Abstract

A general design for high-bandwidth, single-mode, lossless, optical micro-circuitry with fully three-dimensional circuit paths is demonstrated. Our 3D circuit design consists of dense stacking several planar microchip layers into the 2D-3D photonic band gap heterostructures and linking them with vertical interconnects. The 3D microchip enables an extra “dimension” of up to 200 nanometer single-mode wave-guiding in each planar chip layer and 100 nanometer bandwidth chip-to-chip interconnects in a variety of 3D PBG materials, including woodpile, slanted pores, and square spiral 3D PBG materials.

© 2006 Optical Society of America

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Adv. Mat.

L. L. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, “Three-dimensional spiral-architecture photonic crystals obtained by direct laser writing,” Adv. Mat. 17, 541–545 (2005).
[CrossRef]

Adv. Mat.

N. Tétreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John, M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: silicon double inversion of polymer templates,” Adv. Mat. (in press).

Appl. Phys. Lett.

M. Deubel, M. Wegener, A. Kaso, and S. John, “Direct laser writing and characterization of “Slanted Pore” photonic crystals,” Appl. Phys. Lett. 85, 1895–1897 (2004).
[CrossRef]

Appl. Phys. Lett.

A. Chutinan and S. Noda, “Highly confined waveguides and waveguide bends in three-dimensional photonic crystal,” Appl. Phys. Lett. 75, 3739–3741 (1999).
[CrossRef]

Appl. Phys. Lett.

C. Sell, C. Christensen, J. Muehlmeier, G. Tuttle, Z. Y. Li and K. M. Ho, “Waveguide networks in three dimensional layer-by-layer photonic crystals,” Appl. Phys. Lett. 84, 4605–4607 (2004).
[CrossRef]

N. Moll and G. L. Bona, “Bend design for the low-group-velocity mode in photonic crystal-slab waveguides,” Appl. Phys. Lett. 85, 4322–4324 (2004).
[CrossRef]

J. S. Jensen and O. Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2022–2024 (2004).
[CrossRef]

IEEE Trans Electromagn. Compat.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

IEEE Trans. Antennas Propag.

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. Appl. Phys.

R. Hillebrand, S. Senz,W. Hergert, and U. Gösele, “Macroporous-silicon-based three-dimensional photonic crystal with a large complete band gap,” J. Appl. Phys. 94, 2758–2760 (2003).
[CrossRef]

J. Appl. Phys.

D. Roundy, E. Lidorikis, and J. D. Joannopoulos, “Polarization-selective waveguide bends in a photonic crystal structure with layered square symmetry,” J. Appl. Phys. 96, 7750–7752 (2004).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Microwave Opt. Technol. Lett.

M. M. Sigalas, R. Biswas, K. M. Ho, C. M. Soukoulis, D. Turner, B. Vasiliu, S. C. Kothari, and S. Lin, “Waveguide bends in three-dimensional layer-by-layer photonic bandgap materials,” Microwave Opt. Technol. Lett. 23, 56–59 (1999).
[CrossRef]

Nat. Mater.

M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004).
[CrossRef] [PubMed]

Nature

D. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of light in a disordered medium,” Nature 390, 671–671 (1997).
[CrossRef]

J. D. Joannopoulos, P. R. Villeneuve, and S. Fan, “Photonic crystals: Putting a new twist on light,” Nature 386, 143–149 (1997).
[CrossRef]

Opt. Express

Opt. Lett.

M. Deubel, M.Wegener, S. Linden, G. von Freymann and S. John, “3D-2D-3D photonic crystal heterostructures by direct laser writing,” (submitted to Optics Letters).

Photonic Band Gaps and Localization

K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Photonic gaps for electromagnetic waves in periodic dielectric structures: Discovery of the diamond structure,” in Photonic Band Gaps and Localization, C. M. Soukoulis, ed., (Plenum, New York, 1993).

Photonics and Nanostruct. – Fundam. and Appl.

