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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 14 — Jul. 2, 2012
  • pp: 14789–14796

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Suppression of multiple photon absorption in a SiC photonic crystal nanocavity operating at 1.55 μm

Shota Yamada, Bong-Shik Song, Jeremy Upham, Takashi Asano, Yoshinori Tanaka, and Susumu Noda  »View Author Affiliations


Optics Express, Vol. 20, Issue 14, pp. 14789-14796 (2012)
http://dx.doi.org/10.1364/OE.20.014789


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Abstract

We show that a SiC photonic crystal cannot only inhibit two photon absorption completely, but also suppress higher-order multiple photon absorption significantly at telecommunication wavelengths, compared to conventional Si-based photonic crystal nanocavities. Resonant spectra of a SiC nanocavity maintain a Lorentzian profile even at input energies 100 times higher than what can be applied to a Si nanocavity without causing nonlinear effects. Theoretical fitting of the results indicates that the four photon absorption coefficient in the SiC nanocavity is less than 2.0 × 10−5 cm5/GW3. These results will contribute to the development of high-power applications of SiC nanocavities such as harmonic generation, parametric down conversion, and Raman amplification.

© 2012 OSA

1. Introduction

Semiconductor-based nanophotonics have developed rapidly thanks to the established wafer quality and advanced nanofabrication technologies [1

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). [CrossRef] [PubMed]

]. In particular, silicon (Si) and gallium arsenide (GaAs)-based nanophotonic devices such as low-loss waveguides and ultrahigh quality (Q) factor cavities have been demonstrated at the optical communication wavelengths (1.55 μm) [2

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]

–4

N. Ikeda, Y. Sugimoto, Y. Tanaka, K. Inoue, and K. Asakawa, “Low propagation losses in single-line-defect photonic crystal waveguides on GaAs membranes,” IEEE J. Sel. Areas Comm. 23(7), 1315–1320 (2005). [CrossRef]

]. Even though these semiconductors are transparent in the telecommunication range, the phenomenon of multiple photon absorption (MPA) frequently occurs due to high photon densities within nanophotonic structures such as photonic crystal waveguides and nanocavities because they can strongly confine photons within a tiny space. In fact, photonic crystal nanocavities suffer from MPA (particularly, two-photon absorption (TPA)) even at low input powers of a few μW [5

P. E. Barclay, K. Srinivasan, and O. Y. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005). [CrossRef] [PubMed]

–7

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). [CrossRef] [PubMed]

] because of ultrasmall modal volume of the order of a cubic wavelength. In addition to the direct optical absorption due to TPA, carriers generated by TPA contribute to free-carrier absorption and carrier plasma shift, causing additional optical instability to cavity-based devices [5

P. E. Barclay, K. Srinivasan, and O. Y. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005). [CrossRef] [PubMed]

,7

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). [CrossRef] [PubMed]

]. Most strategies for reducing these adverse effects have focused on shortening the lifetime of the generated carriers by using reverse P-i-N diodes to rapidly extract the carriers [8

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005). [CrossRef] [PubMed]

,9

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007). [CrossRef]

]. However, this process is limited by the speed of the electronic response, causing extraction to last on the order of several hundreds of picoseconds. Even under ideal circumstances this approach does not eliminate the initial optical loss incurred by TPA, only the subsequent losses and nonlinearities due to the generated carriers. To fundamentally eliminate the optical losses and non-linear response at high photon densities, the TPA phenomenon itself must be directly addressed. Recently, there have been significant efforts [10

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007). [CrossRef]

,11

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93(5), 051114 (2008). [CrossRef]

] to minimize TPA and its adverse effects using larger electronic bandgap (Eg) materials. This is motivated by the fact that the TPA coefficient decreases as 1/Eg3 [12

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984). [CrossRef]

,13

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. At. Mol. Opt. Phys. 39(12), 2737–2746 (2006). [CrossRef]

