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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 10 — May. 12, 2008
  • pp: 7153–7160
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Optical characterization of photonic crystal slabs using orthogonally oriented polarization filters

Yousef Nazirizadeh, Jürgen G. Müller, Ulf Geyer, Detlef Schelle, Ernst-Bernhard Kley, Andreas Tünnermann, Uli Lemmer, and Martina Gerken  »View Author Affiliations


Optics Express, Vol. 16, Issue 10, pp. 7153-7160 (2008)
http://dx.doi.org/10.1364/OE.16.007153


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Abstract

We present an experimental method for direct analysis of guided-mode resonances in photonic crystal slab structures using transmission measurements. By positioning the photonic crystal slab between orthogonally oriented polarization filters light transmission is suppressed except for the guided-mode resonances. Angle resolved transmission measurements with crossed polarizers are performed to obtain the band structure around the Γ-point. Results are compared to mode simulations. Spatially resolved measurements in a confocal microscope setup are used for homogeneity characterizations. Stitching errors and inhomogeneities in exposure dose down to 1.3% in photonic crystal slabs fabricated by electron beam lithography are observed using this method.

© 2008 Optical Society of America

1. Introduction

Photonic crystal slabs are one-dimensional or two-dimensional periodic structures in a slab of high refractive index material. In these structures two kinds of light confinement are distinguished. In-plane guided modes are modes confined by the high index material without coupling to external radiation [1

1. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999). [CrossRef]

]. Guided-mode resonances are also confined by the high index material but may couple to external radiation [2

2. S. Fan and J. D. Jannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002). [CrossRef]

]. Guided-mode resonances are particularly important in devices where light extraction from the photonic crystal slab is desired. In distributed feedback (DFB) lasers, for instance, the resonator is realized using Bragg reflection in one-dimensional (1D) or two-dimensional (2D) photonic crystal slabs [3

3. S. Wang and S. Sheem, “Two-dimensional distributed-feedback lasers and their applications,” Appl. Phys. Lett. 22, 460–462 (1973). [CrossRef]

,4

4. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999). [CrossRef]

]. First order Bragg reflection corresponds to a guided mode while second order Bragg reflection allows for coupling to external radiation and implies a guided-mode resonance. By choosing a guided-mode resonance as the laser mode a surface emitting laser with nearly diffraction limited emission is obtained [5

5. S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77, 2310–2312 (2000). [CrossRef]

]. In light emitting diodes (LED) the extraction efficiency is increased by introducing a photonic crystal slab structure and employing the interaction of guided-mode resonances with external radiation [6

6. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phs. Rev.Lett. 78, 3294–3297 (1997). [CrossRef]

,7

7. J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000). [CrossRef]

]. Various other passive photonic elements such as narrow linewidth bandpass filters based on photonic crystal slabs are discussed in [8

8. Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661–5674 (2004). [CrossRef] [PubMed]

].

In this paper we present an experimental method for a rapid and non-destructive local optical characterization of photonic crystal slabs. Transmission measurements are performed on photonic crystals slabs placed in a crossed-polarizer configuration in a confocal microscope setup. This allows for the direct characterization of the guided-mode resonances of microscopic structures. In combination with a translation stage the setup is utilized to characterize the spatial homogeneity of macroscopic nanostructured surfaces. Stitching errors and inhomogeneities in exposure dose of photonic crystal slabs fabricated by electron beam lithography are investigated. Unlike lateral transmission measurements these measurements are independent of the lateral termination of the structure and no special preparation is required [21

21. G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Goesele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003). [CrossRef]

].

2. Experimental setup

The experimental setup is shown schematically in Fig. 1(a). The sample is placed on a translation stage in a confocal microscope setup. A halogen lamp is used as a broadband illumination source. Two orthogonally oriented polarization filters (extinction ratio 8,500:1) are placed before and behind the photonic crystal slab. We refer to the first polarization filter as polarizer and to the second polarization filter as analyzer. The polarizer is placed between the halogen lamp and the condenser, and the analyzer behind the objective with a numerical aperture of 0.6. Spatial resolution of 2.5 µm is given due to the combination of a pinhole (100 µm) placed in the detection arm and the magnification of the objective (40×). The spectral distribution of the transmitted light is analyzed with a spectrograph equipped with a CCD camera. To calculate the transmittivity the transmitted intensity is normalized to the detected intensity without a sample for a parallel orientation of polarizer and analyzer. The variable aperture slit-diaphragm is used for angle resolved measurements. Reflection measurements may be performed in a similar configuration using an additional beam splitter. Fig. 1(b) and Fig. 1(c) give the electric field directions, angle definitions, and structural definitions used in the following sections.

