Abstract

An optical refraction prism consisting of metal and dielectric, subwavelength, periodic multilayered thin films has been proposed. The multilayered structure of metal and dielectric thin films has a cylindrical dispersion surface for TM polarized light. The light behaviors are very different from those of conventional glass prisms and photonic crystal superprisms. Refraction and diffraction of the light wave for the metal–dielectric multilayered prism has been investigated by numerical simulations and graphical representation based on the dispersion surface. A prism with 0.2μm period had an angular dispersion of 0.20°/nm for 0.8μm wavelength light. The finite thick metal–dielectric multilayered structure acted as a slab waveguide.

© 2008 Optical Society of America

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References

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2006

2005

2003

2000

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]

1954

S. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466-475 (1954).

Opt. Express

Opt. Lett.

Phys. Rev. B

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]

I. Bulu, H. Caglayan, and E. Ozbay, “Negative refraction and focusing of electromagnetic waves by metallodielectric photonic crystals,” Phys. Rev. B 72, 045124 (2005).
[CrossRef]

Sov. Phys. JETP

S. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466-475 (1954).

Other

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

A. Yariv, “Propagation and coupling of modes in optical dielectric waveguides--periodic waveguides,” in Optical Electronics in Modern Communications, 5th ed. (Oxford U. Press, 1997), pp. 491-540.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the MDMS. The period Λ is shorter than the wavelength of the incident light.

Fig. 2
Fig. 2

Ideal dispersion surface of the MDMS. The period Λ is much shorter than the wavelength, and the metal layers are perfectly conductive.

Fig. 3
Fig. 3

Effective refractive indices with respect to structure period Λ and fill factor f. (a) Real parts of the effective indices, and (b) imaginary parts of the effective indices.

Fig. 4
Fig. 4

Cross section of the effective refractive index surface, which is the dispersion surface normalized by ω c . (a) and (b) are real and imaginary parts of the effective index surface, respectively.

Fig. 5
Fig. 5

Schematic diagram of the metal-clad single-slit waveguide. t is the slit aperture.

Fig. 6
Fig. 6

Real parts of effective refractive indices of the MDMS with respect to normalized thickness of the dielectric layers. The period of the structure is twice the thickness t λ , because the fill factor is fixed at 0.5. The real parts of the effective indices for the single-slit waveguide are shown as light curves. Each curve represents the propagation mode.

Fig. 7
Fig. 7

Magnetic field distribution of the propagating light in the MDMS. Shaded areas mean metal layers. The light curve is the magnetic field distribution for the single-slit waveguide of which the dielectric layer has the same thickness as those of the MDMS.

Fig. 8
Fig. 8

Schematic diagram of the MDMS prism. The structure has 0.2 μ m period with 0.5 fill factor. The apex angle of the prism 2 α is 60°. The light wave is incident on the prism with an angle of θ in = 45 ° from the y axis. The refraction angle θ out is also defined from the y axis.

Fig. 9
Fig. 9

Calculated electric field for the MDMS prism. The squares of the electric field are shown in (a) and (b), of which the wavelengths are 0.8 μ m and 1.0 μ m , respectively.

Fig. 10
Fig. 10

Schematic diagrams of dispersion surfaces to understand the light wave behavior in the MDMS prism. Vertical lines are cross sections of dispersion surfaces of the MDMS, which are rotationally symmetric with respect to the dashed–dotted lines. Circles mean cross sections of dispersion surfaces of the isotropic material outside the MDMS prism. (a) and (b) are the dispersion diagrams for wavelengths of 0.8 μ m and 1.0 μ m , respectively. k in is the wave vector of the incident light, G is the grating constant.

Fig. 11
Fig. 11

Structure of the MDMS slab waveguide that has a finite thickness in the z direction. The incident wave is polarized in the x direction.

Fig. 12
Fig. 12

Calculated electric field distributions in the MDMS slab waveguide. (a) Cross section of the energy density distribution of the electric filed on the x - y plane. (b) Cross section on the x - z plane that is 20 μ m from the input port of the slab waveguide.

Equations (12)

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cos ( β x Λ ) = cos ( k 1 x a ) cos ( k 2 x b ) 1 2 ( n 1 2 n 2 2 k 2 x k 1 x + n 2 2 n 1 2 k 1 x k 2 x ) sin ( k 1 x a ) sin ( k 2 x b ) ,
k 1 x = ( n 1 ω c ) 2 β y 2 ,
k 2 x = ( n 2 ω c ) 2 β y 2 ,
β x 2 n TE 2 + β y 2 n TM 2 = ω 2 c 2 ,
n TE 2 = f n 1 2 + ( 1 f ) n 2 2 ,
1 n TM 2 = f n 1 2 + 1 f n 2 2 .
n 1 = n ̃ ( 1 i ) n ̃ ,
β y 2 = ω 2 c 2 n 2 2 1 f .
( n x , n y , n z ) c ω ( β x , β y , β z ) .
tan ( h t ) = 2 h p h 2 p 2 ,
h = n 2 2 ω 2 c 2 β S y 2 , p = n 2 2 n 1 2 β S y 2 n 1 2 ω 2 c 2 ,
sin ( θ out + α ) = 2 n eff n sin α + sin ( θ in α ) λ Λ cos α n ,

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