Surface Plasmon Resonance

In current scenario optical communication is playing important role and small particle study and subwavelength study is enhancing domains. In SPR light is launched from the one port of the device and the controlled output is taken from the other port of the device, so at the other port light is controlled and also it aperture is also possible in the subwavelength size, since light is travelling inside the boundary betweem metal and dielectric. So it can be decoupled from any small size so that we can overcome diffraction limitation.

When a light fall on the boundary of metal and dielectric, some part of light got trap inside metal-dielectric boundary, because light excites electrons of metal and make them free to flow inside the medium. These electrons make cloud and moves along the boundary. This cloud is known as surface plasmon polariton and frequency of surface plasmon politron is called surface plasmon resonance.

Since the permittivity of the metal are negative. They also have a positive part of permittivity that is imaginary so called gives positive and imaginary refractive index.

Because of surface plasmon some part of light is trapped between metal and dielectric and this light can be guided through the medium and can be used for small power communication and sub-wavelength imaging. 

This can be done in two formate

1. Otto configuration
2. Kreschmann configuration

Otto configuration

In this there is a air gap between metal and dielectric.

Kreshtchmann configuration

in this there is no air gap between metal and dielectric.

SPR can be generated by using gold silver aluminium and also with iron.

Excitation of surface plasmons is based on total internal reflection when an incident beam of p-polarized light strikes an electrically conducting gold layer at the interface of a glass sensor with high RI (Refractive Index) and an external medium (gas or liquid) with low RI. At a given angle, the excitation of surface plasmons takes place resulting in a reduced intensity of the reflected light. (Fig.1). A slight change at the interface (e.g. a change in refractive index or formation of a nanoscale film thickness) will lead to a change in SPR signal, allowing precise measurements of thin film properties as well as surface molecular interactions in real-time.

Surface Plasmon Resonance (SPR) is a physical process that can occur when plane-polarized light hits a metal film under total internal reflection conditions(1).

When a light beam hits a half circular prism, the light is bend towards the plane of interface, when it is passing from a denser medium to a less dense one. Changing the incidence angle (Θ) changes the outcoming light until a critical angle is reached. At this point, all the incoming light is reflected within the circular prism. This is called total internal reflection (TIR).

Although no light is coming out of the prism in TIR, the electrical field of the photons extends about a quarter of a wavelength beyond the reflecting surface.

Now the prism is coated with a thin film of a noble metal on the reflection site. In most cases, gold is used because it gives a SPR signal at convenient combinations of reflectance angle and wavelength. In addition, gold is chemically inert to solutions and solutes typically used in biochemical contexts(1). When the energy of the photon electrical field is just right it can interact with the free electron constellations in the gold surface. These are the outer shell and conduction-band electrons. The incident light photons are absorbed and the energy is transferred to the electrons, which convert into surface plasmons.

Photon and electron behaviour can only be described when they have both wave and particle properties. In accordance with the quantum theory, a plasmon is the particle name of the electron density waves. Therefore, when in a TIR situation the quantum energy of the photons is right, the photons are converted to plasmons leaving a 'gap' in the reflected light intensity.

perfectly matched layer (PML)

A perfectly matched layer (PML) is an artificial absorbing layer for wave equations, commonly used to truncate computational regions in numerical methods to simulate problems with open boundaries, especially in the FDTD and FE methods. The key property of a PML that distinguishes it from an ordinary absorbing material is that it is designed so that waves incident upon the PML from a non-PML medium do not reflect at the interface—this property allows the PML to strongly absorb outgoing waves from the interior of a computational region without reflecting them back into the interior.

PML was originally formulated by Berenger in 1994 for use with Maxwell's equations, and since that time there have been several related reformulations of PML for both Maxwell's equations and for other wave equations. Berenger's original formulation is called a split-field PML, because it splits the electromagnetic fields into two unphysical fields in the PML region. A later formulation that has become more popular because of its simplicity and efficiency is called uniaxial PML or UPML (Gedney, 1996), in which the PML is described as an artificial anisotropic absorbing material. Although both Berenger's formulation and UPML were initially derived by manually constructing the conditions under which incident plane waves do not reflect from the PML interface from a homogeneous medium, both formulations were later shown to be equivalent to a much more elegant and general approach: stretched-coordinate PML (Chew and Weedon, 1994; Teixeira and Chew, 1998). In particular, PMLs were shown to correspond to a coordinate transformation in which one (or more) coordinates are mapped to complex numbers; more technically, this is actually an analytic continuation of the wave equation into complex coordinates, replacing propagating (oscillating) waves by exponentially decaying waves. This viewpoint allows PMLs to be derived for inhomogeneous media such as waveguides, as well as for other coordinate systems and wave equations.

As molecules are immobilized on a sensor surface, the refractive index at the interface between the surface and a solution flowing over the surface changes, altering the angle at which reduced-intensity polarized light is reflected from a supporting glass plane.

The change in angle, caused by binding or dissociation of molecules from the sensor surface, is proportional to the mass of bound material and is recorded in a sensorgram.

When sample is passed over the sensor surface, the sensorgram shows an increasing response as molecules interact. The response remains constant if the interaction reaches equilibrium. When sample is replaced by buffer, the response decreases as the interaction partners dissociate.

Complete profiles of recognition, binding and dissociation are generated in real time. From these profiles, data such as specificity, affinity, kinetic behavior and sample concentration can be determined.
For most applications, a dextran matrix covering the gold layer enables molecules to be immobilized to a sensor surface and provides a hydrophilic environment for interactions. Surface specificity is determined by the nature of the immobilized molecule.

Since light does not penetrate the sample, interactions can be followed in colored, turbid or opaque samples. No labels are required and detection is instantaneous.

This is the full model of SPR generation can be used for the focusing light into very small and thin films, which are smaller as compare to the wavelengths focused inside it.

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Gradient Force: The Gaussian beam has every angle from -180° to 180° so its gradient have a curve, which is negative for positive direction and positive for negative direction on x-axis. So because of Brownian motion of the particle when it comes in this region of intensity gradient, it is always forced toward the center of laser beam. This force ,which attract the particle towards the center of the beam is called as Gradient force. When this gradient force is sufficiently larger as compared to scattering force, the particle will be trapped inside the trap volume.

For Rayleigh particle, the gradient force can be given as:

F_grad = - n_b³r³ /2 (m ²-1/ m ²-2) grad(E²)

Thermal Force:- Mie particles are moving with Browne motion in the open atmosphere so they possase a momentum because of their speed. So they are having a force inside them called as thermal force, since it increases with the temperature. Sice we are woking in very small particles so small change in temperature will require change in Gradient force to trap them.

Thermal force applied to the particle is

|F(f)|² = 4γk_BT

By this we can see that force applied to the particle is depending on the temperature, so if temperature will increase thermal force will also increase and we have to control it so that particle will be trap inside the system. The wave vector because of the Brauny motion is

|X(F)|² = K_BT/ γ(f_c-f)²