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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 25 — Dec. 3, 2012
  • pp: 27242–27252
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Bidirectional scatter measurements of a guided-mode resonant filter photonic crystal structure

M. A. Marciniak, S. R. Sellers, R. B. Lamott, and B. T. Cunningham  »View Author Affiliations


Optics Express, Vol. 20, Issue 25, pp. 27242-27252 (2012)
http://dx.doi.org/10.1364/OE.20.25.027242


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Abstract

This work investigates the Bidirectional Scatter Distribution Function (BSDF) at incident angles other than normal and at 544-nm wavelength of a Guided Mode Resonance Filter (GMRF) Photonic Crystal (PC) structure designed for normally incident light at 532 nm. Strong out-coupling of PC diffraction orders into both the transmitted and reflected hemispheres was observed specifically at a 25.7° incidence angle, which we attribute to this incident angle/wavelength pair being a good match to the ( ± 1, 0) PC grating mode. BSDF measurements at incident angles of 15° and 35° also displayed some out-coupled diffraction, though much lower in magnitude, and are also attributed to being a weaker match to the ( ± 1, 0) PC grating mode. Three-dimensional finite-difference time-domain Maxwell's equation simulations demonstrate that since this GMRF was designed for complete destructive interference of the transmitted light upon normal incidence, stronger out-coupling of the diffraction is expected for modal solutions as the angle of incidence increases.

© 2012 OSA

1. Introduction

Photonic crystals (PC’s) are periodic optical nanostructures that are designed to manipulate the flow of light. Distinct optical phenomena associated with PC structures include negative refraction [1

1. N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, “Optical near-field microscopy of light focusing through a photonic crystal flat lens,” Phys. Rev. Lett. 101(7), 073901 (2008). [CrossRef] [PubMed]

], super-prism [2

2. S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photon. Nano. Fund. Appl. 3(1), 10–18 (2005). [CrossRef]

], self-collimation [3

3. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999). [CrossRef]

] and lensing [4

4. H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008). [CrossRef]

], light trapping [5

5. I. Prieto, B. Galiana, P. A. Postigo, C. Algora, L. J. Martínez, and I. Rey-Stolle, “Enhanced quantum efficiency of Ge solar cells by a two-dimensional photonic crystal nanostructured surface,” Appl. Phys. Lett. 94(19), 191102 (2009). [CrossRef]

] and slow light [6

6. T. R. Nielsen, A. Lavrinenko, and J. Mork, “Slow light in quantum dot photonic crystal waveguides,” Appl. Phys. Lett. 94(11), 113111 (2009). [CrossRef]

], and Fano resonance [7

7. M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94(7), 071101 (2009). [CrossRef]

]. Guided mode resonance filters (GMRF’s) are structures in which a one- or two-dimensional (1- or 2-D) PC is embedded in a planar dielectric structure such that a portion of light incident at a particular angle and wavelength is diffracted into that structure where it resonates. The trapped light is then re-diffracted out of the structure such that it interferes destructively with the otherwise transmitted portion of the beam. At the design angle and wavelength, there can be complete interference and no light transmission [8

8. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef] [PubMed]

11

11. T. Sun and D. Wu, “Guided-mode resonance excitation on multimode planar periodic waveguide,” J. Appl. Phys. 108(6), 063106 (2010). [CrossRef]

]. GMRF structures have been discussed in terms of Wood’s anomaly [12

12. A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 4(10), 1275–1299 (1965). [CrossRef]

], used for bio-sensing [13

13. P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt. 46(12), 2351–2360 (2007). [CrossRef] [PubMed]

,14

14. I. Abdulhalim, M. Auslender, and S. Hava, “Resonant and scatterometric grating-based nanophotonic structures for biosensing,” J. Nanophotonics 1(1), 011680 (2007). [CrossRef]

], and made tunable optically [15

15. F. Yang, G. Yen, G. Rasigade, J. A. N. T. Soares, and B. T. Cunningham, “Optically tuned resonant optical reflectance filter,” Appl. Phys. Lett. 92(9), 091115 (2008). [CrossRef]

