Abstract

Angular distribution of light diffracted out of the plane of two-dimensional photonic crystals (PhC) has been studied in the azimuthal direction with a specially designed waveguide structure. The optical images of the light extraction patterns from the guided photoluminescence light are obtained with laser excitation in the center of the annual structure made on GaN multilayer. For increasing lattice constant, symmetric patterns with varying number of petals according to the symmetry of the PhC are observed. The appearance and disappearance of the petals can be explained using the Ewald construction in the reciprocal space. The dependence of light extraction on the lattice constant and orientation, and incident angle are investigated.

© 2008 Optical Society of America

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  1. S. Noda, "Recent progresses and future prospects of two- and three-dimensional photonic crystals," IEEE J. Lightwave Technol. 24, 4554-4567 (2006).
    [CrossRef]
  2. F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
    [CrossRef] [PubMed]
  3. M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
    [CrossRef]
  4. A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
    [CrossRef]
  5. H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2004).
    [CrossRef]
  6. A. David, C. Meier, R. Sharma, F. S. Diana, S. P. DenBaars, E. Hu, S. Nakamura, C. Weisbuch, and H. Benisty, "Photonic bands in two-dimensionally patterned multimode GaN waveguides for light extraction," Appl. Phys. Lett. 87, 101107-1-101107-3 (2005).
    [CrossRef]
  7. M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
    [CrossRef]
  8. A. David, T. Fujii, E. Matioli, R. Sharma, K. McGroddy, S. Nakamura, S. P. Denbaars, C. Weisbuch, and H. Benisty, "GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510-1-073510-3 (2006).
    [CrossRef]
  9. C. F. Lai, H. C. Kuo, C. H. Chao, H. T. Hsueh, J.-F. T. Wang, W. Y. Yeh, and J. Y. Chi, "Anisotropy of light extraction from two-dimensional photonic crystal light-emitting diodes," Appl. Phys. Lett. 91, 123117-1-123117-3 (2007).
    [CrossRef]
  10. T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
    [CrossRef]
  11. J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
    [CrossRef]
  12. J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
    [CrossRef]
  13. T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
    [CrossRef]

2006 (2)

S. Noda, "Recent progresses and future prospects of two- and three-dimensional photonic crystals," IEEE J. Lightwave Technol. 24, 4554-4567 (2006).
[CrossRef]

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

2004 (4)

H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2004).
[CrossRef]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
[CrossRef]

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
[CrossRef]

2003 (2)

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
[CrossRef]

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

2001 (1)

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

1999 (1)

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Baba, T.

H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2004).
[CrossRef]

Benisty, H.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Bhat, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Boroditsky, M.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Coccioli, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Craford, M. G.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

David, A.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Diana, F. S.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Epler, J. E.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

Erchak, A.

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Fan, S.

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Gardner, N. F.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

Houdré, R.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Ichikawa, H.

H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2004).
[CrossRef]

Jiang, H. X.

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
[CrossRef]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
[CrossRef]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
[CrossRef]

Joannopoulos, J. D.

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Kim, K. H.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
[CrossRef]

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
[CrossRef]

Krames, M. R.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

Krauss, T. F.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Lin, J. Y.

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
[CrossRef]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
[CrossRef]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
[CrossRef]

Meinel, I.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Nakamura, S.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Noda, S.

S. Noda, "Recent progresses and future prospects of two- and three-dimensional photonic crystals," IEEE J. Lightwave Technol. 24, 4554-4567 (2006).
[CrossRef]

Oder, T. N.

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
[CrossRef]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
[CrossRef]

Oesterle, U.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Petroff, P. M.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Rakich, P.

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Rattier, M.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Ripin, D. J.

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

Schwoob, E.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Shakya, J.

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
[CrossRef]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
[CrossRef]

Sharma, R.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Smith, C. J. M.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Vrijen, R.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Weisbuch, C.

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Wierer, J. J.

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

Yablonovitch, E.

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

Appl. Phys. Lett. (8)

M. Boroditsky, T. F. Krauss, R. Coccioli, R. Vrijen, R. Bhat, and E. Yablonovitch, "Light extraction from optically pumped light-emitting diode by thin-slab photonic crystals," Appl. Phys. Lett. 75, 1036-1038 (1999).
[CrossRef]

A. Erchak, D. J. Ripin, S. Fan, P. Rakich, and J. D. Joannopoulos, "Enhanced coupling to vertical radiation using a two-dimensional photonic crystal in a semiconductor light-emitting diode," Appl. Phys. Lett. 78, 563-565 (2001).
[CrossRef]

H. Ichikawa and T. Baba, "Efficiency enhancement in a light-emitting diode with a two-dimensional surface grating photonic crystal," Appl. Phys. Lett. 84, 457-459 (2004).
[CrossRef]

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdré, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

T. N. Oder, K. H. Kim, J. Y. Lin, and H. X. Jiang, "III-nitride blue and ultraviolet photonic crystal light emitting diodes," Appl. Phys. Lett. 84,466-468 (2004).
[CrossRef]

