Abstract

We propose a scheme for on-chip all optical mode conversion based on forward stimulated Brillouin scattering in a hybrid phononic-photonic waveguide. To describe the mode conversion the theoretical model of the FSBS is established by taking into account the radiation pressure and the electrostriction force simultaneously. The numerical simulation is carried out for the mode conversion from the fundamental mode E11x to the higher-order mode E21x. The results indicate that the mode conversion efficiency is affected by the waveguide length and the input pump light power, and the highest efficiency can reach upto 88% by considering the influence of optical and acoustic absorption losses in the hybrid waveguide. Additionally, the conversion bandwidth with approximate 12.5 THz can be achieved in 1550nm communication band. This mode converter on-chip is a promising device in the integrated optical systems, which can effectively increase the capacity of silicon data busses for on-chip optical interconnections.

© 2014 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
  6. S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011).
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    [Crossref]
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    [Crossref] [PubMed]
  14. H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  16. P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2014 (2)

S. Li, C. Zhou, H. Cao, J. Wu, and J. Yu, “Mode conversion and coupling in a slanted grating,” Opt. Lett. 39(7), 1976–1979 (2014).
[Crossref] [PubMed]

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

2013 (2)

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21(25), 31402–31419 (2013).
[Crossref] [PubMed]

2012 (5)

2011 (2)

2010 (2)

2009 (1)

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

2006 (1)

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
[Crossref]

2005 (2)

2002 (1)

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

2001 (1)

1994 (1)

1982 (1)

Ando, T.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

Bahl, G.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Barwicz, T.

Benchabane, S.

Berdagué, S.

Bolle, C.

Bolle, C. A.

Brenn, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Burrows, E. C.

Byrnes, A.

Camacho, R.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

Cao, H.

Carmon, T.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Chen, X.

Corrado, B. J.

Cox, J. A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

Davids, P.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18(14), 14439–14453 (2010).
[Crossref] [PubMed]

Djafari Rouhani, B.

Dong, H.

Eggleton, B. J.

El Boudouti, E. H.

El Hassouani, Y.

Erdogan, T.

Escalante, J. M.

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

Esmaeelpour, M.

Essiambre, R. J.

Essiambre, R.-J.

Facq, P.

Fan, S.

Gnauck, A. H.

Greenberg, M.

Haus, H.

Jarecki, R.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

Johnson, E. G.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
[Crossref]

Kang, M. S.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Laude, V.

Lee, K. S.

Li, C.

Li, S.

Lingle, R.

Marquardt, F.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Martinez, A.

Martínez, A.

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

McCurdy, A.

McCurdy, A. H.

Mehta, A.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
[Crossref]

Mohammed, W.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
[Crossref]

Mumtaz, S.

Murata, T.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

Nakano, H.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

Nakayama, H.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

Nazarkin, A.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Olsson, R. H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

Orenstein, M.

Pant, R.

Papanikolaou, N.

Peckham, D. W.

Pennec, Y.

Pitchumani, M.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
[Crossref]

Poulton, C. G.

Qiu, W.

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21(25), 31402–31419 (2013).
[Crossref] [PubMed]

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

Rakich, P. T.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21(25), 31402–31419 (2013).
[Crossref] [PubMed]

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18(14), 14439–14453 (2010).
[Crossref] [PubMed]

Randel, S.

Reinke, C.

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

Russell, P. S. J.

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Ryf, R.

Shanhui, F.

Shin, H.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21(25), 31402–31419 (2013).
[Crossref] [PubMed]

Sierra, A.

Soljacic, M.

Starbuck, A.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

Steel, M. J.

Thornburg, W. Q.

Tomes, M.

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

Tseng, S.-Y.

Vasseur, J. O.

Wang, Z.

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21(25), 31402–31419 (2013).
[Crossref] [PubMed]

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18(14), 14439–14453 (2010).
[Crossref] [PubMed]

Winzer, P. J.

Wu, J.

Xinpeng, H.

Yamauchi, J.

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

Yu, J.

Zhou, C.

Zhu, X. D.

