Multiple-channel wavelength conversions in a photonic crystal cavity

We demonstrate multiple-channel wavelength conversions of second harmonic and sum frequency generations in a silicon carbide photonic crystal cavity. The cavity is designed to have multiple modes including a nanocavity mode and Fabry–Pérot modes. Multiple-channel wavelength conversions in the nanocavity and Fabry–Pérot modes are shown experimentally. Furthermore, we investigate the polarization characteristics of wavelength-converted light. The experimental results of the polarization are in good agreement with calculation. ©2015 Optical Society of America OCIS codes: (350.4238) Nanophotonics and photonic crystals; (230.5750) Resonators; (190.4223) Nonlinear wave mixing. References and links 1. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407(6804), 608–610 (2000). 2. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). 3. M. Soljacić and J. D. Joannopoulos, “Enhancement of nonlinear effects using photonic crystals,” Nat. Mater. 3(4), 211–219 (2004). 4. T. Uesugi, B. S. Song, T. Asano, and S. Noda, “Investigation of optical nonlinearities in an ultra-high-Q Si nanocavity in a two-dimensional photonic crystal slab,” Opt. Express 14(1), 377–386 (2006). 5. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). 6. X. Yang and C. W. Wong, “Design of photonic band gap nanocavities for stimulated Raman amplification and lasing in monolithic silicon,” Opt. Express 13(12), 4723–4730 (2005). 7. V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, G. Lehoucq, and A. De Rossi, “Kerr-induced all-optical switching in a GaInP photonic crystal Fabry-Perot resonator,” Opt. Express 20(8), 8524–8534 (2012). 8. Y. Takahashi, Y. Inui, M. Chihara, T. Asano, R. Terawaki, and S. Noda, “A micrometre-scale Raman silicon laser with a microwatt threshold,” Nature 498(7455), 470–474 (2013). 9. K. Rivoire, Z. Lin, F. Hatami, W. T. Masselink, and J. Vucković, “Second harmonic generation in gallium phosphide photonic crystal nanocavities with ultralow continuous wave pump power,” Opt. Express 17(25), 22609–22615 (2009). 10. K. Rivoire, Z. Lin, F. Hatami, and J. Vučković, “Sum-frequency generation in doubly resonant GaP photonic crystal nanocavities,” Appl. Phys. Lett. 97(4), 043103 (2010). 11. Y. Ota, K. Watanabe, S. Iwamoto, and Y. Arakawa, “Nanocavity-based self-frequency conversion laser,” Opt. Express 21(17), 19778–19789 (2013). 12. S. Yamada, B. S. Song, S. Jeon, J. Upham, Y. Tanaka, T. Asano, and S. Noda, “Second-harmonic generation in a silicon-carbide-based photonic crystal nanocavity,” Opt. Lett. 39(7), 1768–1771 (2014). 13. H. Nguyen Tan, M. Matsuura, T. Katafuchi, and N. Kishi, “Multiple-channel optical signal processing with wavelength-waveform conversions, pulsewidth tunability, and signal regeneration,” Opt. Express 17(25), 22960– 22973 (2009). 14. N. Chi, L. Xu, K. S. Berg, T. Tokle, and P. Jeppesen, “All-optical wavelength conversion and multichannel 2R regeneration based on highly nonlinear dispersion-imbalanced loop mirror,” IEEE Photon. Technol. Lett. 14(11), 1581–1583 (2002). #229138 $15.00 USD Received 8 Dec 2014; revised 1 Feb 2015; accepted 4 Feb 2015; published 12 Feb 2015 (C) 2015 OSA 23 Feb 2015 | Vol. 23, No. 4 | DOI:10.1364/OE.23.004523 | OPTICS EXPRESS 4523 15. Y. Takahashi, Y. Tanaka, H. Hagino, T. Asano, and S. Noda, “Higher-order resonant modes in a photonic heterostructure nanocavity,” Appl. Phys. Lett. 92(24), 241910 (2008). 16. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4(3), 207–210 (2005). 17. C. Flytzanis and J. Ducuing, “Second-order optical susceptibilities of III-V semiconductors,” Phys. Rev. 178(3), 1218–1228 (1969). 18. S. Yamada, B. S. Song, J. Upham, T. Asano, Y. Tanaka, and S. Noda, “Suppression of multiple photon absorption in a SiC photonic crystal nanocavity operating at 1.55 μm,” Opt. Express 20(14), 14789–14796 (2012). 19. S. H. Kim, G. H. Kim, S. K. Kim, H. G. Park, Y. H. Lee, and S. B. Kim, “Characteristics of a stick waveguide resonator in a two-dimensional photonic crystal slab,” J. Appl. Phys. 95(2), 411–416 (2004). 20. B. S. Song, S. Yamada, T. Asano, and S. Noda, “Demonstration of two-dimensional photonic crystals based on silicon carbide,” Opt. Express 19(12), 11084–11089 (2011). 21. H. Sato, M. Abe, I. Shoji, J. Suda, and T. Kondo, “Accurate measurements of second-order nonlinear optical coefficients of 6H and 4H silicon carbide,” J. Opt. Soc. Am. B 26(10), 1892–1896 (2009).


