Linear polarization state

Let us consider the time evolution of the electric field vector at a given position (z is fixed). If the electric field vibrates in a constant direction (in the x-y plane), the light is said to be linearly polarized. This occurs when = 0 or The angle p of the electric field with respect to the jc axis is given by tan = Ay/Ax for = 0 or tan = - Ay/Ax for 8 = n. If we examine the spatial evolution of the electric field vector at a fixed time (say, t = 0), for a linearly polarized fight, the curve traced by the electric field in space is confined in a plane. For this reason linearly polarized light is also called plane polarized fight. 

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In classical terms, radiation is represented by an electromagnetic wave. The polarization of plane-wave radiation is defined by the way the oscillating electric field evolves in space, in a plane perpendicular to the direction of propagation. The most general polarization state is called elliptical polarization [23], but for luminescence applications the subset of linear polarization states usually suffices. In these cases the electric field vector oscillates along a well defined direction in a plane perpendicular to the direction of propagation. This direction is the polarization direction, and radiation with this characteristic is said to be linearly polarized. 

The laser can be oriented to provide an arbitrary linear polarization state with respect to the vertical. Should a state different from linear be required for illumination purposes, polarizing optics, comprising a quarter-wave plate can be placed between the source and the sample. 

Tj), hence the labeled values are in units of. These contours are displayed as functions of particle aspect ratio r along the ordinate and the effective or spherical volume radius a along the abscissa. The contours have been evaluated for the configuration with illumination and detection in linearly polarized states, hence the detection is assumed to take place at the optimum... 

In the volume case, the particle system is illuminated by a monochromatic plane wave whose propagation direction is along the Z-direction. In the surface case, the incident wave direction forms an angle Oi with respect to the surface normal and it is contained in the Z-Yplane. The scattered intensity is analyzed in the plane Z-Y (scattering plane) as shown in Fig. 1. We consider two linear polarization states of the incident field. The incident wave is 5-polarized when the electric field vibrates parallel to the X axis, and it is P-polarized when the electric field vibrates within the YZ plane. Similarly, we consider two polarization states for the scattered field The co-polarized case when both incident and scattered field have the same polarization states SS or PP) and the cross-polarized case when both fields are perpendicular to each other SP ox PS). 

Assuming the photons propagate in the -z and +z directions, it is also possible to describe the two-photon state vector in terms of the linear polarization states x) and y) using the relations... 

In tire special cases when 5 = 0 or rt, we speak about linear polarization states, where the electric field vector vibrates sinusoidally along a constant direction in the xy plane defined by the ratio of two components (often called plane-polarized light). 

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