Abstract

We report numerical simulations of surface modes in two-dimensional high-index-contrast photonic crystal slabs with a flat dielectric margin of width on the order of the photonic crystal periodicity. Our calculations using plane wave expansion method reveal multiple surface guided modes within the photonic band gap, with some high-order modes exhibit relatively flat dispersion curves. We calculate the finite-length surface waveguide modes transmission and field patterns using two-dimensional finite-difference time-domain method. We verify the surface mode dispersion curves by using spatial Fourier transform of the mode field patterns. Our study on surface modes under small ambient refractive index changes (5 × 10-3) shows that lower order modes exhibit larger wavelength shifts on the order of 1 nm. We also design a 4-port 3-channel bidirectional coupler using a conventional dielectric waveguide side coupled to the multimode surface waveguide.

© 2006 Optical Society of America

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  1. P. Yeh, "Guided waves in layered media," in Optical waves in layered media, (John Wiley & Sons, New York, 1988).
  2. R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
    [CrossRef]
  3. F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 - 15120 (1999).
    [CrossRef]
  4. S. Enoch, E. Popov, and N. Bonod, "Analysis of the physical origin of surface modes on finite-size photonic crystals," Phys. Rev. B 72, 155101 (2005).
    [CrossRef]
  5. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
    [CrossRef]
  6. E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
    [CrossRef]
  7. M. Laroche, R. Carminati, and J.-J. Greffet, "Resonant optical transmission through a photonic crystal in the forbidden gap," Phys. Rev. B 71, 155113 (2005).
    [CrossRef]
  8. W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 - 3917 (2002).
    [CrossRef]
  9. Yu. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 - 4544 (2004).
    [CrossRef]
  10. Y. A. Vlasov, N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett. 29, 2175 - 2177 (2004).
    [CrossRef] [PubMed]
  11. J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
    [CrossRef]
  12. S. Xiao and M. Qiu, "Surface-mode microcavity," Appl. Phys. Lett. 87, 111102 (2005).
    [CrossRef]
  13. K. K. Tsia and A. W. Poon, "Dispersion-guided resonances in two-dimensional photonic-crystal-embedded microcavities," Opt. Express 12, 5711-5722 (2004).
    [CrossRef] [PubMed]
  14. K. K. Tsia and A. W. Poon, "Dispersion-guided and bandgap-guided resonances in semiconductor waveguide-coupled hexagonal photonic-crystal-embedded microcavities," presented at 2005 Conference on Lasers and Electro Optics/ Quantum Electronics and Laser Science Conference (CLEO/QELS), Baltimore, USA, 22-27 May 2005.
  15. M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
    [CrossRef] [PubMed]
  16. D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, "Nanofluidic tuning of photonic crystal circuits," Opt. Lett. 31, 59-61 (2006).
    [CrossRef] [PubMed]
  17. H. Ouyang, C. C. Striemer, and P. M. Fauchet, "Quantitative analysis of sensitivity of porous silicon optical biosensors," Appl. Phys. Lett. 88, 163108 (2006).
    [CrossRef]
  18. E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, "Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity," Opt. Lett. 29, 1093-1095 (2004).
    [CrossRef] [PubMed]

2006 (2)

D. Erickson, T. Rockwood, T. Emery, A. Scherer, and D. Psaltis, "Nanofluidic tuning of photonic crystal circuits," Opt. Lett. 31, 59-61 (2006).
[CrossRef] [PubMed]

H. Ouyang, C. C. Striemer, and P. M. Fauchet, "Quantitative analysis of sensitivity of porous silicon optical biosensors," Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

2005 (3)

S. Xiao and M. Qiu, "Surface-mode microcavity," Appl. Phys. Lett. 87, 111102 (2005).
[CrossRef]

S. Enoch, E. Popov, and N. Bonod, "Analysis of the physical origin of surface modes on finite-size photonic crystals," Phys. Rev. B 72, 155101 (2005).
[CrossRef]

M. Laroche, R. Carminati, and J.-J. Greffet, "Resonant optical transmission through a photonic crystal in the forbidden gap," Phys. Rev. B 71, 155113 (2005).
[CrossRef]

2004 (6)

Yu. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 - 4544 (2004).
[CrossRef]