] or with liquid crystals [16

16. I. Abdulhalim, “Anisotropic layers in waveguides for mode tuning and tunable filtering,” Proc. SPIE 6135, 61350R, 61350R-10 (2006). [CrossRef]

,17

17. F. Yang, G. Yen, and B. T. Cunningham, “Voltage-tuned resonant reflectance optical filter for visible wavelengths fabricated by nanoreplica molding,” Appl. Phys. Lett. 90(26), 261109 (2007). [CrossRef]

] and dyes [18

18. D. W. Dobbs and B. T. Cunningham, “Optically tunable guided-mode resonance filter,” Appl. Opt. 45(28), 7286–7293 (2006). [CrossRef] [PubMed]

]. This work investigates the Bidirectional Scatter Distribution Function (BSDF) of a GMRF at incidence angles and wavelengths other than those for which the structure was designed.

The BSDF is the combination of the BRDF (reflectance) and BTDF (transmittance), and is defined as the scattered radiance, Ls, (W-cm−1-Sr−1) per incident irradiance, Ei (W-cm−2). Practically, since the illuminated area in a BSDF experiment is also the (reflected or transmitted) radiant area, the BSDF can be defined as the collected radiant flux, Φs, per solid angle, Ωs (as defined by the detection aperture and its distance from the sample), per incident flux, Φi, adjusted for the projected area of the source as viewed by the detector (cos θs):

BSDF(θi,ϕi,θs,ϕs)=Ls(θs,ϕs)Ei(θi,ϕi)=Φs/ΩsΦi(θi,ϕi)cosθs(1Sr)
(1)

BSDF measurement of PC’s in the literature is sparse, including periodic nanoarrays [19

19. I. Abdulhalim, “Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit,” Appl. Opt. 46(12), 2219–2228 (2007). [CrossRef] [PubMed]

], 2-D hexagonal PC’s [20

20. S.-T. Wu, M. S. Li, and A. Y.-G. Fuh, “Observation of conical scattering cones from a two-dimensional hexagonal photonic crystal based on a polymer-dispersed liquid crystal,” Opt. Lett. 33(23), 2758–2760 (2008). [CrossRef] [PubMed]

], natural PC’s [21

21. J. Boulengueza, S. Berthiera, and J. P. Vigneron, “Simulations tools for natural photonic structures,” Physica B 394(2), 217–220 (2007). [CrossRef]

23

23. E. Van Hooijdonk, C. Barthou, J. P. Vigneron, and S. Berthier, “Detailed experimental analysis of the structural fluorescence in the butterfly Morpho sulkowskyi (Nymphalidae),” J. Nanophotonics 5(1), 053525 (2011). [CrossRef]

], self-assembled PC’s [24

24. R. V. Nair and R. Vijaya, “Observation of higher-order diffraction features in self-assembled photonic crystals,” Phys. Rev. A 76(5), 053805 (2007). [CrossRef]

], and even including critical dimension metrology [25

25. J. Allgair, D. Benoit, R. Hershey, L. C. Litt, I. Abdulhalim, B. Braymer, M. Faeyrman, J. C. Robinson, U. Whitney, Y. Xu, P. Zalicki, and J. Seligson, “Manufacturing considerations for implementation of scatterometry for process monitoring,” Proc. SPIE 3998, 125–134 (2000). [CrossRef]

27

27. C. J. Raymond, M. R. Murnane, S. Sohail, H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13(4), 1484–1495 (1995). [CrossRef]

]. This work presents novel BSDF and spectral collinear transmittance measurements of a GMRF PC structure, along with supporting analysis.

2. Sample

The GMRF structure studied here was fabricated using a nanoreplica molding process described in detail by Yang et al. (Fig. 1
Fig. 1 (left) SEM view of the nanoreplica mold from a 2-D square lattice PC silicon master. The master is comprised of posts resulting in a nanoreplica mold of 2D square lattice of holes. (right) Cross section schematic view of a 3-PC stack filter with 300-nm period, hole depth of 150 nm, and TiO2 thickness of 67 nm. The schematic cross section is not to scale, as the UVCP layers (layers 1, 3, and 5) are each ~5 μm thick, and the PET substrate is ~250 μm thick [10].
) [10