As a first example the characterization of a hexagonal photonic crystal slab of air holes (r=65 nm) in a Nb2O5 layer (d=150 nm) on a quartz substrate with a periodicity of a=300 nm is considered. Nb2O5 is a promising high-index material for photonic crystals, which is transparent in the visible range. The structure was fabricated by electron beam lithography and a dry etching process. The fabrication procedure for this structure and all other electron beam lithography samples discussed in this publication is detailed in [22

22. M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, A. Tünnermann, R. Iliew, C. Etrich, U. Peschel, and F. Lederer, “Highly efficient waveguide bends in photonic crystal with a low in-plane index contrast,” Opt. Express 11, 3284–3289 (2003). [CrossRef] [PubMed]

, 23

23. M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, A. Tünnermann, R. Iliew, C. Etrich, U. Peschel, and F. Lederer, “High transmission and single-mode operation in low-index-contrast photonic crystal waveguide devices,” Appl. Phys. Lett. 84, 663–665 (2004). [CrossRef]

]. Figure 2(a) shows transmittivity and reflectivity measurements at normal incidence for parallel orientation of polarizer and analyzer on structured (black line) and unstructured (gray line) surface areas. In the unstructured region Fabry-Perot oscillations due to the thin-film are clearly visible for both transmission and reflection. In the structured region, however, these thin-film effects are superimposed with photonic crystal guided-mode resonances. As discussed in [2

2. S. Fan and J. D. Jannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002). [CrossRef]

] these resonances are referred to as Fano-like resonances. The same measurement is repeated in transmission with crossed polarization filters (Fig. 2(b)). The smoothly varying background is suppressed and the guided-mode resonances are revealed. These resonances have the expected symmetric Lorentzian line shape [2

2. S. Fan and J. D. Jannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002). [CrossRef]

]. To explain these results transmission measurements as a function of azimuthal angle ϕ are discussed for a 1D photonic crystal slab in the following.

Fig. 1. (a). Confocal microscope setup for transmission measurements with orthogonally oriented polarization filters. The first and second polarization filter are referred to as polarizer and analyzer respectively. b) Schematic of photonic crystal orientation relative to polarizer and analyzer for normal incidence measurements. Arrows indicate electric field orientation. Azimuthal angle ϕ defines the fraction which couples to the photonic crystal slab (ϕ>0°, θ=0°). c) Schematic drawing of photonic crystal slab for oblique polar angle θ. d is the thickness of the photonic crystal slab, a is the period and 2r is the width (diameter) of the etched pattern in 1D (2D) structures (ϕ=0°, θ>0°).

The considered 1D photonic crystal slab consists of an ITO layer (d=130 nm) with air stripes (2r=50 nm) fabricated by interference lithography with a periodicity of a=350 nm. Figure 3(a) shows transmission with crossed polarization filters for three different azimuthal angles ϕ between the photonic crystal slab and the polarizer (defined in Fig. 1). Only the fraction of light which is perpendicular to the grating lines couples to the guided-mode resonances. And again only the fraction of the guided-mode resonances coupling out of the photonic crystal slab, which points in the direction of the analyzer, passes it. In Fig. 3(b) the intensity of the central mode (530 nm–540 nm) is plotted versus angle ϕ for transmission measurements with crossed polarization filters. The intensity follows a sin(ϕ)2 cos(ϕ)2 curve, which can be derived from Malus’ law and the projection of the polarization filters onto the photonic crystal slab. As expected maxima in transmission are observed at 45° and 135°.

