Abstract

The modal spectral response of an antiresonant reflecting optical waveguide (ARROW) with periodic corrugations or grating is calculated for both shallow and deep gratings with the Method of Lines. The effect of the ARROW layer thickness and the grating depth on the spectral response is studied. It is found that when the ARROW-layer thickness is close to resonance, the ripples in the reflection spectra become smooth and the peak reflectivity drops. This is attributed to the large increase in the leakage loss of the ARROW waveguide near resonance. The ARROW grating is characterized by modal reflectivity spectra, which exhibit a strong polarization discrimination property, in favor of the TE polarization.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
    [CrossRef]
  2. J. Kubica, “Modal propagation within ARROW waveguides,” Opt. Commun. 78, 133–136 (1990).
    [CrossRef]
  3. M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
    [CrossRef]
  4. J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
    [CrossRef]
  5. H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
    [CrossRef]
  6. Z. M. Mao, W. P. Huang, “An ARROW optical wavelength filter: design and analysis,” IEEE J. Lightwave Technol. 11, 1183–1188 (1993).
    [CrossRef]
  7. J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
    [CrossRef]
  8. V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
    [CrossRef]
  9. M. Mann, U. Trutschel, C. Wachter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
    [CrossRef] [PubMed]
  10. J. Gerdes, R. Pregla, “Beam-propagation algorithm based on the method of lines,” J. Opt. Soc. Am. B 8, 389–394 (1991).
    [CrossRef]
  11. U. Rogge, R. Pregla, “Method of lines for the analysis of strip-loaded optical waveguides,” J. Opt. Soc. Am. B 8, 459–463 (1991).
    [CrossRef]
  12. S. F. Helfert, R. Pregla, “Efficient analysis of periodic structures,” IEEE J. Lightwave Technol. 16, 1694–1702 (1998).
    [CrossRef]
  13. V. Vemuri, W. J. Karplus, Digital Computer Treatment of Partial Differential Equations, Prentice-Hall Series in Computational Mathematics (Prentice Hall, Englewood Cliffs, New Jersey, 1981).
  14. T. Itoh, ed., Numerical Techniques for Microwave and Millimeter-Wave Passive Structures (Wiley, New York, 1989).
  15. E. Ahlers, R. Pregla, “3-D modeling of concatenations of straight and curved waveguides by MoL-BPM,” Opt. Quantum Electron. 29, 151–156 (1997).
    [CrossRef]
  16. U. Rogge, “Method of lines for the analysis of dielectric waveguides.” Ph.D. thesis (Fern University, Hagen, Germany, 1991).
  17. H. A. Al-Jamid, M. N. Akram, “A new higher-order finite-difference approximation scheme for the method of lines,” IEEE J. Lightwave Technol. 19, 398–404 (2001).
    [CrossRef]
  18. H. A. Jamid, M. N. Akram, “Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework,” IEEE J. Lightwave Technol. 20, 1204–1209 (2002).
    [CrossRef]
  19. H. A. Jamid, “Frequency-domain PML layer based on the complex mapping of space: boundary condition treatment,” IEEE Microwave Guid. Wave Lett. 10, 356–358 (2000).
    [CrossRef]
  20. J. M. Kubica, “A rigorous design method for antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 6, 1460–1462 (1994).
    [CrossRef]
  21. M. N. Akram, Master’s thesis (King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 2000).

2002 (1)

H. A. Jamid, M. N. Akram, “Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework,” IEEE J. Lightwave Technol. 20, 1204–1209 (2002).
[CrossRef]

2001 (1)

H. A. Al-Jamid, M. N. Akram, “A new higher-order finite-difference approximation scheme for the method of lines,” IEEE J. Lightwave Technol. 19, 398–404 (2001).
[CrossRef]

2000 (1)

H. A. Jamid, “Frequency-domain PML layer based on the complex mapping of space: boundary condition treatment,” IEEE Microwave Guid. Wave Lett. 10, 356–358 (2000).
[CrossRef]

1998 (2)

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

S. F. Helfert, R. Pregla, “Efficient analysis of periodic structures,” IEEE J. Lightwave Technol. 16, 1694–1702 (1998).
[CrossRef]

1997 (1)

E. Ahlers, R. Pregla, “3-D modeling of concatenations of straight and curved waveguides by MoL-BPM,” Opt. Quantum Electron. 29, 151–156 (1997).
[CrossRef]

1996 (1)

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

1995 (1)

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

1994 (1)

J. M. Kubica, “A rigorous design method for antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 6, 1460–1462 (1994).
[CrossRef]

1993 (2)

J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
[CrossRef]

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

1992 (1)

W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
[CrossRef]

1991 (3)

1990 (1)

J. Kubica, “Modal propagation within ARROW waveguides,” Opt. Commun. 78, 133–136 (1990).
[CrossRef]

1986 (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[CrossRef]

Ahlers, E.

E. Ahlers, R. Pregla, “3-D modeling of concatenations of straight and curved waveguides by MoL-BPM,” Opt. Quantum Electron. 29, 151–156 (1997).
[CrossRef]

Akram, M. N.

