Abstract

We demonstrate C-band wavelength conversion in Si photonic-wire waveguides with submicron cross-section by means of nonresonant, nondegenerate four-wave mixing (FWM) using low-power, cw-laser sources. Our analysis shows that for these deeply scaled Si waveguides, FWM can be observed despite the large phase mismatch imposed by strong waveguide dispersion. The theoretical calculations agree well with proof-of-concept experiments. The nonresonant character of the FWM scheme employed allows to demonstrate frequency tuning of the idler from ~20 GHz to>100 GHz thus covering several C-band DWDM channels.

© 2005 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2005

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

2004

B. Jalali, R. Claps, D. Dimitropoulos, V. Raghunathan, “Light generation, amplification, and wavelength conversion via stimulated Raman scattering in silicon microstructures,” Topics in Appl. Phys. 94, 199–238 (2004).
[CrossRef]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713
[CrossRef] [PubMed]

Q. Xu, V. R. Almeida, M. Lipson, “Time-resolved study of Raman gain in highly confined silicon-on-insulator waveguides,” Opt. Express 12, 4437–4442 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-19-4437.
[CrossRef] [PubMed]

T. K. Liang, H. K. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phy. Lett. 85, 3343–3345 (2004).
[CrossRef]

O. Boyraz, B. Jalali, “Demonstration of a silicon Raman laser,” Opt. Express 12, 5269–5273 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-21-5269
[CrossRef] [PubMed]

M. Harjanne, M. Kapulainen, T. Aalto, P. Heimala, “Sub-µs switching time in silicon-on-insulator Mach-Zender thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004).
[CrossRef]

M. W. Geis, S. J. Spector, R. C. Williamson, T. M. Lyszczarz, “Submicrosecond, submilliwatt, silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004).
[CrossRef]

T. K. Liang, H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phy. Lett. 84, 2745–2747 (2004).
[CrossRef]

R. Claps, V. Raghunathan, D. Dimitropoulos, B. Jalali, “Influence of nonlinear absorption on Raman amplification in Silicon waveguides,” Opt. Express 12, 2774–2780 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-12-2774
[CrossRef] [PubMed]

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Spontaneous Raman scattering in ultrasmall silicon waveguides,” Optics Lett. 29, 2755 (2004).
[CrossRef]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Y. A. Vlasov, S. J. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12, 1622–1631 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-8-1622
[CrossRef] [PubMed]

2003

1996

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

1987

R. A. Soref, B. R. Bennett, “Electro-optical effects in Silicon,” IEEE J. Quantum Electron. QE-23, 123–129 (1987).
[CrossRef]

1969

J. J. Wynne,“Optical Third-Order Mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. B 178, 1295–1303 (1969).
[CrossRef]

Aalto, T.

M. Harjanne, M. Kapulainen, T. Aalto, P. Heimala, “Sub-µs switching time in silicon-on-insulator Mach-Zender thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

Aktsipetrov, O. A.

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

Almeida, V. R.

Anderson, M. H.

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

Bennett, B. R.

R. A. Soref, B. R. Bennett, “Electro-optical effects in Silicon,” IEEE J. Quantum Electron. QE-23, 123–129 (1987).
[CrossRef]

Boyraz, O.

Chen, X.

X. Chen, N. C. Panoiu, R. M. Osgood “Full Theoretical Analysis of Pulsed SOI Raman Amplifiers” Integrated Photonics Research and Application2005, Paper IMG3.

Claps, R.

Cohen, O.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Dadap, J. I.

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Spontaneous Raman scattering in ultrasmall silicon waveguides,” Optics Lett. 29, 2755 (2004).
[CrossRef]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713
[CrossRef] [PubMed]

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

Dimitropoulos, D.

Dinu, M.

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

Downer, M. C.

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

Espinola, R. L.

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Spontaneous Raman scattering in ultrasmall silicon waveguides,” Optics Lett. 29, 2755 (2004).
[CrossRef]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713
[CrossRef] [PubMed]

R. L. Espinola, M.-C Tsai, J. T. Yardley, R. M. Osgood, “Fast and low-power thermooptic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003).
[CrossRef]

Fang, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Fukuda, H.

H. Fukuda, T. Tsuchizawa, K. Yamada, T. Watanabe, M. Takahashi, J. Takahashi, S. Itabashi, “Silicon wire waveguides and their applications for microphotonics devices,” Integrated Photonics Research2004, Paper IWA1.

Garcia, H.

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

Geis, M. W.

M. W. Geis, S. J. Spector, R. C. Williamson, T. M. Lyszczarz, “Submicrosecond, submilliwatt, silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004).
[CrossRef]

Hak, D.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Han, Y.