10. F. Yang, G. Yen, and B. T. Cunningham, “Integrated 2D photonic crystal stack filter fabricated using nanoreplica molding,” Opt. Express 18(11), 11846–11858 (2010). [CrossRef] [PubMed]

]. UV-cured polymer (UVCP) atop a polyethylene terephthalate (PET) substrate received the pattern from a silicon master with a 2D square lattice of 150-nm diameter circular posts on a 300-nm period. After UV curing, a thin film of titanium dioxide (TiO2) with high refractive index (n = 2.42 at λ = 532 nm) is sputter deposited on top of the UVCP to serve as a high refractive index layer over the low refractive index (nUVCP = 1.45 at λ = 532 nm) replica-molded grating structure to produce a PC structure that results in resonant optical reflection. A successive nanoreplica molded UVCP layer may then be fabricated atop the TiO2 layer, and the process continued. The structure studied here is a stack of three PC filters. The thicknesses of the UVCP layers that are sandwiched between the TiO2 films are ~5 μm, which is substantially greater than the designed resonant wavelength. As a result, there is no mode coupling between the PC layers, each layer behaves as an independent filter, and there is no requirement for tight tolerance on either the thickness of the UVCP layer or the lateral alignment of upper PC filters with respect to filters beneath.

3. Spectral transmission measurements

Spectral transmission of this three-layer GMRF was measured for off-normal incidence and p-, s- and un-polarized incident light using a Cary 500 Spectraphotometer, a grating monochromator with a Littrow mount. The angular resolution of these measurements was typically 5°; however, for the un-polarized measurements, 1° steps were taken between 24° < θi < 27°. (θi ≈25° will prove of interest later.) These measurements are shown in Figs. 2(a)
Fig. 2 Measured transmittance of the 2-D GMRF for plane of incidence parallel to the grating periodicity (ϕ = 0) for (a) p-, (b) s- and (c) un-polarized light, and (d) plane of incidence at 45° from the grating periodicity (ϕ = 45°). θi steps were made in 5° increments, except in (c) and (d) near the angle of interest, 25°, where 1° steps were made. (e) and (f) Solutions to grating-coupled waveguide analysis of Eq. (5) scaled by Snell's law as described in Eq. (2) for (e) ϕ = 0 and (f) ϕ = 45°. Here, neff = λθ = 0,m = 1/Λ = 532nm/300nm, the design wavelength and periodicity of the measured GRMF.
-2(d).

Analysis of the spectral transmission measurements was performed by developing spectral transmission and reflection simulations for one layer of this GMRF structure in a 3-D finite-difference time-domain (FDTD) Maxwell's equation solver as functions of incident angle and polarization. Specifically, Lumerical FDTD® was used. The structure’s geometry in simulation was built using circular features following the circular posts described for the nanoreplica mold silicon master [10

10. F. Yang, G. Yen, and B. T. Cunningham, “Integrated 2D photonic crystal stack filter fabricated using nanoreplica molding,” Opt. Express 18(11), 11846–11858 (2010). [CrossRef] [PubMed]

]. Figure 3
Fig. 3 Cross section schematic view of the simulated GMRF structure. The unit cell consists one period (Λ = 300 nm) in the x- and y-directions and a 600-nm span in the z-direction. t = 0.25 μm. ε1 = 2.13 and εa = 5.86.
shows a schematic of the simulated structure. Definitions for all refractive indices also followed Yang [10

10. F. Yang, G. Yen, and B. T. Cunningham, “Integrated 2D photonic crystal stack filter fabricated using nanoreplica molding,” Opt. Express 18(11), 11846–11858 (2010). [CrossRef] [PubMed]

]. The unit cell of the simulation consisted of one period (Λ = 300 nm) in the x- and y-directions using Bloch boundary conditions, and a 600-nm span in the z-direction (transverse to the PC layer) with a Perfectly Matched Layer (PML) boundary condition.

