Finite Element Simulation of Surface Plasmon Resonance

Vijay Koju, William M. RobertsonComputational Science Program and Department of Physics and Astronomy, Middle Tennessee State University

Abstract

A surface Plasmon(SP) is an electromagnetic surface mode resulting from the collective oscillation of charge atthe interface between a metal and an insulator. SurfacePlasmon Resonance(SPR) can be used to detect molecularabsorption on surfaces and consequently the phenomenonis of significance for technologies ranging from gene arrays,biomolecules and DNA sensing, and surface electromag-netic field enhancement. SPR sensors can be based oneither attenuated total reflection(ATR) prism coupling ormetallic/dielectric grating coupling. However, the prism-based systems are widely used in practice because theirsensitivity is 2-3 times higher than that of the grating-based sensors. We have been conducting numerical simu-lations on both types of structures to achieve higher sen-sitivity and electromagnetic field enhancement. Moreover,specially designed multilayer structures with alternatinghigh and low refractive index layers have been studiedbecause they support surface electromagnetic waves sim-ilar to surface plasmons but with potentially higher sensi-tivity and field enhancement.

Kretschmann Configuration:Prism - Metal Film - Air

Surface Plasmons are non-radiativeelectromagnetic waves. So, they cannot be directly generated bylight incident on a metal surface.This is due to the fact that althoughSP's exist on a metal surface withoscillation frequencies in the opti-cal range, the SP wavelength isalways smaller that that of lightwith the corresponding frequency. The most common wayto circumvent this problem is to use a prism to couple lightwith SP, as shown in figure 1.

The wavelength of an incident light inside the prism is redu-ced by a factor of the refractive index of the prism. Whenthe light is incident at an appropriate angle, greater thanthe critical angle, it creates an evanescent electromagneticfield in the vicinity of the metal-glass interface. This field,which has a wavelength equal to that of SP, couples with SPand converts the incident light into SP's. This phenomenonis known as Surface Plasmon Resonance (SPR).

When SPR occurs, the total amount of reflected light is greatly reduced which can be observed in their reflectivitycurve as a function of angle of incidence of light.

Figure 1. A schematic diagram of Kretschmann configuration for SP generation.

Finite Element Simulation ofKretschmann Configuration

Electromagnetic wave(transverse magnetic) propagationin the kretschmann configuaration is governed by:

This equation was solved numerically for the 1D case with appropriate boundary condition(Floquet) and initialfield(sinosoidal) in COMSOL, which uses Finite Element Method(FEM).

Figure 3. Magnetic field distributionfor the Kretschmann configuration atthe resonance angle( ). A sharp field enhancement at the interf-ace between silver and air can be clearly observed, which is about 8 times greater than the input field.

Figure 4. Magnetic field distributionacross the media below( ),above( ), and at the resona-nce angle( ). Below and abovethe resonance angle, the SP's are notexcited. The wavelenth of incident lightin free-space was taken to be 632nm.

SiO2-TiO2 Multilayer

A multilayer(1D) is a photonic crystal designed of dielect-ric material with alternating relative permittivity. Thesematerials support SP-like waves, when a defect is intro-duced in their design. However, the sensitivity and fieldenhancement is much higher compared to that from theSP's in metal-air interface.

A 12-layered multilayer with alternating SiO2 and TiO2

was designed with a defect(in the form of extra thickness)in the topmost TiO2 layer.

SiO2-TiO2 Multilayer SimulationResults

Figure 7. Electric field distributionfor the - multilayer atthe resonance angle( ). A sharp field enhancement which is about 48 times greater than the input field is obtained in the last layerof the multilayer.

Figure 8. Electric field distributionacross the media below( ),above( ), and at the resona-nce angle( ). Below and abovethe resonance angle, the SP-like waveare not excited. The wavelenth of incident light in free-space was taken to be 632nm.

Future DirectionsStudy of EM field enhancement in multilayer stuctureswith grating surfaces.Design of optimized multilayer for strong localization ofEM waves which will also give higher sensitivity as abiosensor.Finite Difference Time Domain(FDTD) simulation for EMwave propagation in these structures, which will enableus to see how they behave as time progresses.

References

Figure 2. Top-view fo the magneticfield, z-component (A/m) distributionfor the Kretschmann configuration at the resonance angle( ). Ahigh intensity field is seen at the inter-face which decays rapidly away fromthe interface.

Figure 5. A sharp reduction inthe reflected light is seen at the reso-nance angle( ). This acutereflectivity dip as a function of angleof incidence is the basis for the bio-sensors.The full width at high maxi-mum (FWHM) is approximately 0.310.

Figure 6. Top-view fo the electric field, z-component (V/m) distributionfor the - multilayer at the resonance angle( ). Ahigh intensity field is seen in the lastlayer of which decays rapidly away from the interface.

Figure 9. A sharp reduction inthe reflected light is seen at the reso-nance angle( ). The FWHMis approximately 0.010, which is muchsmaller than that for the Kretschmannconfiguration. This property makes ita better choice for biosensors.

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