Abstract

A micro optical prism and micro lenses with metal-and-dielectric multilayered subwavelength structure (MDMS) are discussed. The MDMS prism has a highly dispersive optical property. Light waves do not spread out in the small prism because of the restriction of propagation direction of light. Optical properties of a curved MDMS prism were investigated by theoretical analysis and numerical simulations. The curved MDMS prism with a structure period of 0.4μm and an apex angle of 90° had angular dispersion of 0.11°nm for light of 1.5μm wavelength. A convexo-plane MDMS lens and a gradient-index MDMS lens were also investigated, and the optical behavior for the curved prism with the convexo-plane lens was demonstrated by a numerical simulation.

© 2010 Optical Society of America

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2008 (1)

2007 (1)

2006 (1)

2005 (6)

2004 (3)

2003 (1)

2000 (2)

H. Yamada, K. Okamoto, A. Kaneko, and A. Sugita, “Dispersion resulting from phase and amplitude errors in arrayed-waveguide grating multiplexers-demultiplexers,” Opt. Lett. 25, 569-571 (2000).
[CrossRef]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Assanto, G.

Ayliffe, P.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Baba, T.

Banabbas, A.

Baumberg, J. J.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Bigot, J.-Y.

Charlton, M. D. B.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Cheben, P.

Chen, Y.-S.

Conti, C.

Dai, D.

Di Falco, A.

Fujita, S.

Gray, S. K.

Halte, V.

He, S.

Hirao, K.

Janz, S.

Joannopoulos, J. D.

Johnson, S. G.

Kameda, S.

Kaneko, A.

Kikuta, H.

Kintaka, K.

Kittaka, S.

Kuebler, S. M.

Lee, T.-W.

Luo, C.

Mansuripur, M.

Matsumoto, T.

Moloney, J. V.

Nakazawa, T.

Netti, M. C.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Nishii, J.

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Ohta, Y.

Okamoto, K.

Oya, K.

Parker, G. J.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Pendry, J. B.

Perney, N.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Powell, I.

Rumpf, R. C.

Sakaue, H.

Z. Wang, O. Yaegashi, H. Sakaue, T. Takahagi, and S. Shingubara, “Bottom-up fill for submicrometer copper via holes of ULSIs by electroless plating,” J. Electrochem. Soc. 151, C781-C785 (2004).
[CrossRef]

Shingubara, S.

Z. Wang, O. Yaegashi, H. Sakaue, T. Takahagi, and S. Shingubara, “Bottom-up fill for submicrometer copper via holes of ULSIs by electroless plating,” J. Electrochem. Soc. 151, C781-C785 (2004).
[CrossRef]

Sugita, A.

Takahagi, T.

Z. Wang, O. Yaegashi, H. Sakaue, T. Takahagi, and S. Shingubara, “Bottom-up fill for submicrometer copper via holes of ULSIs by electroless plating,” J. Electrochem. Soc. 151, C781-C785 (2004).
[CrossRef]

Tal, A.

Tsunemoto, K.

Wang, Z.

Z. Wang, O. Yaegashi, H. Sakaue, T. Takahagi, and S. Shingubara, “Bottom-up fill for submicrometer copper via holes of ULSIs by electroless plating,” J. Electrochem. Soc. 151, C781-C785 (2004).
[CrossRef]

Williams, H. E.

Xie, Y.

Xu, D.-X.

Yaegashi, O.

Z. Wang, O. Yaegashi, H. Sakaue, T. Takahagi, and S. Shingubara, “Bottom-up fill for submicrometer copper via holes of ULSIs by electroless plating,” J. Electrochem. Soc. 151, C781-C785 (2004).
[CrossRef]

Yamada, H.

Yariv, A.

A. Yariv and P. Yhe, “Electromagnetic propagation in periodic media,” in Optical Waves in Crystals (Wiley, 1984), pp. 155-219.

Yhe, P.

A. Yariv and P. Yhe, “Electromagnetic propagation in periodic media,” in Optical Waves in Crystals (Wiley, 1984), pp. 155-219.

Zakharian, A. R.

Zoorob, M. E.

