Abstract

We demonstrate a fast, accurate for weak waveguiding, approximate solution to the problem of computing the modal reflection and transmission coefficients at a discontinuity between two asymmetric multilayer waveguides together with a rigorous solution to check the validity of the approximate but fast approach. The proposed algorithm is analogous to the widely used approximation proposed by Vassallo [Electron. Lett. 21, 333 (1985)] for the case when the medium after discontinuity is uniform and has a large applicability potential for optoelectronic applications. As an example, the case of optoelectronic integration between an active laser diode and a passive waveguide device is analyzed.

© 2005 Optical Society of America

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  1. V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
    [CrossRef]
  2. S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
    [CrossRef]
  3. S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
    [CrossRef]
  4. S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
    [CrossRef]
  5. S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
    [CrossRef]
  6. P. V. Studenkov, M. R. Gokhale, S. R. Forrest, “Efficient coupling in integrated twin-waveguide lasers using waveguide tapers,” IEEE Photon. Technol. Lett. 11, 1096–1098 (1999).
    [CrossRef]
  7. P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
    [CrossRef]
  8. M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
    [CrossRef]
  9. J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
    [CrossRef]
  10. G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
    [CrossRef]
  11. F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
    [CrossRef]
  12. B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
    [CrossRef]
  13. B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
    [CrossRef]
  14. C. Vassallo, “Rigorous and approximate calculations of antireflection layer parameters for travelling-wave diode laser amplifiers,” Electron. Lett. 21, 333–334 (1985).
    [CrossRef]
  15. K. Hirayama, M. Koshiba, “Rigorous analysis of coupling between laser and passive waveguide in multilayer slab waveguide,” J. Lightwave Technol. 11, 1353–1359 (1993).
    [CrossRef]
  16. C. Vassallo, “Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide,” J. Opt. Soc. Am. A 5, 1918–1928 (1988).
    [CrossRef]
  17. C. Vassallo, “Theory and practical calculation of antireflection coatings on semiconductor laser diode and optical amplifiers,” IEE Proc. 137, 193 (1990).
  18. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  19. S.-L. Lee, D. S. L. Mui, L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol. 12, 2073–2079 (1994).
    [CrossRef]
  20. H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless multilayer dielectric waveguides,” IEEE J. Quantum Electron. 31, 411–416 (1995).
    [CrossRef]

2002 (1)

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

2001 (4)

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

2000 (3)

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

1999 (2)

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, S. R. Forrest, “Efficient coupling in integrated twin-waveguide lasers using waveguide tapers,” IEEE Photon. Technol. Lett. 11, 1096–1098 (1999).
[CrossRef]

1998 (2)

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

1997 (1)

G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
[CrossRef]

1995 (1)

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless multilayer dielectric waveguides,” IEEE J. Quantum Electron. 31, 411–416 (1995).
[CrossRef]

1994 (1)

S.-L. Lee, D. S. L. Mui, L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol. 12, 2073–2079 (1994).
[CrossRef]

1993 (1)

K. Hirayama, M. Koshiba, “Rigorous analysis of coupling between laser and passive waveguide in multilayer slab waveguide,” J. Lightwave Technol. 11, 1353–1359 (1993).
[CrossRef]

1990 (1)

C. Vassallo, “Theory and practical calculation of antireflection coatings on semiconductor laser diode and optical amplifiers,” IEE Proc. 137, 193 (1990).

1988 (1)

1985 (1)

C. Vassallo, “Rigorous and approximate calculations of antireflection layer parameters for travelling-wave diode laser amplifiers,” Electron. Lett. 21, 333–334 (1985).
[CrossRef]

Aitchison, J. S.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Andonovic, I.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Aramburu, C.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Baets, R.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Bartolo, R. E.

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

Benech, P.

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless multilayer dielectric waveguides,” IEEE J. Quantum Electron. 31, 411–416 (1995).
[CrossRef]

Bryce, A. C.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Button, C. B.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

Choo, A. G.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Coldren, L. A.

S.-L. Lee, D. S. L. Mui, L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol. 12, 2073–2079 (1994).
[CrossRef]

Dagenais, M.

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

De La Rue, R. M.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

De Mesel, K.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Ding, H.

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless multilayer dielectric waveguides,” IEEE J. Quantum Electron. 31, 411–416 (1995).
[CrossRef]

Forrest, S. R.

