Abstract

We propose and investigate the optimal design of a nonperiodic grating-assisted directional coupler by iterative methods using the beam propagation method. Computer simulations were carried out at wavelengths of 0.8, 1.3, and 1.5 µm, which are often used in optical communications and networking. We found that the complete power coupling lengths can be reduced considerably in comparison with those in the case of the periodic grating-assisted waveguides with the same set of parameters.

© 2001 Optical Society of America

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References

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  1. S. Roland, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
    [CrossRef]
  2. C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
    [CrossRef]
  3. Z. M. Mao, W. P. Huang, “ARROW optical wavelength filter: design and analysis,” J. Lightwave Technol. 11, 1183–1188 (1993).
    [CrossRef]
  4. E. S. Tony, S. K. Chaudhuri, “Directional coupler acoustooptic filter with reduced sidelobe levels,” J. Lightwave Technol. 12, 1144–1151 (1994).
    [CrossRef]
  5. S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
    [CrossRef]
  6. B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 264–269.
  7. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), pp. 251–333.
    [CrossRef]
  8. K. S. Chiang, “Analysis of optical fibers by the effective-index method,” Appl. Opt. 25, 348–354 (1986).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  10. M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
    [CrossRef]
  11. R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
    [CrossRef]
  12. M. Osinski, W. E. Thompson, A. M. Sarangan, A. P. Bogatov, “Theory of angled grating semiconductor lasers: comparison of an analytical model and BPM solution,” in Advanced High-Power Lasers, M. Osinski, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 108–119 (2000).
    [CrossRef]
  13. Y. Tsuji, M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18, 618–623 (2000).
    [CrossRef]
  14. D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. Part II: Grating-assisted couplers,” J. Lightwave Technol. LT-5, 268–273 (1987).
    [CrossRef]
  15. K. Winick, “Design of grating-assisted waveguide couplers with weighted coupling,” J. Lightwave Technol. 9, 1481–1492 (1991).
    [CrossRef]
  16. T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
    [CrossRef]
  17. M. J. Li, S. I. Najafi, “Polarization dependence of grating-assisted waveguide Bragg reflectors,” Appl. Opt. 32, 4517–4521 (1993).
    [CrossRef] [PubMed]

2000 (3)

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Y. Tsuji, M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18, 618–623 (2000).
[CrossRef]

1998 (1)

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

1995 (1)

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

1994 (2)

S. Roland, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
[CrossRef]

E. S. Tony, S. K. Chaudhuri, “Directional coupler acoustooptic filter with reduced sidelobe levels,” J. Lightwave Technol. 12, 1144–1151 (1994).
[CrossRef]

1993 (3)

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Z. M. Mao, W. P. Huang, “ARROW optical wavelength filter: design and analysis,” J. Lightwave Technol. 11, 1183–1188 (1993).
[CrossRef]

M. J. Li, S. I. Najafi, “Polarization dependence of grating-assisted waveguide Bragg reflectors,” Appl. Opt. 32, 4517–4521 (1993).
[CrossRef] [PubMed]

1991 (1)

K. Winick, “Design of grating-assisted waveguide couplers with weighted coupling,” J. Lightwave Technol. 9, 1481–1492 (1991).
[CrossRef]

1987 (1)

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. Part II: Grating-assisted couplers,” J. Lightwave Technol. LT-5, 268–273 (1987).
[CrossRef]

1986 (1)

Bogatov, A. P.

M. Osinski, W. E. Thompson, A. M. Sarangan, A. P. Bogatov, “Theory of angled grating semiconductor lasers: comparison of an analytical model and BPM solution,” in Advanced High-Power Lasers, M. Osinski, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 108–119 (2000).
[CrossRef]

Bouadma, N.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Carenco, A.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Carre, M.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Chaudhuri, S. K.

E. S. Tony, S. K. Chaudhuri, “Directional coupler acoustooptic filter with reduced sidelobe levels,” J. Lightwave Technol. 12, 1144–1151 (1994).
[CrossRef]

Chiang, K. S.

Chik, K. D.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Dugazzaden, A.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Fiddy, M. A.

