Abstract

A significant improvement on the basic design of a channel add-drop multiplexer of the in-plane type, based on the two-dimensional photonic-crystal membrane structure of triangular-lattice holes, has been made to increase the channel-selectivity Q factor as high as 7300, which demonstrates the viability of the original basic design. The three-dimensional finite-difference time-domain simulation shows that theoretically it is possible to design a channel add-drop multiplexer with better than -0.7 dB of the forward-drop insertion loss, -29 dB of the pass-through cross-talk at the center frequency. A revised coupled-mode analysis with an augmented directional coupling gives a good agreement between its parametric analysis and the finite-difference time-domain analysis in regard to the detailed asymmetric forward-drop frequency response of the multiplexer.

© 2005 Optical Society of America

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References

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    [CrossRef]
  2. K. H. Hwang, S. Kim, and G. H. Song, �??Design of a photonic-crystal channel-drop filter based on the two-dimensional triangular-lattice hole structure,�?? in Photonic Crystal Materials and Devices II, A. Adibi, A. Scherer, and S.-Y. Lin, eds., Proc. SPIE 5360, 405�??410 (2004).
    [CrossRef]
  3. H. Takano, Y. Akahane, T. Asano, and S. Noda, �??In-plane-type channel drop filter in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 84, 2226�??2228 (2004).
    [CrossRef]
  4. K. H. Hwang and G. H. Song, �??Design of a two-dimensional photonic-crystal channel-drop filter based on the triangular-lattice holes on the slab structure,�?? in Proc. 30th European Conference on Optical Communication (Stockholm, Sweden, 2004) 5, 76�??77.
  5. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, �??Theoretical analysis of channel drop tunneling processes,�?? Phys. Rev. B 59, 15882�??15892 (1999).
    [CrossRef]
  6. H. A. Haus, Dept. of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, private communications (2002).
  7. C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quantum Electron. 35, 1322�??1331 (1999).
    [CrossRef]
  8. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, USA, 1985).
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    [CrossRef]
  10. K. S. Yee, �??Numerical solution of initial boundary value problems involving Maxwell�??s equations in isotropic media,�?? IEEE Trans. Antennas Propag. 14, 302�??307 (1966).
    [CrossRef]
  11. G. H. Song, S. Kim, and K. H. Hwang, �??FDTD simulation of photonic-crystal lasers and their relaxation oscillation,�?? J. Opt. Soc. Korea 6, 79�??85 (2002).
    [CrossRef]
  12. S. Johnson and J. D. Joannopoulos, Photonic crystals; the road from theory to practice (Kluwer Academic Publishers, Boston/Dordrecht/London, 2002).
    [PubMed]
  13. G. H. Song, �??Theory of symmetry in optical filter responses,�?? J. Opt. Soc. Am. A 11, 2027�??2037 (1994).
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  14. J. Romero-Vivas, D. N. Chigrin, A. V. Lavrinenko, and C. M. S. Torres, �??Resonant add-drop filter based on a photonic quasicrystal,�?? Opt. Express 13, 826�??835 (2005), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-826.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-3-826.</a>
    [CrossRef] [PubMed]

Appl. Phys. Lett. (1)

H. Takano, Y. Akahane, T. Asano, and S. Noda, �??In-plane-type channel drop filter in a two-dimensional photonic crystal slab,�?? Appl. Phys. Lett. 84, 2226�??2228 (2004).
[CrossRef]

ECOC 2004 (1)

K. H. Hwang and G. H. Song, �??Design of a two-dimensional photonic-crystal channel-drop filter based on the triangular-lattice holes on the slab structure,�?? in Proc. 30th European Conference on Optical Communication (Stockholm, Sweden, 2004) 5, 76�??77.

IEEE J. Quantum Electron. (1)

C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, �??Coupling of modes analysis of resonant channel add-drop filters,�?? IEEE J. Quantum Electron. 35, 1322�??1331 (1999).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

S. D. Gedney, �??An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices,�?? IEEE Trans. Antennas Propag. 44, 1630�??1639 (1996).
[CrossRef]

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

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

J. Opt. Soc. Korea (1)

G. H. Song, S. Kim, and K. H. Hwang, �??FDTD simulation of photonic-crystal lasers and their relaxation oscillation,�?? J. Opt. Soc. Korea 6, 79�??85 (2002).
[CrossRef]

Opt. Express (1)

Phys. Rev. B (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, �??Theoretical analysis of channel drop tunneling processes,�?? Phys. Rev. B 59, 15882�??15892 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, �??Channel drop tunneling through localized states,�?? Phys. Rev. Lett. 80, 960�??963 (1998).
[CrossRef]

Proc. SPIE (1)

K. H. Hwang, S. Kim, and G. H. Song, �??Design of a photonic-crystal channel-drop filter based on the two-dimensional triangular-lattice hole structure,�?? in Photonic Crystal Materials and Devices II, A. Adibi, A. Scherer, and S.-Y. Lin, eds., Proc. SPIE 5360, 405�??410 (2004).
[CrossRef]

Other (3)

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, USA, 1985).