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, S. R. Forrest, “Efficient coupling in integrated twin-waveguide lasers using waveguide tapers,” IEEE Photon. Technol. Lett. 11, 1096–1098 (1999).
[CrossRef]

Franzen, A.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Galarza, M.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Gerard, P.

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless multilayer dielectric waveguides,” IEEE J. Quantum Electron. 31, 411–416 (1995).
[CrossRef]

Glesk, I.

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

Gokhale, M. R.

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, S. R. Forrest, “Efficient coupling in integrated twin-waveguide lasers using waveguide tapers,” IEEE Photon. Technol. Lett. 11, 1096–1098 (1999).
[CrossRef]

Hirayama, K.

K. Hirayama, M. Koshiba, “Rigorous analysis of coupling between laser and passive waveguide in multilayer slab waveguide,” J. Lightwave Technol. 11, 1353–1359 (1993).
[CrossRef]

Hou, H.

G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
[CrossRef]

Hu, Y.

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

Hunter, D. K.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Johnson, F. G.

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

Ke, M. L.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

Kim, J. R.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Kim, T. I.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Koshiba, M.

K. Hirayama, M. Koshiba, “Rigorous analysis of coupling between laser and passive waveguide in multilayer slab waveguide,” J. Lightwave Technol. 11, 1353–1359 (1993).
[CrossRef]

Kowalski, O. P.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Lee, H. K.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

Lee, J. S.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Lee, S. D.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Lee, S.-L.

S.-L. Lee, D. S. L. Mui, L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol. 12, 2073–2079 (1994).
[CrossRef]

Lee, Y. H.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Lin, W.

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

Liu, X. F.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

Lopez-Amo, M.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Marsh, J. H.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Moerman, I.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Mui, D. S. L.

S.-L. Lee, D. S. L. Mui, L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol. 12, 2073–2079 (1994).
[CrossRef]

Ott, M. N.

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

Owen, M.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Pamulapati, J.

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

Park, M. W.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Park, S.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Penty, R. V.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Prucnal, P. R.

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

Qian, Y. H.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Qiu, B. C.

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Saini, S. S.

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

Shaw, H. C.

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

Shen, H.

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

Smith, R. E.

G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
[CrossRef]

Stone, D.

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

Stone, D. R.

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

Studenkov, P. V.

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, S. R. Forrest, “Efficient coupling in integrated twin-waveguide lasers using waveguide tapers,” IEEE Photon. Technol. Lett. 11, 1096–1098 (1999).
[CrossRef]

Thomson, J. K.

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

Van Daele, P.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Vassallo, C.

C. Vassallo, “Theory and practical calculation of antireflection coatings on semiconductor laser diode and optical amplifiers,” IEE Proc. 137, 193 (1990).

C. Vassallo, “Reflectivity of multidielectric coatings deposited on the end facet of a weakly guiding dielectric slab waveguide,” J. Opt. Soc. Am. A 5, 1918–1928 (1988).
[CrossRef]

C. Vassallo, “Rigorous and approximate calculations of antireflection layer parameters for travelling-wave diode laser amplifiers,” Electron. Lett. 21, 333–334 (1985).
[CrossRef]

Vawter, G. A.

G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
[CrossRef]

Verstuyft, S.

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

Vusirikala, V.

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

Wei, J.

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

Wendt, J. R.

G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
[CrossRef]

Whaley, R.

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

White, I. H.

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

Xia, F.

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

Yu, J. S.

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

Zhou, W.

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

Electron. Lett. (1)

C. Vassallo, “Rigorous and approximate calculations of antireflection layer parameters for travelling-wave diode laser amplifiers,” Electron. Lett. 21, 333–334 (1985).
[CrossRef]

IEE Proc. (1)

C. Vassallo, “Theory and practical calculation of antireflection coatings on semiconductor laser diode and optical amplifiers,” IEE Proc. 137, 193 (1990).