Using this configuration, the plane wave excitation begins inside the UVCP (ε1 in Fig. 3) and the wavelength was adjusted accordingly. Also, to compare the simulated data directly to measured data, the incident angle was adjusted by Snell's law,
θisim=sin1(1nUVCPsinθimeas)
(2)
where θisim is the incident angle in the simulation, nUVCP is the refractive index of UVCP, and θimeas is the incident angle in the measurements and the incident angle at which all simulation data is presented.

Simulated sweeps in incident angle, θi, wavelength, λ, for s-, p- and un-polarized light, and for azimuthal orientation of the 2-D GMRF structure with respect to the plane of incidence (ϕ = 0 or 45°) were completed. The hemispherical transmission and reflection were measured with two Frequency Domain Power Monitor (FDPM) planes with their normals in the z-direction. The transmission monitor was placed below the structure and the reflection monitor above the source. Results are shown in Fig. 4
Fig. 4 Simulated transmittance and reflectance of the 2-D GRMF structure as a function of incident angle and wavelength for ϕ = 0. (a) and (b) Transmittance for p- and s-polarizations. (c) and (d) Reflectance for p- and s-polarizations. (e) and (f) Transmittance for un-polarized light for ϕ = 0 and ϕ = 45°.
.

The measured data of Figs. 2(a)-2(d) and the simulated data of Fig. 4 can also be analyzed by considering it to be the simple phase-matching problem of a grating-coupled waveguide.
ksin(θi)±m2πΛ=βm=kneff
(3)
where k is the propagation constant, Λ is grating period, and βm is the waveguide propagation constant of the mth mode, where neff is the effective refractive index in which the mth mode propagates. Since GMRF’s are designed for resonance at θi = 0 for the m = 1 mode, neff was approximated here as neff = λθ = 0,m = 1/Λ. For the 2-D GRMF studied here,
kx+ky±iGy±jGx=βi,j
(4)
where kx=ksinθicosϕx^, ky=ksinθisinϕy^, x^ and y^ are unit vectors in the ϕ = 0 and 90° directions, respectively, i and j are integers, |Gx|=|Gy|=2π/Λ and |βi,j| is again the propagation constant of the ith, jth mode. Equation (3) can be rewritten as,
λi,j(θi,ϕ)=λθ=0;i,j=1(Λλi,jsinθisinϕ±i)2+(Λλi,jsinθicosϕ±j)2
(5)
which is plotted in Figs. 2(e) and 2(f) for ϕ = 0 and 45° for λθ = 0;i,j = 1 = 532 nm and Λ = 300 nm. Once again, θi scaled by Snell’s law as described in Eq. (2). Note that this grating-coupled waveguide analysis compares very well with both the measurements of Figs. 2(c) and 2(d) and the simulations of Figs. 4(e) and 4(f).

4. BSDF measurements

The BSDF measurements presented here were made with a Schmitt Measurement Systems, Inc. Complete Angle Scatter Instrument (CASI) using a 544-nm wavelength HeNe laser. The CASI detector is located on a goniometric arm 50 cm away from the sample behind one of four 300-μm to 1.385-cm diameter apertures, implying the solid angle in which the scatter distribution ranged 71 nSr-151 μSr. The detector field of view includes the laser spot on the sample and little significant area outside this, and has a chromatic filter for 544 nm. The CASI also uses a chopper and lock-in detection, making measurements relatively insensitive to ambient light. Calibration experiments against a National Institute of Standards and Technology (NIST) certified reflectance standard showed that the BSDF values are within 2% of the expected value when the system is aligned for the 544-nm source [28

28. B. L. Balling, “A comparative study of the bidirectional reflectance distribution function of several surfaces as a mid-wave infrared diffuse reflectance standard,” MSEE thesis, Air Force Institute of Technology, 2009.

].

The CASI is designed for in-plane measurements; i.e. the collection receiver stays in the plane created by the incident beam and the surface normal of a vertically oriented sample for both reflection and transmission. In this fashion, the polarization angle of incident and scattered light relative to the sample is insensitive to rotation of the sample about a vertical axis on the surface of the sample. The incident laser polarization is neither perfectly linear nor perfectly aligned either vertically or horizontally. Therefore, a polarizer and half-wave plate were used to ensure the largest incident power and rotate an incident linear polarization state into vertical or horizontal alignment. The polarization state of the scattered light was not collected.