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

J. Electrochem. Soc. (1)

Z. Wang, O. Yaegashi, H. Sakaue, T. Takahagi, and S. Shingubara, “Bottom-up fill for submicrometer copper via holes of ULSIs by electroless plating,” J. Electrochem. Soc. 151, C781-C785 (2004).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Microelectron. J. (1)

M. D. B. Charlton, M. E. Zoorob, M. C. Netti, N. Perney, G. J. Parker, P. Ayliffe, and J. J. Baumberg, “Realisation of ultra-low loss photonic crystal slab waveguide devices,”Microelectron. J. 36, 277-281 (2005).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. B (1)

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

Other (1)

A. Yariv and P. Yhe, “Electromagnetic propagation in periodic media,” in Optical Waves in Crystals (Wiley, 1984), pp. 155-219.

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Figures (10)

Fig. 1
Fig. 1

(a) Schematic diagram of a curved MDMS prism (b) and phase-matching conditions at the input and output surfaces. In (b), the lines parallel to the input and output boundaries are cross-sections of the cylindrical dispersion surfaces of the MDMS. The circles are dispersion surfaces of the dielectric. k in and k out are propagation vectors of the incident and output light waves, respectively. β ri is the propagation vector of light refracted at the input surface. β ro and β d are the zero-order and first-order propagation vectors onto the output surface, respectively.

Fig. 2
Fig. 2

Calculated electric field for the curved MDMS prism. (a) The square of the electric field for light of (a) 1.3 μ m wavelength and (b) 1.5 μ m wavelength. The structure period Λ is 0.40 μ m and metal layers are 0.12 μ m thick. The apex angle 2 α is 90°.

Fig. 3
Fig. 3

Angular dispersion with respect to wavelength of light for the curved MDMS prism, the triangular MDMS prism, and conventional planar diffraction gratings. The angular dispersion is normalized by the wavelength of light. Both MDMSs have structure periods of 0.4 μ m and apex angles of 90°. Periods of the diffraction gratings are 0.4 μ m and 4.0 μ m .

Fig. 4
Fig. 4

Normalized angular dispersions of the curved MDMS prism as a function of incident wavelength λ for (a) different structure periods Λ and (b) different apex angles 2 α .

Fig. 5
Fig. 5

(a) Schematic diagram of a convexo-plane MDMS lens and (b) the phase-matching condition expressed by the dispersion surfaces at an incident point. The focal length f is defined as the distance between the output surface and the focusing point of light. In (b), k in is the wave vector of the incident light. β r and v g are the propagation vector and the direction of group velocity in the MDMS, respectively.

Fig. 6
Fig. 6

(a) Calculated intensity distribution for the convexo-plane MDMS lens and (b) the intensity distribution on the plane at 11.5 μ m from the output surface. The wavelength of incident light is 1.5 μ m .

Fig. 7
Fig. 7

Square of the electric field for the curved MDMS prism with the convexo-plane lens. The wavelength of incident light is 1.5 μ m . The lens was designed for a focal length of 11.0 μ m . The beam waist at the focal point is 0.83 μ m at half maximum.

Fig. 8
Fig. 8

Schematic diagram of a gradient-index MDMS lens. The lens width and thickness are 2 x 0 and h, respectively. The structure period increases with distance x from the z axis.

Fig. 9
Fig. 9

(a) Complex effective refractive index with respect to structure period and (b) distribution of the structure period designed for a gradient index lens. The thickness of metal layers was fixed at 0.1 μ m . The designed focal length is 12.0 μ m for a 7.0 μ m thick lens.  

Fig. 10
Fig. 10

(a) Intensity distribution of a light wave converged by the rectangular gradient-index MDMS lens and (b) the cross-section of the intensity at focal plane z = 11.2 μ m .

Equations (12)

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k in = n ω c ( cos θ in , sin θ in ) .
k in t in = β ri t in ,
β ri t in + 2 α n eff ω c = β ro t out ,
k out t out = ( β ro m G ) t out ,
| β ri | cos ( θ ri α ) = n eff ω c ,
| β ro | cos ( θ ro + α ) = n eff ω c .
sin ( θ out α ) = sin ( θ in α ) 2 n eff n α + m λ n Λ ,
P ( x ) = 2 π λ [ n ( h 0 h ( x ) ) + n eff h ( x ) ] .
P ( x ) = 2 π λ f 2 x 2 + C ,
h ( x ) = f 2 x 2 f 2 x 0 2 n eff n .
P ( x ) = 2 π λ h n eff ( x ) .
n eff ( x ) = f 2 x 2 h + C ,

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