H. A. Jamid, M. N. Akram, “Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework,” IEEE J. Lightwave Technol. 20, 1204–1209 (2002).
[CrossRef]

H. A. Al-Jamid, M. N. Akram, “A new higher-order finite-difference approximation scheme for the method of lines,” IEEE J. Lightwave Technol. 19, 398–404 (2001).
[CrossRef]

M. N. Akram, Master’s thesis (King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 2000).

Al-Jamid, H. A.

H. A. Al-Jamid, M. N. Akram, “A new higher-order finite-difference approximation scheme for the method of lines,” IEEE J. Lightwave Technol. 19, 398–404 (2001).
[CrossRef]

Al-Muhanna, M.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Alvarez, T.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Archambault, J. L.

J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
[CrossRef]

Black, R. J.

J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
[CrossRef]

Botez, L.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Brauer, A.

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

Bures, J.

J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
[CrossRef]

Chow, Y. L.

W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
[CrossRef]

Delisle, V.

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

Duguay, M. A.

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[CrossRef]

Gehler, J.

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

Gerdes, J.

Helfert, S. F.

S. F. Helfert, R. Pregla, “Efficient analysis of periodic structures,” IEEE J. Lightwave Technol. 16, 1694–1702 (1998).
[CrossRef]

Huang, W.

W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
[CrossRef]

Huang, W. P.

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

Jamid, H. A.

H. A. Jamid, M. N. Akram, “Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework,” IEEE J. Lightwave Technol. 20, 1204–1209 (2002).
[CrossRef]

H. A. Jamid, “Frequency-domain PML layer based on the complex mapping of space: boundary condition treatment,” IEEE Microwave Guid. Wave Lett. 10, 356–358 (2000).
[CrossRef]

Johnson, R. F. D.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Karplus, W. J.

V. Vemuri, W. J. Karplus, Digital Computer Treatment of Partial Differential Equations, Prentice-Hall Series in Computational Mathematics (Prentice Hall, Englewood Cliffs, New Jersey, 1981).

Karthe, W.

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

Koch, T. L.

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[CrossRef]

Kokubun, Y.

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[CrossRef]

Kubica, J.

J. Kubica, “Modal propagation within ARROW waveguides,” Opt. Commun. 78, 133–136 (1990).
[CrossRef]

Kubica, J. M.

J. M. Kubica, “A rigorous design method for antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 6, 1460–1462 (1994).
[CrossRef]

Lacroix, S.

J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
[CrossRef]

Lederer, F.

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

M. Mann, U. Trutschel, C. Wachter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[CrossRef] [PubMed]

Leine, L.

Mann, M.

Mao, Z. M.

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

Mawst, A.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Nathan, A.

W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
[CrossRef]

Pfeiffer, L.

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[CrossRef]

Pregla, R.

S. F. Helfert, R. Pregla, “Efficient analysis of periodic structures,” IEEE J. Lightwave Technol. 16, 1694–1702 (1998).
[CrossRef]

E. Ahlers, R. Pregla, “3-D modeling of concatenations of straight and curved waveguides by MoL-BPM,” Opt. Quantum Electron. 29, 151–156 (1997).
[CrossRef]

J. Gerdes, R. Pregla, “Beam-propagation algorithm based on the method of lines,” J. Opt. Soc. Am. B 8, 389–394 (1991).
[CrossRef]

U. Rogge, R. Pregla, “Method of lines for the analysis of strip-loaded optical waveguides,” J. Opt. Soc. Am. B 8, 459–463 (1991).
[CrossRef]

Rogge, U.

U. Rogge, R. Pregla, “Method of lines for the analysis of strip-loaded optical waveguides,” J. Opt. Soc. Am. B 8, 459–463 (1991).
[CrossRef]

U. Rogge, “Method of lines for the analysis of dielectric waveguides.” Ph.D. thesis (Fern University, Hagen, Germany, 1991).

Shubair, R. M.

W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
[CrossRef]

Tremblay, H.

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

Trurschel, U.

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

Trutschel, U.

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

M. Mann, U. Trutschel, C. Wachter, L. Leine, F. Lederer, “Directional coupler based on an antiresonant reflecting optical waveguide,” Opt. Lett. 16, 805–807 (1991).
[CrossRef] [PubMed]

Vang, D.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Vemuri, V.

V. Vemuri, W. J. Karplus, Digital Computer Treatment of Partial Differential Equations, Prentice-Hall Series in Computational Mathematics (Prentice Hall, Englewood Cliffs, New Jersey, 1981).

Wachter, C.

Yang, H. N.

