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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

2. Samples and measurement setup

3. Measured results

The intrinsic resonant spectra of the cavities measured using low power CW light are shown as dashed lines in Fig. 2
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.
. 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.

4. Analysis and discussion

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

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

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

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]

]
dadt={jω0(1τv+1τin+1τMPA+1τFCA)}a+12τinS1,
(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

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

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

,13

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]

]
αMPA=β(m)Im-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.
τMPA=ncαMPA,
(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

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
dNedt=1τMPA×Umω×1VMPANeτe,
(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),

τFCA=ncαFCA.
(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).
ω0=εεω0,
(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

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|2τv.
(7)

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

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

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

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(0t) 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

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

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
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).
. 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

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]

].

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

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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