Y. A. Vlasov, N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett. 29, 2175 - 2177 (2004).
[CrossRef] [PubMed]

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

K. K. Tsia and A. W. Poon, "Dispersion-guided resonances in two-dimensional photonic-crystal-embedded microcavities," Opt. Express 12, 5711-5722 (2004).
[CrossRef] [PubMed]

E. Chow, A. Grot, L. W. Mirkarimi, M. Sigalas, and G. Girolami, "Ultracompact biochemical sensor built with two-dimensional photonic crystal microcavity," Opt. Lett. 29, 1093-1095 (2004).
[CrossRef] [PubMed]

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

2002 (1)

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 - 3917 (2002).
[CrossRef]

2001 (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

1999 (1)

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 - 15120 (1999).
[CrossRef]

1993 (1)

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

1991 (1)

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
[CrossRef]

Arjavalingam, G.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

Bonod, N.

S. Enoch, E. Popov, and N. Bonod, "Analysis of the physical origin of surface modes on finite-size photonic crystals," Phys. Rev. B 72, 155101 (2005).
[CrossRef]

Brommer, K. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
[CrossRef]

Carminati, R.

M. Laroche, R. Carminati, and J.-J. Greffet, "Resonant optical transmission through a photonic crystal in the forbidden gap," Phys. Rev. B 71, 155113 (2005).
[CrossRef]

Chow, E.

Emery, T.

Enoch, S.

S. Enoch, E. Popov, and N. Bonod, "Analysis of the physical origin of surface modes on finite-size photonic crystals," Phys. Rev. B 72, 155101 (2005).
[CrossRef]

Erickson, D.

Fan, S.

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 - 3917 (2002).
[CrossRef]

Fauchet, P. M.

H. Ouyang, C. C. Striemer, and P. M. Fauchet, "Quantitative analysis of sensitivity of porous silicon optical biosensors," Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

García-Vidal, F. J.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Girolami, G.

Greffet, J.-J.

M. Laroche, R. Carminati, and J.-J. Greffet, "Resonant optical transmission through a photonic crystal in the forbidden gap," Phys. Rev. B 71, 155113 (2005).
[CrossRef]

Grot, A.

Halevi, P.

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 - 15120 (1999).
[CrossRef]

Joannopoulos, J. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
[CrossRef]

Kim, G.-H.

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

Kim, S.-B.

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

Kim, S.-H.

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

Laroche, M.

M. Laroche, R. Carminati, and J.-J. Greffet, "Resonant optical transmission through a photonic crystal in the forbidden gap," Phys. Rev. B 71, 155113 (2005).
[CrossRef]

Lau, W. T.

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 - 3917 (2002).
[CrossRef]

Lee, Y.-H.

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

Martín-Moreno, L.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

McNab, S. J.

Yu. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 - 4544 (2004).
[CrossRef]

Y. A. Vlasov, N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett. 29, 2175 - 2177 (2004).
[CrossRef] [PubMed]

Meade, R. D.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
[CrossRef]

Mirkarimi, L. W.

Moll, N.

Y. A. Vlasov, N. Moll, and S. J. McNab, "Observation of surface states in a truncated photonic crystal slab," Opt. Lett. 29, 2175 - 2177 (2004).
[CrossRef] [PubMed]

Yu. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 - 4544 (2004).
[CrossRef]

Moreno, E.

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

Notomi, M.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Ouyang, H.

H. Ouyang, C. C. Striemer, and P. M. Fauchet, "Quantitative analysis of sensitivity of porous silicon optical biosensors," Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

Park, H.-G.

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

Poon, A. W.

Popov, E.

S. Enoch, E. Popov, and N. Bonod, "Analysis of the physical origin of surface modes on finite-size photonic crystals," Phys. Rev. B 72, 155101 (2005).
[CrossRef]

Psaltis, D.

Qiu, M.

S. Xiao and M. Qiu, "Surface-mode microcavity," Appl. Phys. Lett. 87, 111102 (2005).
[CrossRef]

Ramos-Mendieta, F.

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 - 15120 (1999).
[CrossRef]

Rappe, A. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
[CrossRef]

Robertson, W. M.

