Abstract

We explain the fundamental physical mechanisms involved in coupling triangular lattice photonic crystal waveguides to conventional dielectric slab waveguides. We show that the two waveguides can be efficiently coupled outside the mode gap frequencies. We especially focus on the coupling of the two structures within the mode gap frequencies and show for the first time that the diffraction from the main photonic crystal structure plays an important role on the reflection of power back into the slab waveguide. The practical importance of this effect and possible strategies to modify it are also discussed.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
  5. S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, �??Experimental demonstration of guiding and bending electromagnetic waves in a photonic crystal,�?? Science 282, 274�??276 (1998).
    [CrossRef] [PubMed]
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    [CrossRef]
  11. A. Jafarpour, E. Chow, C. M. Reinke, J. Huang, A. Adibi, A. Grot, L. W. Mirkarimi, G. Girolami, R. K. Lee, and Y. Xu, �??Large-bandwidth ultra-low-loss guiding in bi-periodic photonic crystal waveguides,�?? App. Phys. B 79, 409-414 (2004).
    [CrossRef]
  12. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, �??Properties of the Slab Modes in Photonic Crystal Optical Waveguides,�?? J. of Lightwave Tech.18, 1554-1564 (2000).
    [CrossRef]
  13. A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, �??Guiding mechanisms in dielectric-core photonic-crystal waveguides,�?? Phys. Rev. B 63, 033308(1-4) (2001).
    [CrossRef]
  14. E. Miyai, M. Okano, M. Mochizuki, and S. Noda, �??Analysis of coupling between two-dimensional photonic crystal waveguide and external waveguide,�?? Appl. Phys. Lett. 81, 3729-3731 (2002).
    [CrossRef]
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    [CrossRef]
  20. A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, �??Role of distributed Bragg reflection in photonic-crystal optical waveguides,�?? Phys. Rev. B 64, 041102(1-4) (2001).
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  21. M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, �??Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,�?? Phys. Rev. B 64, 155113(1-5) 2001.
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  22. T. K. Gaylord, and M. G. Moharam, �??Analysis and Applications of Optical Diffraction by Gratings,�?? Proceedings of the IEEE 73, 894-937 (1985).
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App. Phys. B (1)

A. Jafarpour, E. Chow, C. M. Reinke, J. Huang, A. Adibi, A. Grot, L. W. Mirkarimi, G. Girolami, R. K. Lee, and Y. Xu, �??Large-bandwidth ultra-low-loss guiding in bi-periodic photonic crystal waveguides,�?? App. Phys. B 79, 409-414 (2004).
[CrossRef]

Appl. Phys. Lett. (1)

E. Miyai, M. Okano, M. Mochizuki, and S. Noda, �??Analysis of coupling between two-dimensional photonic crystal waveguide and external waveguide,�?? Appl. Phys. Lett. 81, 3729-3731 (2002).
[CrossRef]

Electron. Lett. (1)

A. Adibi, R. K. Lee, Y. Xu, A. Yariv, and A. Scherer, �??Design of photonic crystal optical waveguides with single mode propagation in the photonic bandgap,�?? Electron. Lett. 36, 1376-1378 (2000).
[CrossRef]

IEEE Trans. Antennas Propagat. (1)

K. S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propagat. AP-14, 302�??307 (1966).

J. Comput. Phys. (1)

J. P. Berenger, �??A perfectly matched layer for the absorption of electromagnetic waves,�?? J. Comput. Phys. 114, 185�??200 (1994).
[CrossRef]

J. of Lightwave Tech. (1)

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, �??Properties of the Slab Modes in Photonic Crystal Optical Waveguides,�?? J. of Lightwave Tech.18, 1554-1564 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (6)

A. Jafarpour, A. Adibi, Y. Xu, and R. K. Lee, �??Mode dispersion in biperiodic photonic crystal waveguides,�?? Phys. Rev. B 68, 233102-233105 (2003).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, A. Yariv, and A. Scherer, �??Guiding mechanisms in dielectric-core photonic-crystal waveguides,�?? Phys. Rev. B 63, 033308(1-4) (2001).
[CrossRef]

N. Stefanou and A. Modinos, �??Impurity bands in photonic insulators,�?? Phys. Rev. B 57, 12127�??12133 (1998).
[CrossRef]

C. T. Chan, Q. L. Yu, and K. M. Ho, �??Order-N spectral method for electromagnetic-waves,�?? Phys. Rev. B 51, 16 635�??16642 (1995).
[CrossRef]

