Abstract

Bragg diffraction is often used as a tool to assess the structural quality of two-dimensional and three-dimensional (3D) photonic crystals. However, direct conclusions from the Laue diagrams to the underlying crystals structure cannot be drawn, as multiple scattering due to the high index contrast takes place. Here we systematically study the scattering of visible light by 3D woodpile photonic crystals with varying internal refractive index contrast Δn, to determine the limits of the single (kinematic) scattering approach. We aim to describe the intensity distribution of diffracting Bragg peaks with analytic expressions similarly to x-ray scattering at electronic crystals. Measured scattering curves of selected Bragg reflections are classified in terms of Δn. We find that the kinematic approach describes the shape and intensity distribution of experimental scattering curves in acceptable accuracy as long as Δn<0.15. The transition between single and multiple scattering is observed for Δn0.160.25 before multiple scattering dominates for larger Δn. The classification of the scattering regimes is confirmed by simulations in terms of numerical solution of Maxwell’s equations.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef]
  3. G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
    [CrossRef]
  4. K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
    [CrossRef]
  5. L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
    [CrossRef]
  6. P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
    [CrossRef]
  7. S. Richel, 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]
  8. C. M. Anderson and K. P. Giapis, “Symmetry reduction in group 4mm photonic crystals,” Phys. Rev. B 56, 7313–7320 (1997).
    [CrossRef]
  9. J. Manzanares-Martinez, P. Castro-Garay, and E. Urrutia-Babuelos, “Analytical determination of the stop band tuning of photonic crystals infilltrated with liquid crystals,” Adv. Studies Theor. Phys. 15, 551–557 (2011).
  10. V. A. Bushuev, B. I. Mantsyzov, and A. A. Skorynin, “Diffraction-induced laser pulse splitting in a linear photonic crystal,” Phys. Rev. A 79, 053811 (2009).
    [CrossRef]
  11. A. Authier, Dynamical Theory of X-ray Diffraction (Oxford, 2001).
  12. J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley, 2001), pp. 11, 318.
  13. B. Brüser and U. Pietsch, “Kinematic and dynamic light scattering from 3D photonic crystals,” Proc. SPIE 7487, 748709 (2009).
    [CrossRef]
  14. S. Orlic, Ch. Müller, and A. Schlösser, “All-optical fabrication of three-dimensional photonic crystals in photopolymers by multiplex-exposure holographic recording,” Appl. Phys. Lett. 99, 131105 (2011).
    [CrossRef]
  15. M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
    [CrossRef]
  16. Nanoscribe Homepage, retrieved 05/11, 2011, http://www.nanoscribe.de/ .
  17. H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
    [CrossRef]
  18. “Cargille Homepage,” retrieved 05/13, 2011, http://www.cargille.com/ .
  19. C. Giacovazzo, Fundamentals of Crystallography, International Union of Crystallography Texts on Crystallography(Oxford, 2002), pp. 14, 825.
  20. B. Brüser, Coherent Light Scattering from Photonic Crystals and Phase Lattices, urn:nbn:de:hbz:467-5513, http://dokumentix.ub.uni-siegen.de/opus/volltexte/2011/551/ .
  21. Rsoft Homepage, retrieved 02/05, 2012, http://www.rsoftdesign.com/products.php?sub=Component+Design&itm=DiffractMOD .

2011

J. Manzanares-Martinez, P. Castro-Garay, and E. Urrutia-Babuelos, “Analytical determination of the stop band tuning of photonic crystals infilltrated with liquid crystals,” Adv. Studies Theor. Phys. 15, 551–557 (2011).

S. Orlic, Ch. Müller, and A. Schlösser, “All-optical fabrication of three-dimensional photonic crystals in photopolymers by multiplex-exposure holographic recording,” Appl. Phys. Lett. 99, 131105 (2011).
[CrossRef]

2010

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

2009

V. A. Bushuev, B. I. Mantsyzov, and A. A. Skorynin, “Diffraction-induced laser pulse splitting in a linear photonic crystal,” Phys. Rev. A 79, 053811 (2009).
[CrossRef]

B. Brüser and U. Pietsch, “Kinematic and dynamic light scattering from 3D photonic crystals,” Proc. SPIE 7487, 748709 (2009).
[CrossRef]

2008

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

2007

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

2004

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

2000

S. Richel, 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]

1997

C. M. Anderson and K. P. Giapis, “Symmetry reduction in group 4mm photonic crystals,” Phys. Rev. B 56, 7313–7320 (1997).
[CrossRef]

1994

H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[CrossRef]

1992

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Als-Nielsen, J.

J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley, 2001), pp. 11, 318.

Anderson, C. M.

C. M. Anderson and K. P. Giapis, “Symmetry reduction in group 4mm photonic crystals,” Phys. Rev. B 56, 7313–7320 (1997).
[CrossRef]

Authier, A.

A. Authier, Dynamical Theory of X-ray Diffraction (Oxford, 2001).

Brennan, T. M.

