Abstract

This Letter proposes a dielectric waveguide with deep-subwavelength mode sizes. Results of both frequency domain and time domain analysis show that the effective mode area is below λ02/400 and can even reach λ02/1000 (λ0 is the wavelength in vacuum). The effective electrical mode area can be comparable to that of a hybrid plasmonic subwavelength confinement waveguide, with reduced optical absorption. In contrast to slot waveguides, which guide light in low-index materials, the proposed structure guides light in high-index materials. Results obtained in this Letter show that the losses are sensitive to the surface roughness on the tens of nanometers scale. The structure can be used to design ring resonators with a quality factor comparable to that of a diffraction-limited dielectric ring resonator with the same standing wave numbers. The property can be applied in nonlinear effect enhancement or laser design with ultralow threshold.

© 2012 Optical Society of America

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2011 (2)

J. Gosciniak, T. Holmgaard, and S. I. Bozhevolnyi, J. Lightwave Technol. 29, 1473 (2011).
[CrossRef]

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

2010 (3)

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

Z. H. Zhu, H. Liu, S. M. Wang, W. M. Ye, X. D. Yuan, and S. N. Zhu, Opt. Lett. 35, 754 (2010).
[CrossRef]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

2009 (3)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

K. Preston and M. Lipson, Opt. Express 17, 1527 (2009).
[CrossRef]

2008 (2)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Q. Xu, D. Fattal, and R. G. Beausoleil, Opt. Express 16, 4309 (2008).
[CrossRef]

2007 (2)

2006 (1)

2004 (1)

1946 (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).

Agrawa, G. P.

Almeida, V. R.

Barios, C. A.

Bartal, G.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Beausoleil, R. G.

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Bozhevolnyi, S. I.

Brien, D. O.

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Eggleton, B. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

Faolain, L. O.

Fattal, D.

Garcia-Vidal, F. J.

Genov, D. A.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Gosciniak, J.

Gramotnev, D. K.

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

Grillet, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

Holmgaard, T.

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Joannopoulos, J.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Krauss, T. F.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

L. O. Faolain, T. P. White, D. O. Brien, X. Yuan, M. D. Settle, and T. F. Krauss, Opt. Express 15, 13129 (2007).
[CrossRef]

Lin, Q.

Lipson, M.

Liu, H.

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Martin-Moreno, L.

Monat, C.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

Moreno, E.

Moss, D. J.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

O’Faolain, L.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Oulton, R. F.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Painter, O. J.

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Preston, K.

Purcell, E. M.

E. M. Purcell, Phys. Rev. 69, 681 (1946).

Rodrigo, S. G.

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Settle, M. D.

Sorger, V. J.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Wang, S. M.

Wang, Y.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

White, T. P.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

L. O. Faolain, T. P. White, D. O. Brien, X. Yuan, M. D. Settle, and T. F. Krauss, Opt. Express 15, 13129 (2007).
[CrossRef]

Xu, Q.

Ye, W. M.

Ye, Z.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Yin, X.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Yuan, X.

Yuan, X. D.

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Zhang, X.

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

Zhu, S. N.

Zhu, Z. H.

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

J. Lightwave Technol. (1)

Nat. Commun. (1)

V. J. Sorger, Z. Ye, R. F. Oulton, Y. Wang, G. Bartal, X. Yin, and X. Zhang, Nat. Commun. 2, 331 (2011).
[CrossRef]

Nat. Photon. (3)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, Nat. Photon. 2, 496 (2008).
[CrossRef]

D. K. Gramotnev and S. I. Bozhevolnyi, Nat. Photon. 4, 83 (2010).
[CrossRef]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, Nat. Photon. 3, 206 (2009).
[CrossRef]

Nature (1)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, Nature 461, 629 (2009).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. (1)

E. M. Purcell, Phys. Rev. 69, 681 (1946).

Supplementary Material (2)

» Media 1: MPG (103 KB)     
» Media 2: MPG (200 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of deep-subwavelength mode optical waveguide. (a) x-z cross section view of dielectric distribution. The waveguide is suspended in air with a high-index material sandwiched by a layer of low-index material; a rectangular groove with two stages is etched in the low-index material layer, and the groove is filled with high-index materials, thus forming a rectangular high-index nanoridge. The high-index material has a permittivity ε1, the low index material ε2, and ε1=11.56, ε2=1. The width w and height h of the waveguide, and the thickness hs of the low-index layer are w=400nm, h=400nm, and hs=50nm. Widths and thicknesses of the two steps are w1, h1, w2, and h2. (b) Magnification of the nanoridge and z component of the electric displacement and electric field across the boundaries between the two dielectric materials.

Fig. 2.
Fig. 2.

x-z cross section view of electrical energy density distribution in the proposed waveguide for a cw propagation with wavelength 1550 nm; the dark region represents the dielectric distribution (Media 1). w1=50nm, h1=35nm, w2=15nm, and h2=15nm. It is obtained from the FDTD method.

Fig. 3.
Fig. 3.

Effective electrical mode areas and effective index of the proposed waveguide. Four different groups of parameters of h1, w2 and h2 are presented. (a) Normalized mode area A0/λ02 against w1 and (b) effective index of the waveguide against w1.

Fig. 4.
Fig. 4.

Transmission spectrum of the 10 μm long proposed waveguide with rough surfaces between high- and low-index layers. N denotes number of random distributed semi-ellipsoids on the surfaces. The inset shows an x-z cross section view of dielectric distribution in the low-index layer. w=400nm, h=400nm, hs=50nm, w1=50nm, h1=35nm, w2=15nm, and h2=15nm.

Fig. 5.
Fig. 5.

(a) Q and waveguide bending loss versus the resonant wavelength of the proposed ring resonator. The inner radius r of the ring is 2.0 μm, w=373nm, h=373nm, hs=50nm, w1=50nm, h1=37.5nm, w2=12.5nm, and h2=12.5nm All modes have similar energy density distribution as shown in Fig. 2. (b) Three-dimensional electrical energy density distribution for a line waveguide coupled with the proposed ring resonator (Media 2). Both the line waveguide and the ring resonator have the same cross section structures shown in Fig. 1(b). The dark gray region represents the dielectric distribution. The propagation wavelength is 1550 nm in vacuum in this structure. Distance between the ring and line is 100 nm.

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