The Quarter Wave plate

Figure 7.25 Set-up for ellipsometry microscopy. Incident linearly polarized light reflects on the surface and becomes eiliptically polarized. The quarter wave plate converts the polarization from elliptical to linear. The analyzer is placed such that it extinguishes all light. If the reflection properties change because a gas is adsorbed, the polarization does not match the setting of the analyzer and light passes through it. Appropriate lenses project an image of the surface onto the CCD camera (adapted from Rotermund [72]).

The plane of vibration of a linearly polarized beam emerging from a quarter-wave plate depends on the phase difference 8 between the interfering ray and is measured by the angle a between the optical axes of the quarter-wave plate and the analyzer ... 

Two special retardation devices find wide application in the design of optical po-larimeters. These are the quarter-wave plate with 8 = jc/2 and the half wave plate with 8 = re. The utility of a quarter-wave plate can be demonstrated by observing its effect on... 

The electric vector, A t, of the light generated by the quarter-wave plate is... 

In practice, the quarter-wave plates will possess some imperfection in retardation. Furthermore, the phase angle of the plates may not be zero relative to the mechanical rotation device. Both sources of error can be taken into account. For example, an imperfect quarter-wave plate with retardation S = tc/2 + (3 and a phase offset of <)> would produce the following Stokes vector for the (P/RQ) 5G,... 

Figure 9. Transient reflectivity signals measured from the Cu film are presented. Panels (a) and (b) show reflectivity signals measured simultaneously with transient rotation and ellipticity, respectively, in order corresponding to the orientation of the quarter wave plate. The latter varies from 78.75° for the bottom trace to -90° for the top trace. Panel (c) shows the signals from panels (a) and (b) in the order that they were actually measured. The peak signal magnitude was normalised to unity in each case.

Figure I. Diagram of experimental apparatus used to obtain IRS and RIKES spectra. The Q-switched ruby is frequency-doubled to pump the dye laser. RIKES and its variations require two polarizers, For IRS the analyzer can be removed and the quarter-wave plate removed or replaced by a half-wave plate.

The origin of the large flash-induced background produced in the RIKES experiments is not immediately evident. However, a rotation of the quarter-wave plate of about 10° yields nearly the same background as observed in the flash experiments. Perhaps turbulence produced by the reaction is the source of this induced ellipticity of the circularly polarized pump. An induced ellipticity combined with a slight rotation of the probe polarization could explain some of the flashed RIKES spectra. 

Figure 3. The sequence of optical hardware needed to view a specimen between crossed circular polars. A quarter wave plate typically introduces a path difference in the range 0.15pm to 0.16pm (approximately 1/4 of the wavelength of Nao light) between the slow and fast rays. The use of crossed circular polars to identify regions of zero birefringence unambiguously is most sensitive if the illumination has a wavelength of exactly four times the path difference introduced by the quarter wave plates.

Because the measurement of accurate magnetic fields is a very difficult task we developed a data reduction procedure using four spectra obtained in two exposures with a turn of the quarter-wave plate by 90. This procedure was labeled as Flip-Fl op Zeeman Measurements (FFZM). 

The electric field (in Jones vector form) of the incident light (before the quarter-wave plate) is... 

In the first step of the measurement, the quarter-wave plate is removed, which is equivalent to P = Q. The light intensity is measured when the polarizer is at the following positions ... 

When the quarter-wave plate is inserted and the polarizer is at 45°, the measured light intensity will be... 

The c axis of the quarter-wave plate is at an angle of n/4- with respect to the linear polarization, which is at an angle nIA) with respect to the x axis in the xy frame. On the... 

A reflection system consists of a linear polarizer on the top, a quarter-wave plate in the middle, and a mirror at the bottom. Calculate the reflection spectrum of the system in the wavelength region from 400 nm to 700 nm. (a) The quarter-wave plate is a regular quarter-wave plate with its principal axis at 45° with respect to the transmission axis of the polarizer, (b) The quarter-wave plate is the broadband quarter-wave plate as shown in Figure 3.8(b). 

It can be assumed that each of the beams focused on the Wollaston prism consists of two such perpendicular beams which, after the quarter-wave plate, result in two circularly polarized beams of opposite rotation. These beams will interfere with each other to yield the original linearly polarized beam. A second polarizer is placed at an angle (90-b) to the first one, allowing 35% of the signal to reach the photomulitiplier. A filter transmitting light at 546 nm precedes the photomultiplier. 

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