Abstract

We report transmission spectra and mode-field distributions of a waveguide-coupled spiral-shaped microdisk resonator on a silicon nitride-on-silica substrate. Our measured and simulated transmission spectra reveal reciprocal transmissions between clockwise and counterclockwise traveling-waves of such microcavity that lacks mirror symmetry. Our measured out-of-plane scattering intensity distributions and simulated steady-state mode-field patterns, however, indicate asymmetric modal distributions that depend on the sense of lightwave circulations and the input-coupling mechanisms. We discuss implications of the observed reciprocal transmissions with asymmetric modal distributions to unidirectional lasing from spiral-shaped microcavities reported in the literature.

© 2007 Optical Society of America

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References

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  1. R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
    [CrossRef]
  2. K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
    [CrossRef] [PubMed]
  3. P. R. Romeo, J. Van Campenhout, P. Regreny, A. Kazmierczak, C. Seassal, X. Letartre, G. Hollinger, D. Van Thourhout, R. Baets, J. M. Fedeli, and L. Di Cioccio, "Heterogeneous integration of electrically driven microdisk based laser sources for optical interconnects and photonic ICs," Opt. Express 14, 3864-3871 (2006).
    [CrossRef]
  4. A. W. Fang, R. Jones, H. Park, O. Cohen, O. Raday, M. J. Paniccia, and J. E. Bowers, "Integrated AlGaInAs-silicon evanescent racetrack laser and photodetector," Opt. Express 15, 2315-2322 (2007).
    [CrossRef] [PubMed]
  5. A. E. Siegman, Lasers (University Science Books, 1986), pp. 532-538.
  6. J. P. Hohimer, G. A. Vawter, and D. C. Craft, "Unidirectional operation in a semiconductor ring diode laser," Appl. Phys. Lett. 62, 1185-1187 (1993).
    [CrossRef]
  7. H. Cao, H. Ling, C. Liu, H. Deng, M. Benavidez, V. A. Smagley, R. B. Caldwell, G. M. Peake, G.A. Smolyakov, P. G. Eliseev, and M. Osiñski, "Large S-section-ring-cavity diode lasers: directional switching, electrical diagnostics, and mode beating spectra," IEEE Photon. Technol. Lett. 17, 282-284 (2005).
    [CrossRef]
  8. J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, "Unidirectional operation of waveguide diode ring lasers," Appl. Phys. Lett. 70, 1192-1194 (1997).
    [CrossRef]
  9. H. Cao, C. Liu, H. Ling, H. Deng, M. Benavidez, V. A. Smagley, and R. B. Caldwell, "Frequency beating between monolithically integrated semiconductor ring lasers," Appl. Phys. Lett. 86, 041101 (2005).
    [CrossRef]
  10. G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, "Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillar," Appl. Phys. Lett. 83, 1710 - 1712 (2003).
    [CrossRef]
  11. M. Kneissl, M. Teepe, N. Miyashita, N. M. Johnson, G. D. Chern, and R. K. Chang, "Current-injection spiral-shaped microcavity disk laser diodes with unidirectional emission," Appl. Phys. Lett. 84, 2485 - 2487 (2004).
    [CrossRef]
  12. T. Ben-Messaoud and J. Zyss, "Unidirectional laser emission from polymer-based spiral microdisks," Appl. Phys. Lett. 86, 241110 (2005).
    [CrossRef]
  13. A. Fujii, T. Nishimura, Y. Yoshida, K. Yoshino, and M. Ozaki, "Unidirectional laser emission from spiral microcavity utilizing conducting polymer," Jpn. J. Appl. Phys. 44, L1091-L1093 (2005).
    [CrossRef]
  14. A. Fujii, T. Takashima, N. Tsujimoto, T. Nakao, Y. Yoshida, and M. Ozaki, "Fabrication and unidirectional laser emission properties of asymmetric microdisks based on poly (p-phenylenevinylene) derivative," Jpn. J. Appl. Phys. 45, L833-L836 (2006).