Appl. Opt. (1)

IEEE Photon. Technol. Lett. (1)

T. Ando, T. Murata, H. Nakayama, J. Yamauchi, and H. Nakano, “Analysis and measurement of polarization conversion in a periodically loaded dielectric waveguide,” IEEE Photon. Technol. Lett. 14(9), 1288–1290 (2002).
[Crossref]

J. Appl. Phys. (1)

J. M. Escalante, A. Martínez, and V. Laude, “Design of single-mode waveguides for enhanced light-sound interaction in honeycomb-lattice silicon slabs,” J. Appl. Phys. 115(6), 064302 (2014).
[Crossref]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

Nat Commun (1)

H. Shin, W. Qiu, R. Jarecki, J. A. Cox, R. H. Olsson, A. Starbuck, Z. Wang, and P. T. Rakich, “Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides,” Nat Commun 4, 1944 (2013).
[Crossref] [PubMed]

Nat. Phys. (2)

G. Bahl, M. Tomes, F. Marquardt, and T. Carmon, “Observation of spontaneous brillouin cooling,” Nat. Phys. 8(3), 203–207 (2012).
[Crossref]

M. S. Kang, A. Nazarkin, A. Brenn, and P. S. J. Russell, “Tightly trapped acoustic phonons in photonic crystal fibres as highly nonlinear artificial Raman oscillators,” Nat. Phys. 5(4), 276–280 (2009).
[Crossref]

Opt. Express (6)

W. Qiu, P. T. Rakich, H. Shin, H. Dong, M. Soljačić, and Z. Wang, “Stimulated Brillouin scattering in nanoscale silicon step-index waveguides: a general framework of selection rules and calculating SBS gain,” Opt. Express 21(25), 31402–31419 (2013).
[Crossref] [PubMed]

C. G. Poulton, R. Pant, A. Byrnes, S. Fan, M. J. Steel, and B. J. Eggleton, “Design for broadband on-chip isolator using Stimulated Brillouin Scattering in dispersion-engineered chalcogenide waveguides,” Opt. Express 20(19), 21235–21246 (2012).
[Crossref] [PubMed]

M. Greenberg and M. Orenstein, “Multimode add-drop multiplexing by adiabatic linearly tapered coupling,” Opt. Express 13(23), 9381–9387 (2005).
[Crossref] [PubMed]

S. Randel, R. Ryf, A. Sierra, P. J. Winzer, A. H. Gnauck, C. A. Bolle, R. J. Essiambre, D. W. Peckham, A. McCurdy, and R. Lingle., “6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6×6 MIMO equalization,” Opt. Express 19(17), 16697–16707 (2011).
[Crossref] [PubMed]

P. T. Rakich, P. Davids, and Z. Wang, “Tailoring optical forces in waveguides through radiation pressure and electrostrictive forces,” Opt. Express 18(14), 14439–14453 (2010).
[Crossref] [PubMed]

Y. Pennec, B. Djafari Rouhani, E. H. El Boudouti, C. Li, Y. El Hassouani, J. O. Vasseur, N. Papanikolaou, S. Benchabane, V. Laude, and A. Martinez, “Simultaneous existence of phononic and photonic band gaps in periodic crystal slabs,” Opt. Express 18(13), 14301–14310 (2010).
[Crossref] [PubMed]

Opt. Lett. (3)

Phys. Rev. X (1)

P. T. Rakich, C. Reinke, R. Camacho, P. Davids, and Z. Wang, “Giant enhancement of stimulated brillouin scattering in the subwavelength limit,” Phys. Rev. X 2, 011008 (2012).

SPIE Opt. Eng. (1)

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng. 45, 074602 (2006).
[Crossref]

Other (9)

G. M. Fernandes, M. Niehus, C. Marques, R. Nogeira, and A. Pinto, “Acousto-Optic Tunable Mode Coupler,” in OSA Technical Digest (Optical Society of America, 2012), JTh2A.2.

E. Dieulesaint and D. Royer, Elastic Waves in Solids II: Generation, Acousto-Optic Interaction, Applications (Springer, 2000).

W. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addision-Wesley, 1962).

J. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

J. Jackson, Classical Electrodynamics (Wiley, 1975).

S. Sriratanavaree, The Characterisation of Acoustic Waves in Optical Waveguides (City University London, 2014).

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2009).