Harjanne, M.

M. Harjanne, M. Kapulainen, T. Aalto, P. Heimala, “Sub-µs switching time in silicon-on-insulator Mach-Zender thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004).
[CrossRef]

Heimala, P.

M. Harjanne, M. Kapulainen, T. Aalto, P. Heimala, “Sub-µs switching time in silicon-on-insulator Mach-Zender thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004).
[CrossRef]

Hu, X.-F.

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

Itabashi, S.

H. Fukuda, T. Tsuchizawa, K. Yamada, T. Watanabe, M. Takahashi, J. Takahashi, S. Itabashi, “Silicon wire waveguides and their applications for microphotonics devices,” Integrated Photonics Research2004, Paper IWA1.

Jalali, B.

Jones, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Kapulainen, M.

M. Harjanne, M. Kapulainen, T. Aalto, P. Heimala, “Sub-µs switching time in silicon-on-insulator Mach-Zender thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2039–2041 (2004).
[CrossRef]

Knights, A. P.

G. T. Reed, A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004).
[CrossRef]

Liang, T. K.

T. K. Liang, H. K. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phy. Lett. 85, 3343–3345 (2004).
[CrossRef]

T. K. Liang, H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phy. Lett. 84, 2745–2747 (2004).
[CrossRef]

Liao, L.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Lipson, M.

Liu, A.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Lowell, J. K.

J. I. Dadap, X.-F. Hu, M. H. Anderson, M. C. Downer, J. K. Lowell, O. A. Aktsipetrov, “Optical second-harmonic electroreflectance spectroscopy of a Si(001) metal-oxide-semiconductor structure,” Phys. Rev. B 53, R7607–R7609 (1996).
[CrossRef]

Lyszczarz, T. M.

M. W. Geis, S. J. Spector, R. C. Williamson, T. M. Lyszczarz, “Submicrosecond, submilliwatt, silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004).
[CrossRef]

McNab, S. J.

Moll, N.

Nicolaescu, R.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Osgood, R. M.

J. I. Dadap, R. L. Espinola, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Spontaneous Raman scattering in ultrasmall silicon waveguides,” Optics Lett. 29, 2755 (2004).
[CrossRef]

R. L. Espinola, J. I. Dadap, R. M. Osgood, S. J. McNab, Y. A. Vlasov, “Raman amplification in ultrasmall silicon-on-insulator wire waveguides,” Opt. Express 12, 3713–3718 (2004). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-16-3713
[CrossRef] [PubMed]

R. L. Espinola, M.-C Tsai, J. T. Yardley, R. M. Osgood, “Fast and low-power thermooptic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003).
[CrossRef]

X. Chen, N. C. Panoiu, R. M. Osgood “Full Theoretical Analysis of Pulsed SOI Raman Amplifiers” Integrated Photonics Research and Application2005, Paper IMG3.

Paniccia, M.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Panoiu, N. C.

X. Chen, N. C. Panoiu, R. M. Osgood “Full Theoretical Analysis of Pulsed SOI Raman Amplifiers” Integrated Photonics Research and Application2005, Paper IMG3.

Quochi, F.

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

Raghunathan, V.

Reed, G. T.

G. T. Reed, A. P. Knights, Silicon Photonics: An Introduction (John Wiley, Chichester, UK, 2004).
[CrossRef]

Rong, H.

H. Rong, A. Liu, R. Jones, O. Cohen, D. Hak, R. Nicolaescu, A. Fang, M. Paniccia, “An all-silicon Raman laser,” Nature 433, 292–294 (2005).
[CrossRef] [PubMed]

Rubin, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Samara-Rubio, D.

A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004).
[CrossRef] [PubMed]

Soref, R. A.

R. A. Soref, B. R. Bennett, “Electro-optical effects in Silicon,” IEEE J. Quantum Electron. QE-23, 123–129 (1987).
[CrossRef]

Spector, S. J.

M. W. Geis, S. J. Spector, R. C. Williamson, T. M. Lyszczarz, “Submicrosecond, submilliwatt, silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004).
[CrossRef]

Takahashi, J.

H. Fukuda, T. Tsuchizawa, K. Yamada, T. Watanabe, M. Takahashi, J. Takahashi, S. Itabashi, “Silicon wire waveguides and their applications for microphotonics devices,” Integrated Photonics Research2004, Paper IWA1.

Takahashi, M.

H. Fukuda, T. Tsuchizawa, K. Yamada, T. Watanabe, M. Takahashi, J. Takahashi, S. Itabashi, “Silicon wire waveguides and their applications for microphotonics devices,” Integrated Photonics Research2004, Paper IWA1.