Introduction
Photonic crystal (PC) nanocavities are well known for their ability to strongly confine light within cavities of a few cubic wavelengths [1,2].Such strong confinement of light is very effective for the enhancement of nonlinear optical phenomena [3] such as two-photon absorption [4], up-down wavelength conversion [5], Raman scattering [6], and the Kerr effect [7].In particular, semiconductor-based PC nanocavities have been studied intensively because such materials can exhibit intrinsic nonlinear coefficients and are used in other optoelectronic components [8].Wavelength conversions, such as second harmonic generation (SHG) and sum frequency generation (SFG), in PC nanocavities have been demonstrated experimentally using semiconductors made of gallium phosphide (GaP) [9,10], gallium arsenide (GaAs) [11], and silicon carbide (SiC) [12].Such approaches to wavelength conversion have focused mainly on the use of a single nanocavity mode, which results in a high Q factor and small modal volume.Although wavelength conversion in the PC cavity using two resonant modes has been demonstrated recently [10], multiple-channel wavelength conversions-which are important for compact all-optical signal processing, wavelength multiplexing, regeneration [13,14], and other techniques-have not been demonstrated clearly yet.
Thus, in this paper, we experimentally demonstrate the multiple-channel wavelength conversions of SHG and SFGs in a PC cavity by exploiting the nonlinear optical behavior and large electronic band gap of the hexagonal polytype (6H) of silicon carbide (SiC) and multiple resonant modes formed in a heterostructured PC cavity [15].The hexagonal SiC has secondorder nonlinear optical coefficients [16] comparable to those of other nonlinear semiconductors [17], and is an attractive material for realizing nonlinear photonic devices without optical absorption [18].The heterostructured PC cavity has several resonant modes, including the nanocavity mode and Fabry-Pérot (FP) modes, with considerable mode overlaps and high Q factors that enable multiple-channel wavelength conversions.Furthermore, we experimentally investigated the polarization characteristics of the SFG light for identification of the contributing modes and compared these with the calculated results.

