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Excitation of guided waves in layered structures with negative refraction

Ilya V. Shadrivov, Richard W. Ziolkowski, Alexander A. Zharov, and Yuri S. Kivshar

Open Access Open Access

Abstract

We study the electromagnetic beam reflection from layered structures that include the so-called double-negative metamaterials, also called left-handed metamaterials. We predict that such structures can demonstrate a giant lateral Goos-Hänchen shift of the scattered beam accompanied by a splitting of the reflected and transmitted beams due to the resonant excitation of surface waves at the interfaces between the conventional and double-negative materials as well as due to the excitation of leaky modes in the layered structures. The beam shift can be either positive or negative, depending on the type of the guided waves excited by the incoming beam. We also perform finite-difference time-domain simulations and confirm the major effects predicted analytically.

©2005 Optical Society of America

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Supplementary Material (5)

Media 1: GIF (665 KB)     
Media 2: GIF (816 KB)     
Media 3: GIF (428 KB)     
Media 4: GIF (1527 KB)     
Media 5: GIF (365 KB)     

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Figures (10)
Fig. 1.
Fig. 1. Schematic geometry of the excitation of surface waves in a three-layer structure that includes a DNG medium.

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Fig. 2.
Fig. 2. (a,b) Relative beam shift, Δ r , and beam width, Wr , vs. incidence angle (in degrees). (c,d) Relative shift and width of the reflected beam vs. normalized gap width 2πd/λ at a/λ=100/2π. In (c,d) the angle of incidence corresponds to the point of maximum shift in (a).

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Fig. 3.
Fig. 3. (a) Relative beam shift and (b) reflection coefficient vs. the imaginary part of the dielectric permittivity, for a/λ=100/2π and d/λ=3/2π. Insets show the profiles of the reflected beam.

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Fig. 4.
Fig. 4. Distribution of the electric field after the excitation of (a) backward surface wave (665K), and (b) forward surface wave (815K).

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Fig. 5.
Fig. 5. Temporal variation of the amplitudes of the incident (solid) and surface (dashed) waves.

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Fig. 6.
Fig. 6. (a) Geometry of the layered structure. (b) Dependence of the normalized wave number h of the guided modes in the center slab whose thickness is L, for odd (dashed) and even (solid) modes. The vertical dashed line in the lower figure corresponds to the thickness L5λ/2π used in our calculations.

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Fig. 7.
Fig. 7. Dependence of the relative shifts of the (a) reflected and (b) transmitted beams versus the angle of incidence, for L=5λ 0/2π and d=λ 0, and several values of the waist of the incident beam a: aλ 0 (dotted), a=5λ 0 (dashed), and a10λ 0 (solid). The vertical lines indicate the position of the slab eigenmodes. The insert shows an enlargement of the domain marked by the dashed box in the main figure.

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Fig. 8.
Fig. 8. Dependence of the relative shift of the (a) reflected and (b) transmitted beams versus the thickness d of the air gaps between the DNG slab and the high-index slabs when L=5λ 0/2π, a=λ 0, and k x0=1.1862π/λ 0. Dependence of the relative shift of the (c) reflected and (d) transmitted beams versus the waist a of the incident beam when L=5λ 0/2π, dλ 0, and k x0=1.1862π/λ 0.

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Fig. 9.
Fig. 9. Intensity distribution of the electric field for the excitation of (a) backward guided waves (430K) and (b) forward leaky waves guided by the air gaps (1.5M).

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Fig. 10.
Fig. 10. (a) (365K) Contour plot of the x-component of the Poynting vector (blue corresponds to positive values, while yellow corresponds to negative values), (b) Profile of the x-component of the instantaneous Poynting vector as a function of z (normal to the interfaces) at the middle point of the simulation domain.

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Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Δ r = d Φ r d k x ,
E r , t ( x ) 1 2 π ∫ − ∞ ∞ { R ( k x ) , T ( k x ) } E ¯ i ( k x ) d k x ,
Δ r , t ( n ) = ∫ − ∞ ∞ x n ∣ E r , t ( x ) ∣ 2 dx a n ∫ − ∞ ∞ ∣ E r , t ( x ) ∣ 2 dx ,
R = ( α 1 + 1 ) ( α 2 + 1 ) − ( α 1 − 1 ) ( α 2 − 1 ) e 2 i k z 2 d ( α 1 − 1 ) ( α 2 + 1 ) − ( α 1 + 1 ) ( α 2 − 1 ) e 2 i k z 2 d ,
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