Abstract

An integrated total internal reflection prism is demonstrated that generates a transversely localized evanescent wave along the boundary between a photonic crystal and an etched out trench. The reflection can be described by either the odd symmetry of the Bloch wave or a tangential momentum matching condition. In addition, the Bloch wave propagates through the photonic crystal in a negative refraction regime, which manages diffraction within the prism. A device with three input channels has been fabricated and tested that illuminates different regions of the reflection interface. The reflected wave is then sampled by a photonic wire array, where the individual channels are resolved. Heterodyne near field scanning optical microscopy is used to characterize the spatial phase variation of the evanescent wave and its decay constant.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
  2. R. C. Reddick, R. J. Warmack, T. R. Ferrel, "New form of scanning optical microscopy," Phys. Rev. B 39, 767-770 (1990).
    [CrossRef]
  3. N. J. Harrick, Internal Reflection Spectroscopy, (Interscience, New York, 1967).
  4. A. Yariv, Optical Electronics in Modern Communications, (Oxford, New York, 1997).
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  6. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
    [CrossRef] [PubMed]
  7. K. Sakoda, Optical Properties of Photonic Crystals, (Springer Series, Berlin, 2001).
  8. W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band Structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1991).
    [CrossRef]
  9. H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwavecircuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-Index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
    [CrossRef]
  15. B. Momeni, J. Huang, M. Solatani, M. Askari, S. Mohammadi, M. Rakhshandehroo, and A. Adibi "Compact wavelength demultiplexing using focusing negative index photonic crystal superprisms," Opt. Express 14, 2413 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B. 71, 045111 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  21. M. L. M. Balisteri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Local observations of phase singularities in optical fields in waveguide structures" Phys. Rev. Lett. 85, 294 (2000).
    [CrossRef]
  22. P. Tortora, M. Abashin, I. Märki, W. Nakagawa, L. Vaccaro, M. Salt, H. P. Herzig, U. Levy, and Y. Fainman "Observation of amplitude and phase in ridge and photonic crystal waveguides operating at 1.55 μm by use of Heterodyne Scanning Near-Field Optical Microscopy," Opt. Lett. 30, 2885 (2005).
    [CrossRef] [PubMed]
  23. E. Schonbrun, Q. Wu, W. Park, T. Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal" Appl. Phys. Lett. 90, 041113 (2007).
    [CrossRef]

2007 (1)

E. Schonbrun, Q. Wu, W. Park, T. Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal" Appl. Phys. Lett. 90, 041113 (2007).
[CrossRef]

2006 (3)

2005 (5)

T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect" J. Select. Areas. Commun. 23, 1341 (2005).
[CrossRef]

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B. 71, 045111 (2005).
[CrossRef]

B. Lombardet, L. A. Dunbar, R. Ferrini, and R. Houdre, "Fourier analysis of Bloch wave propagation in photonic crystals" J. Opt. Soc. Am. B 22, 1179-1190 (2005).
[CrossRef]

I. De Leon and F. S. Roux, "Fourier analysis of reflection and refraction in two-dimensional photonic crystals" Phys. Rev. B 71, 235105 (2005).
[CrossRef]

P. Tortora, M. Abashin, I. Märki, W. Nakagawa, L. Vaccaro, M. Salt, H. P. Herzig, U. Levy, and Y. Fainman "Observation of amplitude and phase in ridge and photonic crystal waveguides operating at 1.55 μm by use of Heterodyne Scanning Near-Field Optical Microscopy," Opt. Lett. 30, 2885 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

2003 (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

2000 (1)

M. L. M. Balisteri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Local observations of phase singularities in optical fields in waveguide structures" Phys. Rev. Lett. 85, 294 (2000).
[CrossRef]

1999 (2)

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, "Photonic crystal polarization splitter," Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

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, 1212-1214 (1999).
[CrossRef]

1991 (1)

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band Structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1991).
[CrossRef]

1990 (1)

R. C. Reddick, R. J. Warmack, T. R. Ferrel, "New form of scanning optical microscopy," Phys. Rev. B 39, 767-770 (1990).
[CrossRef]

1981 (1)

D. Axelrod, "Cell-substrate contacts illuminated with total internal reflection fluorescence," J. Cell. Biol. 89, 141-145 (1981).
[CrossRef] [PubMed]

Appl. Phys. Lett. (2)

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, 1212-1214 (1999).
[CrossRef]

E. Schonbrun, Q. Wu, W. Park, T. Yamashita, C. J. Summers, M. Abashin and Y. Fainman, "Wave front evolution of negatively refracted waves in a photonic crystal" Appl. Phys. Lett. 90, 041113 (2007).
[CrossRef]

Electron. Lett. (1)

Y. Ohtera, T. Sato, T. Kawashima, T. Tamamura, and S. Kawakami, "Photonic crystal polarization splitter," Electron. Lett. 35, 1271-1272 (1999).
[CrossRef]

J. Cell. Biol. (1)

D. Axelrod, "Cell-substrate contacts illuminated with total internal reflection fluorescence," J. Cell. Biol. 89, 141-145 (1981).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

J. Select. Areas. Commun. (1)

T. Yamashita and C. J. Summers, "Evaluation of self-collimated beams in photonic crystals for optical interconnect" J. Select. Areas. Commun. 23, 1341 (2005).
[CrossRef]

Nature (1)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-929 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. B (3)

I. De Leon and F. S. Roux, "Fourier analysis of reflection and refraction in two-dimensional photonic crystals" Phys. Rev. B 71, 235105 (2005).
[CrossRef]