E. Dieulesaint and D. Royer, Elastic Waves in Solids I: Generation, Acousto-Optic Interaction, Applications (Springer, 2000).

S. Gevorgian, A. K. Tagantsev, and A. K. Vorobiev, Tuneable Film Bulk Acoustic Wave Resonators (Springer, 2013).

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Figures (6)

Fig. 1
Fig. 1 (a) Schematic diagram of the mode conversion based on the FSBS. (b) Energy conservation diagram of FSBS process. (c) Phase matching diagram during the FSBS.
Fig. 2
Fig. 2 (a) The optical waveguide cross-section. (b, c) The E 11 x and E 21 x field profiles. (d, e) The x and y components of the electrostriction force generated by E 11 x mode, respectively. (f, g) The x and y components of radiation pressure-induced boundary force, respectively, produced by E 11 x mode. (h, i) The x and y components of the electrostriction force generated by E 21 x mode, respectively. (j, k) The x and y components of radiation pressure-induced boundary force, respectively, produced by E 21 x mode.
Fig. 3
Fig. 3 (a) The x-z plan view of the waveguide. (b) Displacement field pattern of the phononic mode. (c) Phononic band structure for phononic crystal slab (purple dots indicate the phononic dispersion relationship without defect). (d) Phononic dispersion relationship and group velocity for the guided phononic mode.
Fig. 4
Fig. 4 (a) The optical dispersion relationship and the propagation constant difference (red curve) among the guided optical modes with frequency difference at 6.7 GHz. (b) The optical wave vector mismatch curve (blue) and the acoustic dispersion curve (red).
Fig. 5
Fig. 5 The optical and acoustic powers vary with the hybrid waveguide length: (a) by considering the electrostriction force only; (b) by considering the radiation pressure only; (c) by considering both the electrostriction force and the radiation pressure.
Fig. 6
Fig. 6 (a) Efficient length as a function of the input pump light power for hybrid waveguide under different optical absorption losses. (b) Mode conversion efficiency varies with waveguide width under the given length and pump power. (c) Mode conversion efficiency varies with input pump power under different hybrid waveguide lengths.

Equations (12)

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E m (z,t)= 1 2 e m (x,y) A m (z,t) e i( β m z w m t) +c.c
σ ij = 1 2 ε 0 n 4 p ijkl E k E l
T ij rp = ε 0 ε(x,y)[ E i E j 1 2 δ ij E 2 ]
p r xx = 1 4 ε 0 γ E 1x E 2x * 1 4 ε 0 n 4 p 12 E 1z E 2z * + 1 4 ε 0 ε(x,y)[ E 1x E 2x * E 1 E 2 * ] p r yy = 1 4 ε 0 n 4 p 12 E 1x E 2x * 1 4 ε 0 n 4 p 12 E 1z E 2z * 1 4 ε 0 ε(x,y) E 1 E 2 * p r zz = 1 4 ε 0 n 4 p 12 E 1x E 2x * 1 4 ε 0 γ E 1z E 2z * + 1 4 ε 0 ε(x,y)[ E 1z E 2z * E 1 E 2 * ]
F j = i p r ij
2 ρ t 2 Γ ' 2 ρ t v 2 2 ρ=F
ρ(z,t)= 1 2i C(z,t)U(x,y)exp[i(qzΩt)]+c.c
C(z,t) z = ( Ω 2 Ω a 2 +iΩ Γ B ) 2iq v 2 C(z,t) F* U * (x,y)exp[i(Ωtqz)]dxdy q v 2
2 E 1 c 2 ε 2 E t 2 αn c E t = 1 c 2 ε 0 2 P NL t 2
P NL = ε 0 ρ 0 1 γρE
d A 1 (z) dz = γ ω 1 2 4 c 2 β 1 ρ 0 U * (x,y) e 2 (x,y) e 1 * (x,y)dxdy A 2 (z)C(z) αn 2 n eff1 A 1 (z)
d A 2 (z) dz = γ ω 2 2 4 c 2 β 2 ρ 0 U * (x,y) e 1 (x,y) e 2 * (x,y)dxdy A 1 (z)C(z) αn 2 n eff2 A 2 (z)

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