]. However, complete inhibition of TPA has yet to be demonstrated experimentally because the tested bandgaps e.g. AlxGa1-xAs (Eg = 1.6~1.8 eV) are smaller than the energy of a pair of photons (2ћω~1.6 eV). Thus, it is desirable to utilize a sufficiently wide bandgap material to completely inhibit TPA and its side effects [14

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the Optical Absorption of ZnO Single Crystals in the Presence of an Intense Midinfrared Laser Field,” Phys. Rev. Lett. 107(16), 167407 (2011). [CrossRef] [PubMed]

]. Very recently, we have developed photonic crystals made of silicon carbide (SiC), a wide bandgap material having Eg of 3.0 eV, and demonstrated both broadband operation from infrared to visible wavelengths and superior thermal stability [15

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). [CrossRef] [PubMed]

–17

S. Yamada, B. S. Song, T. Asano, and S. Noda, “Silicon carbide-based photonic crystal nanocavities for ultra-broadband operation from infrared to visible wavelengths,” Appl. Phys. Lett. 99(20), 201102 (2011). [CrossRef]

]. In this work, we investigate the robustness of SiC photonic crystal nanocavity performance at high input powers. We compare the response of SiC and Si nanocavities to high input powers and demonstrate that SiC nanocavities inhibit TPA completely and also suppress higher-order MPA.

2. Samples and measurement setup

In order to investigate the superiority of SiC-based photonic crystals for the suppression of MPA phenomena at infrared ranges, we compare experimentally the optical response of a SiC photonic crystal nanocavity and a conventional Si nanocavity. We prepared Si and SiC photonic crystal nanocavities (see inset of Fig. 1 .) having similar resonant wavelength and Q factors: To realize similar resonant wavelengths near 1.55 μm, the lattice constant of the SiC photonic crystal was made larger than that of the Si because of the lower refractive index of SiC (nSiC = 2.5~2.7, nSi = 3.48). Furthermore, air-hole shifted cavities and heterostructured cavities are adopted for the Si an SiC photonic crystals, respectively, to obtain similarly high Q factors (8,000 and 10,000, respectively) [1

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). [CrossRef] [PubMed]

,15

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). [CrossRef] [PubMed]

]. The calculated modal volumes of the Si and SiC cavities are 0.73 (λ/n)3 and 1.71 (λ/n)3, respectively. An input waveguide is introduced nearby in order to couple light evanescently into each cavity. Detailed fabrication procedures of Si and SiC photonic crystal structures are described in references 15

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). [CrossRef] [PubMed]

and 18

B. S. Song, T. Nagashima, T. Asano, and S. Noda, “Resonant-wavelength control of nanocavities by nanometer-scaled adjustment of two-dimensional photonic crystal slab structures,” IEEE Photon. Technol. Lett. 20(7), 532–534 (2008). [CrossRef]

. The fabricated cavities are measured by the setup shown in Fig. 1. At first, we measured the intrinsic or linear characteristics of the cavities using a wavelength-tunable, continuous wave (CW) light source (λ = 1.52~1.63 μm) where input power to the waveguides are set to be as low as a few nW. The spectra are obtained by scanning the wavelength while measuring the intensity of light emitted from each cavity using an ultrasensitive photoreceiver. Next, we investigated the nonlinear characteristics of the cavities by inputting higher-intensity light pulses (up to 64 pJ). For this purpose, we used a wavelength-tunable, pulsed light source (λ = 1.53~1.56 μm, pulse width = 4 ps, repetition rate = 50 MHz), where the center wavelengths were tuned to the resonant wavelength of the cavities, and the spectra of light emitted from the cavities were measured using an optical spectrum analyzer (OSA) with a resolution of 0.1 nm.

Fig. 1 Schematic picture of the optical setup used to measure the characteristics of nanocavities at high input energies. Insert images of nanocavities used in experiment.