J. J. Wierer, M. R. Krames, J. E. Epler, N. F. Gardner, and M. G. Craford, "InGaN/GaN quantum-well heterostructure light-emitting diodes employing photonic crystal structures," Appl. Phys. Lett. 84, 3885-3887 (2004).
[CrossRef]

J. Shakya, K. H. Kim, J. Y. Lin, and H. X. Jiang, "Enhanced light extraction in III-nitride ultraviolet photonic crystal light-emitting diodes," Appl. Phys. Lett. 85, 142-144 (2004).
[CrossRef]

T. N. Oder, J. Shakya, J. Y. Lin, and H. X. Jiang, "III-nitride photonic crystals," Appl. Phys. Lett. 83, 1231-1233 (2003).
[CrossRef]

IEEE J. Lightwave Technol. (1)

S. Noda, "Recent progresses and future prospects of two- and three-dimensional photonic crystals," IEEE J. Lightwave Technol. 24, 4554-4567 (2006).
[CrossRef]

Nano lett. (1)

F. S. Diana, A. David, I. Meinel, R. Sharma, C. Weisbuch, S. Nakamura, and P. M. Petroff, "Photonic Crystal-assisted light extraction from a Colloidal Quantum Dot/GaN Hybrid Structure," Nano lett. 6, 1116-1120 (2006).
[CrossRef] [PubMed]

Other (3)

A. David, T. Fujii, E. Matioli, R. Sharma, K. McGroddy, S. Nakamura, S. P. Denbaars, C. Weisbuch, and H. Benisty, "GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510-1-073510-3 (2006).
[CrossRef]

C. F. Lai, H. C. Kuo, C. H. Chao, H. T. Hsueh, J.-F. T. Wang, W. Y. Yeh, and J. Y. Chi, "Anisotropy of light extraction from two-dimensional photonic crystal light-emitting diodes," Appl. Phys. Lett. 91, 123117-1-123117-3 (2007).
[CrossRef]

A. David, C. Meier, R. Sharma, F. S. Diana, S. P. DenBaars, E. Hu, S. Nakamura, C. Weisbuch, and H. Benisty, "Photonic bands in two-dimensionally patterned multimode GaN waveguides for light extraction," Appl. Phys. Lett. 87, 101107-1-101107-3 (2005).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

(a). Schematic diagram of the MOCVD-grown GaN-based blue LED structure (dominant λ=470 nm) with annular PhC region. (b) The top-view scanning electron microscopy (SEM) micrograph of square PhCs on blue LED with the lattice constant a=260 nm and the diameter of air holes d=180 nm, and the etch depth t=120 nm. (c) The µ-PL and CCD imaging system setup, where M.: mirror; T.L.: tube lens; D.M.: dichroic mirror; O.: objective.

Fig. 2.
Fig. 2.

CCD images taken with square lattices with a=(a) 260 nm, (b) 410 nm, (c) 600 nm. The central bright region in all the photos is due to the unguided PL light excited by the focused laser beam impinging normally in the center.

Fig. 3.
Fig. 3.

(a). The Ewald construction for square lattice PhC with a=260 nm. (b) The projection of the Ewald sphere construction on the waveguide plane. (c) The locus of resultant wavevectors for multimode propagation. The direction of the arrows indicates the increasing mode order.

Fig. 4.
Fig. 4.

Reciprocal lattice for square PhC with a=410nm along the (b) ΓX, (c) ΓM, and (d) ΓXΓM directions with the Ewald spheres explaining the disappearance of the ΓM petals shown in (a).

Fig. 5.
Fig. 5.

Reciprocal lattice for triangular lattice PhC with a=600nm along the (b) ΓM, (c) ΓK, (d) ΓKΓM, (e) ΓK2ΓM, and (f) ΓK3ΓM directions with the Ewald spheres explaining the disappearance of the ΓK petals in (a).

Fig. 6.
Fig. 6.

(a). Reciprocal lattice and Ewald construction for a/λ increases above the cutoff and just start to couple with the shortest lattice vector G ΓX in the ΓX directions. (b) Shows the situation in the ΓM direction with the resultant wavevector fall outside the NA circle and will not be seen by the NA=0.32 objective. (c) Shows the situation when the a/λ increases further to have the nk0 just start to leave the NA circle to disappear from the CCD image.

Fig. 7.
Fig. 7.

Map showing regions with different number of petals. The formulas on the right of the figure are the boundary for regions for NA=1. The insets showed the observed 8-fold (a=260 nm) and 16-fold (a=410nm) symmetry patterns. The regions of various petals are shown with different colors. The directions of the petals are shown in the parenthesis. The “+” and “-” signs indicate the lower and upper boundary for the regions. The highest mode order number is designated as ‘m’ with nm =1.7 (Sapphire) and the maximum index is n=2.5 (GaN).

Fig. 8.
Fig. 8.

(a). The observed image when the laser light scanned along the ΓM directions. The intensity scale is shown in the side bar. (b) Schematic shows the incident angles and the normal incident lines for the two directions, where S is the focused laser beam. (c) and (d) show the polar plots of angular dependence of light extraction with the lattice orientation in the (c) ΓK and (d) ΓM directions, respectively.

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