Supercontinuum generation in planar rib ... - OSA Publishing

Supercontinuum generation in planar rib waveguides enabled by anomalous dispersion O. Fedotova Institute of Solid State and Semiconductor Physics, Belarus National Academy of Sciences, P.Brovki str. 17, Minsk 220072, Belarus

A. Husakou, J. Herrmann Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Str. 2a, D-12489 Berlin, Germany [email protected]

Abstract: We predict and numerically study supercontinuum generation extending over almost two octaves in planar rib waveguides, with anomalous dispersion at the input wavelength provided by the waveguide contribution. Such planar nonlinear waveguides generating broadband coherent radiation can be intergrated with other components to constitute a building block in intergrated optical circuits. © 2006 Optical Society of America OCIS codes: (130.4310) Integrated Optics, Nonlinear; (190.5530) Nonlinear optics, Pulse propagation and solitons

References and links 1. J. K. Ranka, R. S. Windeler, and A. J. Stentz, ”Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 25-27 (2000). 2. A. Husakou and J. Herrmann, ”Supercontinuum generation of higher-order solitons by fission in photonic crystal fibers,” Phys. Rev. Lett. 87, 203901 (2001). 3. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, ”Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers,” Phys. Rev. Lett. 88, 173901 (2002). 4. A. Ortigosa-Blanch, J. C. Knight, and P. St. J. Russel, ”Pulse breaking and supercontinuum generation with 200-fs pump pulses in photonic crystal fibers,” J. Opt. Soc. Am. B 19, 2567-2572 (2002). 5. K. M. Hillingsoe, H. N. Paulsen, J. Thogersen, S. R. Keiding, and J. J. Larsen, ”Initial steps of supercontinuum generation in photonic crystal fibers,” J. Opt. Soc. Am. B 20, 1887-1893, (2003) 6. J. M. Dudley, L. Provino, N. Grossard, H. Maillotte, R. S. Windeler, B. J. Eggleton, and S. Coen, ”Supercontinuum generation in air-silica microstructured fibers with nanosecond and femtosecond pulse pumping,” J. Opt. Soc. Am. B 19, 765-771 (2002). 7. A. Husakou and J. Herrmann, ”Supercontinuum generation in photonic crystal fibers made from highly nonlinear glasses,” Appl. Phys. B 77, 227-234 (2003). 8. K. M. Hilligsoe, T. V. Andersen, H. N. Paulsen, C. K. Nielsen, K. Molmer, S. Keiding, R. Kristiansen, K. P. Hansen, and J. J. Larsen, ”Supercontinuum generation in a photonic crystal fibers with two zero dispersion wavelengths,” Opt. Express 12, 1045-1054 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-6-1045. 9. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, ”Fundamental noise limitations to supercontinuum generation in microstructure fibers,” Phys. Rev. Lett. 90, 113904 (2003). 10. T. Udem, R. Holzwarth, and T. W. H¨ansch, ”Optical frequency metrology,” Nature 416, 233-237 (2002). 11. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, ”Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure fiber,” Opt. Lett. 26, 608-610 (2001).

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Received 20 December 2005; revised 26 January 2006; accepted 5 February 2006

20 February 2006 / Vol. 14, No. 4 / OPTICS EXPRESS 1512

12. A. Bassi, J. Swartling, C. D’Andrea, A. Pifferi, A. Torricelli, and R. Cubeddu, ”Time-resolved spectrophotometer for turbid media based on supercontinuum generation in a photonic crystal fiber,” Opt. Lett. 29, 2405-2407 (2004). 13. See special issues JOSA B 19 issue 9, Appl. Phys. B 77 issue 2-3, and P. St. J. Russel, Science 299, 358 (2003). 14. H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, and M. Paniccia, ”An all-silicon Raman laser,” Nature 433, 292-294 (2005). 15. V. R. Almelda, C. A. Barrlos, R. R. Papenucci, and M. Lipson, ”All-optical control of light on a silicon chip,” Nature 431, 1081-1084 (2004). 16. O. Boyraz, T. Indukuri, and B. Jalali, ”Self-phase-modulation induced spectral broadening in silicon waveguides,” Opt. Express 12, 829-834 (2004),http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-5-829. 17. S. Spalter, H. Y. Hwang, J. Zimmermann, G. Lenz, T. Katsufuji, S-W. Cheong, and R.E. Slusher, ”Strong selfphase modulation in planar chalcogenide glass waveguide,” Opt. Lett. 27, 363-365 (2002). 18. Y. Ruan, W. Li, R. Jarvis, N. Madsen, A. Rode, and B. Luther-Davies, ”Fabrication and characterization of low loss rib chalcogenide waveguides made by dry etching,” Opt. Express 12, 5140-5145 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5140. 19. M. J. Adams, An introduction to optical waveguides (John Wiley and Sons, Chichester-New York-BrisbaneToronto, 1981). 20. Handbook of Optics, M. Bass (ed.) (McGRAW-HILL, New York, 1995).