    [CrossRef]
  15. N. Tsujimoto, T. Takashima, T. Nakao, K. Masuyama, A. Fujii, and M. Ozaki, "Laser emission from spiral-shaped microdisc with waveguide of conducting polymer," J. Phys. D 40, 1669-1672 (2007).
    [CrossRef]
  16. R. M. Audet, M. A. Belkin, J. A. Fan, F. Capasso, E. Narimanov, D. Bour, S. Corzine, J. Zhu, and G. Höfler, "Current Injection Spiral-Shaped Chaotic Microcavity Quantum Cascade Lasers," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper CTuE4.
  17. A. Tulek and Z. V. Vardeny, "Unidirectional laser emission from π-conjugated polymer microcavities with broken symmetry," Appl. Phys. Lett. 90, 161106 (2007).
    [CrossRef]
  18. T. Y. Kwon, S. Y. Lee, M. S. Kurdoglyan, S. Rim, C. M. Kim, and Y. J. Park, "Lasing modes in a spiral-shaped dielectric microcavity," Opt. Lett. 31, 1250 - 1252 (2006).
    [CrossRef] [PubMed]
  19. S. Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C. M. Kim, "Quasiscarred resonances in a spiral-shaped microcavity," Phys. Rev. Lett. 93, 164102 (2004).
    [CrossRef] [PubMed]
  20. C. M. Kim, S. Y. Lee, J. W. Ryu, T. Y. Kwon, S. Rim J. Lee, and J. Cho, "Characteristics of lasing modes in a spiral-shaped microcavity," Prog. Theor. Phys.sSuppl. 166, 112-118 (2007).
    [CrossRef]
  21. R. K. Chang, G. E. Fernandes, and M. Kneissl, "The Quest for Uni-Directionality with WGMs in μ-Lasers: Coupled Oscillators and Amplifiers," in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 47-51.
  22. G. D. Chern, G. E. Fernandes, R. K. Chang, Q. Song, L. Xu, M. Kneissl, and N. M. Johnson, "High-Q-preserving coupling between a spiral and a semicircle μ-cavity," Opt. Lett. 32, 1093-1095 (2007).
    [CrossRef] [PubMed]
  23. J. Y. Lee and A. W. Poon, "Spiral micropillar resonator-based unidirectional channel drop filters," in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 62-65.
  24. J. Y. Lee and A. W. Poon, "Spiral-shaped microdisk resonator-based channel drop filters on a silicon nitride chip," in Proceedings of IEEE 3rd International Conference on Group IV Photonics, (IEEE, 2006), pp. 19 - 21.
  25. A. W. Poon, J. Y. Lee, and C. Chan, "Spiral microdisk resonator-based channel filters on a silicon chip: probing the out-of-plane scattering spectra," in Proceedings of International Symposium on Biophotonics, Nanophotonics and Metamaterials, (IEEE, 2006), pp. 234 - 239.
  26. J. Y. Lee, X. Luo, and A. W. Poon, "Spiral-shaped microdisk resonator channel drop/add filters: asymmetry in modal distributions," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD116.
    [CrossRef]
  27. R. J. Potton, "Reciprocity in optics," Rep. Prog. Phys. 67, 717-754 (2004).
    [CrossRef]
  28. M. Nieto-Vesperinas and E. Wolf, "Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape," J. Opt. Soc. Am. A. 3, 2038 - 2046 (1986).
    [CrossRef]
  29. M. Born and E. Wolf, Principles of Optics 7th edition (Cambridge, Cambridge University Press, 1999), pp. 724-726.
  30. G. S. Agarwal and S. Dutta Gupta, "Reciprocity relations for reflected amplitudes," Opt. Lett. 27, 1205 - 1207 (2002).
    [CrossRef]
  31. S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
    [CrossRef]
  32. FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.
  33. E. E. Narimanov and V. A. Podolskiy, "Dynamical localization in spiral microlasers with unidirectional emission," in Conference on Lasers and Electro-Optics 2004, (IEEE and Optical Society of America, 2004), paper IThI5.
  34. H. Chen, J. Y. Lee, A. W. Poon, and H. K. Tsang, "Non-evanescently pumped Raman silicon lasers using spiral-shaped microdisks," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD114.
    [CrossRef]

2007 (5)