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Observation of surface photons on periodic dielectric arrays," Opt. Lett. 7, 528-531 (1993).
[CrossRef]

Rockwood, T.

Scherer, A.

Shinya, A.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Sigalas, M.

Striemer, C. C.

H. Ouyang, C. C. Striemer, and P. M. Fauchet, "Quantitative analysis of sensitivity of porous silicon optical biosensors," Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

Takahashi, C.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Takahashi, J.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Tsia, K. K.

Vlasov, Y. A.

Vlasov, Yu. A.

Yu. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 - 4544 (2004).
[CrossRef]

Xiao, S.

S. Xiao and M. Qiu, "Surface-mode microcavity," Appl. Phys. Lett. 87, 111102 (2005).
[CrossRef]

Yamada, K.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Yang, J.-K.

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

Yokohama, I.

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Appl. Phys. Lett. (4)

J.-K. Yang, S.-H. Kim, G.-H. Kim, H.-G. Park, Y.-H. Lee, and S.-B. Kim, "Slab-edge modes in two-dimensional photonic crystals," Appl. Phys. Lett. 84, 3016-3018 (2004).
[CrossRef]

S. Xiao and M. Qiu, "Surface-mode microcavity," Appl. Phys. Lett. 87, 111102 (2005).
[CrossRef]

W. T. Lau and S. Fan, "Creating large bandwidth line defects by embedding dielectric waveguides into photonic crystal slabs," Appl. Phys. Lett. 81, 3915 - 3917 (2002).
[CrossRef]

H. Ouyang, C. C. Striemer, and P. M. Fauchet, "Quantitative analysis of sensitivity of porous silicon optical biosensors," Appl. Phys. Lett. 88, 163108 (2006).
[CrossRef]

J. Appl. Phys. (1)

Yu. A. Vlasov, N. Moll, and S. J. McNab, "Mode mixing in asymmetric double-trench photonic crystal waveguides," J. Appl. Phys. 95, 4538 - 4544 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. B (5)

E. Moreno, F. J. García-Vidal, and L. Martín-Moreno, "Enhanced transmission and beaming of light via photonic crystal surface modes," Phys. Rev. B 69, 121402 (2004).
[CrossRef]

M. Laroche, R. Carminati, and J.-J. Greffet, "Resonant optical transmission through a photonic crystal in the forbidden gap," Phys. Rev. B 71, 155113 (2005).
[CrossRef]

R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Electromagnetic Bloch waves at the surface of a photonic crystal," Phys. Rev. B 44, 10961 - 10964 (1991).
[CrossRef]

F. Ramos-Mendieta and P. Halevi, "Surface electromagnetic waves in two-dimensional photonic crystals: effect of the position of the surface plane," Phys. Rev. B 59, 15112 - 15120 (1999).
[CrossRef]

S. Enoch, E. Popov, and N. Bonod, "Analysis of the physical origin of surface modes on finite-size photonic crystals," Phys. Rev. B 72, 155101 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I. Yokohama, "Extremely large group-velocity dispersion of line-defect waveguides in photonic crystal slabs," Phys. Rev. Lett. 87, 253902 (2001).
[CrossRef] [PubMed]

Other (2)

P. Yeh, "Guided waves in layered media," in Optical waves in layered media, (John Wiley & Sons, New York, 1988).

K. K. Tsia and A. W. Poon, "Dispersion-guided and bandgap-guided resonances in semiconductor waveguide-coupled hexagonal photonic-crystal-embedded microcavities," presented at 2005 Conference on Lasers and Electro Optics/ Quantum Electronics and Laser Science Conference (CLEO/QELS), Baltimore, USA, 22-27 May 2005.

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Figures (8)

Fig. 1
Fig. 1

Schematic of a two-dimensional photonic crystal slab surface waveguide in the z-direction (GK symmetry direction) with a dielectric margin of width m. The waveguide has a finite length of L. Shaded frame indicates the PML region in the FDTD simulation domain. (b) Unit cell adopted (dashed-line box) in the plane wave expansion calculation using super-cell approach. (c) Schematic of a 4-port device comprising a finite-length surface waveguide side coupled to a strip waveguide. Port 1: input, Port 2: throughput, Port 3: forward couple, and Port 4: backward couple.

Fig. 2.
Fig. 2.

