Abstract

Two optical beams of the same frequency but different wave vectors propagating through a homogeneous dielectric medium can exchange photons with each other and/or undergo mutually induced phase shifts as a result of a stimulated Rayleigh emission underpinning the coupling term of the Poynting theorem. Quadrature states of the same optical wave exchange power as they propagate through a homogeneous and linear dielectric medium. Consequently, coupling of photons between two optical waveguides takes place in the shared cladding region.

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References

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  1. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).
  2. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  3. A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” J. Lightwave Technol. 5, 1652–1659 (1987).
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  4. K. Inoue and T. Mukai, “Signal wavelength dependence of gain saturation in a fiber optical parametric amplifier,” Opt. Lett. 26, 10–12 (2001).
    [CrossRef]
  5. K. Inoue and T. Mukai, “Spectral hole in the amplified spontaneous emission spectrum of a fiber optical parametric amplifier,” Opt. Lett. 26, 869–871 (2001).
    [CrossRef]
  6. D. Marcuse, Principles of Quantum Electronics (Academic, 1980).
  7. W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  9. W. P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11, 963–983 (1994).
    [CrossRef]
  10. Q. Yishen, L. Denfeng, L. Gaoming, and L. Denfeng, “Rigorous vectorial coupled-mode theory for the isotropic waveguide with anisotropic disturbance,” J. Opt. Soc. Am. B 23, 120–125 (2006).
    [CrossRef]
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    [CrossRef]
  12. E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. 22, 988–993 (1986).Two sets of wave equations are mixed up to generate an “interaction” between the guided modes of the individual waveguides. One set of equations involves the normal, even and odd, modes of the coupler, and the other set involves the modes of the individual waveguides. But no physical effect underpins this mathematical technique. Equally, the incoming guided mode of one waveguide is instantly converted, at the input to the coupler, into a superposition of the normal modes. But no explanation is provided as to how the propagation constant of the incoming photons is converted into the propagation constants of the normal modes.
    [CrossRef]
  13. S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008). http://www.ece.rutgers.edu/~orfanidi/ewa
  14. E. A. J. Marcatili, L. L. Buhl, and R. C. Alferness, “Experimental verification of the improved coupled-mode equations,” Appl. Phys. Lett. 49, 1692–1694 (1986).
    [CrossRef]
  15. R. R. A. Syms and R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
    [CrossRef]
  16. M. Xu, F. Li, T. Wang, J. Wu, L. Lu, L. Zhou, and Y. Su, “Design of an electro-optic modulator based on a silicon-plasmonic hybrid phase shifter,” J. Lightwave Technol. 31, 1170–1177 (2013).
    [CrossRef]
  17. A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
    [CrossRef]
  18. A. Vatarescu, “Nonperiodic power coupling in highly birefringent nonlinear optical fibers,” Appl. Phys. Lett. 49, 1409–1411 (1986).
    [CrossRef]
  19. T. Zhu, X. Bao, L. Chen, H. Liang, and Y. Dong, “Experimental study on stimulated Rayleigh scattering in optical fibers,” Opt. Express 18, 22958 (2010).
    [CrossRef]
  20. C. L. Tang, “Spontaneous and stimulated parametric processes,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, 1975), p. 419.

2013

2010

2009

2006

2001

1994

1989

R. R. A. Syms and R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

1987

A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” J. Lightwave Technol. 5, 1652–1659 (1987).
[CrossRef]

1986

E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. 22, 988–993 (1986).Two sets of wave equations are mixed up to generate an “interaction” between the guided modes of the individual waveguides. One set of equations involves the normal, even and odd, modes of the coupler, and the other set involves the modes of the individual waveguides. But no physical effect underpins this mathematical technique. Equally, the incoming guided mode of one waveguide is instantly converted, at the input to the coupler, into a superposition of the normal modes. But no explanation is provided as to how the propagation constant of the incoming photons is converted into the propagation constants of the normal modes.
[CrossRef]

E. A. J. Marcatili, L. L. Buhl, and R. C. Alferness, “Experimental verification of the improved coupled-mode equations,” Appl. Phys. Lett. 49, 1692–1694 (1986).
[CrossRef]

A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
[CrossRef]

A. Vatarescu, “Nonperiodic power coupling in highly birefringent nonlinear optical fibers,” Appl. Phys. Lett. 49, 1409–1411 (1986).
[CrossRef]

Alferness, R. C.

E. A. J. Marcatili, L. L. Buhl, and R. C. Alferness, “Experimental verification of the improved coupled-mode equations,” Appl. Phys. Lett. 49, 1692–1694 (1986).
[CrossRef]

Bao, X.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Buhl, L. L.

E. A. J. Marcatili, L. L. Buhl, and R. C. Alferness, “Experimental verification of the improved coupled-mode equations,” Appl. Phys. Lett. 49, 1692–1694 (1986).
[CrossRef]

Chen, L.

Denfeng, L.

Dong, Y.

Gaoming, L.

Huang, W. P.

Inoue, K.

Li, F.

Liang, H.

Louisell, W. H.

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).

Lu, L.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Marcatili, E.

E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. 22, 988–993 (1986).Two sets of wave equations are mixed up to generate an “interaction” between the guided modes of the individual waveguides. One set of equations involves the normal, even and odd, modes of the coupler, and the other set involves the modes of the individual waveguides. But no physical effect underpins this mathematical technique. Equally, the incoming guided mode of one waveguide is instantly converted, at the input to the coupler, into a superposition of the normal modes. But no explanation is provided as to how the propagation constant of the incoming photons is converted into the propagation constants of the normal modes.
[CrossRef]

Marcatili, E. A. J.