N. Tsujimoto, T. Takashima, T. Nakao, K. Masuyama, A. Fujii, and M. Ozaki, "Laser emission from spiral-shaped microdisc with waveguide of conducting polymer," J. Phys. D 40, 1669-1672 (2007).
[CrossRef]

A. Tulek and Z. V. Vardeny, "Unidirectional laser emission from π-conjugated polymer microcavities with broken symmetry," Appl. Phys. Lett. 90, 161106 (2007).
[CrossRef]

C. M. Kim, S. Y. Lee, J. W. Ryu, T. Y. Kwon, S. Rim J. Lee, and J. Cho, "Characteristics of lasing modes in a spiral-shaped microcavity," Prog. Theor. Phys.sSuppl. 166, 112-118 (2007).
[CrossRef]

A. W. Fang, R. Jones, H. Park, O. Cohen, O. Raday, M. J. Paniccia, and J. E. Bowers, "Integrated AlGaInAs-silicon evanescent racetrack laser and photodetector," Opt. Express 15, 2315-2322 (2007).
[CrossRef] [PubMed]

G. D. Chern, G. E. Fernandes, R. K. Chang, Q. Song, L. Xu, M. Kneissl, and N. M. Johnson, "High-Q-preserving coupling between a spiral and a semicircle μ-cavity," Opt. Lett. 32, 1093-1095 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (4)

H. Cao, H. Ling, C. Liu, H. Deng, M. Benavidez, V. A. Smagley, R. B. Caldwell, G. M. Peake, G.A. Smolyakov, P. G. Eliseev, and M. Osiñski, "Large S-section-ring-cavity diode lasers: directional switching, electrical diagnostics, and mode beating spectra," IEEE Photon. Technol. Lett. 17, 282-284 (2005).
[CrossRef]

H. Cao, C. Liu, H. Ling, H. Deng, M. Benavidez, V. A. Smagley, and R. B. Caldwell, "Frequency beating between monolithically integrated semiconductor ring lasers," Appl. Phys. Lett. 86, 041101 (2005).
[CrossRef]

T. Ben-Messaoud and J. Zyss, "Unidirectional laser emission from polymer-based spiral microdisks," Appl. Phys. Lett. 86, 241110 (2005).
[CrossRef]

A. Fujii, T. Nishimura, Y. Yoshida, K. Yoshino, and M. Ozaki, "Unidirectional laser emission from spiral microcavity utilizing conducting polymer," Jpn. J. Appl. Phys. 44, L1091-L1093 (2005).
[CrossRef]

2004 (3)

M. Kneissl, M. Teepe, N. Miyashita, N. M. Johnson, G. D. Chern, and R. K. Chang, "Current-injection spiral-shaped microcavity disk laser diodes with unidirectional emission," Appl. Phys. Lett. 84, 2485 - 2487 (2004).
[CrossRef]

S. Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C. M. Kim, "Quasiscarred resonances in a spiral-shaped microcavity," Phys. Rev. Lett. 93, 164102 (2004).
[CrossRef] [PubMed]

R. J. Potton, "Reciprocity in optics," Rep. Prog. Phys. 67, 717-754 (2004).
[CrossRef]

2003 (2)

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, "Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillar," Appl. Phys. Lett. 83, 1710 - 1712 (2003).
[CrossRef]

2002 (2)

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

G. S. Agarwal and S. Dutta Gupta, "Reciprocity relations for reflected amplitudes," Opt. Lett. 27, 1205 - 1207 (2002).
[CrossRef]

1997 (1)

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, "Unidirectional operation of waveguide diode ring lasers," Appl. Phys. Lett. 70, 1192-1194 (1997).
[CrossRef]

1993 (1)

J. P. Hohimer, G. A. Vawter, and D. C. Craft, "Unidirectional operation in a semiconductor ring diode laser," Appl. Phys. Lett. 62, 1185-1187 (1993).
[CrossRef]

1986 (1)

M. Nieto-Vesperinas and E. Wolf, "Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape," J. Opt. Soc. Am. A. 3, 2038 - 2046 (1986).
[CrossRef]

Appl. Phys. Lett. (8)

J. J. Liang, S. T. Lau, M. H. Leary, and J. M. Ballantyne, "Unidirectional operation of waveguide diode ring lasers," Appl. Phys. Lett. 70, 1192-1194 (1997).
[CrossRef]