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

Filoche, M.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Fouchet, S.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Francois, S.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Gopinath, A.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Helfert, S.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Herve-Gruyer, G.

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

Huang, W. P.

Z. M. Mao, W. P. Huang, “ARROW optical wavelength filter: design and analysis,” J. Lightwave Technol. 11, 1183–1188 (1993).
[CrossRef]

Koshiba, M.

Larocque, C.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Li, M. J.

Liang, T.

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

Mao, Z. M.

Z. M. Mao, W. P. Huang, “ARROW optical wavelength filter: design and analysis,” J. Lightwave Technol. 11, 1183–1188 (1993).
[CrossRef]

Marcuse, D.

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. Part II: Grating-assisted couplers,” J. Lightwave Technol. LT-5, 268–273 (1987).
[CrossRef]

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), pp. 251–333.
[CrossRef]

Najafi, S. I.

Osinski, M.

M. Osinski, W. E. Thompson, A. M. Sarangan, A. P. Bogatov, “Theory of angled grating semiconductor lasers: comparison of an analytical model and BPM solution,” in Advanced High-Power Lasers, M. Osinski, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 108–119 (2000).
[CrossRef]

Pregla, R.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Puetz, N.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Roland, S.

S. Roland, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
[CrossRef]

Rolland, C.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Saleh, B. E.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 264–269.

Sarangan, A. M.

M. Osinski, W. E. Thompson, A. M. Sarangan, A. P. Bogatov, “Theory of angled grating semiconductor lasers: comparison of an analytical model and BPM solution,” in Advanced High-Power Lasers, M. Osinski, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 108–119 (2000).
[CrossRef]

Scarmozzino, R.

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

Shepherd, F.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Teich, M. C.

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 264–269.

Testorf, M. E.

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

Thompson, W. E.

M. Osinski, W. E. Thompson, A. M. Sarangan, A. P. Bogatov, “Theory of angled grating semiconductor lasers: comparison of an analytical model and BPM solution,” in Advanced High-Power Lasers, M. Osinski, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 108–119 (2000).
[CrossRef]

Tony, E. S.

E. S. Tony, S. K. Chaudhuri, “Directional coupler acoustooptic filter with reduced sidelobe levels,” J. Lightwave Technol. 12, 1144–1151 (1994).
[CrossRef]

Tsuji, Y.

Winick, K.

K. Winick, “Design of grating-assisted waveguide couplers with weighted coupling,” J. Lightwave Technol. 9, 1481–1492 (1991).
[CrossRef]

Wu, C.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Xu, J. M.

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

Ziolkowski, R. W.

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

Appl. Opt. (2)

IEEE J. Sel. Top. Quantum Electron. (1)

R. Scarmozzino, A. Gopinath, R. Pregla, S. Helfert, “Numerical techniques for modeling guided-wave photonic devices,” IEEE J. Sel. Top. Quantum Electron. 6, 150–162 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

T. Liang, R. W. Ziolkowski, “Grating assisted waveguide-to-waveguide couplers,” IEEE Photon. Technol. Lett. 10, 693–695 (1998).
[CrossRef]

S. Francois, S. Fouchet, N. Bouadma, A. Dugazzaden, M. Carre, G. Herve-Gruyer, M. Filoche, A. Carenco, “Polarization-independent filtering in a grating-assisted horizontal directional coupler,” IEEE Photon. Technol. Lett. 7, 780–782 (1995).
[CrossRef]

C. Wu, C. Rolland, F. Shepherd, C. Larocque, N. Puetz, K. D. Chik, J. M. Xu, “InGaAsP/InP vertical directional coupler filter with optimally designed wavelength tunability,” IEEE Photon. Technol. Lett. 5, 457–459 (1993).
[CrossRef]

J. Lightwave Technol. (5)

Z. M. Mao, W. P. Huang, “ARROW optical wavelength filter: design and analysis,” J. Lightwave Technol. 11, 1183–1188 (1993).
[CrossRef]

E. S. Tony, S. K. Chaudhuri, “Directional coupler acoustooptic filter with reduced sidelobe levels,” J. Lightwave Technol. 12, 1144–1151 (1994).
[CrossRef]