S. R. Kennedy, M. J. Brett, H. Miguez, O. Toader and S. John, “Optical properties of a three-dimensional silicon square spiral photonic crystal,” Photonics and Nanostruct. –Fundam. and Appl. 1, 37–42 (2003).
[CrossRef]

Phys. Rev. A

M. Florescu and S. John, “Resonance fluorescence in photonic band gap waveguide architectures: engineering the vacuum for all-optical switching,” Phys. Rev. A 69, 053810 (2004).
[CrossRef]

R. Z. Wang and S. John, “Engineering the electromagnetic vacuum for controlling light with light in a photonicband-gap microchip,” Phys. Rev. A 70, 043805 (2004).
[CrossRef]

Phys. Rev. B

A. Chutinan and S. John, “Light localization for broadband integrated optics in three dimensions,” Phys. Rev. B 72, 161316(R) (2005).
[CrossRef]

M. L. Povinelli, S. G. Johnson, S. Fan, and J. D. Joannopoulos, “Emulation of two-dimensional photonic crystal defect modes in a photonic crystal with a three-dimensional photonic band gap,” Phys. Rev. B 64, 075313 (2001).
[CrossRef]

P. R. Villeneuve, S. Fan, and J. D. Joannopoulos, “Microcavities in Photonic Crystals: mode symmetry, tunability and coupling efficiency,” Phys. Rev. B 54, 7837-8942 (1996).
[CrossRef]

Phys. Rev. E

O. Toader and S. John, “Square spiral photonic crystals: Robust architecture for microfabrication of materials with large three-dimensional photonic band gaps,” Phys. Rev. E 66, 016610 (2002).
[CrossRef]

A. Chutinan and S. John, “Diffractionless flow of light in two and three-dimensional photonic band gap heterostructures: theory, design rules, and simulations,” Phys. Rev. E 71, 026605 (2005).
[CrossRef]

O. Toader and S. John, “Slanted-pore photonic band-gap materials,” Phys. Rev. E 71, 036605 (2005).
[CrossRef]

Phys. Rev. Lett.

O. Toader, M. Berciu, and S. John, “Photonic band gaps based on tetragonal lattices of slanted pores,” Phys. Rev. Lett. 90, 233901 (2003).
[CrossRef] [PubMed]

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopoulos, “Donor and acceptor modes in photonic band structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[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]

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

S. John, “Electromagnetic absorption in a disordered medium near a photon mobility edge,” Phys. Rev. Lett. 53, 2169–2172 (1984).
[CrossRef]

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

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]

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

Science

O. Toader and S. John, “Proposed square spiral microfabrication architecture for large three-dimensional photonic band gap crystals,” Science 292, 1133–1135 (2001).
[CrossRef] [PubMed]

Solid State Commun.

K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimension: New layer- by- layer periodic structures,” Solid State Comm. 89, 413 (1994).
[CrossRef]

Other

Strictly speaking, the two bands can be represented by two bases polarized in any two orthogonal directions in the x-y plane since they are doubly degenerate. However, it is more convenient to consider them as polarized along the x- and y- directions, respectively, as in the text.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic Press, Orlando, FL, 1985).

C. M. Soukoulis, ed., Photonic Crystals and Light Localization in the 21st Century (Kluwer Academic, Dordrecht, 2001).

K. Iizuka, Elements of Photonics (Wiley-Interscience, New York, 2002).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of a 3+1D optical micro-chip for the woodpile 3D PBG architecture. The bottom, intermediate, and top cladding sections of the 3D micro-chip (consisting of the woodpile 3D PBG material) are separated to help visualize the 2D micro-chip layers (square lattice of red rods). The vertical waveguide is created by removing certain parts of dielectric rods along the y-direction marked by yellow and green (see text). A part of the bottom cladding section (inside the black wire frame) is made transparent to show end segment of the vertical waveguide (green) in (a). The transparent white strips are guides for the eyes. The y-z cross sections at the centers of the lower and upper 2D PC waveguides are shown in (b) and (c), respectively. The upper 2D PC waveguide is shifted to the +x-direction by 0.5a relative to the lower 2D PC waveguide. The orange rod in the upper 2D micro-chip layer in (c) and the dark blue woodpile rods in (b) and (c) are not shown in (a) for the sake of visualization of other features.

Fig. 2.
Fig. 2.

