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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 17 — Aug. 22, 2005
  • pp: 6564–6571
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Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum

A. Rosenberg, Michael W. Carter, J. A. Casey, Mijin Kim, Ronald T. Holm, Richard L. Henry, Charles R Eddy, V. A. Shamamian, K. Bussmann, Shouyuan Shi, and Dennis W. Prather  »View Author Affiliations


Optics Express, Vol. 13, Issue 17, pp. 6564-6571 (2005)
http://dx.doi.org/10.1364/OPEX.13.006564


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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

Recent theoretical work has identified and characterized a class of modes in photonic crystal slabs dubbed guided resonances [1

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]

]. These resonant modes are guided in the sense of having their electric field distribution confined within the photonic crystal slab. However, unlike other resonances that exist in photonic crystals, guided resonances are also strongly coupled to radiation modes. The latter property of guided resonances holds promise for several potential applications, such as the efficient extraction of light originating from emitting layers that could be incorporated into photonic crystal slabs and the filtering of externally incident light [2

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]

].

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

The photonic crystal slabs investigated in this study consist of patterned films of GaN (a wide band gap semiconductor) on sapphire substrates. As shown in Fig. 2, these asymmetrical structures allow almost no guided modes below the light line (which defines the lower-frequency limit of the radiation continuum). This is quite different from the case of the symmetrical (free-standing) membranes studied in the past [1–5

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]

], which can show band gaps in the guided modes even for membranes with moderate values of refractive index. Note also that since so few guided modes exist in the asymmetrical case studied here, no band gaps appear for the guided modes, as seen in Fig. 2. The absence of band gaps results both from the mixing of odd- and even-parity modes, caused by the asymmetry, and also from the relatively low refractive index contrast between the photonic crystal slab and the substrate (e.g., approximately 2.37 for GaN and 1.8 for sapphire).

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.

To identify the guided resonant modes present in our photonic crystal slabs, we examined the E-field distribution patterns of the Γ-point modes identified in Fig. 2(a). As described previously [1

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]

], the guided resonances are distinguished by having their field distribution strongly confined to the spatial region occupied by the photonic crystal slab. By contrast, non-resonant modes have a field intensity distribution that quickly radiates away from the slab and into the surrounding medium. Examples of resonant field patterns are shown in Figs. 2(b) and (c). Note that the field patterns of the resonant modes displayed in Figs. 2(b) and (c) do not share the full (square) symmetry of the photonic crystal lattice.

Normal-incidence transmission measurements were carried out by illuminating the photonic crystal slabs with a weakly focused halogen-bulb source. The transmitted light was collected by an infinity-corrected near-IR microscope objective and analyzed in two fiber-coupled spectrometers equipped with array detectors, covering the wavelength range between 400 nm and 1.7 μm. Since the transmission was measured relative to an unpatterned area of the same GaN film, transmission results in excess of 1 indicate spectral regions where the GaN photonic crystal pattern serves to reduce the impedance mismatch between the unpatterned GaN film on sapphire and the ambient. Several different samples with various hole sizes and array spacings were measured. In each case, the optical transmission results were compared to transmission calculations for the specific sets of parameters determined by imaging the fabricated structures with SEM and AFM instruments. The transmission calculations were performed by FDTD techniques, using perfectly matched layer boundary conditions on the surfaces of the computational domain parallel to the slab and repeating boundary conditions in the four other directions. For the purposes of this study, we considered only the normal incidence direction in both the measurements and simulations. We found the experimental transmission results to be very sensitive to both propagation direction and focusing conditions, and we took great care to ensure that the measurements were done along the direction normal to the slab faces and that the optical beam was as weakly focused as possible while still allowing for the efficient collection of transmitted light. We estimate both the divergence of the beam at the sample position and any deviations from normal incidence to be less than 1°.

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.

Typical transmission results for a GaN on sapphire photonic crystal slab are shown in Fig. 3. Several spectral features associated with the guided resonant modes discussed above are easily identified in the measured spectrum and are matched well by corresponding features in the calculated transmission spectrum. In particular, the inset of Fig. 3 shows, in greater detail, the two resonant modes identified as ω1 and ω2 in Fig. 2. The agreement between the measured and calculated spectra is generally very good. (Note that both the measured and calculated spectra in Fig. 3 are for unpolarized light.) The asymmetrical (Fano) lineshapes observed in some cases result from the coupling between the resonant modes and the continuum of radiation states, as described previously [1

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]

]. At shorter wavelengths, the reduced broadband transmission in the measured spectra may be due to enhanced scattering resulting from residual fabrication errors in the photonic crystal array, which are not included in the simulations. Nevertheless, the detailed agreement between the measured and calculated spectra, including spectral positions and lineshapes (or linewidths), is excellent in general, as exemplified by the inset of Fig. 3.

Careful examination of the E-field patterns for the several Γ-point modes appearing in Fig. 2(a), combined with a comparison of Figs. 2(a) and 3, indicates that only a subset of the Γ-point modes which are resonant also give rise to corresponding spectral features (resonances) in the normal-incidence transmission spectrum. The resonant modes which are “missing” from this spectrum (in both experiments and FDTD simulations) are those which share the full symmetry of the photonic crystal lattice. These modes cannot be excited by externally incident plane waves [9

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

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

]. This observation is analogous to the null-coupling effect observed previously for certain photonic bands in 2D photonic crystals [11

11. A. Rosenberget al., “ Near-infrared two-dimensional photonic band-gap materials,” Opt. Lett. 21, 830 (1996), and references therein. [CrossRef] [PubMed]

].