Fig. 2. Transmittivity and reflectivity measurements of a photonic crystal slab with hexagonal geometry of holes in a 150 nm Nb2O5 (n=2.3 for wavelength λ=500 nm) layer with a periodicity of a=300 nm. Black lines indicate measurements on structured and gray lines on unstructured regions (θ=0°). a) Polarizer and analyzer with parallel orientation. Superposition of guided-mode resonances and background. b) Transmittivity measurement with crossed polarization filters. Direct observation of guided-mode resonances. Inset: SEM image of hexagonal photonic crystal.
Fig. 3. Transmission measurements with crossed polarization filters performed on 1D photonic crystal slab with a periodicity of a=350 nm, structured in a 130 nm ITO (n=1.87 for λ=500 nm) layer on a glass substrate. θ=0°, while ϕ is varied from 0° to 180°. a) Transmission spectra at three different angles ϕ. Inset: SEM image of 1D photonic crystal. b) Central mode intensity (530 nm–540 nm) versus angle ϕ. Maxima at ϕ=45° and ϕ=135°.

The absolute value of transmittivity with crossed polarization filters depends on the coupling efficiency of external radiation to the photonic crystal and the polarization conversion properties [13

13. M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526 (2001). [CrossRef] [PubMed]

,14

14. A. D. Bristow, V. N. Astratov, R. Shimada, I. S. Culshaw, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, and T. F. Krauss, “Polarization conversion in the reflectivity properties of photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 880–884 (2002). [CrossRef]

]. As a comparison the insertion of an ideal polarization filters with an azimuthal orientation of ϕ=45° instead of the photonic crystal slab is considered. The transmittivity of this configuration is 25% following the sin(ϕ)2 cos(ϕ)2 relation. For 2D hexagonal photonic crystal slabs the transmittivity values show maxima in intervals of Δϕ=60° as reported in [13

13. M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526 (2001). [CrossRef] [PubMed]

]. Between these maxima the transmittivity is reduced, but larger than zero. Thus, transmission measurements between crossed polarizers may be performed at any azimuthal angle ϕ. The transmittivity values in Fig. 2(b) are lower due to the weaker coupling to the external radiation.

3. Angle resolved transmission measurements

Dark field microscopy, which also suppresses the background light, is a common method for visual characterization of photonic crystal slabs. However, the spectral information gained with this method has no defined angular orientation. Using the proposed method with crossed polarization filters, measurements at angles other than normal incidence are possible. By performing angle resolved measurements (varying polar angle θ in Γ - M direction) the band structure of the photonic crystal slab can be obtained locally. The band structure measurements are limited to the part lying above the light line since only guided-mode resonances are observed.

Fig. 4. Angle resolved transmission measurements on a photonic crystal slab with hexagonal geometry in Γ - M direction. Polar angle θ is varied from 0° to 8° a) Transmission measurements under various angles. The intensity plot is normalized to the transmittivity without sample. b) Band structure calculation for the measured photonic crystal slab. Assuming a radius of r=85 nm the best fit to the measurements was observed.

We place a variable aperture slit-diaphragm in the condenser plane for the illumination. By opening the aperture incrementally and subtracting consecutive results, a differential measurement for angular illumination is obtained. This configuration allows for the band structure evaluation at each spatial position. An example of a measurement of a photonic crystal slab on a glass substrate with a hexagonal geometry consisting of 85 nm - holes etched into a Nb2O5 layer (d=250 nm) with a periodicity a=295 nm is shown in Fig. 4(a). The guided-mode resonances can be distinguished clearly. The guided-mode resonance intensities correspond to the coupling strength to external radiation. From the width in wavelength the guided-mode resonance quality factor may be obtained.

For comparison the theoretical band structure is plotted in Fig. 4(b). It is computed with a code developed by Andreani et al. [24

24. L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006). [CrossRef]

] that determines photonic mode dispersion and losses using a guided-mode expansion method, which consists of expanding the magnetic field on the basis of guided modes of an effective homogeneous waveguide and calculating out-of-plane diffraction losses by perturbation theory. For this calculation we considered hexagonal arranged holes with a radius r=85 nm in a 250 nm Nb2O5 layer on a glass substrate with a periodicity of a=295 nm. The dispersion of Nb2O5 is included in our calculations by performing piecewise calculations for wavelength ranges of 5 nm. Good agreement between experimental and theoretical results is observed.

