Abstract

We demonstrate that guided resonant modes can be readily observed in asymmetrical photonic crystal slabs on high-index substrates. In spite of the high radiative loss associated with all optical modes in these cases, the guided resonant modes are found to give rise to strong high-Q features in the transmission spectra. Since these photonic crystal structures are far more robust and easier to fabricate than the free-standing photonic crystal membranes used in previous studies of guided resonant modes, detailed studies of relevant optical phenomena and the implementation of proposed applications are greatly simplified.

©2005 Optical Society of America

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References

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  1. Shanhui Fan and J.D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002); Shanhui Fanet al, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569 (2003).
    [Crossref]
  2. See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
    [Crossref]
  3. K.B. Crozieret al, “Two-dimensional photonic crystals at visible wavelengths,” in CLEO/QELS and PhAST 2004 (OS A Washington, DC, 2004), CWG2.
  4. Onur Kilicet al, “Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,” Opt. Lett. 29, 2782 (2004).
    [Crossref] [PubMed]
  5. F. Raineriet al, “Nonlinear optical manipulation of Fano resonances in 2D photonic crystal slabs,” in CLEO/QELS and PhAST 2003 (OS A Washington, DC, 2004), QThPDA1.
  6. C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).
  7. David S.Y. Hsuet al, “Using Ni masks in inductively coupled plasma etching of high density hole patterns in GaN,” J. Vac. Sci. Technol. B (to be published).
  8. D. Coquillatet al, “Equifrequency surfaces in a two-dimensional GaN-based photonic crystal,” Opt. Express 12, 1097 (2004), and references therein.
    [Crossref] [PubMed]
  9. T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
    [Crossref]
  10. Shanhui Fan, Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305 (personal communication, 2005).
  11. A. Rosenberget al., “ Near-infrared two-dimensional photonic band-gap materials,” Opt. Lett. 21, 830 (1996), and references therein.
    [Crossref] [PubMed]

2004 (2)

2003 (1)

See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
[Crossref]

2001 (1)

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[Crossref]

1996 (1)

Coquillat, D.

Crozier, K.B.

K.B. Crozieret al, “Two-dimensional photonic crystals at visible wavelengths,” in CLEO/QELS and PhAST 2004 (OS A Washington, DC, 2004), CWG2.

Culbertson, J.C

C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).

Eddy, C.R.

C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).

Fan, Shanhui

See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
[Crossref]

Shanhui Fan and J.D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002); Shanhui Fanet al, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569 (2003).
[Crossref]

Shanhui Fan and J.D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002); Shanhui Fanet al, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569 (2003).
[Crossref]

Shanhui Fan, Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305 (personal communication, 2005).

Henry, R.L.

C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).

Holm, R.T.

C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).

Hsu, David S.Y.

David S.Y. Hsuet al, “Using Ni masks in inductively coupled plasma etching of high density hole patterns in GaN,” J. Vac. Sci. Technol. B (to be published).

Joannopoulos, J.D.

Shanhui Fan and J.D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002); Shanhui Fanet al, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569 (2003).
[Crossref]

Kilic, Onur

Ochiai, T.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[Crossref]

Raineri, F.

F. Raineriet al, “Nonlinear optical manipulation of Fano resonances in 2D photonic crystal slabs,” in CLEO/QELS and PhAST 2003 (OS A Washington, DC, 2004), QThPDA1.

Rosenberg, A.

Sakoda, K.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[Crossref]

Solgaard, Olav

See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
[Crossref]

Suh, Wojoo

See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
[Crossref]

Twigg, M.E.

C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).

Yanik, M.F.

See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
[Crossref]

Appl. Phys. Lett. (1)

See, for example, Wojoo Suh, M.F. Yanik, Olav Solgaard, and Shanhui Fan, “Displacement-sensitive photonic crystal structures based on guided resonance in photonic crystal slabs,” Appl. Phys. Lett. 82, 1999 (2003).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (1)

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[Crossref]

Other (6)

Shanhui Fan, Dept. of Electrical Engineering, Stanford University, Stanford, CA 94305 (personal communication, 2005).

K.B. Crozieret al, “Two-dimensional photonic crystals at visible wavelengths,” in CLEO/QELS and PhAST 2004 (OS A Washington, DC, 2004), CWG2.

F. Raineriet al, “Nonlinear optical manipulation of Fano resonances in 2D photonic crystal slabs,” in CLEO/QELS and PhAST 2003 (OS A Washington, DC, 2004), QThPDA1.

C.R. Eddy, R.T. Holm, R.L. Henry, J.C Culbertson, and M.E. Twigg, “Investigation of a three-step epilayer growth approach of GaN thin films to minimize compensation,” J. Electron. Mater. (to be published).

David S.Y. Hsuet al, “Using Ni masks in inductively coupled plasma etching of high density hole patterns in GaN,” J. Vac. Sci. Technol. B (to be published).

Shanhui Fan and J.D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B65, 235112 (2002); Shanhui Fanet al, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A20, 569 (2003).
[Crossref]

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Figures (5)
Fig. 1.
Fig. 1. Schematic layout (a), SEM (b) and AFM (c) images of typical photonic crystal patterns used in this study.

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Fig. 2.
Fig. 2. Band structure (a) of an asymmetrical photonic crystal slab consisting of a square lattice of air holes patterned in a GaN (n=2.37) film on a sapphire (n=1.8) substrate, with an AlN (n=2.1) nucleation layer. The holes have a radius of 0.27a, where a is the lattice spacing. The GaN has a thickness of 0.52a, and the AlN has a thickness of 0.05a. The gray region is the continuum of radiation modes. The spatial distribution of the electric field is shown in (b) and (c) for two resonant modes identified in (a) as ω1 and ω2, respectively. The cross-sectional views in (b) and (c) (see dotted lines) show the corresponding confinement of the field inside the photonic crystal slab.

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Fig. 3.
Fig. 3. Comparison between the measured transmission spectrum (black) and the spectrum simulated by an FDTD calculation (blue). The parameters of the photonic crystal slab are as in Fig. 2, with a=490 nm. The inset shows more clearly the resonances at 885 nm and 915 nm, corresponding to the modes at ω1 and ω2 (respectively) identified in Fig. 2.

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Fig. 4.
Fig. 4. Frequency dependence on hole size of the resonant modes identified in Fig. 2 as ω1 and ω2, as well as of two higher frequency modes. The inset shows the dependence of Q on hole size for the resonant mode at ω1. Solid symbols represent calculated values and open symbols represent measured values. The lines are guides to the eyes.

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Fig. 5.
Fig. 5. Transmission spectra calculated by FDTD for an asymmetrical photonic crystal slab as the substrate index is varied. The photonic crystal slab consists of a square array of holes with radius of 0.15a in a GaN film (index of 2.37) with thickness of 0.54a (where a is the lattice spacing). The substrate index n varies between 2.135 and 1.8, as indicated in the figure. Note that at n=2.135 there is sufficient index contrast to observe a single weak resonance, while near n=2.0 a second resonance appears (as discussed in the text).

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