3. Measured results

The intrinsic resonant spectra of the cavities measured using low power CW light are shown as dashed lines in Fig. 2 . From the spectra, we see that the cavities have similar resonant wavelengths (λSi = 1.539 μm and λSiC = 1.559 μm) and Q factors (QSi = 8,000 and QSiC = 10,000). The solid lines in Fig. 2 show the spectra of the Si and SiC nanocavities measured for various input energies of pulsed light. Here, the input energy is defined as the energy of the light pulse actually coupled into the waveguides, and was estimated from the transmission intensity of the waveguides as schematically shown in Fig. 1. In the case of the Si nanocavity, as the input energy is increased, the peak wavelengths of the spectra shift toward shorter wavelengths even at input energies as low as 0.6 pJ. This phenomenon is due to the decrease of refractive index caused by the plasma effect of the MPA-generated carriers. Furthermore, the peak intensities in the Si cavity do not increase with input energy. This can be attributed to the MPA itself and the free carrier absorption by the MPA generated carriers. By contrast, the waveforms in the SiC cavity spectra do not change: no shift of the resonant wavelength was observed even at input energies of 64 pJ, which are 100 times higher than the maximum energy that can be applied to the Si nanocavity without causing deformation of the waveform. Furthermore, the peak intensities for the SiC cavity simply increased linearly with input energy, indicating that nonlinear absorption doesn’t occur. Note that the input energy of 64 pJ is the maximum performance of our measurement system and not a limit imposed by MPA in the SiC nanocavity. It is clear that the SiC-based photonic crystal can sufficiently suppress MPA for this wavelength (~1.56 μm) at least up to input pulse energies of 64 pJ.

Fig. 2 Spectra of the vertical emission from the nanocavities for various input energies. (a) In Si higher energies lead to spectral blue shift due to TPA without significant increase in overall emission. (b) In SiC peak emission increases linearly with input energy and shows complete inhibition of TPA.

4. Analysis and discussion

In order to analyze the experimental results shown in Fig. 2 theoretically, we built on the model described in [7

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). [CrossRef] [PubMed]

] and developed a nonlinear response model including MPA and its side effects in a photonic crystal structure. The photonic crystal structure consists of a waveguide and a cavity to form a two-port system shown schematically in Fig. 3 . Here, a is defined as the amplitude whose magnitude squared corresponds to the energy within the cavity (U = |a|2). S1 is the amplitude whose magnitude squared corresponds to the light power introduced into the waveguide. S2 is the amplitude whose magnitude squared corresponds to the light power emitted from the cavity to free space.

Fig. 3 The model of two-port system consisting of a waveguide and a cavity.

The equation for the evolution of the cavity mode in time can be expressed using coupled-mode theory (CMT) [19

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999). [CrossRef]

]
da dt= { j ω′0− ( 1 τv+ 1 τ in+ 1 τ MPA+ 1 τ FCA)}a+ 1 2 τ in S1,
(1)
where ω'0 is the resonant angular frequency. The terms 1/τin and 1/τv are the rates of energy decay into the waveguide and free space, respectively, which are obtained from the measured results of transmission and emission spectra [20

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13(4), 1202–1214 (2005). [CrossRef] [PubMed]

]. The term 1/τMPA and 1/τFCA are the rate of additional absorption due to MPA and consequent free-carrier absorption (FCA), respectively. The optical absorption coefficient (αMPA) of m-photon absorption can be generally expressed as [12

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984). [CrossRef]

,13

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. At. Mol. Opt. Phys. 39(12), 2737–2746 (2006). [CrossRef]

]
α MPA= ∑ β (m) I m-1= β (2)I+ β (3) I2+ β (4) I3+...,
(2)
where I is the light intensity and β(m) is m-photon photon absorption coefficient that is dependent on the electronic band structure of the material. In the case of the cavity, I is replaced by the energy U in the nanocavity and αMPA is replaced by 1/τMPA by the following equation.
τ MPA= n c α MPA,
(3)
where n is the refractive index of material and c is the velocity of light in the vacuum. Si-based nanophotonic structures suffer mainly from two photon absorption (TPA, i.e. m = 2) rather than higher-order photon absorption at input pulse energies of ~pJ [7

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). [CrossRef] [PubMed]