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

M. A. Duguay, Y. Kokubun, T. L. Koch, L. Pfeiffer, “Antiresonant reflecting optical waveguides in SiO2-Si multilayer structures,” Appl. Phys. Lett. 49, 13–15 (1986).
[CrossRef]

Electron. Lett. (1)

J. Gehler, A. Brauer, W. Karthe, U. Trurschel, M. A. Duguay, “ARROW based optical wavelength filter in silica,” Electron. Lett. 31, 547–548 (1995).
[CrossRef]

IEEE J. Lightwave Technol. (6)

S. F. Helfert, R. Pregla, “Efficient analysis of periodic structures,” IEEE J. Lightwave Technol. 16, 1694–1702 (1998).
[CrossRef]

J. L. Archambault, R. J. Black, S. Lacroix, J. Bures, “Loss calculations for anti-resonant waveguides,” IEEE J. Lightwave Technol. 11, 416–423 (1993).
[CrossRef]

W. Huang, R. M. Shubair, A. Nathan, Y. L. Chow, “The modal characteristics of ARROW structures,” IEEE J. Lightwave Technol. 10, 1015–1022 (1992).
[CrossRef]

H. A. Al-Jamid, M. N. Akram, “A new higher-order finite-difference approximation scheme for the method of lines,” IEEE J. Lightwave Technol. 19, 398–404 (2001).
[CrossRef]

H. A. Jamid, M. N. Akram, “Analysis of deep waveguide gratings: an efficient cascading and doubling algorithm in the method of lines framework,” IEEE J. Lightwave Technol. 20, 1204–1209 (2002).
[CrossRef]

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

IEEE Microwave Guid. Wave Lett. (1)

H. A. Jamid, “Frequency-domain PML layer based on the complex mapping of space: boundary condition treatment,” IEEE Microwave Guid. Wave Lett. 10, 356–358 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

J. M. Kubica, “A rigorous design method for antiresonant reflecting optical waveguides,” IEEE Photon. Technol. Lett. 6, 1460–1462 (1994).
[CrossRef]

H. N. Yang, M. Al-Muhanna, A. Mawst, L. Botez, D. Vang, T. Alvarez, R. F. D. Johnson, “High-power single-mode simplified antiresonant reflecting optical waveguide (s-arrow) distributed feedback semiconductor lasers,” IEEE Photon. Technol. Lett. 10, 1079–1081 (1998).
[CrossRef]

V. Delisle, U. Trutschel, H. Tremblay, M. A. Duguay, F. Lederer, “High finesse wavelength selective coupler based on ARROW,” IEEE Photon. Technol. Lett. 8, 791–793 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

J. Kubica, “Modal propagation within ARROW waveguides,” Opt. Commun. 78, 133–136 (1990).
[CrossRef]

Opt. Lett. (1)

Opt. Quantum Electron. (1)

E. Ahlers, R. Pregla, “3-D modeling of concatenations of straight and curved waveguides by MoL-BPM,” Opt. Quantum Electron. 29, 151–156 (1997).
[CrossRef]

Other (4)

U. Rogge, “Method of lines for the analysis of dielectric waveguides.” Ph.D. thesis (Fern University, Hagen, Germany, 1991).

M. N. Akram, Master’s thesis (King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia, 2000).

V. Vemuri, W. J. Karplus, Digital Computer Treatment of Partial Differential Equations, Prentice-Hall Series in Computational Mathematics (Prentice Hall, Englewood Cliffs, New Jersey, 1981).

T. Itoh, ed., Numerical Techniques for Microwave and Millimeter-Wave Passive Structures (Wiley, New York, 1989).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

ARROW grating structure.

Fig. 2
Fig. 2

n eff (real part) of TE and TM modes versus ARROW layer thickness.

Fig. 3
Fig. 3

Modal loss of TE and TM modes versus ARROW layer thickness.

Fig. 4
Fig. 4

ARROW TE1 and TE2 mode profile transformation. (a) d ARROW = 0.1 μm, (b) d ARROW = 0.19 μm, (c) d ARROW = 0.198 μm, (d) d ARROW = 0.225 μm, (e) d ARROW = 0.3 μm.

Fig. 5
Fig. 5

Modal reflectivity of shallow ARROW grating at antiresonance and near resonance TE1 and TM1 modes.

Fig. 6
Fig. 6

Modal reflectivity of deep ARROW grating operating at anti resonance TE1 and TM1 modes.

Fig. 7
Fig. 7

Modal reflectivity of deep ARROW grating operating near resonance TE and TM modes.

Fig. 8
Fig. 8

Modal reflectivity of deep ARROW grating for higher-order TE and TM modes operating (a) at antiResonance, d ARROW = 0.1 μm and (b) near resonance, d ARROW = 0.19 μm.

Fig. 9
Fig. 9

Modal reflectivity of deeper ARROW grating, TE1 and TM1 modes, 10% groove depth.

Tables (1)

Tables Icon

Table 1 Effective-Index of Different ARROW Modes and the Corresponding Error [neff(Exact) - neff(MoL)]

Equations (7)

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

x  x1+jσ,
dx  dx1+jσ,
exp+jkx1+jσ=exp+jkxexp-kσx
2ψx, zx2+2ψx, zz2+ko2n2xψx, z=0
d2Ψdz2+S2Ψ=0,
S21Δx2-211-21001-211-2+ko2n12n220n320nM2
Ψ=exp+jSzA+exp-jSzB.

Metrics