Measurements out of the plane of incidence are accomplished by rotating the sample about a horizontal axis on its surface. The CASI system is basically designed for in-plane measurements; however, by rotating the sample about its horizontal axis, it is possible to collect out-of-plane BSDF data. The θi and θs values produced by the CASI from a tilted sample assume the sample is vertical. Therefore, a geometric coordinate transformation was applied to the BSDF measurements to ensure the results are presented in the sample-centered coordinate system. The transform used here was described in detail by Germer [29

29. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999). [CrossRef]

].

The BSDF of this PC structure, designed to be a GMRF for normally incident light at 532 nm, was measured at 544 nm. In-plane results for transmittance and reflectance distributions for ϕ = 0 are shown in Fig. 5
Fig. 5 In-plane Log(BTDF) of GMRF structure measured at λ = 544 nm for (a) p- and (b) s-polarizations, and in-plane Log(BRDF) measurements for (c) p- and (d) s-polarizations. Note that the collinear transmittance/specular reflectance peaks at θi = θt,r have magnitudes greater than 10 Sr−1 as do the m = −1 diffraction order peaks in (c) and (d).
. The ridges at θi = θt,r show the collinear transmittance/specular reflectance. The curved ridges at the lower right of the BRDF plots ((c) and (d)) correspond to the m = −1 diffraction grating order,
sinθm=mλΛ+sinθi
(6)
Note the increased retro-reflection in the BRDF at θi ≈25° and the corresponding increased transmittance at that incident angle in BTDF ((a) and (b)), and the lower-magnitude ridges apparent at θi ≈25° and θt,r ≈25° in all plots.

The data for in-plane s-polarized BTDF and BRDF at θi = 25.7° is shown in Figs. 6(a)
Fig. 6 (a) and (b) In-plane Log(BSDF) of the GMRF (design wavelength of 532 nm) measured at 544 nm at θi = 25.7°. BTDF is shown in red and BRDF in blue. (a) Log-linear plot: The BRDF occlusion region around θr = −25.7° is due to the detector blocking the incident beam. (b) Log-polar plot: The green arrow shows the incident angle of 25.7°. (c) Photo of both in-plane and out-of-plane reflected scatter centered about the specular direction at θi = 25.7°. (d) and (e) Out-of-plane Log(BRDF) at θi = 25.7° for (d) p- and (e) s-polarizations.
and 6(b). Here, it is obvious that the increased scatter is due to out-coupled diffraction orders. Out-of-plane BRDF measurements were also made at θi = 15° and 35°. Although some out-coupled diffraction was also observed at these angles, its magnitude was much less than that at 25.7°. Note the missing BRDF data in Fig. 6(a) at ~21° < θs < ~29° is due to the detector occluding the incident laser. Figure 6(c) is a photograph of the reflected diffraction pattern over a ~5° solid angle centered on the specular direction at θi = 25.7°. Out-of-plane BRDF measurements for both p- and s-polarizations are shown in Figs. 6(d) and 6(e). The appearance of this data is due to the nature of the out-of-plane measurements being made as individual slices across the reflectance hemisphere. For this reason, it was difficult to capture all the out-of-plane diffraction orders, making this an incomplete measurement set.

To analyze the BSDF measured at λ = 544 nm and θi = 25.7° further, a second Lumerical FDTD® simulation was performed, modeling the GMRF structure as a single-layer 2-D PC sandwiched by 500 nm of UVCP on the top and bottom. Grating orders and their strengths were calculated in all directions. In the z-direction (again, transverse to the PC layer), only specular grating orders were calculated. However, in the x- and y-directions, multiple grating orders were calculated and their strengths determine power propagating parallel to the grating periodicity. These results are shown in Fig. 7
Fig. 7 Normalized x/y transmission for seven points along the (0, −1), ( ± 1, 0) and (0, 1) modes corresponding to the λ and θi points shown in the inset. The inset shows the transmittance of s-polarized radiation as a function of wavelength and incident angle. The A, B, and C points on the inset correspond to the λ and θi values at which the grating orders are plotted in Fig. 8.
, where normalized x/y transmission corresponding to the wavelength and incident angle points shown in the inset is plotted. The inset shows s-polarization transmittance as a function of λ and θi, similar to Fig. 4(b). Since the GMRF was designed for destructive interference of the design wavelength (532 nm) upon transmission at normal incidence, normalized x/y transmission of the m = 1 modes at θi = 0 is zero, as expected. The x/y transmission of all the modes then increases with incident angle.