]. However for SiC, β(2) and β(3) are fundamentally excluded because the Eg of SiC is larger than the combined energy of two or even three photons at 1.55 μm, so the first term to be considered is β (4). The MPA-generated carrier densities (Ne) are expressed as
d Ne dt= 1 τ MPA× U mℏω× 1 V MPA− Ne τe,
(4)
where VMPA is MPA-generated free carriers’ volume in a nanophotonic structure and τe is the decay rate of the free carriers. 1/τFCA is determined from Ne by Eq. (5),

τ FCA= n c α FCA.
(5)

The resonant angular frequency ω'0 is assumed to be determined by the original resonant frequency of the cavity ω0 and the frequency shift caused by the refractive index decrease due to plasma effect of the MPA-generated free-carriers as show by Eq. (6).
ω′0= ε′ε ω0,
(6)
where ε is the original dielectric constant of material, and ε' is the dielectric constant in the presence of free-carriers. Here, the increase of refractive index due to the temperature increase is ignored because the duration of the input pulse used in the experiment is as short as 4 ps and the response time of the temperature increase is much longer than either the pulse duration or the photon lifetime in the nanocavities. Furthermore, the refractive index increase due to the Kerr effect is negligibly small compared to the refractive index decrease due to carrier plasma effect [7

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). [CrossRef] [PubMed]

]. The light power radiated from the cavity (measured light in experiment) can be expressed as

S2= |a|2 τv.
(7)

To perform the nonlinear CMT simulation, we solve Eqs. (1)-(7) simultaneously, using the physical parameters of Si and SiC [7

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). [CrossRef] [PubMed]

,21

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

,22

N. T. Son, O. Kordina, A. O. Konstantinov, W. M. Chen, E. Sörman, B. Monemar, and E. Janzén, “Electron effective masses and mobilities in high-purity 6H-SiC chemical vapor deposition layers,” Appl. Phys. Lett. 65(25), 3209–3211 (1994). [CrossRef]

], where the input light is set to be a Gaussian pulse: S1 = Aexp(-t2/Δt2)exp(jω0t) with Δt = 4 ps.

Generally, it is difficult to determine accurate MPA coefficients because they are strongly dependent on material bandgaps and qualities (e.g. free carrier density, defects and crystallographic orientation) [21

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

,23

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

]. In particular, βSiC(4) is unknown in the telecommunication range. Therefore, we determined values of βSi(2) and βSiC(4) by fitting the above CMT simulations to the experimental results shown in Fig. 2. The calculated results of nonlinear optical response of the Si nanocavity for various βSi(2) are plotted in Fig. 4 . For the purposes of comparison, we show the spectra for βSi(2) set to 2.0 cm/GW and 0.5 cm/GW in Figs. 4(a) and 4(b), respectively. The waveforms and peak wavelengths for the former are inconsistent with the experimental results shown in Fig. 2(a) while the latter matches experiment quite closely. In order to determine the value of βSi(2) more clearly from experiment, we plot the calculated the normalized peak intensity and the shift of the peak wavelengths for various input energies as a function of βSi(2), as shown in Figs. 4(c) and 4(d), respectively. The experimental results for each input energy, plotted as solid circles, consistently indicate βSi(2) of ~0.5 cm/GW (shaded region in the figures). The value of the βSi(2) is in good agreement with the value reported in [21

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

].

Fig. 4 Calculated results of optical responses of a Si cavity for various βSi(2). (a), (b) The spectra of βSi(2) = 2.0 cm/GW and 0.5 cm/GW in the Si cavity. (c), (d) The normalized peak intensity and peak wavelength shift for various βSi in the Si cavity, respectively (here, experimental results are also plotted as the solid circles).