H. Cao, C. Liu, H. Ling, H. Deng, M. Benavidez, V. A. Smagley, and R. B. Caldwell, "Frequency beating between monolithically integrated semiconductor ring lasers," Appl. Phys. Lett. 86, 041101 (2005).
[CrossRef]

G. D. Chern, H. E. Tureci, A. D. Stone, R. K. Chang, M. Kneissl, and N. M. Johnson, "Unidirectional lasing from InGaN multiple-quantum-well spiral-shaped micropillar," Appl. Phys. Lett. 83, 1710 - 1712 (2003).
[CrossRef]

M. Kneissl, M. Teepe, N. Miyashita, N. M. Johnson, G. D. Chern, and R. K. Chang, "Current-injection spiral-shaped microcavity disk laser diodes with unidirectional emission," Appl. Phys. Lett. 84, 2485 - 2487 (2004).
[CrossRef]

T. Ben-Messaoud and J. Zyss, "Unidirectional laser emission from polymer-based spiral microdisks," Appl. Phys. Lett. 86, 241110 (2005).
[CrossRef]

J. P. Hohimer, G. A. Vawter, and D. C. Craft, "Unidirectional operation in a semiconductor ring diode laser," Appl. Phys. Lett. 62, 1185-1187 (1993).
[CrossRef]

A. Tulek and Z. V. Vardeny, "Unidirectional laser emission from π-conjugated polymer microcavities with broken symmetry," Appl. Phys. Lett. 90, 161106 (2007).
[CrossRef]

S. Fan, "Sharp asymmetric line shapes in side-coupled waveguide-cavity systems," Appl. Phys. Lett. 80, 908-910 (2002).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Cao, H. Ling, C. Liu, H. Deng, M. Benavidez, V. A. Smagley, R. B. Caldwell, G. M. Peake, G.A. Smolyakov, P. G. Eliseev, and M. Osiñski, "Large S-section-ring-cavity diode lasers: directional switching, electrical diagnostics, and mode beating spectra," IEEE Photon. Technol. Lett. 17, 282-284 (2005).
[CrossRef]

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

M. Nieto-Vesperinas and E. Wolf, "Generalized Stokes reciprocity relations for scattering from dielectric objects of arbitrary shape," J. Opt. Soc. Am. A. 3, 2038 - 2046 (1986).
[CrossRef]

J. Phys. D (1)

N. Tsujimoto, T. Takashima, T. Nakao, K. Masuyama, A. Fujii, and M. Ozaki, "Laser emission from spiral-shaped microdisc with waveguide of conducting polymer," J. Phys. D 40, 1669-1672 (2007).
[CrossRef]

Jpn. J. Appl. Phys. (2)

A. Fujii, T. Nishimura, Y. Yoshida, K. Yoshino, and M. Ozaki, "Unidirectional laser emission from spiral microcavity utilizing conducting polymer," Jpn. J. Appl. Phys. 44, L1091-L1093 (2005).
[CrossRef]

A. Fujii, T. Takashima, N. Tsujimoto, T. Nakao, Y. Yoshida, and M. Ozaki, "Fabrication and unidirectional laser emission properties of asymmetric microdisks based on poly (p-phenylenevinylene) derivative," Jpn. J. Appl. Phys. 45, L833-L836 (2006).
[CrossRef]

Nature (1)

K. J. Vahala, "Optical microcavities," Nature 424, 839-846 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

S. Y. Lee, S. Rim, J. W. Ryu, T. Y. Kwon, M. Choi, and C. M. Kim, "Quasiscarred resonances in a spiral-shaped microcavity," Phys. Rev. Lett. 93, 164102 (2004).
[CrossRef] [PubMed]

Prog. Theor. Phys.s (1)

C. M. Kim, S. Y. Lee, J. W. Ryu, T. Y. Kwon, S. Rim J. Lee, and J. Cho, "Characteristics of lasing modes in a spiral-shaped microcavity," Prog. Theor. Phys.sSuppl. 166, 112-118 (2007).
[CrossRef]

Rep. Prog. Phys. (1)

R. J. Potton, "Reciprocity in optics," Rep. Prog. Phys. 67, 717-754 (2004).
[CrossRef]

Other (12)

A. E. Siegman, Lasers (University Science Books, 1986), pp. 532-538.

R. K. Chang and A. J. Campillo, eds., Optical Processes in Microcavities (World Scientific, Singapore, 1996).
[CrossRef]

FullWAVE, Rsoft Inc. Research Software, http://www.rsoftinc.com.