Tsai, M.-C

R. L. Espinola, M.-C Tsai, J. T. Yardley, R. M. Osgood, “Fast and low-power thermooptic switch on thin silicon-on-insulator,” IEEE Photon. Technol. Lett. 15, 1366–1368 (2003).
[CrossRef]

Tsang, H. K.

T. K. Liang, H. K. Tsang, “Role of free carriers from two-photon absorption in Raman amplification in silicon-on-insulator waveguides,” Appl. Phy. Lett. 84, 2745–2747 (2004).
[CrossRef]

T. K. Liang, H. K. Tsang, “Efficient Raman amplification in silicon-on-insulator waveguides,” Appl. Phy. Lett. 85, 3343–3345 (2004).
[CrossRef]

Tsuchizawa, T.

H. Fukuda, T. Tsuchizawa, K. Yamada, T. Watanabe, M. Takahashi, J. Takahashi, S. Itabashi, “Silicon wire waveguides and their applications for microphotonics devices,” Integrated Photonics Research2004, Paper IWA1.

Vlasov, Y. A.

Watanabe, T.

H. Fukuda, T. Tsuchizawa, K. Yamada, T. Watanabe, M. Takahashi, J. Takahashi, S. Itabashi, “Silicon wire waveguides and their applications for microphotonics devices,” Integrated Photonics Research2004, Paper IWA1.

Williamson, R. C.

M. W. Geis, S. J. Spector, R. C. Williamson, T. M. Lyszczarz, “Submicrosecond, submilliwatt, silicon-on-insulator thermooptic switch,” IEEE Photon. Technol. Lett. 16, 2514–2516 (2004).
[CrossRef]

Wynne, J. J.

J. J. Wynne,“Optical Third-Order Mixing in GaAs, Ge, Si, and InAs,” Phys. Rev. B 178, 1295–1303 (1969).
[CrossRef]

Xu, Q.

Yamada, K.

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Figures (6)

Fig. 1.
Fig. 1.

Energy-level diagrams for (a) general FWM and (b) CARS processes.

Fig. 2.
Fig. 2.

(a) Converted wavelength and phase mismatch vs. pump-wavelength separation. (b) Conversion efficiency versus phase mismatch for Δλ=0.148 nm at two possible propagation losses of α=3.5 dB/cm (solid line) and 0.1 dB/cm (dash-dot line).

Fig. 3.
Fig. 3.

(a) Experimental setup. (b) Spectra of pump and signal lasers. The pump longitudinal modes are separated by Δλ=0.148 nm.

Fig. 4.
Fig. 4.

Output spectra for several signal wavelengths at λ s =1545.5, 1548.5, 1550.5, 1552.5, and 1555.5 nm in the presence of the pump laser at λ p ~1435 nm.

Fig. 5.
Fig. 5.

(a) Output spectrum for λ s =1550.5 nm and the associated FWM peaks denoted by ±1, …,±5 using copropagating pump and signal sources. (b) Output spectrum using counterpropagating pump and signal sources. Note the absence of the FWM peaks as expected for this geometry.

Fig. 6.
Fig. 6.

FWM output power dependence on the (a) pump and (b) signal powers.

Equations (11)

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ω o ± = ω s ± ( ω p 1 ω p 2 )
Δ β = β o ± [ β s ± ( β p 1 β p 2 ) ]
d E p 1 d z + 1 2 α p 1 E p 1 = i γ p 1 ( E p 1 2 + 2 E p 2 2 + 2 E s 2 + 2 E o 2 ) E p 1
+ 2 i γ p 1 E s * E p 2 E o exp ( i Δ β z )
d E p 2 d z + 1 2 α p 2 E p 2 = i γ p 2 ( E p 2 2 + 2 E p 1 2 + 2 E s 2 + 2 E o 2 ) E p 2
+ 2 i γ p 2 E p 1 E s E o * exp ( i Δ β z )
d E s d z + 1 2 α s E s = i γ s ( E s 2 + 2 E p 1 2 + 2 E p 2 2 + 2 E o 2 ) E s
+ 2 i γ s E p 1 * E p 2 E o exp ( i Δ β z )
d E o d z + 1 2 α o E o = i γ o ( E o 2 + 2 E p 1 2 + 2 E p 2 2 + 2 E s 2 ) E o
+ 2 i γ o E p 1 E s E p 2 * exp ( i Δ β z )
d E o d z + 1 2 α o E o 2 i γ o E p 1 E s E p 2 * exp ( i Δ β z ) .

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