Abstract

We present a technique for manipulating the dispersive properties of low index periodic structures using microfluidic materials that fill the lattice with various fluids of different refractive indices. In order to quantify the modulation of the optical properties of the periodic structure we use Equi-frequency contours (EFC) data to calculate the frequency dependant refractive index and the refractive angle. We further introduce various types of defects by selectively filling specific lattice sites and measuring the relative change in the index of refraction. Finally we design and optically characterize an adaptive low index photonic crystal based lens with tunable optical properties using various microfluidics. We also present experimental results for a silicon based PhC lens used an optical coupling element.

© 2005 Optical Society of America

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References

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," IEEE J. Sel. Topics Quantum Electron.

J. Witzens, M. Loncar, and A. Scherer, "Self-collimation in planar photonic crystals," IEEE J. Sel. Topics Quantum Electron. 8, (2002).
[CrossRef]

App. Phys. Lett.

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

Appl. Opt.

Appl. Phys. Lett.

Y. Y. Huang, Y. Xu, and A. Yariv, "Fabrication of functional microstructured optical fibers through a selective-filling technique," Appl. Phys. Lett. 85. 5182-5184, (2004).
[CrossRef]

IEEE Photonics Technology Letters

H. C. Nguyen, P. Domachuk, M. J. Steel, and B. J. Eggleton, "Experimental and finite difference time domain technique characterization of transverse in-line photonic crystal fiber," IEEE Photonics Technology Letters 16. 1852-1854, (2004).
[CrossRef]

Journal of Microlithography Microfabrica

D. M. Pustai, A. Sharkawy, S. Y. Shi, G. Jin, J. Murakowski, and D. W. Prather, "Characterization and analysis of photonic crystal coupled waveguides," Journal of Microlithography Microfabrication and Microsystems 2. 292-299, (2003).
[CrossRef]

Opt. Commun.

T. Sondergaard, A. Bjarklev, J. Arentoft, M. Kristensen, J. Erland, J. Broeng, and S. E. B. Libori, "Designing finite-height photonic crystal waveguides: confinement of light and dispersion relations," Opt. Commun. 194. 341-351, (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

H. Kosaka, T. Kawashima, AkihisaTomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami,"Superprism Phenomena in Photnic Crystals," Phys. Rev. B 58. R10096-R10099, (1998).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "Microcavities in Photonic Crystals: Mode Symmetry, Tunability, and Coupling Efficiency," Phys. Rev. B 54. 7837-7842, (1996).
[CrossRef]

Phys. Rev. Lett.

P. Halevi, "Photonic Crystal optics and Homogenization of 2D periodic Composites," Phys. Rev. Lett. 82. 719-722, (1999).
[CrossRef]

Other

S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The road from Theory to Practice. Norwell, MA: Kluwer Academic Publishers, (2002).

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Figures (12)

Fig. 1.
Fig. 1.

Photonic Crystal Capillary Hole Structure

Fig. 2.
Fig. 2.

Dispersion surface and EFC contours of the capillary glass structure calculated for a TE polarized wave at normalized frequency=0.7733

Fig. 3.
Fig. 3.

Multiple EFC contours extracted for the capillary hole structure at normalized frequency on 0.7733 will cause an incident plane wave to split and propagate along different directions. A plane wave propagating though a homogenous medium with a circular EFC (blue) incident with a wavevector ko will propagate along kp 2 due to the EFC from the 2nd band and along kp 3 due to the EFC from the 3rd band.

Fig. 4(a).
Fig. 4(a).

Propagation angle Fig.

Fig. 4(b).
Fig. 4(b).

Effective refractive index

Fig. 5.
Fig. 5.

Modulating the dispersive properties of the capillary glass structure using a one dimensional defect pattern, (a) Capillary glass structure filled every other lattice site with various microfluidics (b) Equi-frequency contours for the modulated periodic structure in (a) using fluids with n=1.46, n-1.52 and n=1.66 (c) Spectral variation of the effective refractive index of the structure in (a) under different fluids. Incident angle is 5 degrees (d) Spectral variation of the angular dispersion through the structure in (a) with different fluids using a fixed incident angle of 5 degrees

Fig. 6.
Fig. 6.

Modulating the dispersive properties of the capillary glass structure using a two dimensional defect pattern, (a) Capillary glass structure filled every two lattice site with various microfluidics (b) Equifrequency contours for the modulated periodic structure in (a) using fluids with n=1.46, n-1.52 and n=1.66 (c) Spectral variation of the effective refractive index of the structure in (a) under different fluids. Incident angle is 9 degrees.

Fig. 7.
Fig. 7.

Equi-frequency contours for the capillary glass structure for a three lattice sites defect pattern (filling every three lattice sites).

Fig. 8.
Fig. 8.

A Photonic crystal based lens in the capillary glass structure analyzed in section 4. A normally incident plane wave with a normalized frequency of 0.55 is used to excited the lens structure and produced a focus at 45micon. The transmission and diffraction efficiencies were numerically measured to be 92% and 88% respectively.

Fig. 9.
Fig. 9.

A Photonic crystal based lens in the capillary glass structure filled with an index matching fluid n=1.55. A normally incident plane wave with a normalized frequency of 0.55 is used to excited the lens structure and produced a focus at 22micon. The transmission and diffraction efficiencies were numerically measured to be 92% and 85% respectively.

Fig. 10.
Fig. 10.

A Photonic crystal based lens in the capillary glass structure filled with an index matching fluid n=1.55. An oblique plane wave at normalized frequency of 0.55 is incident with 5 degrees off axis is used to excite the lens structure and produced a focus at 25micon the transmission and diffraction efficiencies were numerically measured to be 92% and 77% respectively

Fig. 11.
Fig. 11.

A photonic crystal based lens in silicon background can be used as a coupling element in a Photonic crystal based circuit. (a) SEM image of a fabricated lens coupling structure (b) Steady state simulation results for the structure in (a). (c) Experimental characterization of the device in (a) at 1300nm.

Tables (1)

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Table 1. Modulating Focal Point of PhC Designed Lens using various Fluids at Different Wavelengths

Equations (2)

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V g = k ω ( k ) = ω k x x ̂ + ω k y y ̂
k x 2 + k y 2 = ( k o n eff ) 2

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