IEEE J. Quantum Electron. (1)

H. Ding, P. Gerard, P. Benech, “Radiation modes of lossless multilayer dielectric waveguides,” IEEE J. Quantum Electron. 31, 411–416 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (13)

V. Vusirikala, S. S. Saini, R. E. Bartolo, M. Dagenais, D. R. Stone, “Compact mode expanders using resonant coupling between a tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 203–205 (1998).
[CrossRef]

S. S. Saini, Y. Hu, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, J. Pamulapati, M. N. Ott, H. C. Shaw, M. Dagenais, “Lossless 1 3 2 optical switch monolithically integrated on a passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 12, 840–842 (2000).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, H. Shen, W. Zhou, M. Dagenais, “Passive active resonant coupler (PARC) platform with mode expander,” IEEE Photon. Technol. Lett. 12, 1025–1027 (2000).
[CrossRef]

S. S. Saini, F. G. Johnson, D. R. Stone, W. Zhou, H. Shen, M. Dagenais, “A 2 × 2 crosspoint switch fabricated on the passive active resonant coupler (PARC) platform,” IEEE Photon. Technol. Lett. 13, 203–205 (2001).
[CrossRef]

S. S. Saini, V. Vusirikala, R. Whaley, F. G. Johnson, D. Stone, M. Dagenais, “Compact mode expanded lasers using resonant coupling between a 1.55-μm InGaAsP tapered active region and an underlying coupling waveguide,” IEEE Photon. Technol. Lett. 10, 1232–1234 (1998).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, S. R. Forrest, “Efficient coupling in integrated twin-waveguide lasers using waveguide tapers,” IEEE Photon. Technol. Lett. 11, 1096–1098 (1999).
[CrossRef]

P. V. Studenkov, M. R. Gokhale, W. Lin, I. Glesk, P. R. Prucnal, S. R. Forrest, “Monolithic integration of an all-optical Mach–Zehnder demultiplexer using an asymmetric twin-waveguide structure,” IEEE Photon. Technol. Lett. 13, 600–602 (2001).
[CrossRef]

M. Galarza, K. De Mesel, S. Verstuyft, C. Aramburu, I. Moerman, P. Van Daele, R. Baets, M. Lopez-Amo, “1.55-μm InP–InGaAsP Fabry–Perot lasers with integrated spot size converters using antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 14, 1043–1045 (2002).
[CrossRef]

J. R. Kim, J. S. Lee, S. Park, M. W. Park, J. S. Yu, S. D. Lee, A. G. Choo, T. I. Kim, Y. H. Lee, “Spot-size converter integrated polarization insensitive semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 11, 967–969 (1999).
[CrossRef]

G. A. Vawter, R. E. Smith, H. Hou, J. R. Wendt, “Semiconductor laser with tapered-rib adiabatic-following fiber coupler for expanded output-mode diameter,” IEEE Photon. Technol. Lett. 9, 425–427 (1997).
[CrossRef]

F. Xia, J. K. Thomson, M. R. Gokhale, P. V. Studenkov, J. Wei, W. Lin, S. R. Forrest, “An asymmetric twin-waveguide high-bandwidth photodiode using a lateral taper coupler,” IEEE Photon. Technol. Lett. 13, 845–847 (2001).
[CrossRef]

B. C. Qiu, X. F. Liu, M. L. Ke, H. K. Lee, A. C. Bryce, J. S. Aitchison, J. H. Marsh, C. B. Button, “Monolithic fabrication of 2 × 2 crosspoint switches in InGaAs–InAlGaAs multiple quantum wells using quantum-well intermixing,” IEEE Photon. Technol. Lett. 13, 1292–1294 (2001).
[CrossRef]

B. C. Qiu, Y. H. Qian, O. P. Kowalski, A. C. Bryce, J. S. Aitchison, R. M. De La Rue, J. H. Marsh, M. Owen, I. H. White, R. V. Penty, A. Franzen, D. K. Hunter, I. Andonovic, “Fabrication of 2 × 2 crosspoint switches using a sputtered SiO2intermixing technique,” IEEE Photon. Technol. Lett. 12, 287–289 (2000).
[CrossRef]

J. Lightwave Technol. (2)

S.-L. Lee, D. S. L. Mui, L. A. Coldren, “Explicit formulas of normalized radiation modes in multilayer waveguides,” J. Lightwave Technol. 12, 2073–2079 (1994).
[CrossRef]

K. Hirayama, M. Koshiba, “Rigorous analysis of coupling between laser and passive waveguide in multilayer slab waveguide,” J. Lightwave Technol. 11, 1353–1359 (1993).
[CrossRef]

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

Other (1)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Cited By

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Figures (6)

Fig. 1
Fig. 1

Schematic of the waveguide configuration for which the modal reflectivity is computed: (a) structure 1 and (b) structure 2.