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

Brüser, B.

B. Brüser and U. Pietsch, “Kinematic and dynamic light scattering from 3D photonic crystals,” Proc. SPIE 7487, 748709 (2009).
[CrossRef]

Busch, K.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Bushuev, V. A.

V. A. Bushuev, B. I. Mantsyzov, and A. A. Skorynin, “Diffraction-induced laser pulse splitting in a linear photonic crystal,” Phys. Rev. A 79, 053811 (2009).
[CrossRef]

Castro-Garay, P.

J. Manzanares-Martinez, P. Castro-Garay, and E. Urrutia-Babuelos, “Analytical determination of the stop band tuning of photonic crystals infilltrated with liquid crystals,” Adv. Studies Theor. Phys. 15, 551–557 (2011).

Depine, R. A.

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

Deubel, M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Dorado, L. A.

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

Dowling, J. P.

H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[CrossRef]

Essig, S.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

Feldmann, J.

S. Richel, 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]

Giacovazzo, C.

C. Giacovazzo, Fundamentals of Crystallography, International Union of Crystallography Texts on Crystallography(Oxford, 2002), pp. 14, 825.

Giapis, K. P.

C. M. Anderson and K. P. Giapis, “Symmetry reduction in group 4mm photonic crystals,” Phys. Rev. B 56, 7313–7320 (1997).
[CrossRef]

Gombert, A.

S. Richel, 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]

Gourly, P. L.

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

Hammons, B. E.

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Kallinger, C.

S. Richel, 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]

Ledermann, A.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

Lemmer, U.

S. Richel, 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]

Linden, S.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Lozano, G.

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

Mantsyzov, B. I.

V. A. Bushuev, B. I. Mantsyzov, and A. A. Skorynin, “Diffraction-induced laser pulse splitting in a linear photonic crystal,” Phys. Rev. A 79, 053811 (2009).
[CrossRef]

Manzanares-Martinez, J.

J. Manzanares-Martinez, P. Castro-Garay, and E. Urrutia-Babuelos, “Analytical determination of the stop band tuning of photonic crystals infilltrated with liquid crystals,” Adv. Studies Theor. Phys. 15, 551–557 (2011).

McMorrow, D.

J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley, 2001), pp. 11, 318.

Miguez, H.

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

Mingaleev, S.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Müller, Ch.

S. Orlic, Ch. Müller, and A. Schlösser, “All-optical fabrication of three-dimensional photonic crystals in photopolymers by multiplex-exposure holographic recording,” Appl. Phys. Lett. 99, 131105 (2011).
[CrossRef]

Orlic, S.

S. Orlic, Ch. Müller, and A. Schlösser, “All-optical fabrication of three-dimensional photonic crystals in photopolymers by multiplex-exposure holographic recording,” Appl. Phys. Lett. 99, 131105 (2011).
[CrossRef]

Pereira, S.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Pietsch, U.

B. Brüser and U. Pietsch, “Kinematic and dynamic light scattering from 3D photonic crystals,” Proc. SPIE 7487, 748709 (2009).
[CrossRef]

Richel, S.

S. Richel, 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]

Scherf, U.

S. Richel, 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]

Schinca, D.

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

Schlösser, A.

S. Orlic, Ch. Müller, and A. Schlösser, “All-optical fabrication of three-dimensional photonic crystals in photopolymers by multiplex-exposure holographic recording,” Appl. Phys. Lett. 99, 131105 (2011).
[CrossRef]

Skorynin, A. A.

V. A. Bushuev, B. I. Mantsyzov, and A. A. Skorynin, “Diffraction-induced laser pulse splitting in a linear photonic crystal,” Phys. Rev. A 79, 053811 (2009).
[CrossRef]

Soukoulis, C. M.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Sozuer, H. S.

H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[CrossRef]

Staude, I.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

Thiel, M.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

Tkeshelashvili, L.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Urrutia-Babuelos, E.

J. Manzanares-Martinez, P. Castro-Garay, and E. Urrutia-Babuelos, “Analytical determination of the stop band tuning of photonic crystals infilltrated with liquid crystals,” Adv. Studies Theor. Phys. 15, 551–557 (2011).

Vawter, G. A.

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

von Freymann, G.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Warren, M. E.

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

Wegener, M.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Wittwer, V.

S. Richel, 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]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

Adv. Funct. Mater.

G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. 20, 1038–1052 (2010).
[CrossRef]

Adv. Studies Theor. Phys.

J. Manzanares-Martinez, P. Castro-Garay, and E. Urrutia-Babuelos, “Analytical determination of the stop band tuning of photonic crystals infilltrated with liquid crystals,” Adv. Studies Theor. Phys. 15, 551–557 (2011).

Appl. Phys. Lett.

