Abstract

We propose a novel ultra-low loss single-mode hollow-core waveguide using subwavelength high-contrast grating (HCG). We analyzed and simulated the propagation loss of the waveguide and show it can be as low as 0.006dB/m, three orders of magnitude lower than the lowest loss of the state-of-art chip-scale hollow waveguides. This novel HCG hollow-core waveguide design will serve as a basic building block in many chip-scale integrated photonic circuits enabling system-level applications including optical interconnects, optical delay lines, and optical sensors.

© 2009 Optical Society of America

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  1. H. Ou "Different index contrast silica-on-silicon waveguides by PECVD," Electron. Lett. 2, 212-213 (2003)
    [CrossRef]
  2. P. Y. Yu and M. Cardona, Fundamentals of Semiconductors: Physics and Material Properties (Springer, 2001)
  3. J. N. McMullin, R. Narendra, and C. R. James, "Hollow metallic waveguides in silicon V-grooves," IEEE Photon. Technol. Lett. 5, 1080-1082 (1993).
    [CrossRef]
  4. Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 1091-1093 (2004).
    [CrossRef]
  5. P. Roberts, F. Couny, H. Sabert, B. Mangan, D. Williams, L. Farr, M. Mason, A. Tomlinson, T. Birks, J. Knight, and P. St. J. Russell, "Ultimate low loss of hollow-core photonic crystal fibres," Opt. Express 13, 236-244 (2005).
    [CrossRef] [PubMed]
  6. C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
    [CrossRef]
  7. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
    [CrossRef]
  8. M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nature Photon. 2, 180-184 (2008).
    [CrossRef]
  9. Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Tunable VCSEL with ultra-thin high contrast grating for high-speed tuning," Opt. Express 16, 14221-14226 (2008).
    [CrossRef] [PubMed]
  10. Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, "Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating," Opt. Express 16, 17282-17287 (2008).
    [CrossRef] [PubMed]
  11. J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, (Princeton University Press, 1995).
  12. V. Karagodsky, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, C.A. 94720, Y. Zhou, M.C.Y. Huang, and C. J. Chang-Hasnain are preparing a manuscript to be called "full-wave analysis and design rules for high-contrast gratings."
  13. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981).
    [CrossRef]
  14. Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Large fabrication tolerance for VCSELs using high-contrast grating," IEEE Photon. Technol. Lett. 20, 434-436 (2008).
    [CrossRef]
  15. H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
    [CrossRef]
  16. K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
    [CrossRef]
  17. E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2102 (1969).
  18. B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005).
    [CrossRef]

2008

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nature Photon. 2, 180-184 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Large fabrication tolerance for VCSELs using high-contrast grating," IEEE Photon. Technol. Lett. 20, 434-436 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Tunable VCSEL with ultra-thin high contrast grating for high-speed tuning," Opt. Express 16, 14221-14226 (2008).
[CrossRef] [PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, "Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating," Opt. Express 16, 17282-17287 (2008).
[CrossRef] [PubMed]

2007

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

2005

2004

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 1091-1093 (2004).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

2003

H. Ou "Different index contrast silica-on-silicon waveguides by PECVD," Electron. Lett. 2, 212-213 (2003)
[CrossRef]

2002

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

1993

J. N. McMullin, R. Narendra, and C. R. James, "Hollow metallic waveguides in silicon V-grooves," IEEE Photon. Technol. Lett. 5, 1080-1082 (1993).
[CrossRef]

1985

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

1981

1969

E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2102 (1969).

Akahane, Y.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005).
[CrossRef]

Asano, T.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005).
[CrossRef]

Asghari, M.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Birks, T.

Chang-Hasnain, C. J.

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Large fabrication tolerance for VCSELs using high-contrast grating," IEEE Photon. Technol. Lett. 20, 434-436 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Tunable VCSEL with ultra-thin high contrast grating for high-speed tuning," Opt. Express 16, 14221-14226 (2008).
[CrossRef] [PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, "Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating," Opt. Express 16, 17282-17287 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nature Photon. 2, 180-184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Couny, F.

Cutler, C.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

Day, I. E.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Drake, J.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Farr, L.

Gaylord, T. K.

Goodman, J.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

Harpin, A.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nature Photon. 2, 180-184 (2008).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Large fabrication tolerance for VCSELs using high-contrast grating," IEEE Photon. Technol. Lett. 20, 434-436 (2008).
[CrossRef]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, "Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating," Opt. Express 16, 17282-17287 (2008).
[CrossRef] [PubMed]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Tunable VCSEL with ultra-thin high contrast grating for high-speed tuning," Opt. Express 16, 14221-14226 (2008).
[CrossRef] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Jackson, K.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

James, C. R.