Many applications in scientific research, engineering, optical communication and medicine require coherent optical sources of radiation with a wide spectral range, or supercontinuum (SC). The recent discovery of SC generation covering more than two octaves ocurring in microstructure fibers (MF) with nJ input pulses[1] encouraged tremendous research activities to explain the origin of this spectral broadening process[2, 3], to explore its properties in different ranges of parameters[4, 5, 6, 7, 8, 9], and to develop numerous applications in areas like frequency metrology[10], optical coherence tomography[11], absorption spectroscopy[12], and others (for an overview, see[13] and references therein). The SC generation in MF in the anomalous dispersion range is connected with the splitting of the input pulse into several fundamental solitons, which emit phase-matched non-solitonic radiation[2, 3]. The threshold of this highly efficient mechanism is significantly lower than for self-phase modulation or any other known spectral broadening process. The high application potential of SC sources based on MF rises the question whether this process can also be realized in other waveguide structures, such as planar rib waveguides. The fabrication and investigation of low-loss rib waveguides have been given much attention recently because of its application for photonic integrated circuits. In particular, nonlinear effects in silicon waveguides like Raman lasing in a waveguide cavity on a silicon chip[14], optical swithing[15], or self-phase-modulation induced spectral broadening[16] has been studied for silicon-based optoelectronic applications in integrated optics. Surprisingly, the possibility to achieve SC from planar rib waveguides has not attracted much effort. Up to now only very narrow spectra has been observed, e.g. a 20-nm spectrum from rib waveguides made from highly nonlinear chalcogenide glass based on self-phase modulation[17, 18]. In the present paper we study the perspective for generating supercontinuum spectra in planar rib waveguide structures based on radiation and fission of solitons. The anomalous dispersion region due to the waveguide contribution to dispersion is the critical condition of the soliton broadening process in MF. However, it is not a priori evident whether the waveguide contribution to dispersion due to spatial confinement of the field can enable this mechanism also in planar rib waveguides. First, it is not clear whether a broad region of anomalous dispersion in the optical range can be reached at all due to the existence of a cut-off which is absent in MF. Second, modification of dispersion in rib waveguides is quantitatively less significant than in MF; and third, typical materials used in integrated optics tend to have strong dispersion and/or no broadband transmission. We show that for specific glasses with low bulk group velocity dispersion (GVD) as waveguide material, and appropriate waveguide parameters the waveguide #10047 - $15.00 USD

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contribution to dispersion leads to a significant shift of the zero-GVD wavelength and anomalous dispersion in the visible range. This enables the spectral broadening mechanism of fission and radiation of solitons in a rib waveguide, similar as in MF. As a result of our study we predict that for certain waveguides and input pulse parameters a 2-octaves-broad supercontinuum can be achieved in a planar rib waveguide. The realization of a small-scale and reliable coherent light source with extremely broad spectra has the potential to find applications in various fields. Combined with a microchip laser as pump source[6], such SC source could be a basis for a compact low-cost microspectrometer for biochemical sensing and spectroscopy. Integrated with other components it could constitute a building block for integrated optical circuits. Depending on the requirements of applications, the supercontinuum can be used as a whole or after spectral reshaping by optical filtering or slicing. We consider a planar rib waveguide with a geometry as given in Fig. 1(a), consisting of a region above the ribbed layer (region I), a layer with rib (region II), and a substrate (region III), with refractive indices n I (ω ), nII (ω ), nIII (ω ). The z-independent structure consists of a layer with thickness f with a rib characterized by the width a and total thickness d. The refraction index difference between the neighboring layers in such structures can result in optical waveguiding, i.e. the fundamental mode is localized in the rib region. Waveguiding can be observed for n II (ω )2 > nI (ω )2 , nII (ω )2 > nIII (ω )2 , whereby any of the indices may be complex characterizing a metallic layer. x mode in a waveguide by the approximate effectiveWe describe the dispersion of the E 00 index approach[19]. In a first step, the effective refractive indices of the central part of the rib nd (ω ), and of the side parts of the structure n f (ω ), are determined, considering each part as an infinite in x direction asymmetric planar waveguide. The following implicit equation for the effective refractive indices n d, f (ω ) of the fundamental TE mode of the respective asymmetric planar waveguide is used[19]: 2π n2II (ω ) − n2d, f (ω ) = λ 2 2 n (ω ) − n2I (ω ) n (ω ) − n2III (ω ) −1 d, f −1 d, f tan + tan n2II (ω ) − n2d, f (ω ) n2II (ω ) − n2d, f (ω ) ld, f ×