Grating orders and their directions for three of the λ and θi locations shown in the inset of Fig. 7, A, B and C, are shown in Fig. 8
Fig. 8 Spherical plots of grating orders and their directions. (A) λ = 532 nm and θi = 0°, (B) λ = 700 nm and θi = 25°, and (C) λ = 544 nm and θi = 25°. The black dotted lines represent the incident light, the blue lines represent the specular reflection, and the red and green lines represent the light transmitted in the x- and y-directions.
. The black dotted lines represent the incident light, the blue lines represent the specular reflection, and the red and green lines represent the magnitude of the power transmitted in the x- and y-directions. (A) For normal incidence at 532 nm, essentially no power is transmitted into the structure. (B) For off-normal incidence at wavelengths not corresponding to a grating-coupled mode, x/y transmission is also minimal. But (C), for off-normal incidence at wavelengths corresponding to coupled modes, x/y transmission is significant, and leads to the out-coupling seen in our BSDF measurements.

5. Conclusion

Acknowledgments

The research was supported by the Air Force Research Laboratory, Wright-Patterson AFB OH. The views expressed in this paper are those of the authors and do not necessarily reflect the official policy or position of the Air Force, the Department of Defense or the U.S. Government.

References and links

1.

N. Fabre, L. Lalouat, B. Cluzel, X. Mélique, D. Lippens, F. de Fornel, and O. Vanbésien, “Optical near-field microscopy of light focusing through a photonic crystal flat lens,” Phys. Rev. Lett. 101(7), 073901 (2008). [CrossRef] [PubMed]

2.

S. N. Tandon, M. Soljacic, G. S. Petrich, J. D. Joannopoulos, and L. A. Kolodziejski, “The superprism effect using large area 2D-periodic photonic crystal slabs,” Photon. Nano. Fund. Appl. 3(1), 10–18 (2005). [CrossRef]

3.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Self-collimating phenomena in photonic crystals,” Appl. Phys. Lett. 74(9), 1212–1214 (1999). [CrossRef]

4.

H. Kurt, E. Colak, O. Cakmak, H. Caglayan, and E. Ozbay, “The focusing effect of graded index photonic crystals,” Appl. Phys. Lett. 93(17), 171108 (2008). [CrossRef]

5.

I. Prieto, B. Galiana, P. A. Postigo, C. Algora, L. J. Martínez, and I. Rey-Stolle, “Enhanced quantum efficiency of Ge solar cells by a two-dimensional photonic crystal nanostructured surface,” Appl. Phys. Lett. 94(19), 191102 (2009). [CrossRef]

6.

T. R. Nielsen, A. Lavrinenko, and J. Mork, “Slow light in quantum dot photonic crystal waveguides,” Appl. Phys. Lett. 94(11), 113111 (2009). [CrossRef]

7.

M. Galli, S. L. Portalupi, M. Belotti, L. C. Andreani, L. O’Faolain, and T. F. Krauss, “Light scattering and Fano resonances in high-Q photonic crystal nanocavities,” Appl. Phys. Lett. 94(7), 071101 (2009). [CrossRef]

8.

S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef] [PubMed]

9.

N. Ganesh and B. T. Cunningham, “Photonic-crystal near-ultraviolet reflectance filters fabricated by nanoreplica molding,” Appl. Phys. Lett. 88(7), 071110 (2006). [CrossRef]

10.

F. Yang, G. Yen, and B. T. Cunningham, “Integrated 2D photonic crystal stack filter fabricated using nanoreplica molding,” Opt. Express 18(11), 11846–11858 (2010). [CrossRef] [PubMed]

11.

T. Sun and D. Wu, “Guided-mode resonance excitation on multimode planar periodic waveguide,” J. Appl. Phys. 108(6), 063106 (2010). [CrossRef]

12.