J. N. McMullin, R. Narendra, and C. R. James, "Hollow metallic waveguides in silicon V-grooves," IEEE Photon. Technol. Lett. 5, 1080-1082 (1993).
[CrossRef]

Kern, J.

Knight, J.

Koyama, F.

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 1091-1093 (2004).
[CrossRef]

Liang, T. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Mangan, B.

Marcatili, E. A. J.

E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2102 (1969).

Mason, M.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

McMullin, J. N.

J. N. McMullin, R. Narendra, and C. R. James, "Hollow metallic waveguides in silicon V-grooves," IEEE Photon. Technol. Lett. 5, 1080-1082 (1993).
[CrossRef]

Moewe, M.

Moharam, M. G.

Moslehi, B.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

Narendra, R.

J. N. McMullin, R. Narendra, and C. R. James, "Hollow metallic waveguides in silicon V-grooves," IEEE Photon. Technol. Lett. 5, 1080-1082 (1993).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Newton, S.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

Noda, S.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005).
[CrossRef]

Ou, H.

H. Ou "Different index contrast silica-on-silicon waveguides by PECVD," Electron. Lett. 2, 212-213 (2003)
[CrossRef]

Roberts, P.

Roberts, S. W.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Russell, P. St. J.

Sabert, H.

Sakurai, Y.

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 1091-1093 (2004).
[CrossRef]

Shaw, H. J.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

Song, B.

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005).
[CrossRef]

Tomlinson, A.

Tsang, H. K.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Tur, M.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

Williams, D.

Wong, C. S.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Yunfei, D.

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Zhou, Y.

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Tunable VCSEL with ultra-thin high contrast grating for high-speed tuning," Opt. Express 16, 14221-14226 (2008).
[CrossRef] [PubMed]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, "Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating," Opt. Express 16, 17282-17287 (2008).
[CrossRef] [PubMed]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Large fabrication tolerance for VCSELs using high-contrast grating," IEEE Photon. Technol. Lett. 20, 434-436 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nature Photon. 2, 180-184 (2008).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

Appl. Phys. Lett.

H. K. Tsang, C. S. Wong, T. K. Liang, I. E. Day, S. W. Roberts, A. Harpin, J. Drake, and M. Asghari "Optical dispersion, two-photon absorption and self-phase modulation in silicon waveguides at 1.5 µm wavelength", Appl. Phys. Lett. 80, 416-418, (2002).
[CrossRef]

Bell Syst. Tech. J.

E. A. J. Marcatili, "Dielectric rectangular waveguide and directional coupler for integrated optics," Bell Syst. Tech. J. 48, 2071-2102 (1969).

Electron. Lett.

H. Ou "Different index contrast silica-on-silicon waveguides by PECVD," Electron. Lett. 2, 212-213 (2003)
[CrossRef]

IEEE Photon. Technol. Lett.

J. N. McMullin, R. Narendra, and C. R. James, "Hollow metallic waveguides in silicon V-grooves," IEEE Photon. Technol. Lett. 5, 1080-1082 (1993).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, "Ultrabroadband mirror using low-index cladded subwavelength grating," IEEE Photon. Technol. Lett. 16, 518-520 (2004).
[CrossRef]

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, "Large fabrication tolerance for VCSELs using high-contrast grating," IEEE Photon. Technol. Lett. 20, 434-436 (2008).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

K. Jackson, S. Newton, B. Moslehi, M. Tur, C. Cutler, J. Goodman, H. J. Shaw, "Optical fiber delay-line signal processing," IEEE Trans. Microwave Theory Tech. 33, 193-204, (1985).
[CrossRef]

J. Opt. Soc. Am.

Jpn. J. Appl. Phys.

Y. Sakurai and F. Koyama, "Control of group delay and chromatic dispersion in tunable hollow waveguide with highly reflective mirrors," Jpn. J. Appl. Phys. 43, 1091-1093 (2004).
[CrossRef]

Nat. mat

B. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Mat. 4, 207-210 (2005).
[CrossRef]

Nature Photon.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A surface-emitting laser incorporating a high-index-contrast subwavelength grating," Nature Photon. 1, 119-122 (2007).
[CrossRef]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, "A nanoelectromechanical tunable laser," Nature Photon. 2, 180-184 (2008).
[CrossRef]

Opt. Express

Other

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

V. Karagodsky, Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, C.A. 94720, Y. Zhou, M.C.Y. Huang, and C. J. Chang-Hasnain are preparing a manuscript to be called "full-wave analysis and design rules for high-contrast gratings."