(a) Schematic of the woodpile 3D PBG material. (b) Band structure for the woodpile structure using a tetragonal lattice for the Bloch vectors along the z-direction. There are two pairs of doubly degenerate bands below the PBG. The arrow points to the mode for which the electric displacement field distribution is shown in (c) and (d). This corresponds to the first band at the Bloch vector 0.25 [2π/c]. Large amplitudes of the y-component of electric displacement field in the x-y plane are shown as red shading at the center of the (c) first and (d) third layers. Except for the different envelope wave vector, the field pattern shown here is similar to that of the first band at the Z-point discussed in the text and Appendix. The numbers 1-4 denote the positions and stacking order of the woodpile layers.

Fig. 3.
Fig. 3.

(a) Schematic of the vertical waveguide in the woodpile. Parts of dielectric rods with the length l are removed from the first and third layers in each unit cell along the z-direction. (b) Dispersion relation for the vertical waveguide consisting of the zig-zag pattern of the removed dielectric rods of length l=0.5a. A single waveguide mode spans the frequency range a/λ=0.380-0.417.

Fig. 4.
Fig. 4.

Time-averaged electric field intensity for the woodpile based circuit with both in-plane and vertical bends at the frequency a/λ=0.39. An inset shows transmission and reflection spectra for the U-turn (solid lines) and the in-plane 90° bend (solid lines with circles).

Fig. 5.
Fig. 5.

(a) Schematic for the SP 2 PBG architecture depicting two slanted pores drilled in each unit cell of the square lattice. (b) The SP 2 structure with structural parameters c=1.2a and r=0.28a. The top surface shows the plane z=(1/8)c.

Fig. 6.
Fig. 6.

Schematics of the unit cell of (a) the SP 2 PBG architecture and (b) the woodpile PBG structure. The vertical waveguide for each structure is created by removing parts of dielectric marked by yellow in each of (a) and (b). The zig-zag pattern of removed dielectric is a common feature of both waveguides.

Fig. 7.
Fig. 7.

Schematic of the 3+1D optical micro-chip using the SP 2 3D PBG architecture. The bottom, second, and third cladding sections of the micro-chip (consisting of the SP 2 3D PBG material) are separated to help visualize the 2D micro-chip layers. (The topmost cladding section is not shown). The vertical waveguide, connecting the bottom and the second micro-chip layers, is created by removing certain parts of dielectric rods along the y-direction marked by yellow and green (corresponding to the U-turn interconnect of the woodpile based 3+1D circuits shown in Fig. 1(a)). The left surface showing the vertical waveguide (highlighted by black wire frame) corresponds to the cross-section y=0.5a (see Fig. 6(a)).

Fig. 8.
Fig. 8.

Transmission and reflection spectra for two different vertical U-turn bends in the SP 2 based 3D circuits, the first with a vertical interconnect of length 3.75c (red) and the second with length 7.75c (black). The corresponding spectra for a simple 90° in-plane bend are superimposed (blue).

Fig. 9.
Fig. 9.

(a) Schematic for the square spiral depicting a coil in each unit cell of the square lattice. (b) The inverse diamond:5 structure with structural parameters c=1.2a and r=0.28a. The top surface shows the plane z=0.

Fig. 10.
Fig. 10.

(a) Schematic of the unit cell of the square spiral structure. The vertical waveguide is created by removing a zig-zag pattern of dielectric marked by yellow. (b) Transmission and reflection spectra for a vertical U-turn bends in the square spiral based 3D circuits. The length of vertical interconnect is 3.75c.

Fig. 11.
Fig. 11.

Schematic of the 3+1D optical micro-chip using the inverse square spiral 3D PBG architecture. The bottom, second, and third cladding sections of the micro-chip (consisting of the inverse square spiral 3D PBG material) are separated to help visualize the 2D micro-chip layers. (The topmost cladding section is not shown). The vertical waveguide, connecting the bottom and the second micro-chip layers, is created by removing a zig-zag pattern of dielectric rods along the y-direction marked by yellow and green. This pattern of removed dielectric is the same as for the U-turn interconnects of the woodpile based 3+1D circuits shown in Fig. 1(a) and that of the SP 2 based 3+1D circuits shown in Fig. 7. The left surface showing the vertical waveguide (highlighted with black wire frame) corresponds to the cross-section y=0.7a (see Fig. 10(a)).

Fig. 12.
Fig. 12.

Schematic describing electric field amplitude at positions along the z-direction for the first band of the woodpile structure. The Bloch vector is equal to π/c. The +, - signs represent positive and negative values, respectively.

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