A. Hessel and A. A. Oliner, “A new theory of Wood's anomalies on optical gratings,” Appl. Opt. 4(10), 1275–1299 (1965). [CrossRef]

13.

P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt. 46(12), 2351–2360 (2007). [CrossRef] [PubMed]

14.

I. Abdulhalim, M. Auslender, and S. Hava, “Resonant and scatterometric grating-based nanophotonic structures for biosensing,” J. Nanophotonics 1(1), 011680 (2007). [CrossRef]

15.

F. Yang, G. Yen, G. Rasigade, J. A. N. T. Soares, and B. T. Cunningham, “Optically tuned resonant optical reflectance filter,” Appl. Phys. Lett. 92(9), 091115 (2008). [CrossRef]

16.

I. Abdulhalim, “Anisotropic layers in waveguides for mode tuning and tunable filtering,” Proc. SPIE 6135, 61350R, 61350R-10 (2006). [CrossRef]

17.

F. Yang, G. Yen, and B. T. Cunningham, “Voltage-tuned resonant reflectance optical filter for visible wavelengths fabricated by nanoreplica molding,” Appl. Phys. Lett. 90(26), 261109 (2007). [CrossRef]

18.

D. W. Dobbs and B. T. Cunningham, “Optically tunable guided-mode resonance filter,” Appl. Opt. 45(28), 7286–7293 (2006). [CrossRef] [PubMed]

19.

I. Abdulhalim, “Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit,” Appl. Opt. 46(12), 2219–2228 (2007). [CrossRef] [PubMed]

20.

S.-T. Wu, M. S. Li, and A. Y.-G. Fuh, “Observation of conical scattering cones from a two-dimensional hexagonal photonic crystal based on a polymer-dispersed liquid crystal,” Opt. Lett. 33(23), 2758–2760 (2008). [CrossRef] [PubMed]

21.

J. Boulengueza, S. Berthiera, and J. P. Vigneron, “Simulations tools for natural photonic structures,” Physica B 394(2), 217–220 (2007). [CrossRef]

22.

D. G. Stavenga, H. L. Leertouwer, P. Pirih, and M. F. Wehling, “Imaging scatterometry of butterfly wing scales,” Opt. Express 17(1), 193–202 (2009). [CrossRef] [PubMed]

23.

E. Van Hooijdonk, C. Barthou, J. P. Vigneron, and S. Berthier, “Detailed experimental analysis of the structural fluorescence in the butterfly Morpho sulkowskyi (Nymphalidae),” J. Nanophotonics 5(1), 053525 (2011). [CrossRef]

24.

R. V. Nair and R. Vijaya, “Observation of higher-order diffraction features in self-assembled photonic crystals,” Phys. Rev. A 76(5), 053805 (2007). [CrossRef]

25.

J. Allgair, D. Benoit, R. Hershey, L. C. Litt, I. Abdulhalim, B. Braymer, M. Faeyrman, J. C. Robinson, U. Whitney, Y. Xu, P. Zalicki, and J. Seligson, “Manufacturing considerations for implementation of scatterometry for process monitoring,” Proc. SPIE 3998, 125–134 (2000). [CrossRef]

26.

I. Kallioniemi, J. Saarinen, and E. Oja, “Optical scatterometry of subwavelength diffraction gratings: neural-network approach,” Appl. Opt. 37(25), 5830–5835 (1998). [CrossRef] [PubMed]

27.

C. J. Raymond, M. R. Murnane, S. Sohail, H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B 13(4), 1484–1495 (1995). [CrossRef]

28.

B. L. Balling, “A comparative study of the bidirectional reflectance distribution function of several surfaces as a mid-wave infrared diffuse reflectance standard,” MSEE thesis, Air Force Institute of Technology, 2009.

