Near-Field Distributions

To investigate the EM properties of the hole-array/planar multilayer system, and subsequently reveal the origin of magnetic activity within

it, we calculated the field distributions within the structures using finite element method (FEM) based commercial software, FEMLAB (COMSOL). We analyzed the amplitudes of Ex, Ez and Hy at the different resonance

wavelengths for two structures used in the previous section (Dx = 300 nm

and Dy = 180 nm). Fig. 7.5 illustrates the schematic of the top view of an

unit cell, where the y = 200 nm and y = 400 nm lines correspond to the x-z planes that are at the centre of the unit cell and at the the centre of the neighboring unit cells, respectively.

Figure 7.5: Top view of an unit cell.

We first simulated the field distributions within the structure having effective parameters shown in Fig. 7.2 (Dx = 300 nm). The calculated |Ex|,

|Ez| and |Hy| at λ = 550 nm (the wavelength of the first reflection minimum)

and λ = 880 nm (the wavelength of the effective µ minimum) are displayed in Fig. 7.6 and Fig.7.7, respectively. Here |Ex| and Hy are the superposition

of the incident field and the reflected field, whereas the |Ez| is due to the

§ 7. New Designs for Optical Metamaterials 154

two resonances are also presented as arrows in the |Hy| plots.

The |Ex| and |Ez| profiles shown in Fig. 7.6 indicate that the electric

response of the structure at λ = 550 nm is mainly related to the excitation of a SPP resonance on the dielectric spacer/planar Ag interface; whereas |Ex|

and |Ez| shown in Fig. 7.7 suggest that the electric response of the structure

at λ = 880 nm is governed by the LSP modes on the edges of the metallic holes near the dielectric spacer/hole-array interface.

The nature of the different plasmon resonances at these two wavelengths can be clearly identified from the Ez profile, since it represents the field

scattered by the subwavelength hole arrays. At λ = 550 nm, the |Ez|

maximum occurs on the dielectric spacer/planar Ag film interface near the centre of the unit cell and decays exponentially away from the interface, which is the character of the SPP resonance. Owing to the ohmic loss of the metal, the amplitude of this SPP field decreases rapidly along the y-direction and reaches its minimum near the centre of the neighboring unit cells. There also exists a LSP resonance at this wavelength, which is excited on the air superstrate/Ag interface at the edges of the subwavelength holes. However, the amplitudes of SPP and LSP fields reveal that the SPP resonance is the dominant mode at λ = 500 nm. The large Ez that is opposite to the SPP

field on the other side of the dielectric spacer (dielectric spacer/Ag hole-array interface) is caused by the strong field enhancement from the SPP excitation on the planar Ag film, which induces a charge density redistribution on the patterned layer around that area. Owing to the interaction between the SPP and LSP resonances, the field pattern exhibits an irregular shape within the dielectric spacer.

On the other hand, the LSP resonance becomes the dominant mode at λ = 880 nm. As illustrated in Fig. 7.7, at this wavelength, the |Ez|

Figure 7.6: Field distributions in the structure of Fig. 7.2 at λ = 550 nm. The arrows in |Hy| graphs represent the electric displacement.

§ 7. New Designs for Optical Metamaterials 156

Figure 7.7: Field distributions in the structure of Fig. 7.2 at λ = 880 nm. The arrows in |Hy| graphs represent the electric displacement.

maximum occurs on the dielectric spacer/Ag hole-array interface at the edges of the metallic hole; the enhanced near-field extends to the planar Ag film underneath, and induces a replica charge distribution with opposite sign near the surface of the Ag film. Therefore, the |Ez| pattern shows a well defined

rectangular shape within the spacer layer.

The large |Hy| observed near the interfaces of the planar Ag film at 550

nm is just a subsidiary of the strong electric field enhancement from SP excitation (including both SPPs and LSPs) within the structure. The electric displacement vectors reveal that near the centre of the unit cell (y = 200 nm plane), the currents within the metallic components of the hole-array layer and the planar Ag film counterpart underneath are parallel (symmetric mode), whereas near the the centre of the neighboring unit cells (y = 400 nm plane), the magnitude of the current is negligible on the planar Ag film. The lack of effective circulating current loops at this wavelength implies that there is no magnetic resonance within the structure. In contrast, the electric displacement vectors shown in Fig. 7.7 clearly indicate the existence of the circular current loops within the structure at λ = 880 nm. Here the currents in the metallic components of the hole-array layer and their counterparts in the planar Ag film underneath are antiparallel (antisymmetric mode), which are closed through the displacement currents within the dielectric spacer near the edges of the hole. These circular currents generate the magnetic field to counteract the incident magnetic field and subsequently produce negative µ. In the previous section, we studied the effects of varying pattern linewidth along the magnetic field of incident light (Dx in Fig.7.1) on the magnetic

activity of the structure, and observed that magnetic resonance wavelength increases with the decreased linewidth. To understand this phenomenon, we calculated the field distributions within the structure having effective

§ 7. New Designs for Optical Metamaterials 158

parameters shown in Fig. 7.4 (Dx = 180 nm). The results of |Ex|, |Ez|

and |Hy|, as well as the electric displacement vectors, at λ = 1040 nm (the

wavelength of the effective µ minimum) are displayed in Fig. 7.8.

Figure 7.8 shows that the Ex and Ez component within the structure

follow the similar fashion as that in Fig. 7.7, however, the magnetic field distribution within the structure is somewhat different here, particularly near the centre of the neighboring unit cells. At the centre of the unit cell, the magnetic field highly concentrates in the space between the Ag lattice and the planar Ag film (|Hy| in Fig. 7.8a). The electric displacement (arrows)

clearly indicates the existence of circular current loops in this region, which leads to the magnetic activity, and subsequently, the negative µ. At the centre of the neighboring unit cells (|Hy| in Fig. 7.8b), the strength of the

Hy component is relatively weak within the structure.

The magnetic response of the hole-array/planar multilayer structure involves the contributions from two regions, as shown in Fig. 7.9: one is formed by the continuous metallic lines parallel to H-field and the planar film beneath them; the other is formed by the metallic components between these lines and the planar film beneath them, as labelled by region 1 and region 2 in Fig. 7.9, respectively.

In general the contribution from region 1 is the primary factor that determines the magnetic response of the structures; however, as the width of the region 1 increases (i.e., a large Dx), the role of region 2 also rises.

The electric displacement (arrows) in Fig. 7.8b shows that only one current loop is excited for structure with small Dx (Dx = 180 nm here). In contrast,

Fig. 7.7b reveals that the excitation of two anti-phase current loops in regions 1 and 2 when Dx of the structure is set to 300 nm. The existence of two

Figure 7.8: Field distributions in the structure for Fig. 7.4 at λ = 1040 nm. The arrows in |Hy| graphs represent the electric displacement.

§ 7. New Designs for Optical Metamaterials 160

Figure 7.9: Two regions of an unit cell that have different magnetic responses (top view).

in a reduction in the total effective inductance, hence a higher L-C resonance frequency and a shorter resonance wavelength.

To sum up, the near-field distributions and the electric displacement vectors at different resonance wavelengths reveal the existence of SPP and LSP resonance within the the structure, and the latter gives rise to the magnetic resonance and the negative µ. Due to the 2D nature of the hole arrays, the overall magnetic response of the structure is a superposition of the effects from two functional parts of the unit cell, which leads to the unusual trend observed in Section 7.2.2.2, i.e., the magnetic resonance wavelength decreases as the pattern linewidth along incident H-field increases.