(a) - (c) PWE-calculated projected dispersion diagrams for PC surface waveguides of (a) m = 0.1a, (b) m = 0.7a, and (c) m = 1.2a. Surface modes A0 – A4 are highlighted. (d) – (g) PWE-calculated field patterns of modes (d) A0 in m = 0.1a waveguide, (e) A1, (f) A2 in m = 0.8a waveguide, and (g) A3 in m = 1.2a waveguide. (h) PWE-calculated surface waveguide modes (A0 – A5) zone edge frequencies with margin width spanning from 0.1a to 2.0a. 1st PC band lines are zone-edge frequency boundaries. Lines are for visual aid.

Fig. 3
Fig. 3

(a) Surface modes k span (Δk) for n g exceeding 50 as a function of the zone-edge frequency. Lines are for visual aid. (b)–(d) Dispersion diagrams highlighting mode A3 dispersion curves in waveguides with m = 1.1a, m = 1.7a, and m = 1.9a.

Fig. 4.
Fig. 4.

(a) PWE-calculated projected dispersion diagram for a surface waveguide with a margin width of 0.8a. Symbols are k-vectors retrieved from FDTD-simulated field patterns for modes A1 (oe-14-16-7368-i001) and A2 (oe-14-16-7368-i002). Dashed line shows the light line. (b) FDTD-simulated transmission spectra and (c) reflection spectra for L = 16a (blue) and L = 32a (red). (d), (e) Zoom-in view of transmission bands for modes A1 and A2.

Fig. 5
Fig. 5

FDTD-simulated time-averaged steady-state H-field intensity patterns of (a) mode Al and (b) mode A2 in m = 0.8a surface waveguides. The waveguide length L = 32a. (c) and (d) FDTD-simulated time-averaged steady-state H-field amplitude patterns. (e) and (f) Fourier analysis of the field patterns of modes (e) A1, and (f) A2. Arrows indicate minor peaks positions in the k-space.

Fig. 6.
Fig. 6.

(a) PWE-calculated projected dispersion diagram for a surface waveguide with a margin width of 1.5a. Symbols are k-vectors retrieved from the FDTD-simulated H-field patterns for modes A3 (oe-14-16-7368-i003) and A4 (oe-14-16-7368-i004). FDTD-simulated H-field patterns for modes (b) A3, and (d) A4. Fourier analysis of field patterns of (d) A3, and (e) A4.

Fig. 7
Fig. 7

(a) Mode A1 transmission spectra of the surface photonic crystal waveguide m = 0.6a, and L = 32a with different ambient refractive indices: 1.33 and 1.335. (b) Fractional frequency shifts as a function of center frequency under ambient refractive index changes from 1.33 to 1.335, for modes Al(oe-14-16-7368-i005), A2(oe-14-16-7368-i006), and A3(oe-14-16-7368-i007). (c) – (e) Time-averaged E-field intensity for (c) mode A1 at ~0.216 (c/a), (d) mode A2 at ~0.227 (c/a), and (e) mode A3 at ~0.238 (c/a).

Fig. 8.
Fig. 8.

(a) Simulated spectra of the 4-port 3-channel bi-directional coupler. Port 2: black line, port 3: blue line, and port 4: red line. (b) PWE-calculated dispersion diagram of surface modes A1 (red) and A2 (blue), and of the strip waveguide (purple). Two intersections at (k1 ω 1) and (k2 , ω 2) correspond to the two resonant coupling. (c) - (e) Time-averaged steady-state H-field intensity patterns for (c) forward coupling to port 3 (λ = 1.3114 μm), (d) throughput transmission to port 2 (λ = 1.49 μm), and (e) backward coupling to port 4 (λ = 1.5494 μm). Dashed-line windows denote the coupling regions for Fourier transform analysis. (f), (g) Fourier-transformed k-space representation at (f) λ = 1.3114 μm, and (g) λ = 1.5494 μm. (h) Schematic extended dispersion diagram (1st and part of 2nd BZ’s). Strip waveguide mode projected wavevector k WG2 matches with surface mode projected wavevector kA2 . Strip waveguide mode projected wavevector kWG1 matches with counter-propagating surface mode projected wavevector kA1 . L.L. is light line.

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