(1)

where ld = d, l f = f and λ is the vacuum wavelength of the light. In a second step it is assumed that the effective refractive index n(ω ) of the waveguide is given by the effective n(ω ) of a symmetric planar three-layer waveguide with thickness a and refractive indices of the layers n f (ω ), nd (ω ), n f (ω ). It also can be found by solving the equation similar to (1) with n I (ω ) = nIII (ω ) = n f (ω ), nII (ω ) = nd (ω ), l = a, and the unknown is n(ω ) instead of n d, f (ω ). Though not exact, this model is sufficient to describe the waveguide contribution to dispersion for the considered structures. We have found two waveguide structures with layers of Air-TaFD5 glass-SiO 2 and Air-SiO2 -Ag (denotations correspond to regions I-II-III) which have a sufficient nonlinear suspectibility and a moderate bulk dispersion of the rib material. The explicit dependence of the bulk refractive indices on the wavelength is described by Sellmeyer formulas[20]. The modification of the GVD for the both cases is illustrated in Fig. 1 (b),(c) with structure parameters presented in the caption. Crucial GVD modification was established in the Air-TaFD5-SiO2 structure in comparison with the bulk GVD of TaFD5, resulting in a broad anomalous-GVD region in the visible and near IR [Fig. 1(b)] with two zero-GVD wavelengths at 1150 and 2075 nm. This broad region of anomalous dispersion is still far from the cutoff, which we estimate at above 4.5 μ m with our approximate model. Higher-order modes have cutoffs at approximately 1.5μ m or below and therefore high losses in the considered spectral #10047 - $15.00 USD

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4.0

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Fig. 1. Planar rib waveguide structure (a) and GVD in an Air-TaFD5-SiO2 (b) and an AirSiO2 -Ag (c) structure. In (b) and (c), both the bulk GVD of the central layer (dashed green curves) and the GVD of the guiding structure (solid red curves) are shown. The parameters are a = 4.0 μ m, d = 1.0 μ m, f = 0.5 μ m for (b) and a = 4.0 μ m, d = 0.5 μ m, f = 0.25 μ m for (c).

region, thus coupling to them can be neglected. For the Air-SiO 2 -Ag structure, no additional zeros of the GVD occur, but the zero-GVD wavelength is shifted to a shorter wavelength [Fig. 1(c)]. As it will be shown, this effect has a critical influence on the spectral broadening mechanism in the waveguide. The pulse evolution in the waveguide was simulated by the first-order propagation equation without slowly-varying envelope approximation and with account of dispersion to all orders, neglecting the back-propagating waves[2]: iω PNL (z, ω ) ∂ E(z, ω ) = iω [n(ω ) − ng]/c + ∂z 2n(ω )ε0 c

(2)

where E(z, ω ) is the Fourier transform of the electric field in the fundamental mode, n(ω ) is the effective refractive index of the waveguide determined as described above, c/n g is the velocity of the moving coordinate frame, and PNL (z, ω ) is the Fourier transform of the nonlinear polarization, PNL (z,t) = χ3 ε0 E(z,t){(1− f )E(z,t)2 + f [Ω+ ν 2 /Ω]

∞ 0

sin(Ωτ ) exp(−ντ )E 2 (t − τ )d τ } (3)

which includes the Kerr nonlinearity and the Raman response. Here χ 3 is the nonlinear thirdorder polarizability, f is the fractional contribution of the Raman response, 2π /Ω is the Raman period and 1/ν is the Raman decay time. The nonlinear parameters are taken identical to the parameters of the rib material: n 2 = 3χ3 /(4cε0 n2II ) = 3 × 10−16 cm2 /W, f = 0.18, 2π /Ω = 30 fs, 1/ν = 70 fs for the structure with a fused silica rib and n 2 = 8 × 10−16 cm2 /W, f = 0 for #10047 - $15.00 USD