E. E. Narimanov and V. A. Podolskiy, "Dynamical localization in spiral microlasers with unidirectional emission," in Conference on Lasers and Electro-Optics 2004, (IEEE and Optical Society of America, 2004), paper IThI5.

H. Chen, J. Y. Lee, A. W. Poon, and H. K. Tsang, "Non-evanescently pumped Raman silicon lasers using spiral-shaped microdisks," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD114.
[CrossRef]

M. Born and E. Wolf, Principles of Optics 7th edition (Cambridge, Cambridge University Press, 1999), pp. 724-726.

R. K. Chang, G. E. Fernandes, and M. Kneissl, "The Quest for Uni-Directionality with WGMs in μ-Lasers: Coupled Oscillators and Amplifiers," in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 47-51.

J. Y. Lee and A. W. Poon, "Spiral micropillar resonator-based unidirectional channel drop filters," in Proceedings of 8th International Conference on Transparent Optical Networks, (IEEE, 2006), 1, pp. 62-65.

J. Y. Lee and A. W. Poon, "Spiral-shaped microdisk resonator-based channel drop filters on a silicon nitride chip," in Proceedings of IEEE 3rd International Conference on Group IV Photonics, (IEEE, 2006), pp. 19 - 21.

A. W. Poon, J. Y. Lee, and C. Chan, "Spiral microdisk resonator-based channel filters on a silicon chip: probing the out-of-plane scattering spectra," in Proceedings of International Symposium on Biophotonics, Nanophotonics and Metamaterials, (IEEE, 2006), pp. 234 - 239.

J. Y. Lee, X. Luo, and A. W. Poon, "Spiral-shaped microdisk resonator channel drop/add filters: asymmetry in modal distributions," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper JThD116.
[CrossRef]

R. M. Audet, M. A. Belkin, J. A. Fan, F. Capasso, E. Narimanov, D. Bour, S. Corzine, J. Zhu, and G. Höfler, "Current Injection Spiral-Shaped Chaotic Microcavity Quantum Cascade Lasers," in Conference on Lasers and Electro-Optics 2007, (IEEE and Optical Society of America, 2007), paper CTuE4.

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Figures (9)

Fig. 1.
Fig. 1.

(a)–(c) Schematics of the spiral-shaped microdisk resonator-based filter configurations. The configurations assume different wavelength-selective filter functionalities depending on the input-coupling port. (a) Notch filter: the arrows depict the evanescently in-coupled CCW traveling-waves that do not favor out-coupling to the notch-waveguide. (b) Drop filter: the arrows depict the evanescently in-coupled CW traveling-waves that favor partial transmission to the notch-waveguide. (c) Add-only filter: the arrows depict the non-evanescently in-coupled CCW traveling-waves that do not favor out-coupling to the notch-waveguide. The throughput-port transmissions (labeled with “*”) of notch and drop filters are reciprocal related. The drop-port transmission of drop filter and the throughput-port transmission of add-only filter (labeled with “**”) are also reciprocal related. (d) SEM of the fabricated spiral-shaped microdisk filter in silicon nitride. The two red circles denote the evanescent-coupling region and the notch junction. The coordinates define the fiber scanning directions for the out-of-plane scattering measurements. Left inset: zoom-in view SEM of the evanescent-coupling region. Right inset: zoom-in view SEM of the notch junction. (e) Schematic of the experimental setup for transmission and out-of-plane scattering measurements of the three filter configurations. Bottom inset: optical micrograph of the spiral-shaped microdisk filter with arrows denoting the three filter operations.

Fig. 2.
Fig. 2.