Design of a SiC cavity for multiple-channel wavelength conversions
To obtain multiple resonances in a SiC PC nanocavity, we used a heterostructured cavity [16] consisting of waveguides with three different lattice constants (a 1 < a 2 < a 3 ) as shown in Fig. 1(a).The band diagram along the waveguide direction (x) is shown schematically in Fig. 1(b), wherein two kinds of resonant modes are formed: a nanocavity (NC) mode caused by the mode gap at a frequency below the band edge of the PC 1 waveguide (lowest line) and FP modes [15] due to the long (PC 1 + PC 2 + PC 3 + PC 2 + PC 1 ) waveguide at frequencies above the band edge of PC 1 (upper lines).The FP modes are generated by reflection at both ends of the long waveguide due to the photonic bandgap effect [15,19].It is worth noting that many FP resonant modes can be controlled by adjusting the length of the PC 1 waveguide and satisfying the FP condition [19].To quantitatively investigate the multiple resonant modes of the cavity, we calculated the resonant spectrum of a SiC-based nanocavity.These geometric parameters are set equal to those of the fabricated sample.The lattice constants in the x direction are a 1 = 534 nm, a 2 = 537 nm, and a 3 = 550 nm, while the lattice constant in the y direction equals 3 a 1 for all regions.The radii of each air hole and the thickness of the SiC slab are 0.26a 1 and 0.6a 1 , respectively.The respective lengths of each PC waveguide are 2a 3 , 2a 2 , and 27a 1 ; the refractive index of the SiC is set to 2.5 at the telecommunication range.The resonant spectrum of the nanocavity is calculated using a 3D finite-difference time-domain (FDTD) method.As seen in Fig. 1(c), there are four peaks: λ 0 = 1563 nm, λ 1 = 1555 nm, λ 2 = 1551 nm, and λ 3 = 1547 nm.It can be seen from Fig. 1(d), which demonstrates the electric field distribution of each mode, that λ 0 is a NC mode, while λ 1 , λ 2 , and λ 3 are FP modes.Other FP modes shorter than λ 3 exist in principle; however, only the NC mode and the three FP modes specified above are relevant to the following experiments.It is also worth noting that the radiation intensity of the NC mode is not necessarily larger than that of the FP modes, but only appears so because the spectrum of the radiated light is monitored from the center region (PC 3 ) of the cavity shown in Fig. 1(a).Detailed calculations reveal that the Q factors for the individual modes (λ 0 , λ 1 , λ 2 , and λ 3 ) are 1.6 × 10 7 , 2 × 10 5 , 1.5 × 10 5 , and 9.4 × 10 3 and the calculated modal volumes are 1.66 (λ/n) 3 , 7.54 (λ/n) 3 , 7.72 (λ/n) 3 , and 7.74 (λ/n) 3 , respectively.

Fabricated SiC PC cavity and fundamental characteristics
On the basis of the aforementioned design, we fabricated a SiC PC cavity with varied lattice constants (a 1 = 534 nm, a 2 = 537, nm, and a 3 = 550 nm) as seen in the scanning electron microscope image of Fig. 2(a).The details of this fabrication process are provided in [20].An input waveguide with a width of 1.125 3  × a 1 is placed parallel to the cavity at an interval of 4 rows.The optical setup for measuring the fundamental and wavelength-converted characteristics of the cavity is shown schematically in Fig. 2(b).The wavelength-tunable (1510-1610 nm), continuous-wave (CW) laser is incident on the input waveguide and the light propagating along the waveguide is evanescently coupled to the cavity.The fundamental resonant spectrum of the cavity is obtained by changing the wavelength of the laser and measuring the intensity of the radiated light from the cavity.Wavelength-converted light is measured by a short-pass filter and a spectrometer with Si detectors.Additionally, a pinhole is used to isolate nanocavity radiation from light scattered from elsewhere on the device.As seen in the measured resonant spectrum of Fig. 2(c), there are four distinct peaks corresponding to one NC mode (λ 0 = 1562.0nm) and three FP modes (λ 1 = 1553.0nm, λ 2 = 1549.4nm, and λ 3 = 1547.3nm).Although there are minor differences between the measured and calculated resonant wavelengths, the experimental results agree well with the values shown in Fig. 1(c).From this spectrum, the quality factors of the individual modes (λ 0 , λ 1 , λ 2 , λ 3 ) are estimated to be 9 × 10 3 , 4.5 × 10 3 , 4 × 10 3 , and 3.5 × 10 3 , respectively.The difference between the calculated and experimental Q factors may be due to additional optical loss resulting in defect states in the SiC wafer rather than due to the variation of the slab thickness and hole size [20].