Fig. 2
Fig. 2

Field distribution in the active (lasing) and passive sections of the waveguide: (a) the shallow etch stops above the QWs and (b) the deep etch stops below the QW and above the optical trap layer.

Fig. 3
Fig. 3

Amplitude of reflection coefficients r0, r1, r2, in the left waveguide, amplitude of transmission coefficients t0, t1 in the right waveguide, radiated power in the Pr left, left waveguide, in the Pr right right waveguide, and total radiated power Pr versus the thickness of the active layer in structure 1 for TE0 incidence from the left waveguide. (a) Results computed with the exact method reported in Ref. 15 and (b) results computed with the fast, approximate but accurate method proposed in this paper.

Fig. 4
Fig. 4

Amplitude of reflection coefficients r0, r1, r2, in the left waveguide, amplitude of transmission coefficients t0, t1, in the right waveguide, radiated power in the Pr left, left waveguide, in the Pr right, right waveguide, and total radiated power Pr versus the thickness of the active layer in structure 1 for TE1 incidence from the left waveguide. (a) Results computed with the exact method reported in Ref. 15 and (b) results computed with the fast, approximate but accurate method proposed in this paper.

Fig. 5
Fig. 5

(a) Amplitude of the reflection and transmission coefficients and (b) radiated power in the left (lasing) and right (passive) waveguides versus thickness of the p cladding above the active region that remains after etching.

Fig. 6
Fig. 6

Schematic diagram of the multilayer waveguide.

Tables (1)

Tables Icon

Table 1 Numerical Results for Two Etching Depths

Equations (37)