(a) Measured TE-polarized throughput-port transmission spectra of notch (blue line) and drop (green line) filters. The multimode spectra show essentially identical spectral features, suggesting reciprocal transmissions between the evanescently in-coupled CCW and CW traveling-waves. (b) Measured TE-polarized drop-port transmission spectrum of drop filter (green line) and throughput-port spectrum of add-only filter (red line). The multimode spectra essentially overlap albeit with some mismatches. Most of the modal features in (a) find corresponding resonances in (b). The waveguide transmission intensity is normalized to the input-coupling lensed-fiber transmission intensity.

Fig. 3.
Fig. 3.

Measured out-of-plane scattering spectra near the notch junction region for (a) notch, (b) drop, and (c) add-only filters. (d) Light scattering spectra near the notch junction (x = 50 μm, y = -5 μm). The estimated Q values are labeled. We see no clear evidence for distinct Q values between CW and CCW traveling-wave modes. (e) Measured throughout- and drop-port transmission spectra of drop filter for reference. (f)-(g) Light scattering intensity profiles at resonances of (f) 1552.06 nm, and (g) 1553.02 nm. The profiles suggest input-port dependent modal distributions. The intensity profile width is estimated by the distance between the 5% of the maximum intensity and the cavity rim.

Fig. 4.
Fig. 4.

Measured out-of-plane scattering spectra near the evanescent-coupling region for (a) notch, (b) drop, and (c) add-only filters. The intensity profiles display distinct spatial and spectral features among the three filter configurations, and also from those near the notch junction. (d) Light scattering spectra near the evanescent-coupling region (x = 0 μm, y = 0 μm). The estimated Q values are labeled. (e) Measured throughout- and drop-port transmission spectra of drop filter for reference. (f)-(g) Light scattering intensity profiles at resonances of (f) 1552.06 nm, and (g) 1553.02 nm. The profiles suggest input-port dependent modal distributions.

Fig. 5.
Fig. 5.

(a) FDTD-simulated TE-polarized throughput-port transmission spectra of notch (blue dashed line) and drop (green line) filters. The multimode spectra overlap with each other, indicating reciprocal transmissions. The resonances within a FSR are labeled as A1, B1, C1, D1, E1, F1, G1, and H1. (b) FDTD-simulated TE-polarized drop-filter drop-port transmission spectrum (green line) and add-only filter throughput-port transmission spectrum (red dashed line). The multimode transmission spectra are identical, with corresponding resonances in the throughput-port transmission spectra in (a).

Fig. 6.
Fig. 6.

FDTD-simulated cavity internal-field spectra along the x-direction near the notch junction for (a) notch, (b) drop, and (c) add-only filters. (d) Simulated internal-field spectra at the notch junction (x = 19 μm, y = 0 μm). (e) Simulated drop-filter throughput- and drop-port transmission spectra for reference. (f), (g) Simulated internal-field intensity profiles at resonances (f) H1 (1532.72 nm), and (g) A2 (1535.13 nm). The intensity profile width is estimated by the distance between the 5% of the maximum intensity and the cavity rim.

Fig. 7.
Fig. 7.

FDTD-simulated internal-field spectra along the x-direction near the evanescent coupling region for (a) notch-, (b) drop-, and (c) add-only filters. (d) Simulated internal-field spectra near the side-coupled waveguide (x = 1 μm, y = 0 μm). (e) Simulated drop-filter throughput- and drop-port transmission spectra for reference. (f)-(g) Simulated internal-field intensity profiles at resonances (f) H1 (1532.72 nm), and (g) A2 (1535.13 nm). The intensity profile width is estimated by the distance between the 5% of the maximum intensity and the cavity rim.

Fig. 8.
Fig. 8.

FDTD-simulated TE-polarized input-coupling H -field patterns at wavelength of 1512.52 nm (resonance A1), and the corresponding spatial Fourier transforms, for (a), (d) notch filter, (b), (e) drop filter, and (c), (f) add-only filter. The Fourier transform is applied over the dashed rectangular windows depicted in (a)-(c). Only the Fourier component amplitudes above the half-maximum are shown in (d)-(f).

Fig. 9.
Fig. 9.

FDTD-simulated TE-polarized steady-state resonance mode H -field patterns for notch (left column), drop (center column), and add-only (right column) filters. (a)-(c) resonance A1, (d)-(f) resonance H1, and (g)-(i) resonance A2.

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