E. A. J. Marcatili, L. L. Buhl, and R. C. Alferness, “Experimental verification of the improved coupled-mode equations,” Appl. Phys. Lett. 49, 1692–1694 (1986).
[CrossRef]

Marcuse, D.

D. Marcuse, Principles of Quantum Electronics (Academic, 1980).

Mu, J.

Mukai, T.

Orfanidis, S. J.

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008). http://www.ece.rutgers.edu/~orfanidi/ewa

Peall, R. G.

R. R. A. Syms and R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

Su, Y.

Syms, R. R. A.

R. R. A. Syms and R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

Tang, C. L.

C. L. Tang, “Spontaneous and stimulated parametric processes,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, 1975), p. 419.

Vatarescu, A.

A. Vatarescu, “Light conversion in nonlinear monomode optical fibers,” J. Lightwave Technol. 5, 1652–1659 (1987).
[CrossRef]

A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
[CrossRef]

A. Vatarescu, “Nonperiodic power coupling in highly birefringent nonlinear optical fibers,” Appl. Phys. Lett. 49, 1409–1411 (1986).
[CrossRef]

Wang, T.

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Wu, J.

Xu, M.

Yishen, Q.

Zhou, L.

Zhu, T.

Appl. Phys. Lett.

E. A. J. Marcatili, L. L. Buhl, and R. C. Alferness, “Experimental verification of the improved coupled-mode equations,” Appl. Phys. Lett. 49, 1692–1694 (1986).
[CrossRef]

A. Vatarescu, “Intensity discrimination through nonlinear power coupling in birefringent fibers,” Appl. Phys. Lett. 49, 61–63 (1986).
[CrossRef]

A. Vatarescu, “Nonperiodic power coupling in highly birefringent nonlinear optical fibers,” Appl. Phys. Lett. 49, 1409–1411 (1986).
[CrossRef]

IEEE J. Quantum Electron.

E. Marcatili, “Improved coupled-mode equations for dielectric guides,” IEEE J. Quantum Electron. 22, 988–993 (1986).Two sets of wave equations are mixed up to generate an “interaction” between the guided modes of the individual waveguides. One set of equations involves the normal, even and odd, modes of the coupler, and the other set involves the modes of the individual waveguides. But no physical effect underpins this mathematical technique. Equally, the incoming guided mode of one waveguide is instantly converted, at the input to the coupler, into a superposition of the normal modes. But no explanation is provided as to how the propagation constant of the incoming photons is converted into the propagation constants of the normal modes.
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Commun.

R. R. A. Syms and R. G. Peall, “Mode confinement and modal overlap in electro-optic channel waveguide devices,” Opt. Commun. 74, 46–48 (1989).
[CrossRef]

Opt. Express

Opt. Lett.

Other

D. Marcuse, Principles of Quantum Electronics (Academic, 1980).

W. H. Louisell, Quantum Statistical Properties of Radiation (Wiley, 1973).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, 1984).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

C. L. Tang, “Spontaneous and stimulated parametric processes,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, 1975), p. 419.

S. J. Orfanidis, Electromagnetic Waves and Antennas (Rutgers University, 2008). http://www.ece.rutgers.edu/~orfanidi/ewa

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Figures (1)

Fig. 1.
Fig. 1.

Diagram of the longitudinal stages of the comprehensive coupling effects between the two waveguides of a directional coupler.

Equations (21)

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E(k,φ)=Eo(z)f(r)eiφei(ωtk·r)u,
f2(x,y,z)dxdy=1,
P(z)=0.5εoncEo2(z).
2E1+(kon)2E1=(E1·ε/ε)ω2μoP2,
2H1+(kon)2H1=iωε×E1iω×P2,
·P1=iωD1·E1*iωB1·H1*iωP2·E1*,
dE12/dz=2γE1E2sinθ,
dE(k1)/dz=i[kon+γ(E2/E1)cosθ]E1γE2sinθ,
dθ/dz=(k2k1)·uz+γ[(E1/E2)(E2/E1)]cosθ,
Eout=(E2+iE1)ei(ωtk·r)=Eo[cos(γz)+isin(γz)]ei(ωtk·r),
ReEout=Eo[cos(γz)cos(ωtk·r)sin(γz)sin(ωtk·r)],
ea=(paeiφpa+qaeiφqa)fa(r)ei(ωtka·r),
eb=(pbeiφpb+qbeiφqb)fb(r)ei(ωtkb·r),
κ12(z)=γ(x,y,z)f1(x,y,z)f2(x,y,z)dxdy,
dqa2/dz=2(κaapasinθpa,qa+κabpbsinθpb,qa+κabqbsinθqb,qa)qa,
dφqa/dz=(κaapacosθpa,qa+κabpbcosθpb,qa+κabqbcosθqb,qa)/qa,
dθpb,qa/dz=βbβa+d(φpbφqa)/dz,
H^int=χ(a^2a^1+a^1a^2),
da^1/dt=(i/)[a^1,H^int]=iχa^2.
Psp=χ2hPpumpΩ·Δz/(πnλ4),
×H1=(εoE1+P1)/t+P2/t.

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