Similarly, we investigated the optical responses of the SiC nanocavity for various βSiC(4) as shown in Fig. 5 . Even when βSiC(4) is set to be as small as 2.0 × 10−4 cm5/GW3 the peak resonant wavelengths are visibly shifted toward shorter wavelengths as seen in the spectra of Fig. 5(a). Figures 5(b), 5(c) and 5(d) show that peak intensity and peak wavelength of the SiC cavity are maintained, even at the extremely high energies seen in experiment (Fig. 2(b)), when βSiC(4) is less than 2.0 × 10−5 cm5/GW3. This implies that no nonlinear effects occur. Through additional calculations we checked that the significant suppression of multiple photon absorption in the SiC cavity is due not to the modal volume of the cavity but to the wide electronic bandgap of the material. An amplified higher-power laser source and higher input coupling efficiency [5

P. E. Barclay, K. Srinivasan, and O. Y. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005). [CrossRef] [PubMed]

] in the experimental setup provides higher input energy, it would cause four photon absorption in the SiC cavity and allow the value of βSiC(4) to be identified definitely. The small βSiC(4) means that even when a strong light intensity of 1 GW/cm2 is inputted in SiC photonic crystal nanocavity, the optical absorption loss is as small as 2.0 × 10−5 /cm. This is an experimental verification of the very small multiple photon absorption of SiC material at the telecommunication range. It implies that SiC-based photonic crystals not only completely inhibit the undesirable nonlinear phenomena of two and three photon absorption, but also sufficiently suppress four photon absorption to be unobservable up to an input energy of 64 pJ at telecommunication wavelength range.

Fig. 5 Calculated results of optical responses of a SiC cavity for various βSiC(4). (a), (b) The spectra of βSiC(4) = 2.0 × 10−4 cm5/GW3 and 2.0 × 10−5 cm5/GW3 in the SiC cavity. (c), (d) The normalized peak intensity and peak wavelength shift for various βSi in SiC cavity, respectively (here, experimental results are also plotted as the solid circles in shaded region).

5. Conclusion

In summary, we experimentally demonstrated that photonic crystals made of SiC can completely inhibit two-photon and three-photon absorption at telecommunication wavelengths of 1.55 μm. We compared SiC-based and Si-based nanocavities with high Q factors of ~10,000, and found that the SiC-based nanocavity suppresses nonlinear absorption and to below detectable levels and exhibits no change of resonant spectrum shift even at input energies 100 times higher than that is maximally allowed for equivalent Si-based nanocavities to maintain optically stable operation. We believe these results will open a route for the realization of nanophotonics devices that are very optically stable without multiple photon absorption even at high input energies, and will lead to applications such as harmonic generation [24

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011). [CrossRef]

], parametric down conversion, and Raman amplification with very high efficiency and low loss.

Acknowledgments

This work was supported by the Japan Society for the Promotion of Science (JSPS) through its “Funding Program for World-Leading Innovation R&D on Science and Technology (FIRST Program),” a Grant-in-Aid from the MEXT Japan, and the WCU program (R32-2008-000-10204-0) of the National Research Foundation of Korea (NRF).

References and links

1.

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). [CrossRef] [PubMed]

2.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics 1(8), 449–458 (2007). [CrossRef]

3.

J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express 17(6), 4752–4757 (2009). [CrossRef] [PubMed]

4.

N. Ikeda, Y. Sugimoto, Y. Tanaka, K. Inoue, and K. Asakawa, “Low propagation losses in single-line-defect photonic crystal waveguides on GaAs membranes,” IEEE J. Sel. Areas Comm. 23(7), 1315–1320 (2005). [CrossRef]

5.

P. E. Barclay, K. Srinivasan, and O. Y. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express 13(3), 801–820 (2005). [CrossRef] [PubMed]

6.

M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express 13(7), 2678–2687 (2005). [CrossRef] [PubMed]

7.

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). [CrossRef] [PubMed]

8.

H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature 433(7027), 725–728 (2005). [CrossRef] [PubMed]

9.

H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics 1(4), 232–237 (2007). [CrossRef]

10.

H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett. 90(23), 231102 (2007). [CrossRef]

11.

H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett. 93(5), 051114 (2008). [CrossRef]

12.

B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B 1(1), 67–72 (1984). [CrossRef]

13.

H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. At. Mol. Opt. Phys. 39(12), 2737–2746 (2006). [CrossRef]

14.