Y. Tsuji, M. Koshiba, “Guided-mode and leaky-mode analysis by imaginary distance beam propagation method based on finite element scheme,” J. Lightwave Technol. 18, 618–623 (2000).
[CrossRef]

D. Marcuse, “Directional couplers made of nonidentical asymmetric slabs. Part II: Grating-assisted couplers,” J. Lightwave Technol. LT-5, 268–273 (1987).
[CrossRef]

K. Winick, “Design of grating-assisted waveguide couplers with weighted coupling,” J. Lightwave Technol. 9, 1481–1492 (1991).
[CrossRef]

Opt. Commun. (1)

M. E. Testorf, M. A. Fiddy, “Simulation of light propagation in planar-integrated free-space optics,” Opt. Commun. 176, 365–372 (2000).
[CrossRef]

Opt. Quantum Electron. (1)

S. Roland, “All-optical switching in the directional coupler caused by nonlinear refraction due to cascaded second-order nonlinearity,” Opt. Quantum Electron. 26, 415–431 (1994).
[CrossRef]

Other (4)

B. E. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991), pp. 264–269.

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, New York, 1991), pp. 251–333.
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

M. Osinski, W. E. Thompson, A. M. Sarangan, A. P. Bogatov, “Theory of angled grating semiconductor lasers: comparison of an analytical model and BPM solution,” in Advanced High-Power Lasers, M. Osinski, H. T. Powell, K. Toyoda, eds., Proc. SPIE3889, 108–119 (2000).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Directional coupler structure.

Fig. 2
Fig. 2

Schematic of a grating-assisted directional coupler.

Fig. 3
Fig. 3

Simulation of power exchange in the periodic grating-assisted directional coupler with the following parameters: n 1 = 1.47, n 2 = 1.48, n s = 1.45, λ = 1.3 µm, d 1 = d 2 = 2 µm, b = 0.4 µm, s = 1 µm, and grating period Λ = 138 µm.

Fig. 4
Fig. 4

Flow chart of iterative method I for the design of the nonperiodic grating-assisted directional coupler with BPM.

Fig. 5
Fig. 5

Schematic of the nonperiodic grating-assisted directional coupler with a minimum length constraint.

Fig. 6
Fig. 6

Flow chart of iterative method III for the design of the nonperiodic grating-assisted directional coupler with BPM.

Fig. 7
Fig. 7

Input power profile over the directional coupler cross section at z = 0.

Fig. 8
Fig. 8

Simulation of power exchange in the nonperiodic grating-assisted directional coupler with the following parameters: n 1 = 1.47, n 2 = 1.48, n s = 1.45, λ = 1.3 µm, d 1 = d 2 = 2 µm, b = 0.4 µm, and s = 1 µm.

Fig. 9
Fig. 9

Simulation of power exchange in the grating-assisted directional coupler with the following parameters: n 1 = 1.47, n 2 = 1.48, n s = 1.45, λ = 0.8 µm, d 1 = d 2 = 1 µm, b = 0.2 µm, and s = 0.5 µm. (a) The periodic grating with Λ = 76 µm, (b) the nonperiodic grating with l min = dz = 0.2 µm, (c) the nonperiodic grating with l min = 10 µm.

Fig. 10
Fig. 10

Simulation of power exchange in the nonperiodic grating-assisted directional coupler with the following parameters: n 1 = 1.47, n 2 = 1.48, n s = 1.45, λ = 1.55 µm, d 1 = d 2 = 2 µm, b = 0.4 µm, s = 1 µm. (a) The periodic grating with Λ = 150 µm, (b) the nonperiodic grating with β = 1, (c) the nonperiodic grating with β = 0.99.

Tables (1)

Tables Icon

Table 1 Comparison of Computer Simulation Results

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

fz4bπcos2πΛ z,
Λ=2πβ1-β2,
L=π2κˆg,
κˆg=bn22-ns20/μ0πns2n22βeβo×n24+ns42n22ns2 βeβ0HyeHyo±HyexHyoxx=x2,
P2zP1z=01.

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