We have also investigated the effect of hole size within a specific pattern (i.e., a square array with fixed nearest-neighbor spacing but varying hole sizes) on the positions of the guided resonances. As shown in Fig. 4, we find excellent agreement between the measured and calculated positions of the spectral features corresponding to these modes. This agreement clearly validates both our FDTD simulation results and the precision of the fabrication process developed for the GaN photonic crystal slabs studied here.

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.

In order to clarify the role of the substrate in the observation of these guided resonant modes, it is interesting to consider more closely the effect of the substrate index in the asymmetric photonic crystal slabs investigated here. The effect of substrate index is demonstrated by the calculated transmission spectra in Fig. 5, for two resonant modes corresponding to ω1 and ω2 in Fig. 2. (This correspondence of modes holds true in spite of the fact that the band structure in Fig. 2 is calculated for r=0.27a, while Fig. 5 is associated with r=0.15a.) A series of spectra is shown in Fig. 5 for (hypothetical) substrate indices ranging from 2.135 (relatively close to the GaN index of 2.37) to 1.8 (the approximate value for the sapphire substrate). At low index contrast (high substrate index), only a very weak resonance appears, corresponding to ω2 in Fig. 2. (In the limiting case where the substrate index matches that of the photonic crystal slab, no resonances are expected (or observed).) As shown in Fig. 5, this resonance shifts to higher frequency with increasing index contrast (decreasing substrate index), and at a certain value of index contrast (near 2.0) a second resonance appears, corresponding to ω1 in Fig. 2. Thus, there appears to be a minimum index contrast value required to observe a particular resonance in the transmission spectrum, and this minimum index contrast is specific to each resonance. The second resonance does not appear to be due to a “splitting” in the traditional sense, since the separation between the two resonances in Fig. 5 does not extrapolate to a vanishing value at any size of index contrast. We do not currently have an explanation for what appears to be a non-monotonic change in the strengths of the resonances as the substrate index is varied. Although not included in Fig. 5, a closer look at spectra corresponding to much lower substrate index values (i.e., higher index contrast), approaching the symmetric case of a free-standing membrane, shows that the frequency separation has a mild dependence on index contrast, implying that each resonance shifts with index contrast at a slightly different rate. Also, we note in Fig. 5 that the asymmetry of the lineshapes, discussed in detail in Ref. [1

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]

], is stronger at larger index contrast and shows an apparent sign reversal at low index contrast.

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).

In conclusion, we have demonstrated that guided resonances can be readily observed in asymmetrical photonic crystal slabs, where the presence of a substrate greatly increases the radiative coupling of the modes in the photonic crystal slab. These structures typically do not exhibit band gaps in the guided mode spectrum, particularly when the index of refraction contrast between the slab and the substrate is only moderately high, as is the case (examined here) for a GaN photonic crystal slab on a sapphire substrate. In addition to the effects on optical properties discussed above, asymmetrical structures consisting of photonic crystal slabs supported by a substrate also have a number of practical advantages over their symmetrical counterparts (free-standing membranes) for potential applications, including ease of fabrication, mechanical robustness and improved thermal properties. Our results demonstrate that it is not necessary to fabricate very thin large-area free-standing membranes in order to access many of the properties of guided resonant modes discussed previously. Therefore, optical components or devices based on these narrow (high-Q) resonances are far easier to fabricate and hence much more practical than previously believed.

Acknowledgments

We acknowledge technical assistance from S. Bounnak (Sachs-Freeman Associates, Inc.) and J.A. Murakowski (Univ. of DE).

References and Links

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 Jr., 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]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(120.2440) Instrumentation, measurement, and metrology : Filters
(230.3990) Optical devices : Micro-optical devices
(230.5750) Optical devices : Resonators

ToC Category:
Research Papers

History
Original Manuscript: July 19, 2005
Revised Manuscript: August 12, 2005
Published: August 22, 2005

Citation
A. Rosenberg, Michael Carter, J. Casey, Mijin Kim, Ronald Holm, Richard Henry, Charles Eddy, V. Shamamian, K. Bussmann, Shouyuan Shi, and Dennis Prather, "Guided resonances in asymmetrical GaN photonic crystal slabs observed in the visible spectrum," Opt. Express 13, 6564-6571 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-17-6564


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References

  1. Shanhui Fan and J.D. Joannopoulos, �??Analysis of guided resonances in photonic crystal slabs,�?? Phys. Rev. B 65, 235112 (2002); Shanhui Fan et al., �??Temporal coupled-mode theory for the Fano resonance in optical resonators,�?? J. Opt. Soc. Am. A 20, 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. Crozier et al., �??Two-dimensional photonic crystals at visible wavelengths,�?? in CLEO/QELS and PhAST 2004 (OSA, Washington, DC, 2004), CWG2.
  4. Onur Kilic et al., �??Photonic crystal slabs demonstrating strong broadband suppression of transmission in the presence of disorders,�?? Opt. Lett. 29, 2782 (2004). [CrossRef] [PubMed]
  5. F. Raineri et al., �??Nonlinear optical manipulation of Fano resonances in 2D photonic crystal slabs,�?? in CLEO/QELS and PhAST 2003 (OSA, Washington, DC, 2004), QThPDA1.
  6. C.R. Eddy, Jr., 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. Hsu et 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. Coquillat et 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. Rosenberg et al., �??Near-infrared two-dimensional photonic band-gap materials,�?? Opt. Lett. 21, 830 (1996), and references therein. [CrossRef] [PubMed]

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