4. Spatially resolved optical characterization

During the fabrication process of nano-photonic devices the monitoring of photonic crystal slab homogeneities is necessary. Here we consider a photonic crystal slab consisting of holes (r=115 nm) in a Nb2O5 layer (d=250 nm) with hexagonal geometry (periodicity a=330 nm) fabricated using electron beam lithography. To obtain a visual impression of the quality of the photonic crystal field, an image of the field is taken with a single lens reflex camera in a conventional, non-confocal microscope setup. Again crossed polarization filters are used to suppress background light. Figure 5(a) shows a false color plot of the red image channel. Two main disadvantages of this fabrication method are clearly visible: stitching errors, which appear as squares in the structure, and drift in the exposure dose, which shows up as a color shift. To observe absolute values for these errors transmission spectra as a function of wavelength and position were recorded for a scan over the 150 µm field with 12.5 µm step size (Fig 5(b)). We observe a drift of 7 nm in the guided-mode resonance wavelength, which is due to changes in the photonic crystal parameters. Such a drift of 1.3% over the entire photonic crystal filed is difficult to observe with SEM.

Fig. 5. Transmission measurements on a photonic crystal slab with hexagonal geometry (θ=0°). a) False color plot of red image channel using orthogonally oriented polarization filters. Dotted line indicates position of scan shown in Fig. 5(b). b) Spectrally and spatially resolved transmission measurements at normal incidence. 1.3% drift in photonic modes is observed.

5. Conclusion

We present a method for optical characterization of 1D and 2D photonic crystal slabs based on spectrally resolved reflection and transmission measurements using two crossed polarization filters, one placed before and one behind the photonic crystal slab. This configuration suppresses the background light, thus guided-mode resonances can be observed directly. A confocal microscope setup is used to perform angle and spatially resolved transmission measurements. Angle resolved transmission measurements were used to reveal the band structure at an arbitrary position. Spatially resolved transmission measurements were performed for rapid and accurate homogeneity characterization of photonic crystal slabs fabricated by electron beam lithography.

Acknowledgments

We acknowledge financial support by the Volkswagen Foundation and the German Federal Ministry for Education and Research BMBF (Project No. 03X5514).

References and links

1.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999). [CrossRef]

2.

S. Fan and J. D. Jannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002). [CrossRef]

3.

S. Wang and S. Sheem, “Two-dimensional distributed-feedback lasers and their applications,” Appl. Phys. Lett. 22, 460–462 (1973). [CrossRef]

4.

M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos, and O. Nalamasu, “Laser action from two-dimensional distributed feedback in photonic crystals,” Appl. Phys. Lett. 74, 7–9 (1999). [CrossRef]

5.

S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, “A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure,” Appl. Phys. Lett. 77, 2310–2312 (2000). [CrossRef]

6.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, “High extraction efficiency of spontaneous emission from slabs of photonic crystals,” Phs. Rev.Lett. 78, 3294–3297 (1997). [CrossRef]

7.

J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, “Bragg scattering from periodically microstructured light emitting diodes,” Appl. Phys. Lett. 77, 3340–3342 (2000). [CrossRef]

8.

Y. Ding and R. Magnusson, “Resonant leaky-mode spectral-band engineering and device applications,” Opt. Express 12, 5661–5674 (2004). [CrossRef] [PubMed]

9.

V. N. Astratov, M. S. Skolnick, S. Brand, T. F. Krauss, O. Z. Karimov, R. M. Stevenson, D. M. Whittaker, I. Culshaw, and R. M. De La Rue, “Experimental technique to determine the band structure of two-dimensional photonic lattices,” IEEE Proc. Optoelectron. 145, 398–402 (1998). [CrossRef]

10.

V. N. Astratov, R. M. Stevenson, I. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss, and R. M. De La Rue, “Heavy photon dispersion in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000). [CrossRef]

11.

M. Galli, D. Bajoni, M. Belotti, F. Paleari, M. Patrini, G. Guizzetti, D. Gerace, M. Agio, L. C. Andreani, D. Peyrade, and Y. Chen, “Measurement of photonic mode dispersion and linewidths in silicon-on-insulator photonic crystal slabs,” IEEE J. Sel. Areas Commun. 23, 1402–1410 (2005). [CrossRef]

12.

K. B. Crozier, V. Lousee, O. Kilic, S. Kim, S. Fan, and O. Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelengths,” Phys. Rev. B 73, 115126 (2006). [CrossRef]

13.

M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob, and G. J. Parker, “Optical trirefringence in photonic crystal waveguides,” Phys. Rev. Lett. 86, 1526 (2001). [CrossRef] [PubMed]

14.