P. Y. Yu and M. Cardona, Fundamentals of Semiconductors: Physics and Material Properties (Springer, 2001)

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Figures (8)

Fig. 1.
Fig. 1.

(a) Schematic of high contrast grating (HCG). High index gratings (blue) are surrounded by low index material, typically air. The incident angle, θ, is measured from the plane of the grating. High reflectivity in a sub-wavelength grating (Λ < λ) can be achieved by proper choice of grating parameters (b) Schematic of a 1D HCG hollow-core slab waveguide structure consisting of two reflecting HCGs. (c) Ray optics model for guided mode in a hollow-core slab waveguide. Two reflective surfaces extend infinitely in the y-z plane and light propagates in the z direction. The spacing D between the planes forms the core of the waveguide. Light within the core can be expressed via a plane wave expansion, where the plane waves within the core are characterized by the wave vector k.

Fig. 2:
Fig. 2:

Excellent agreement is obtained between ray optics and full wave analysis. (a) Relation between the waveguide spacing D and the angle of incidence θ, obtained by the analytical solution is compared with the ray optics approximation. (b) Symmetric mode profile of the fundamental mode obtained by the analytical solution for D =15 um and compared to the ray optics approximation. The data for both figures corresponds to: tg /λ = 0.258, Λ/λ = 0.423 , η=0.45 and εr =3.62.

Fig. 3.
Fig. 3.

Calculation of waveguide loss α (dB/m) at 1.55 um for a 15-μm core slab HCG-HW as a function of (a) grating period and semiconductor width (b) thickness and semiconductor width (c) wavelength. 0.1dB/m and 0.01dB/m lines are labeled in the plots.

Fig. 4.
Fig. 4.

Propagation loss of 1D slab HCG-HW vs θ for the first four TE modes in a 15 μm HCG-HW. Due to symmetry, one can avoid launching into the second order mode. Hence the difference between the first and third order modes is the most important for modal screening. In this case, the loss of 3rd mode (2nd lowest odd order mode) is drastically higher, 200 times, than that of the 1st mode.

Fig. 5.
Fig. 5.

(a) Simulated electric field intensity profile of HCG-HW. Color is labeled in log scale. The field intensity outside the HCG-HW is only 10-8 of the intensity at the center of the hollow core. (b) Normalized electrical field at the center of the HCG-HW as a function of waveguide length. Linear regression is used to fit the curve as plotted in the red dash line. A waveguide propagation loss of 0.006±0.0024dB/m with 95% fitting confidence bounds is obtained.

Fig. 6.
Fig. 6.

(a) Schematic of a 2D rectangular HCG-HW. (b) Schematic of HCG cladding grating in 2D rectangular HCG-HW. There are two incident characteristic angles θ and φ, which are the angle between incident beam and y-z plane and the angle between incident beam and x-z plane, respectively. (c) A round trip ray trace looking along the z axis direction. The sizes of the hollow-core in x and y direction are Dx and Dy , respectively.

Fig. 7.
Fig. 7.

Schematic of the hollow-core waveguide based on photonic heterostructure geometry. Light is confined vertically due to the high-contrast gratings while horizontal confinement is achieved due to effective index difference between core and cladding regions. Effective index method is used to analyze the structure in the lateral direction (y) as shown in the right figure.

Fig. 8.
Fig. 8.

Transverse intensity profile calculated using effective index method for a heterostructure waveguide with a height of 3.2 um and a height of 10 um. By changing the grating period in core and cladding regions, we obtain an index difference of 1% corresponding to an optical confinement factor of 78%.

Equations (9)

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α ( dB / m ) = 10 L log ( P t P i ) = 10 L log ( R N ) = 10 L log ( R ) = 10 tan θ D log ( R )
α ( dB / m ) 4.3 θ D δ
k x D = 2 π λ sin θ · D = ; m = 1,2 , . . .
( E y ) core = m ρ m cos ( k xm x ) e i ( k z + m k g ) z
k xm 2 + ( k z + m k g ) 2 = k 0 2 ,
( E y ) grating = n A n cos ( β n x + ϕ n ) e i Γ n z + B n cos ( β n x + ψ n ) e i Γ n z
( E y ) outside = m τ m e i k xm x e i ( k z + m k g ) z
k x = k sin θ = 2 π sin θ / λ , k x D x = ; m = 1,2 , . . .
k y = k sin φ = 2 π sin φ / λ , k y D y = ; n = 1,2 , . . .

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