Abstract

A nonuniform-shape photonic crystal taper integrated with a single-mode optical fiber and a photonic crystal waveguide for high-efficiency mode coupling is presented. The curvature of the tapering section is varied by the parameter α. For values of α set to 2 and 0.5, concave and convex tapers are obtained, respectively. Numerical calculations yield an average coupling efficiency greater than 97% at a short taper length of 20.52 μm for the convex-shape taper. Subsequently, the value of the parameter α is varied for investigating the effects of curvature on coupling efficiency and compactness of different types of taper.

© 2005 Optical Society of America

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References

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Appl. Phys. Lett. (1)

M. Palamaru and Ph. Lalanne, �??Photonic crystal waveguides: out-of-plane losses and adiabatic mode conversion,�?? Appl. Phys. Lett. 78, 1466�??1468 (2001).
[CrossRef]

Bell Syst. Tech. J. (1)

D. Marcuse, �??Radiation losses of tapered dielectric slab waveguides,�?? Bell Syst. Tech. J. 49, 273�??290 (1969).

IEE Proceedings (1)

C. C. Constantinou and R. C. Jones, �??Path-integral analysis of arbitrarily tapered multimode, graded-index waveguide: the inverse-square-law and parabolic tapers,�?? IEE Proceedings 139, 365�??375 (1992).

IEEE J. Quantum Electron. (3)

W. K. Burns and A. F. Milton, �??Mode conversion in planar-dielectric separating waveguide,�?? IEEE J. Quantum Electron. 11, 32�??39 (1975).
[CrossRef]

D. Falco, C. Conti, and C. G. Someda, �??Coupling and decoupling of electromagnetic waves in parallel 2-D photonic crystal waveguides,�?? IEEE J. Quantum Electron. 38, 47�??53 (2002).
[CrossRef]

D. Tailaert, W. Bogaerts, P. Bienstman, T. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, �??An out-of plane grating coupler for efficient butt coupling between compact planar waveguides and single mode fibres,�?? IEEE J. Quantum Electron. 38, 949�??954 (2002).
[CrossRef]

J. Appl. Phys. (1)

H. Benisty, �??Modal analysis of optical guides with two-dimensional photonic band-gap boundaries,�?? J. Appl. Phys. 79, 7483�??7492 (1996).
[CrossRef]

J. Lightwave Technol. (3)

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

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

P. Pottier, I. Ntakis, and R. M. De La Rue, �??Photonic crystal continuous taper for low-loss direct coupling into photonic crystal channel waveguides and further device functionality,�?? Opt. Commun. 223, 339�??347 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

S. G. Johnson, P. R. Villeneuve, S. H. Fan, and J. D. Joannopoulos, �??Linear waveguide in photonic crystal slab,�?? Phys. Rev. B 62, 8212�??8222 (2000).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis and J. D. Joannopoulos, �??Adiabatic theorem and continuous couple-mode theory for efficient taper transition�?? Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Radio Sci. (1)

G. O. Olaofe, �??Scattering by two cylinders,�?? Radio Sci. 5, 1351�??1360 (1970).
[CrossRef]

Other (2)

F. Sporleder and H. G. Unger, Waveguide tapers transition and couplers (IEE, 1979).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton U. Press, 1995).

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Figures (9)

Fig. 1.
Fig. 1.

Top: General layout of taper waveguide. Bottom: Diagram showing step analysis for mode conversion in a taper waveguide.

Fig. 2.
Fig. 2.

Tapered-waveguide shapes for different values of α. For α = 1, the taper shape corresponds to the linear taper. For α = 2 and α = 0.5, the taper shape corresponds to concave and convex taper, respectively.

Fig. 3.
Fig. 3.

Schematic layout of the PC taper: (a) linear; (b) convex; (c) concave.

Fig. 4.
Fig. 4.

Field distribution of the simulation layout: (a) linear taper; (b) convex taper; (c) concave taper.

Fig. 5.
Fig. 5.

Normalized field intensity of the propagating wave as a function of taper position for different taper shapes.

Fig. 6.
Fig. 6.

Transmission spectra for the various taper shapes: (a) and (b) linear PC taper for l = 9.69 μm and 18.24 μm; (c) and (d) nonuniform PC taper l = 9.69 μm and 18.24 μm.

Fig. 7.
Fig. 7.

Normalized loss power versus relative position for a linear taper with (a) l = 9.69 μm and (b) l = 18.24 μm. The area under the curve gives the total loss for the taper.

Fig. 8.
Fig. 8.

Transmittance vs taper length plots for different values of α. (a) Convex shaped taper for values of α = 0.333, 0.5, 0.667. (b) Concave shaped taper for values of α = 1, 1.5, 2, 3

Fig. 9.
Fig. 9.

Spectrum distortion for concave taper of length 5.7 μm.

Tables (1)

Tables Icon

Table 1. Saturated Length and Maximum Transmittance for Different Values of α

Equations (8)

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

z ( x ) = m λ 2 n core 2 n g 2
r = ( β 1 β 2 β 1 + β 2 ) exp ( i 2 β 1 )
c = 2 β 1 β 2 ( β 1 + β 2 ) I 1,2 I 1,1 I 2,2 exp [ i ( β 1 + β 2 ) ]
I α , γ = E α E γ dz α , γ = 1,2
n g = c ( ω k ) 1
z = d i + ( d i d o ) [ ( 1 x l ) α 1 ]
ψ ( P ) = ψ inc ( P ) + v = 1 N m = m = + b n , m H m ( 1 ) ( k 0 R n ( P ) ) exp ( jm θ n ( P ) )
S v = [ n J m ( k 0 r ) J m ( k 0 nr ) γ J m ( k 0 r ) J m ( k 0 nr ) n H m ( k 0 r ) J m ( k 0 nr ) γ H m ( k 0 r ) J m ( k 0 nr ) ]

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