A. D. Bristow, V. N. Astratov, R. Shimada, I. S. Culshaw, M. S. Skolnick, D. M. Whittaker, A. Tahraoui, and T. F. Krauss, “Polarization conversion in the reflectivity properties of photonic crystal waveguides,” IEEE J. Quantum Electron. 38, 880–884 (2002). [CrossRef]

15.

Y. A. Vlasov, M. Deutsch, and D. J. Norris, “Single-domain spectroscopy of self-assembled photonic crystals,” Appl. Phys. Lett. 76, 1627–1629 (2000). [CrossRef]

16.

M. Gerken, R. Boschert, R. Bornemann, U. Lemmer, D. Schelle, M. Augustin, E.-B. Kley, and A. Tünnermann, “Transmission measurements for the optical characterization of 2D-photonic crystals,” Proc. SPIE 5963, Optical Systems Design (2005). [CrossRef]

17.

G. A. Turnbull, P. Andrew, M. J. Jory, W. L. Barnes, and I. D. W. Samuel, “Relationship between photonic band structure and emission characteristics of a polymer distributed feedback laser,” Phys. Rev. B 64, 125122 (2001). [CrossRef]

18.

G. A. Turnbull, P. Andrew, W. L. Barnes, and I. D. W. Samuel, “Photonic mode dispersion of a two-dimensional distributed feedback polymer laser,” Phys. Rev. B 67, 165107 (2003). [CrossRef]

19.

K. Sakai, E. Miyai, T. Sakaguchi, D. Ohnishi, T. Okano, and S. Noda, “Lasing band-edge identification for a surface-emitting photonic crystal laser,” IEEE J. Sel. Areas Commun. 23, 1335–1340 (2005). [CrossRef]

20.

R. Harbers, P. Strasser, D. Caimi, R. F. Mahrt, N. Moll, D. Erni, W. Baechtold, B. J. Offrein, and U. Scherf, “Enhanced feedback and experimental band mapping of organic photonic-crystal lasers,” J. Opt. A: Pure Appl. Opt. 8, 273–277 (2006). [CrossRef]

21.

G. von Freymann, W. Koch, D. C. Meisel, M. Wegener, M. Diem, A. Garcia-Martin, S. Pereira, K. Busch, J. Schilling, R. B. Wehrspohn, and U. Goesele, “Diffraction properties of two-dimensional photonic crystals,” Appl. Phys. Lett. 83, 614–616 (2003). [CrossRef]

22.

M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, A. Tünnermann, R. Iliew, C. Etrich, U. Peschel, and F. Lederer, “Highly efficient waveguide bends in photonic crystal with a low in-plane index contrast,” Opt. Express 11, 3284–3289 (2003). [CrossRef] [PubMed]

23.

M. Augustin, H.-J. Fuchs, D. Schelle, E.-B. Kley, S. Nolte, A. Tünnermann, R. Iliew, C. Etrich, U. Peschel, and F. Lederer, “High transmission and single-mode operation in low-index-contrast photonic crystal waveguide devices,” Appl. Phys. Lett. 84, 663–665 (2004). [CrossRef]

24.

L. C. Andreani and D. Gerace, “Photonic-crystal slabs with a triangular lattice of triangular holes investigated using a guided-mode expansion method,” Phys. Rev. B 73, 235114 (2006). [CrossRef]

OCIS Codes
(120.7000) Instrumentation, measurement, and metrology : Transmission
(220.4241) Optical design and fabrication : Nanostructure fabrication
(050.5298) Diffraction and gratings : Photonic crystals

ToC Category:
Photonic Crystals

History
Original Manuscript: February 25, 2008
Revised Manuscript: April 18, 2008
Manuscript Accepted: April 19, 2008
Published: May 2, 2008

Citation
Yousef Nazirizadeh, Jürgen Müller, Ulf Geyer, Detlef Schelle, Ernst-Bernhard Kley, Andreas Tünnermann, Uli Lemmer, and Martina Gerken, "Optical characterization of photonic crystal slabs using orthogonally oriented polarization filters," Opt. Express 16, 7153-7160 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-10-7153