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

E y , inc = i left inc i f i ( x ) .
i left ( inc i + r i ) f i ( x ) + 0 f k a ϕ r a * left ( x ,     k ) d k + 0 f k b ϕ r b * left ( x ,     k ) d k = j right t j g j ( x ) + 0 g k a ϕ r a * right ( x ,     k ) d k + 0 g k b ϕ r b * right ( x ,     k ) d k ,
i left ( inc i - r i ) n ef     i k 0 f i ( x ) - 0 f k a ( N 1 left 2 k 0 2 ) - k 2 ) 1 / 2 ϕ r a * left ( x ,     k ) d k - 0 f k b ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 ϕ r b * left ( x ,     k ) d k = j right t j n ef j k 0 g j ( x ) + 0 g k a ( N 1 right 2 k 0 2 - k 2 ) 1 / 2 ϕ r a * right ( x ,     k ) d k + 0 g k b ( N 1 right 2 k 0 2 ) - k 2 ) 1 / 2 ϕ r b * right ( x ,     k ) d k ,
i left [ ( inc i + r i ) + n ef i left n ef 1 left ( inc i - r i ) ] f i ( x ) + 0 [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] × [ f k a ϕ r a * left ( x ,     k ) + f k b ϕ r b * left ( x ,     k ) ] d k = j right t j n ef j right n ef 1 left g j ( x ) + 0 [ g k a ϕ r a * right ( x ,     k ) + g k b ϕ r b * right ( x ,     k ) ] [ 1 + ( N 1 right 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k .
g k a i left [ ( inc i + r i ) + n ef i left n ef 1 lef t ( inc i - r i ) ] - f i ( x ) ϕ r a right ( k ,     x ) d x { 1 + [ ( N 1 right 2 k 0 2 - k 2 ) ] 1 / 2 n ef 1 left k 0 } i l e f t 2 inc i - f i ( x ) ϕ r a right ( k ,     x ) d x { 1 + [ ( N 1 right 2 k 0 2 - k 2 ) ] 1 / 2 n ef 1 left k 0 } , g k b i left [ ( inc i + r i ) + n ef i left n ef 1 left ( inc i - r i ) ] - f i ( x ) ϕ r b right ( k ,     x ) d x { 1 + [ ( N 1 right 2 k 0 2 - k 2 ) ] 1 / 2 n ef 1 left k 0 } i left 2 inc i - f i ( x ) ϕ r b right ( k ,     x ) d x { 1 + [ ( N 1 right 2 k 0 2 - k 2 ) ] 1 / 2 n ef 1 left k 0 } ,
t j i left [ ( inc i + r i ) + n ef i left n ef 1 left ( inc i - r i ) ] - f i ( x ) g j * ( x ) d x n ef j right / n ef 1 left i left 2 inc i - f i ( x ) g j * ( x ) d x n ef j right / n ef 1 left .
r i = - inc i + j t j - g j ( x ) f i * ( x ) d x + 0 g k a ( - f i * ( x ) φ r a * right ( x ,     k ) d x ) d k + 0 g k b ( - f i * ( x ) φ r b * right ( x ,     k ) d x ) d k = - inc i + j t j - g j ( x ) f i * ( x ) d x + 0 g k a f k a * d k + 0 g k b f k b * d k ,
f k a * = - f i * ( x ) ϕ r a * right ( x ,     k ) d x ,             - g j ( x ) f i * ( x ) d x
P r ,     left = C 0 N 1 left k 0 ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef ,     1 left k 0 × ( f k a 2 + f k b 2 ) d k , P r ,     right = C 0 N 1 right k 0 ( N 1 right 2 k 0 2 - k 2 ) 1 / 2 n ef ,     1 left k 0 × ( g k a 2 + g k b 2 ) d k , R i = C r i 2 n ef , i left n ef ,     1 left , T j = C t j 2 n ef ,     j right n ef ,     1 left ,
C = 1 i n ef ,     i left n ef ,     1 1 inc i 2 .
Γ g = α i + α m = α i + 1 2 L a ln 1 R 1 R 2 ,
η ex = 1 2 L a ln 1 R 1 R 2 α + 1 2 L a ln 1 R 1 R 2 ,
P 1 P 2 = R 2 R 1 ( 1 - R 1 ) ( 1 - R 2 ) .
η p = T a - p η ex ( 1 - R 2 ) ( 1 - R 1 R 2 ) R 1 ( R 1 + R 2 ) .
φ r ( x ,     k ) = 1 2 π × { A 1 ( k ) exp ( i k 1 x ) + B 1 ( k ) exp ( - i k 1 x ) x x 1 , k 1 = k A N - 1 ( k ) exp [ i k N - 1 ( x - x N - 2 ) ] + B N - 1 ( k ) exp [ - i k N - 1 ( x - x N - 2 ) ] x N - 2 < x x N - 1 , k N - 1 = [ k 2 + k 0 2 ( N N - 1 2 - N 1 2 ) ] 1 / 2 , A N ( k ) exp [ i k N ( x - x N - 1 ) ] + B N ( k ) exp [ - i k N ( x - x N - 1 ) ] x < x N - 1 , k N = [ k 2 + k 0 2 ( N N 2 - N 1 2 ) ] 1 / 2
( A i B i ) = 1 2 k i [ exp ( - i k i d i ) ( k i + k i + 1 ) exp ( - i k i d i ) ( k i - k i + 1 ) exp ( i k i d i ) ( k i - k i + 1 ) exp ( i k i d i ) ( k i + k i + 1 ) ] ( A i + 1 B i + 1 ) = M i ( A i + 1 B i + 1 ) ,
( A i + 1 B l + 1 ) = 1 2 k i + 1 [ exp ( i k i d i ) ( k i + 1 + k i ) exp ( - i k i d i ) ( k i + 1 - k i ) exp ( i k i d i ) ( k i + 1 - k i ) exp ( - i k i d i ) ( k i + 1 + k i ) ] ( A i B i ) .