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the structure with the rib made of TaFD5 glass. Equation (2) is solved by the split-step Fourier method with fourth-order Runge-Kutta nonlinear step. 1

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Fig. 2. Supercontinuum generation in a Air-TaFD5-SiO2 structure. For input pulses with FWHM of 150 fs, central wavelength of 1185 nm, and intensity of 0.2 TW/cm2 the spectrum (a) and temporal shape (b) are shown after the propagation of a 10-cm-long waveguide. In (c), the spectrum is shown after the propagation of 10 cm in bulk TaFD5 with the same input parameters. The dotted green curves present the input spectrum.

The calculated output spectrum at z = 10 cm in the TaFD5 glass-silica structure is presented in Fig. 2(a) (red curve) for a 150-fs input pulse with peak intensity of 0.2 TW/cm 2 , centered at 1170 nm (e.g., from a Cr:forsterite laser) in the anomalous dispersion region. A quite flat two-octave broad spectrum reaching from 750 nm to 2400 nm is generated. The corresponding temporal field distribution is shown in Fig. 2(b), where we can see many spikes in the interval between −0.6 and 0.6 ps corresponding to fundamental solitons with different frequencies in the anomalous-GVD interval. Due to higher-order dispersion, each of these solitons generates non-solitonic radiation at frequencies determined by the phase-matching condition. Because the solitons have distinct central frequencies, the resulting radiation covers a broad spectral range. In the studied TaFD5 glass-silica waveguide, the non-solitonic radiation is emitted both on blue- and red-shifted frequencies, enabled by the existence of two zero-GVD wavelengths in this structure, similar as in some MF[7, 8]. The analysis of the output spectra at shorter propagation distance reveals a considerable spectral broadening already at 4-5 cm propagation length; with propagation beyond 10 cm the broadening saturates, limited by strong normal GVD below 750 nm and above 2400 nm. Note however, that a 10 cm-long waveguide can still be practically implemented, if one uses spiral design to avoid ultralong chips with the curved rib forming a spiral line on the surface. The dependence of the spectral broadening on the input wavelength (not shown) shows that the optimum wavelength is in the anomalous GVD region near the zero-GVD wavelength, similar to previous results[2]. The role of the waveguide contribution to dispersion is illustrated in Fig. 2(c), where the spectrum (dashed line) is given for the same input intensity and and other parameters as in Fig. 2(a), but after propagation through bulk TaFD5 glass. The spectrum is much narrower, and shows modulations very typical for self-phase modulation. Indeed, this is an expected result since the input wavelength of 1170 nm lies in the normal GVD region of bulk TaFD5 and therefore supercontinuum generation by solitons is impossible. For the Air-SiO2 -Ag structure, we also obtain a broad spectrum shifted to the visible in #10047 - $15.00 USD

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10

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Fig. 3. Supercontinuum generation in an Air-SiO2-Ag structure. For input pulses with FWHM duration of 150 fs, central wavelength of 798 nm, and intensity of 0.5 TW/cm2 the spectrum (a) and temporal shape (b) are shown after the propagation of a 4-cm-long waveguide. Dotted green curve is the input spectrum.

comparison with the Air-TaFD5-SiO 2 structure. The output spectrum formed in Air-SiO 2 -Ag structure by a 150-fs pulse of 0.5 TW/cm 2 peak intensity centered at 798 nm and the corresponding temporal field distribution at L = 4 cm propagation length are presented in Fig. 3. A spectrum of around 1 octave extending from 600 nm to 1150 nm is predicted, and many spikes in the temporal shape identified as fundamental solitons are observed. The spectral width is smaller than for the Air-TaFD5-SiO 2 structure presented in Fig. 2, because phase-matching is inhibited outside of the narrow region of moderate dispersion. In summary, ultrawide spectral broadening is predicted in planar rib waveguide structures with a spectral width up to two octaves. A wide spectral region of anomalous dispersion which arises in these structures due to the waveguide contribution plays a crucial role for the formation of the supercontinuum, because it enables the effective mechanism of soliton fission and radiation. The spectral range of the generated supercontinua can be tuned in a large extent by the choice of the input frequency and tailoring of the waveguide dispersion using different rib materials and parameters. The predictions of this work can find applications as a novel coherent supercontinuum source in the framework of integrated optics. The financial support from DFG and DAAD is acknowledged.

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