. M. J. Steel and J. R. M. Osgood, “Elliptical-hole photonic crystal fibers,” Opt. Lett. 26, 229–231 (2001). [CrossRef]
10. T. P. Hansen, J. Broeng, S. E. B. Libori, E. Knudsen, A. Bjarklev, J. R. Jensen, and H. Simonsen, “Highly birefringent index-guiding photonic crystal fibers,” IEEE Photon. Technol. Lett. 13, 588–590 (2001). [CrossRef]
11. A. Ortigosa-Blanch, J. C. Knight, and P. St. J. Russell, “Pulse breaking and supercontinuum generation with 200-fs pump pulses in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 2567 (2002). [CrossRef]
12. A. Apolonski, B. Povazay, A. Unterhuber, W. Drexler, W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Spectral shaping of a supercontinuum in a cobweb photonic- crystal fiber with sub-20-fs pulses,” J. Opt. Soc. Am. B 19, 2165 (2002). [CrossRef]
13. M. Lehtonen, G. Genty, H. Ludvigsen, and M. Kaivola, “Supercontinuum generation in a highly birefringent microstructured fiber,” Appl. Phys. Lett. 82, 2197–2199 (2003). [CrossRef]
14. M. Hu, C. Y. Wang, L. Chai, and A. Zheltikov, “Frequency-tunable anti-Stokes line emission by eigenmodes of a birefringent microstructure fiber,” Opt. Express 12, 1932–1937 (2004). [CrossRef] [PubMed]
15. A. A. Ivanov, M. V. Alfimov, A. M. Zheltikov, M. Szpulak, W. Urbanczyk, and J. Wójcik, “Polarization-controlled vectorial spectral transformations of femtosecond pulses in a birefringent photonic-crystal fiber,” J. Opt. Soc. Am. B 23, 986–991 (2006). [CrossRef]
16. M. Hu, C. Wang, Y. Li, L. Chai, and A. M. Zheltikov, “Polarization-demultiplexed two-color frequency conversion of femtosecond pulses in birefringent photonic-crystal fibers,” Opt. Express 13, 5947–5952 (2005). [CrossRef] [PubMed]
17. M. -L. Hu, C. -Y. Wang, Y. -J. Song, Y. -F. Li, L. Chai, E. Serebryannikov, and A. Zheltikov, “Mode-selective mapping and control of vectorial nonlinear-optical processes in multimode photonic-crystal fibers,” Opt. Express 14, 1189–1198 (2006). [CrossRef] [PubMed]
18. K. Suzuki, H. Kubota, S. Kawanishi, M. Tanaka, and M. Fujita, “Optical properties of a low-loss polarization-maintaining photonic crystal fiber,” Opt. Express 9, 676–680 (2001). [CrossRef] [PubMed]
20. M. Fiorentino, J. E. Sharping, P. Kumar, A. Porzio, and R. S. Windeler, “Soliton squeezing in microstructure fiber,” Opt. Lett. 27, 649–651 (2002). [CrossRef]
21. M. Fiorentino, J. E. Sharping, P. Kumar, and A. Porzio, “Amplitude squeezing in a Mach-Zehnder interferometer: numerical analysis of experiments with microstructure fiber,” Opt. Express 10, 128–138 (2002). [PubMed]
22. A. M. Zheltikov, “Birefringence of guided modes in photonic wires: Gaussian-mode analysis,” Opt. Commun. 252, 78–83 (2005). [CrossRef]
23. P. Szarniak, M. Foroni, R. Buczynski, D. Pysz, P. Wasylczyk, P. Gaboardi, F. Poli, A. Cucinotta, S. Selleri, and R. Stępien, “Nonlinear photonic crystal fiber with high birefringence made of silicate glass,” in Photonic Crystal Materials and Devices III (i.e. V), R. M. De La Rue, P. Viktorovitch, C. Lopez, and M. Midrio, eds., Proc. SPIE 6182, 618220, (2006).
24. D. Pysz, R. Stępien, P. Szarniak, R. Buczynski, and T. Szoplik, “Highly birefringent photonic crystal fibers with a square lattice,” in Lightguides and their Applications II, J. Wojcik and W. Wojcik, eds., Proc. SPIE 5576, 81–87 (2004). [CrossRef]
25. A. Cucinotta, S. Selleri, L. Vincetti, and M. Zoboli, “Holey Fiber Analysis through the Finite-Element Method,” IEEE Photon. Technol. Lett. 14, 1530–1532 (2002). [CrossRef]
26. E. Silvestre, M. V. Andres, and P. Andres, “Biorthonormal-basis method for the vector description of optical-fiber modes,” J. Lightwave Technol. 16, 923–928 (1998). [CrossRef]
27. A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Femtosecond pulses in nanophotonics” Phys. Usp. 47, 687–704 (2004). [CrossRef]
28. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, and G. Korn,“Experimental Evidence for Supercontinuum Generation by Fission of Higher-Order Solitons in Photonic Fibers,” Phys. Rev. Lett. 88, 173901 (2002). [CrossRef] [PubMed]
29. W. J. Wadsworth, A. Ortigosa-Blanch, J. C. Knight, T. A. Birks, T. P. M. Mann, and P. St. J. Russell, “Supercontinuum generation in photonic crystal fibers and optical fiber tapers: a novel light source,” J. Opt. Soc. Am. B 19, 2148–2155 (2002). [CrossRef]
31. S. O. Konorov, D. A. Akimov, E. E. Serebryannikov, A. A. Ivanov, M. V. Alfimov, and A. M. Zheltikov, “Cross-correlation FROG CARS with frequency-converting photonic-crystal fibers,” Phys. Rev. E 70, 057601 (2004). [CrossRef]
32. H. N. Paulsen, K. M. Hilligsøe, J. Thøgersen, S. R. Keiding, and J. J. Larsen “Coherent anti-Stokes Raman scattering microscopy with a photonic crystal fiber based light source,” Opt. Lett. 28, 1123–1125 (2003). [CrossRef] [PubMed]
33. A. M. Zheltikov, “Nanoscale nonlinear optics in photonic-crystal fibres,” J. Opt. A: Pure Appl. Opt. 8, S47–S72 (2006). [CrossRef]