A. Adibi, Y. Xu, R. K. Lee, M. Loncar, A. Yariv, and A. Scherer, �??Role of distributed Bragg reflection in photonic-crystal optical waveguides,�?? Phys. Rev. B 64, 041102(1-4) (2001).
[CrossRef]

M. Qiu, K. Azizi, A. Karlsson, M. Swillo, and B. Jaskorzynska, �??Numerical studies of mode gaps and coupling efficiency for line-defect waveguides in two-dimensional photonic crystals,�?? Phys. Rev. B 64, 155113(1-5) 2001.
[CrossRef]

Phys. Rev. Lett. (4)

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

S. John, �??Strong localization of photons in certain disordered dielectric superlattices,�?? Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

A. Chutinan, S. John, and O. Toader, �??Diffractionless flow of light in all-optical microchips,�?? Phys. Rev. Lett. 90, 123901(1-4) (2003).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, �??High transmission through sharp bends in photonic crystal waveguides,�?? Phys. Rev. Lett. 77, 3787�??3790 (1996).
[CrossRef] [PubMed]

Proceedings of the IEEE (1)

T. K. Gaylord, and M. G. Moharam, �??Analysis and Applications of Optical Diffraction by Gratings,�?? Proceedings of the IEEE 73, 894-937 (1985).
[CrossRef]

Science (1)

S. Lin, E. Chow, V. Hietala, P. R. Villeneuve, and J. D. Joannopoulos, �??Experimental demonstration of guiding and bending electromagnetic waves in a photonic crystal,�?? Science 282, 274�??276 (1998).
[CrossRef] [PubMed]

Other (3)

L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits (Wiley, New York, 1995).

T. Tamir, Guided-wave optoelectronics (Springer-Verlag, New York 1990).
[CrossRef]

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

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Figures (7)

Fig. 1.
Fig. 1.

Coupling of a slab waveguide to a triangular lattice PCW. The PCW is made by removing one row of air holes from a perfect PC. The thicknesses of both waveguides are the same and are equal to d=27 calculation cells. The PC lattice constant is a=24, and the radius of the air holes is r=0.3a. For designing single mode waveguide we increased the radii of the air holes next to the guiding region to r’=0.4a. The permittivity of dielectric used for the core of the slab waveguide and PCW is 7.9. Perfectly matched layers are used around the structure.

Fig. 2.
Fig. 2.

(a) One period of the PCW with the magnetic field pattern of the fundamental even TM mode. (b) Dispersion diagram of the first two TM modes of the PCW in part (a). The odd mode exists outside the PBG and only the even mode remains inside the bandgap. The mode gap corresponds to the frequencies within the PBG with no allowed guided mode.

Fig. 3
Fig. 3

(a) The transmission and reflection spectra of the power coupled from the slab waveguide to the PCW. A TM Huygens source is placed at x=x 0=40 and the transmitted and reflected powers at different frequencies are calculated at x=x 1=450 and x=x 2=20, respectively. Note that reflection coefficient within the mode gap is less than 100%. (b) The magnetic field profile at the normalized frequency a/λ = 0.28 inside the mode gap. The diffraction of power into the air above and below the dielectric slab is clear.

Fig. 4.
Fig. 4.

A slab waveguide coupled to a perfect PC structure with r=0.3a (and a=24). Different diffracted orders are shown in the figure. Other properties of the structure are similar to those summarized in the captions of Fig. 1.

Fig. 5.
Fig. 5.

The 2D spatial Fourier transform of the magnetic field above the slab waveguide for the case of a slab waveguide coupled to: (a) a PCW as shown in Fig. 1 and (b) a perfect PC structure with r=0.3a every where and no defect as shown in Fig. 4. All properties of the structures in (a) and (b) are the same as those in the caption of Fig. 1 and Fig. 4, respectively.

Fig. 6.
Fig. 6.

(a) The slab waveguide with TM0 mode as a superposition of two plane waves with incident angles of θ=±48.8°. (b)The variation of the approximate relative strength of different diffraction orders with the incident angle for the structure in Fig. 4 calculated using the grating theory with approximations described in the text. The dashed line corresponds to the incident angle of 48.8°

Fig. 7.
Fig. 7.

(a) A slab waveguide coupled to a PCW with uniform perturbation of ±0.2a in the center of air holes in the y direction next to the interface. (b) The transmission and reflection spectra of the power coupled from slab waveguide to this perturbed structure with x=x 0=40, x=x 1=450, and x=x 2=20.

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