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References

  1. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos and L. A. Kolodziejski, "Guided modes in photonic crystal slabs," Phys. Rev. B 60, 5751-5758 (1999). [CrossRef]
  2. S. Fan and J. D. Jannopoulos, "Analysis of guided resonances in photonic crystal slabs," Phys. Rev. B 65,235112 (2002). [CrossRef]
  3. S. Wang and S. Sheem, "Two-dimensional distributed-feedback lasers and their applications," Appl. Phys. Lett. 22, 460-462 (1973). [CrossRef]
  4. M. Meier, A. Mekis, A. Dodabalapur, A. Timko, R. E. Slusher, J. D. Joannopoulos and O. Nalamasu, "Laser action from two-dimensional distributed feedback in photonic crystals," Appl. Phys. Lett. 74, 7-9 (1999). [CrossRef]
  5. S. Riechel, C. Kallinger, U. Lemmer, J. Feldmann, A. Gombert, V. Wittwer, and U. Scherf, "A nearly diffraction limited surface emitting conjugated polymer laser utilizing a two-dimensional photonic band structure," Appl. Phys. Lett. 77, 2310-2312 (2000). [CrossRef]
  6. Q1. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and E. F. Schubert, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Phs. Rev.Lett. 78, 3294-3297 (1997). [CrossRef]
  7. J. M. Lupton, B. J. Matterson, I. D. W. Samuel, M. J. Jory, and W. L. Barnes, "Bragg scattering from periodically microstructured light emitting diodes," Appl. Phys. Lett. 77, 3340-3342 (2000). [CrossRef]
  8. Y. Ding and R. Magnusson, "Resonant leaky-mode spectral-band engineering and device applications," Opt. Express 12,5661-5674 (2004). [CrossRef] [PubMed]
  9. Q2. V. N. Astratov, M. S. Skolnick, S. Brand, T. F. Krauss, O. Z. Karimov, R. M. Stevenson, D. M. Whittaker, I. Culshaw and R. M. De La Rue, "Experimental technique to determine the band structure of two-dimensional photonic lattices," IEEE Proc. Optoelectron. 145, 398-402 (1998). [CrossRef]
  10. V. N. Astratov, R. M. Stevenson, I. Culshaw, D. M. Whittaker, M. S. Skolnick, T. F. Krauss and R. M. De La Rue, "Heavy photon dispersion in photonic crystal waveguides," Appl. Phys. Lett. 77, 178-180 (2000). [CrossRef]
  11. M. Galli, D. Bajoni, M. Belotti, F. Paleari, M. Patrini, G. Guizzetti, D. Gerace, M. Agio, L. C. Andreani, D. Peyrade and Y. Chen, "Measurement of photonic mode dispersion and linewidths in silicon-on-insulator photonic crystal slabs," IEEE J. Sel. Areas Commun. 23, 1402-1410 (2005). [CrossRef]
  12. K. B. Crozier, V. Lousee, O. Kilic, S. Kim, S. Fan and O. Solgaard, "Air-bridged photonic crystal slabs at visible and near-infrared wavelengths," Phys. Rev. B 73, 115126 (2006). [CrossRef]
  13. M. C. Netti, A. Harris, J. J. Baumberg, D. M. Whittaker, M. B. D. Charlton, M. E. Zoorob and G. J. Parker, "Optical trirefringence in photonic crystal waveguides," Phys. Rev. Lett. 86, 1526 (2001). [CrossRef] [PubMed]
  14. A. D. Bristow, V. N. Astratov, R. Shimada, I. S. Culshaw, M. S. Skolnick, D. M. Whittaker, A. Tahraoui and T. F. Krauss, "Polarization conversion in the reflectivity properties of photonic crystal waveguides," IEEE J. Quantum Electron. 38, 880-884 (2002). [CrossRef]
  15. Y. A. Vlasov, M. Deutsch, and D. J. Norris, "Single-domain spectroscopy of self-assembled photonic crystals," Appl. Phys. Lett. 76, 1627-1629 (2000). [CrossRef]
  16. M. Gerken, R. Boschert, R. Bornemann, U. Lemmer, D. Schelle, M. Augustin, E.-B. Kley, and A. Tünnermann, "Transmission measurements for the optical characterization of 2D-photonic crystals," Proc. SPIE 5963, Optical Systems Design (2005). [CrossRef]
  17. G. A. Turnbull, P. Andrew, M. J. Jory, W. L. Barnes and I. D. W. Samuel, "Relationship between photonic band structure and emission characteristics of a polymer distributed feedback laser," Phys. Rev. B 64, 125122 (2001). [CrossRef]
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