P. L. Gourly, M. E. Warren, G. A. Vawter, T. M. Brennan, and B. E. Hammons, “Optical Bloch waves in a semiconductor photonic lattice,” Appl. Phys. Lett. 60, 2714–2716 (1992).
[CrossRef]

S. Richel, 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]

S. Orlic, Ch. Müller, and A. Schlösser, “All-optical fabrication of three-dimensional photonic crystals in photopolymers by multiplex-exposure holographic recording,” Appl. Phys. Lett. 99, 131105 (2011).
[CrossRef]

J. Mod. Opt.

H. S. Sozuer and J. P. Dowling, “Photonic band calculations for woodpile structures,” J. Mod. Opt. 41, 231–239 (1994).
[CrossRef]

Nat. Mater.

M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef]

Phys Rev B

L. A. Dorado, R. A. Depine, D. Schinca, G. Lozano, and H. Miguez, “Experimental and theoretical analysis of the intensity of beams diffracted by three-dimensional photonic crystals,” Phys Rev B 78, 075102 (2008).
[CrossRef]

Phys. Rep.

K. Busch, G. von Freymann, S. Linden, S. Mingaleev, L. Tkeshelashvili, and M. Wegener, “Periodic nanostructures for photonics,” Phys. Rep. 444, 101–202 (2007).
[CrossRef]

Phys. Rev. A

V. A. Bushuev, B. I. Mantsyzov, and A. A. Skorynin, “Diffraction-induced laser pulse splitting in a linear photonic crystal,” Phys. Rev. A 79, 053811 (2009).
[CrossRef]

Phys. Rev. B

C. M. Anderson and K. P. Giapis, “Symmetry reduction in group 4mm photonic crystals,” Phys. Rev. B 56, 7313–7320 (1997).
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef]

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Proc. SPIE

B. Brüser and U. Pietsch, “Kinematic and dynamic light scattering from 3D photonic crystals,” Proc. SPIE 7487, 748709 (2009).
[CrossRef]

Other

“Cargille Homepage,” retrieved 05/13, 2011, http://www.cargille.com/ .

C. Giacovazzo, Fundamentals of Crystallography, International Union of Crystallography Texts on Crystallography(Oxford, 2002), pp. 14, 825.

B. Brüser, Coherent Light Scattering from Photonic Crystals and Phase Lattices, urn:nbn:de:hbz:467-5513, http://dokumentix.ub.uni-siegen.de/opus/volltexte/2011/551/ .

Rsoft Homepage, retrieved 02/05, 2012, http://www.rsoftdesign.com/products.php?sub=Component+Design&itm=DiffractMOD .

A. Authier, Dynamical Theory of X-ray Diffraction (Oxford, 2001).

J. Als-Nielsen and D. McMorrow, Elements of Modern X-ray Physics (Wiley, 2001), pp. 11, 318.

Nanoscribe Homepage, retrieved 05/11, 2011, http://www.nanoscribe.de/ .

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1.
Fig. 1.

Scanning electron micrograph of an as-prepared WP PhC before infiltration of the liquids. Sketch of the bct (left) and fcc (right) unit cell is shown as inset.

Fig. 2.
Fig. 2.

Sketch of the experimental setup used to record scattering intensities as a function of incident and exit angle.

Fig. 3.
Fig. 3.

Schematic of the scattering geometry. Crystal rotation is possible via three axes ω, ψ, and φ. The detector can be rotated around the θ-axis.

Fig. 4.
Fig. 4.

2D Ewald construction. For a thin WP PhC the reciprocal lattice points are degenerated into ellipses along 001. The decomposition of the transfer wave vector q, is shown as well as the in-plane reciprocal lattice vector G⃗.

Fig. 5.
Fig. 5.

Laue diffraction picture from a WP PhC (a) with Δn0.01 (b) and with a maximum contrast of Δn0.52. The incidence direction is parallel to [001]. The transmitted beam in the center is blocked by a beam stop. The arrangement of the first order diffraction peaks [(10L)—circles] displays the square plane symmetry of the h, k plane. Due to the particular scattering geometry the (20L) reflections will appear outside of the screen.

Fig. 6.
Fig. 6.

Set of scattering curves of the (20L) reflection for a WP PhC after removal of the RI liquids.

Fig. 7.
Fig. 7.

Scans throughout the (20L) reflection of WP PhC filled with RI liquids. For clarity, the curves are vertically displaced.

Fig. 8.
Fig. 8.

Kinematic fits to the corrected scattering curves of the (20L) reflection for selected refractive-index contrasts.

Fig. 9.
Fig. 9.

R2 factor versus refractive index of the index-matching fluid in the WP PhC. The range where the kinematic approximation applies is indicated.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

θ=arcsin(sin(ω)+λ/d)ω,
d=a/(h2+k2)1/2.
q=2πneffλ1(λdneffsin(ω)neff)2+2πneffλcos(arcsin(-sin(ω)nneff)).
L=qc/2π.
ΔωλD*cosθ
I(sin(NπL)Nsin(πL)·Δn·cos(π2(h+k+L)))2.
R2=1(IexpIkin)2Ikin2,

Metrics