H. A. Haus, Dept. of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, private communications (2002).

S. Johnson and J. D. Joannopoulos, Photonic crystals; the road from theory to practice (Kluwer Academic Publishers, Boston/Dordrecht/London, 2002).
[PubMed]

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Figures (6)

Fig. 1.
Fig. 1.

(a) Geometry of a stick-shape resonator located between two waveguide buses. (b) Schematic of a two-dimensional photonic-crystal channel-add-drop multiplexer based on the membrane structure of the triangular-lattice holes.

Fig. 2.
Fig. 2.

(a) Even-symmetric and (b) odd-symmetric resonance modes for the mirror plane perpendicular to the line-defect waveguides.

Fig. 3.
Fig. 3.

Basic configuration of a channel-drop multiplexer with two symmetric resonators between two waveguide buses.

Fig. 4.
Fig. 4.

Schematic side view of the computational domain for 3D FDTD simulation of the photonic-crystal channel add-drop multiplexer.

Fig. 5.
Fig. 5.

Analysis of the two-dimensional photonic crystal which contains a line defect. (a) The supercell structure for the analysis. (b) The resulting band structure diagram. Parameters used for the analysis are the following: The dielectric constant: ε/ε 0=11.56. The radii of the normal holes and the modified side holes: r=0.300a and rs =0.265a with a being the lattice constant. The notation of Γ 0 K * Γ 1 ¯ in the reciprocal space for the supercell followed that of [12]. The blue-shaded range represents the inside of the light cone. The two yellow-shaded ranges denote the frequency ranges supporting a single TE-like guided-mode.

Fig. 6.
Fig. 6.

The dB-scale frequency responses of the designed channel-drop filter. The plotted data have been normalized to the power of the incoming waves at the input port. The solid curves show the results by the 3D FDTD simulation. The (a) dotted and (b) dash-dot curves represent the data from the coupled-mode analysis with (a) nonzero and (b) zero directional coupling between the two parallel waveguide buses, respectively. Red; forward drop. Blue; pass-through. Green; backward drop.

Equations (21)

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d 𝓐 L d t = [ i 2 π ν 0 + τ out 1 + 2 τ bus 1 ] 𝓐 L i μ 𝓐 R + σ 2 𝒮 + 1 + σ 1 𝒮 ̂ + 2 + σ 1 𝒮 + 3 + σ 2 𝒮 ̂ + 4 ,
d 𝓐 R d t = [ i 2 π ν 0 + τ out 1 + 2 τ bus 1 ] 𝓐 R i μ L + σ 2 𝒮 ̂ + 1 + σ 1 𝒮 + 2 + σ 2 𝒮 ̂ + 3 + σ 1 𝒮 + 4 ,
σ = τ bus 1 .
A L ( ν ) 𝓐 L ( t ) exp ( i 2 π ν t ) d t ,
S ̂ + 1 = S ̂ 2 = e i β L [ cos ( δ β L ) S + 1 + i sin ( δ β L ) S + 3 σ 2 * A L ] ,
S ̂ + 2 = S ̂ 1 = e i β L [ cos ( δ β L ) S + 2 + i sin ( δ β L ) S + 4 σ 2 * A R ] ,
S ̂ + 3 = S ̂ 4 = e i β L [ cos ( δ β L ) S + 3 + i sin ( δ β L ) S + 1 σ 2 * A L ] ,
S ̂ + 4 = S ̂ 3 = e i β L [ cos ( δ β L ) S + 4 + i sin ( δ β L ) S + 2 σ 2 * A R ] ,
S 1 = e i β L [ cos ( δ β L ) S ̂ + 2 + i sin ( δ β L ) S ̂ + 4 σ 1 * A L ] ,
S 2 = e i β L [ cos ( δ β L ) S ̂ + 1 + i sin ( δ β L ) S ̂ + 3 σ 1 * A R ] ,
S 3 = e i β L [ cos ( δ β L ) S ̂ + 4 + i sin ( δ β L ) S ̂ + 2 σ 1 * A L ] ,
S 4 = e i β L [ cos ( δ β L ) S ̂ + 3 + i sin ( δ β L ) S ̂ + 1 σ 1 * A R ] ,
R ( ν ) S 1 ( ν ) S + 1 ( ν ) , T ( ν ) S 2 ( ν ) S + 1 ( ν ) , D b ( ν ) S 3 ( ν ) S + 1 ( ν ) , D f ( ν ) S 4 ( ν ) S + 1 ( ν )
μ 2 σ 2 sin ( β d ) = 0 ,
β d = [ m 1 2 ] π
Q 2 π ν 0 U d U d t .
Q = ν 0 Δ ν ,
Q 1 = [ 8 , 120 1 + 5 , 560 1 ] 2 = 6 , 600 1 ,
4 τ bus 1 = 2 π ν 0 Q in 1 , 2 τ out 1 = 2 π ν 0 Q out 1 ,
β d = 8.565 π , δ β L = 0.045 ,
μ = 2 σ 2 sin ( β d ) × 1.005 2 σ 2 × 0.987

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