S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the Optical Absorption of ZnO Single Crystals in the Presence of an Intense Midinfrared Laser Field,” Phys. Rev. Lett. 107(16), 167407 (2011). [CrossRef] [PubMed]

15.

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). [CrossRef] [PubMed]

16.

S. Yamada, B. S. Song, T. Asano, and S. Noda, “Experimental investigation of thermo-optic effects in SiC and Si photonic crystal nanocavities,” Opt. Lett. 36(20), 3981–3983 (2011). [CrossRef] [PubMed]

17.

S. Yamada, B. S. Song, T. Asano, and S. Noda, “Silicon carbide-based photonic crystal nanocavities for ultra-broadband operation from infrared to visible wavelengths,” Appl. Phys. Lett. 99(20), 201102 (2011). [CrossRef]

18.

B. S. Song, T. Nagashima, T. Asano, and S. Noda, “Resonant-wavelength control of nanocavities by nanometer-scaled adjustment of two-dimensional photonic crystal slab structures,” IEEE Photon. Technol. Lett. 20(7), 532–534 (2008). [CrossRef]

19.

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron. 35(9), 1322–1331 (1999). [CrossRef]

20.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13(4), 1202–1214 (2005). [CrossRef] [PubMed]

21.

M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett. 82(18), 2954–2956 (2003). [CrossRef]

22.

N. T. Son, O. Kordina, A. O. Konstantinov, W. M. Chen, E. Sörman, B. Monemar, and E. Janzén, “Electron effective masses and mobilities in high-purity 6H-SiC chemical vapor deposition layers,” Appl. Phys. Lett. 65(25), 3209–3211 (1994). [CrossRef]

23.

Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express 15(25), 16604–16644 (2007). [CrossRef] [PubMed]

24.

S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys. 7(2), 138–141 (2011). [CrossRef]

OCIS Codes
(190.4390) Nonlinear optics : Nonlinear optics, integrated optics
(230.5750) Optical devices : Resonators
(230.5298) Optical devices : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: April 12, 2012
Revised Manuscript: May 31, 2012
Manuscript Accepted: June 2, 2012
Published: June 18, 2012

Citation
Shota Yamada, Bong-Shik Song, Jeremy Upham, Takashi Asano, Yoshinori Tanaka, and Susumu Noda, "Suppression of multiple photon absorption in a SiC photonic crystal nanocavity operating at 1.55 μm," Opt. Express 20, 14789-14796 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-14789