( A 1 B 1 ) = ( m 11 tot m 12 tot m 21 tot m 22 tot ) ( A N 0 ) = M tot ( A N 0 ) ,
B 1 a = A 1 a * = m 21 tot m 11 tot A 1 a ,             ( m 21 tot * m 11 tot * ) 1 / 2 , B 1 a = A 1 a * ,     A N a = A 1 a m 11 tot ,     B N a = 0 ,
I = - ϕ r ( x ,     k ) ϕ r * ( x ,     k ) d x = δ ( k - k )
( A 1 B 1 ) = ( m 11 tot m 12 tot m 21 tot m 22 tot ) ( A N B N ) = M tot ( A N B N ) , A 1 = A 1 * ,             A N = A N * .
A N a = B N a = B 0 = 1 ( m 11 tot + m 12 tot 2 + k N k ) 1 / 2 , A 1 a = m 11 tot + m 12 tot ( m 11 tot + m 12 tot 2 + k N k ) 1 / 2 , B 1 a = m 21 tot + m 22 tot ( m 11 tot + m 12 tot 2 + k N k ) 1 / 2 .
0 = ( A 1 a A 1 b * + A 1 a * A 1 b ) + k N k ( A N a A N b * + A N a * A N b ) .
A 1 b = i exp [ i arg ( m 11 tot + m 12 tot * ) ] ( { 1 + k k N i m 22 tot exp [ i arg ( m 11 tot + m 12 tot * ) ] + i m 12 tot exp [ - i arg ( m 11 tot + m 12 tot * ) ] } 2 ) 1 / 2 B 1 b = A 1 b * ,
A N b = ( m 22 tot A 1 b - m 12 tot B 1 b ) det M tot , B N b = A N b * = - ( m 21 tot A 1 b + m 11 tot B 1 b ) det M tot .
( A 1 b B 1 b )     or     ( A N b B N b )
( A i b B i b ) .
( A N b B N b ) ,
( A 1 b B 1 b )
( A 1 a B 1 a ) = ( 1 2 1 2 ) ,             ( A N a B N a ) = ( 1 2 1 2 ) , ( A 1 b B 1 b ) = ( i 2 - i 2 ) ,             ( A N b B N b ) = ( i 2 - i 2 ) .
ψ g left = j right c j ψ g , j right + 0 c k a ϕ k a * right ( x ,     k ) d k + 0 c k b ϕ k b * right ( x ,     k ) d k , j right c j 2 + 0 c k a 2 d k + 0 c k b 2 d k = 1 .
f k a = - i left ( inc i + r i ) - f i ( x ) ϕ r a left ( x ,     k ) d x + j right t j - g j ( x ) ϕ r a left ( x ,     k ) d x + 0 g k a d k [ - ϕ r a * right ( x ,     k ) ϕ r a left ( x ,     k ) * d x ] + 0 g k b d k [ - ϕ r b * right ( x ,     k ) ϕ r a left ( x ,     k ) d x ] .
g k a [ 1 + ( N 1 right 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] = i left [ ( inc i + r i ) + ( inc i - r i ) n ef i left n ef 1 left ] - f i ( x ) ϕ r a right ( x ,     k ) d x - j right t j - g j ( x ) ϕ r a right ( x ,     k ) d x + 0 f k a [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k [ - ϕ r a * left ( x ,     k ) ϕ r a right ( x ,     k ) d x ] + 0 f k b [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k [ - ϕ r b * left ( x ,     k ) ϕ r a right ( x ,     k ) d x ]
I = 0 f k b [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k [ - φ r b * left ( x ,     k ) φ r a right ( x ,     k ) d x ] = 0 f k b [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k [ 0 φ r b * left ( x ,     k ) φ r a right ( x ,     k ) d x ] + i = 2 N - 1 f k b [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k [ x i - 1 x i φ r b * left ( x ,     k ) φ r a right ( x ,     k ) d x ] + 0 f k b [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] d k [ - x N - 1 φ r b * left ( x ,     k ) φ r a right ( x ,     k ) d x ] = I 1 ( k ) + i = 2 N - 1 0 f k b [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ] I i ( k ,     k ) d k + I N ( k ) .
I i ( k ,     k ) = k i left * [ A i left * ( k ) - B i left * ( k ) ] [ A i right ( k ) + B i right ( k ) ] - k i + 1 left * [ A i + 1 left * ( k ) - B i + 1 left * ( k ) ] [ A i + 1 right ( k ) + B i + 1 right ( k ) ] i ( k i * left 2 - k i right 2 ) + k i right [ A i left * ( k ) + B i left * ( k ) ] [ A i right ( k ) - B i right ( k ) ] - k i + 1 right [ A i + 1 left * ( k ) + B i + 1 left * ( k ) ] [ A i + 1 right ( k ) - B i + 1 right ( k ) ] i ( k i * left 2 - k i right 2 )
I 1 ( k ) = real [ A 1 right ( k ) A 1 left * ( k ) ] f k b × [ 1 - ( N 1 left 2 k 0 2 - k 2 ) 1 / 2 n ef 1 left k 0 ]
I N ( k ) = { real [ A n right ( k ) A N left * ( k 2 + Δ left 2 - Δ right 2 ) ] f b k 2 + Δ left 2 - Δ right 2 [ 1 - ( N N left 2 k 0 2 - k 2 + Δ right 2 ) 1 / 2 n ef 1 left k 0 ] ( k 2 - Δ right 2 ) 1 / 2 ( k 2 - Δ right 2 + Δ left 2 ) 1 / 2 if k > Δ right 0 if 0 k Δ right .

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