29.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane,” Rev. Sci. Instrum. 70(9), 3688–3695 (1999). [CrossRef]

OCIS Codes
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(290.1483) Scattering : BSDF, BRDF, and BTDF
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: August 10, 2012
Manuscript Accepted: September 12, 2012
Published: November 19, 2012

Citation
M. A. Marciniak, S. R. Sellers, R. B. Lamott, and B. T. Cunningham, "Bidirectional scatter measurements of a guided-mode resonant filter photonic crystal structure," Opt. Express 20, 27242-27252 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-25-27242


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References

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  11. T. Sun and D. Wu, “Guided-mode resonance excitation on multimode planar periodic waveguide,” J. Appl. Phys.108(6), 063106 (2010). [CrossRef]
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  13. P. C. Mathias, N. Ganesh, L. L. Chan, and B. T. Cunningham, “Combined enhanced fluorescence and label-free biomolecular detection with a photonic crystal surface,” Appl. Opt.46(12), 2351–2360 (2007). [CrossRef] [PubMed]
  14. I. Abdulhalim, M. Auslender, and S. Hava, “Resonant and scatterometric grating-based nanophotonic structures for biosensing,” J. Nanophotonics1(1), 011680 (2007). [CrossRef]
  15. F. Yang, G. Yen, G. Rasigade, J. A. N. T. Soares, and B. T. Cunningham, “Optically tuned resonant optical reflectance filter,” Appl. Phys. Lett.92(9), 091115 (2008). [CrossRef]
  16. I. Abdulhalim, “Anisotropic layers in waveguides for mode tuning and tunable filtering,” Proc. SPIE6135, 61350R, 61350R-10 (2006). [CrossRef]
  17. F. Yang, G. Yen, and B. T. Cunningham, “Voltage-tuned resonant reflectance optical filter for visible wavelengths fabricated by nanoreplica molding,” Appl. Phys. Lett.90(26), 261109 (2007). [CrossRef]
  18. D. W. Dobbs and B. T. Cunningham, “Optically tunable guided-mode resonance filter,” Appl. Opt.45(28), 7286–7293 (2006). [CrossRef] [PubMed]
  19. I. Abdulhalim, “Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit,” Appl. Opt.46(12), 2219–2228 (2007). [CrossRef] [PubMed]
  20. S.-T. Wu, M. S. Li, and A. Y.-G. Fuh, “Observation of conical scattering cones from a two-dimensional hexagonal photonic crystal based on a polymer-dispersed liquid crystal,” Opt. Lett.33(23), 2758–2760 (2008). [CrossRef] [PubMed]
  21. J. Boulengueza, S. Berthiera, and J. P. Vigneron, “Simulations tools for natural photonic structures,” Physica B394(2), 217–220 (2007). [CrossRef]
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  23. E. Van Hooijdonk, C. Barthou, J. P. Vigneron, and S. Berthier, “Detailed experimental analysis of the structural fluorescence in the butterfly Morpho sulkowskyi (Nymphalidae),” J. Nanophotonics5(1), 053525 (2011). [CrossRef]
  24. R. V. Nair and R. Vijaya, “Observation of higher-order diffraction features in self-assembled photonic crystals,” Phys. Rev. A76(5), 053805 (2007). [CrossRef]
  25. J. Allgair, D. Benoit, R. Hershey, L. C. Litt, I. Abdulhalim, B. Braymer, M. Faeyrman, J. C. Robinson, U. Whitney, Y. Xu, P. Zalicki, and J. Seligson, “Manufacturing considerations for implementation of scatterometry for process monitoring,” Proc. SPIE3998, 125–134 (2000). [CrossRef]
  26. I. Kallioniemi, J. Saarinen, and E. Oja, “Optical scatterometry of subwavelength diffraction gratings: neural-network approach,” Appl. Opt.37(25), 5830–5835 (1998). [CrossRef] [PubMed]
  27. C. J. Raymond, M. R. Murnane, S. Sohail, H. Naqvi, and J. R. McNeil, “Metrology of subwavelength photoresist gratings using optical scatterometry,” J. Vac. Sci. Technol. B13(4), 1484–1495 (1995). [CrossRef]
  28. B. L. Balling, “A comparative study of the bidirectional reflectance distribution function of several surfaces as a mid-wave infrared diffuse reflectance standard,” MSEE thesis, Air Force Institute of Technology, 2009.
  29. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane,” Rev. Sci. Instrum.70(9), 3688–3695 (1999). [CrossRef]

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