Experiments and discussion on wavelength conversions
To investigate the SHG characteristics of the cavity, we observed SHG emission when the CW input laser was set to the fundamental wavelength of each resonant mode.Figure 3(a) shows the SHG spectra measured by the spectrometer with CW input set to λ 0 (NC mode).It is found that the peak wavelength corresponds to half of the input wavelength, λ 0 /2 = 781.0nm.The detailed factors, such as input-power dependence, conversion efficiency, and radiation patterns of SHG in a PC cavity, are described in [12].In addition, we observed SHG at input wavelengths of λ 1 , λ 2 , and λ 3 (FP modes).For example, the SHG light for λ 1 is generated in the cavity, as shown in Fig. 3(b).The SHG wavelengths for all NC and FP modes are plotted as circles in Fig. 3(f).This clearly demonstrates the multiple-wavelength conversions of SHG in the PC cavity that arise through excitation of multi-resonant modes.
Next, we added an additional CW input laser source to simultaneously stimulate two distinct fundamental resonant modes.Additional wavelength conversions occur when two fundamental modes are excited simultaneously by two CW lasers.Figure 3(c) shows the spectrum of the wavelength-converted light radiated from the cavity with inputs of λ 0 and λ 1 .
Here, we see three peaks in the spectrum of the cavity.The shortest and longest peak wavelengths coincide with the SHG wavelengths in Figs.3(a) and 3(b), respectively; the middle peak corresponds to half the sum of the resonant wavelengths λ 0 and λ 1 , which implies SFG.As shown in Figs.3(d) and 3(e), other SFG spectra are also measured by fixing the wavelength of one laser (λ 0 ), while changing the wavelengths (λ 2 and λ 3 ) of the second one.In principle, SFG between the FP modes (e.g.λ 1 and λ 2 ) are generated, but we cannot observe them experimentally.This is considered to be because the SFG light in FP-FP cases is spread along the length of the waveguide (compared to that in NC-FP cases), resulting in a reduced power collection by our measurement system.Figure 3(f) demonstrates these multiplechannel SHG and SFGs in the photonic cavity.If a cavity were to be designed with an even greater number of modes, we expect that a dense multiple-channel nanophotonic device with various wavelength conversions would result.FP mode1(λ 1 ) SHG Fig. 3. Measured spectrum of wavelength conversion in the cavity at (a) λ 0 , (b) λ 1 , (c) both λ 0 and λ 1 , (d) both λ 0 and λ 2 , and (e) both λ 0 and λ 3 .(f) a plot of the wavelengths of the second harmonic generation (SHG) and sum frequency generation (SFG) for a fixed λ 0 with additional inputs of λ 1 , λ 2 , and λ 3 .
Furthermore, we investigated the polarization characteristics of the individual SFG light outputs.Here, the x direction, parallel to the cavity length (Fig. 1(a)), is defined as 0° (180°).When λ 0 and λ 1 are incident in the cavity, the measured SFG light for λ 0 + λ 1 is non-polarized, as shown in Fig. 4(a).On the other hand, the SFG light for λ 0 + λ 2 and λ 0 + λ 3 is primarily polarized along the x direction, as shown in Figs.4(b) and 4(c), respectively.To analyze the experimental polarization characteristics of the SHG light, we calculated the electrical distributions of the SFG light and polarization properties of the radiated light from the cavity.Because SFG is produced by second nonlinear electric polarization, the SFG polarization of ( ) P ω ω + is expressed generally as where ( ) ω are the second-order susceptibility [21] of SiC and the electric fields of the cavity modes for ω 1 and ω 2 , respectively.Because the hexagonal polytype of SiC was used and the electric field ( ) z E ω is negligible in comparison with the in-plane components of ( ) x E ω and ( ) y E ω , the polarization can be simplified into component of ( ) The electric fields of the cavity modes for ω 1 and ω 2 are calculated using a FDTD method as mentioned in Section 2.Then, the cavity is excited according to Eq. ( 2) and the polarization characteristics of the radiated SFG light are obtained.Figures 4(d

Conclusion
In summary, we demonstrated the multiple-channel wavelength conversions of SHG and SFG in a PC cavity.A cavity with multiple resonances of NC and FP modes was designed using a nonlinear SiC PC structure.The resonant NC and FP modes were identified experimentally by measurements using the fabricated SiC PC cavity.When the individual modes were excited by varying the wavelengths of input light, the multiple-channel wavelength conversions of SHG and SFG were demonstrated experimentally.Additionally, the polarization characteristics of the SFG light were investigated experimentally.The experimental results agreed well with calculation, indicating that these results may further stimulate the development of easily integrable light sources with short wavelengths as well as the conversion of photons for quantum information processing and communication.

Fig. 1 .
Fig. 1.(a) Schematic image of a heterostructured nanocavity.(b) Schematic picture of the band diagram along the waveguide direction.A nanocavity mode occurs below the band-edge frequency of PC 1 and the FP modes occur above this frequency.(c) The calculated fundamental resonance spectrum of the cavity.(d) The electric field distribution of each mode.