E. Schonbrun, T. Yamashita, W. Park, and C. J. Summers, "Negative-Index imaging by an index-matched photonic crystal slab," Phys. Rev. B 73, 195117 (2006).
[CrossRef]

R. C. Reddick, R. J. Warmack, T. R. Ferrel, "New form of scanning optical microscopy," Phys. Rev. B 39, 767-770 (1990).
[CrossRef]

Phys. Rev. B. (1)

Z. Ruan, M. Qiu, S. Xiao, S. He, and L. Thylen, "Coupling between plane waves and Bloch waves in photonic crystals with negative refraction," Phys. Rev. B. 71, 045111 (2005).
[CrossRef]

Phys. Rev. Lett. (3)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylen, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

W. M. Robertson, G. Arjavalingam, R. D. Meade, K. D. Brommer, A. M. Rappe, and J. D. Joannopoulos, "Measurement of photonic band Structure in a two-dimensional periodic dielectric array," Phys. Rev. Lett. 68, 2023 (1991).
[CrossRef]

M. L. M. Balisteri, J. P. Korterik, L. Kuipers and N. F. van Hulst, "Local observations of phase singularities in optical fields in waveguide structures" Phys. Rev. Lett. 85, 294 (2000).
[CrossRef]

Other (6)

H. Kosaka, T. Kawashima, A. Tomita, T. Sato, and S. Kawakami, "Photonic crystals for micro lightwavecircuits using wavelength-dependent angular beam steering," Appl. Phys. Lett. 74, 1370-1372 (1999).
[CrossRef]

K. Sakoda, Optical Properties of Photonic Crystals, (Springer Series, Berlin, 2001).

N. J. Harrick, Internal Reflection Spectroscopy, (Interscience, New York, 1967).

A. Yariv, Optical Electronics in Modern Communications, (Oxford, New York, 1997).

H. Raether, Surface plasmons on smooth and rough surfaces and on gratings, (Springer-Verlag, Berlin, 1988).

W. Park, "Modeling of photonic crystals" in Handbook of Theoretical and Computational Nanotechnology Vol. 7, M. Rieth and W. Schommers, ed., (American Scientific Publishers, Stevenson Ranch, CA, 2006), pp. 263-327.

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Figures (7)

Fig. 1.
Fig. 1.

Photonic Crystal total internal reflection prisms. The prism is a triangular lattice of holes and the incident medium is air. If a mode in the second photonic band is excited, the wave can couple into the prism through the ΓM interface, but not out the ΓK interface. A) shows a beam normally incident into the prism, where the excited Bloch wave has parallel momentum, kpc , and Poynting, Spc , vectors. The energy of the wave is then obliquely incident into the reflection interface. B) shows a beam obliquely incident into the PC that negatively refracts across the boundary. The Bloch wave has a large angle between its kpc , which bends positively, and Spc , which bends negatively. The energy of the wave is normally incident into the reflection interface, yet still experiences TIR.

Fig. 2.
Fig. 2.

A) Scanning electron micrograph (SEM) of the fabricated device. The insets show the crystal terminations for the prism input and reflection interfaces. The front half of the prism is surrounded by silicon slab, and behind the prism is an etched out air trench. B) Numerical simulation of the time averaged square of the Ez (out-of-plane) field. The wave is incident from the bottom right and exits the bottom left. The numerically simulated device is three times smaller than the fabricated device, so diffraction is negligible.

Fig. 3.
Fig. 3.

The Fourier spectrum of the numerically simulated complex field. The spectrum has five major components, the incident, reflected, and transmitted waves on kSi , the incident Bloch wave ki-pc , and the reflected Bloch wave kr-Pc . The energy of the incident kSi and kpc waves travel towards the upper left and the energy of the reflected ksi and kpc waves travel towards the lower left similar to Fig. 2(B). The evanescent wave spectrum lies just beyond the kair , circle and is difficult to resolve in this figure because the wave only occupies a small fraction of the area in real space. Most of the energy in the incident and reflected Bloch waves is carried by the indicated unfolded EFS in the neighboring reciprocal lattice cells. Other EFS harmonic components are significantly weaker.

Fig. 4.
Fig. 4.

Far-field scattering images of the PC prism. The center input waveguide is illuminated. The scattering images are superimposed on an SEM image to show the device geometry. In each photograph, the input waveguide is at the upper-left, the TIR prism is in the upper-right and the output waveguide array is along the bottom. A) shows 1542 nm TM polarized illumination, which creates a highly confined output spot that primarily illuminates two output waveguides. B) shows 1559 nm TM polarized illumination, which has high efficiency and small out-of-plane scattering at each device interface. Scattering from the output waveguide array is significantly brighter than any other region indicating the small losses at the other interfaces. C, D) show 1542 and 1559 nm TE polarized illumination respectively, which does not couple into the PC prism.

Fig. 5.
Fig. 5.

Cross-section of the output photonic wire array for excitation of each input waveguide. The diffraction curve is calculated with a gaussian beam model and is normalized to the peak height of the other curves.

Fig. 6.
Fig. 6.

The amplitude and phase images along the reflection interface collected by the HNSOM superimposed on the SEM image to show the geometry. The inset to the amplitude image shows the field amplitude averaged over a 10 μm cross-section plotted vs. Y. The inset to the phase image shows the evanescent field phase one sample above the interface in the air region plotted vs. X.

Fig 7.
Fig 7.

The Fourier spectrum of the complex field values collected by the HNSOM. The arrows show the incident Bloch wave, ki-pc , the reflected Bloch wave, ki-PC , and the evanescent wave, k ev . The dotted circle shows the air light line at 1552 nm. The insets show the windowed regions after being inverse transformed back to the spatial domain, a dotted line outlines the prism.

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