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References

  1. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature425(6961), 944–947 (2003). [CrossRef] [PubMed]
  2. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nat. Photonics1(8), 449–458 (2007). [CrossRef]
  3. J. Cardenas, C. B. Poitras, J. T. Robinson, K. Preston, L. Chen, and M. Lipson, “Low loss etchless silicon photonic waveguides,” Opt. Express17(6), 4752–4757 (2009). [CrossRef] [PubMed]
  4. N. Ikeda, Y. Sugimoto, Y. Tanaka, K. Inoue, and K. Asakawa, “Low propagation losses in single-line-defect photonic crystal waveguides on GaAs membranes,” IEEE J. Sel. Areas Comm.23(7), 1315–1320 (2005). [CrossRef]
  5. P. E. Barclay, K. Srinivasan, and O. Y. Painter, “Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper,” Opt. Express13(3), 801–820 (2005). [CrossRef] [PubMed]
  6. M. Notomi, A. Shinya, S. Mitsugi, G. Kira, E. Kuramochi, and T. Tanabe, “Optical bistable switching action of Si high-Q photonic-crystal nanocavities,” Opt. Express13(7), 2678–2687 (2005). [CrossRef] [PubMed]
  7. 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. Express14(1), 377–386 (2006). [CrossRef] [PubMed]
  8. H. Rong, R. Jones, A. Liu, O. Cohen, D. Hak, A. Fang, and M. Paniccia, “A continuous-wave Raman silicon laser,” Nature433(7027), 725–728 (2005). [CrossRef] [PubMed]
  9. H. Rong, S. Xu, Y. H. Kuo, V. Sih, O. Cohen, O. Raday, and M. Paniccia, “Low-threshold continuous-wave Raman silicon laser,” Nat. Photonics1(4), 232–237 (2007). [CrossRef]
  10. H. Oda, K. Inoue, Y. Tanaka, N. Ikeda, Y. Sugimoto, H. Ishikawa, and K. Asakawa, “Self-phase modulation in photonic-crystal-slab line-defect waveguides,” Appl. Phys. Lett.90(23), 231102 (2007). [CrossRef]
  11. H. Oda, K. Inoue, A. Yamanaka, N. Ikeda, Y. Sugimoto, and K. Asakawa, “Light amplification by stimulated Raman scattering in AlGaAs-based photonic-crystal line-defect waveguides,” Appl. Phys. Lett.93(5), 051114 (2008). [CrossRef]
  12. B. S. Wherrett, “Scaling rules for multiphoton interband absorption in semiconductors,” J. Opt. Soc. Am. B1(1), 67–72 (1984). [CrossRef]
  13. H. Garcia and R. Kalyanaraman, “Phonon-assisted two-photon absorption in the presence of a dc-field: the nonlinear Franz–Keldysh effect in indirect gap semiconductors,” J. Phys. At. Mol. Opt. Phys.39(12), 2737–2746 (2006). [CrossRef]
  14. S. Ghimire, A. D. DiChiara, E. Sistrunk, U. B. Szafruga, P. Agostini, L. F. DiMauro, and D. A. Reis, “Redshift in the Optical Absorption of ZnO Single Crystals in the Presence of an Intense Midinfrared Laser Field,” Phys. Rev. Lett.107(16), 167407 (2011). [CrossRef] [PubMed]
  15. B. S. Song, S. Yamada, T. Asano, and S. Noda, “Demonstration of two-dimensional photonic crystals based on silicon carbide,” Opt. Express19(12), 11084–11089 (2011). [CrossRef] [PubMed]
  16. S. Yamada, B. S. Song, T. Asano, and S. Noda, “Experimental investigation of thermo-optic effects in SiC and Si photonic crystal nanocavities,” Opt. Lett.36(20), 3981–3983 (2011). [CrossRef] [PubMed]
  17. S. Yamada, B. S. Song, T. Asano, and S. Noda, “Silicon carbide-based photonic crystal nanocavities for ultra-broadband operation from infrared to visible wavelengths,” Appl. Phys. Lett.99(20), 201102 (2011). [CrossRef]
  18. B. S. Song, T. Nagashima, T. Asano, and S. Noda, “Resonant-wavelength control of nanocavities by nanometer-scaled adjustment of two-dimensional photonic crystal slab structures,” IEEE Photon. Technol. Lett.20(7), 532–534 (2008). [CrossRef]
  19. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “Coupling of modes analysis of resonant channel add-drop filters,” IEEE J. Quantum Electron.35(9), 1322–1331 (1999). [CrossRef]
  20. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express13(4), 1202–1214 (2005). [CrossRef] [PubMed]
  21. M. Dinu, F. Quochi, and H. Garcia, “Third-order nonlinearities in silicon at telecom wavelengths,” Appl. Phys. Lett.82(18), 2954–2956 (2003). [CrossRef]
  22. N. T. Son, O. Kordina, A. O. Konstantinov, W. M. Chen, E. Sörman, B. Monemar, and E. Janzén, “Electron effective masses and mobilities in high-purity 6H-SiC chemical vapor deposition layers,” Appl. Phys. Lett.65(25), 3209–3211 (1994). [CrossRef]
  23. Q. Lin, O. J. Painter, and G. P. Agrawal, “Nonlinear optical phenomena in silicon waveguides: Modeling and applications,” Opt. Express15(25), 16604–16644 (2007). [CrossRef] [PubMed]
  24. S. Ghimire, A. D. DiChiara, E. Sistrunk, P. Agostini, L. F. DiMauro, and D. A. Reis, “Observation of high-order harmonic generation in a bulk crystal,” Nat. Phys.7(2), 138–141 (2011). [CrossRef]

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