Quarter-wave retardation plate

The system described here is based on the principles of ellipsometry (47). Figure 8 gives a block diagram of our experimental setup. The Psi-meter consists of a 2 mW helium-neon polarized laser source, a quarter wave retardation plate to generate circularly polarized light, a synchronously rotating polarizer to... 

Figure 1 Block diagram of a typical electrical birefringence apparatus using either square-pulse (for transient electrical birefringence) or oscillating field (for dynamic electrical birefringence) perturbations. P, polarizer A, analyzer A/4, quarter-wave retardation plate P.S., power supply P.M.T., photomultiplier tube HP-214A, wave-form generator. (Reprinted with permission from Ref. 41. Copyright 1994 American Chemical Society.)...

Crystalline materials with precisely known birefringences are normally used for this purpose, with mica being commonly used. It is difficult, however, to machine most bi-refringent crystals so that a retardation of precisely rc/2 is produced. This is because the thicknesses of the crystal calculated using equaiton (9.1) may be too thin to be practical. Instead, multiple ordered quarter-wave plates can be fabricated with retardation, 8 = 2nj + n/2, where j = 1,2,3,... If a single-order quarter-wave retardation is required, this can be achieved by combining two multiple-order quarter-wave plates of retardation 8 = 2nj + k/2 and 8 = 2nj + jt + n/2, at a relative orientation of 90°. 

Fig. 6.3-5 shows the spectra taken with a CdSe calibration plate on a Bruker IF.S-66 FT-IR spectrometer. Theoretically four curves should result. For calibration purposes, however, it is only necessary to record two curves, as the two other curves are mirror images of the latter. The curves shown in the figure were taken with only a single orientation of the CdSe calibration plate, but one with parallel and another with crossed polarizers. They are the results of 32 coadded interferograms transformed without apodization. As result we chose a power spectrum, since this is less noisy. A further advantage is that we do not need to use the (in the case of calibration spectra) complicated phase correction. The curves cross at certain points. Interpolating between those crossings, we get a curve with which we can multiply our spectra for the correction of Bessel function dependance. We also clearly can identify the node of the Bessel function at about 2450 cm . The modulator was tuned to quarter wave retardation at 1111 cm. ... 

In a similar fashion, we can tailor the thickness to give a quarter wave retardation of r=71/2. Such a wave plate is useful for converting to and from circularly polarized light. For a quarter wave plate with its fast axis aligned to the y axis (y/=0), the Jones matrix will be... 

The effect of the retardation plate on the e-o crystal is to impart a further phase shift [e.g., % 2 phase shift for a quarter wave (A74) plate] on the y component. The total phase shift between the y and x components thus becomes... 

In frequency regions where absorption is small the two indices of refraction , and n2 give rise to the phenomenon of double refraction. One of the most common uses for this property is in making wave retarders such as quarter-wave plates incident light linearly polarized with equal x and y field components is phase shifted upon transmission because of the two different phase velocities c/w, and c/n2. An entire field, usually referred to as crystal optics, arises out of this and further applications of crystal anisotropy. 

Figure 4.11 Two optical retarders. F fast axis, S slow axis. In both cases the incident beam is polarized under 45°. Left a quarter wave plate retards the slow component of the polarization by 7t/2 and elliptical polarization is achieved. Right a half-wave plate rotates the plane of polarization from 45° to -45°.

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... 

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,... 

Retardation plates are frequently used in polarimetry instruments. Quarter-wave and half wave plates are most often used and may be fabricated in either wavelength-dependent or achromatic forms. 

Following this work, we investigated the possibility of polarization state control with a simple quarter waveplate (QWP). We were interested to determine whether a QWP could be employed in the scattered light beam to measure the SCP form of ROA. In this position there would be no thermal effects due to laser heating. Further, the QWP is a relatively thin object which probably would suffer only small thermal effects even if it were placed in the laser beam. We found that if the QWP were zeroth order, a 0+ A / 4 plate rather than an n+A / 4 plate where n is some integer, typically 30 or 40, representing the number of full wave retardations, the SCP form of ROA could be successfully measured [32]. 

The second case refers to generating circularly polarized light by means of birefringent retarders. If the azimuth a of the electric vector is set at 45° and 6 at kKll (vdAn = kl4) respectively, the emerging radiation turns out to be circularly polarized. Such an optical element is often called quarter wave plate since 6 = kitl2 means a quarter wave displacement between the ordinary and extraordinary wave. The necessity of setting the azimuth at -i-45° arises from the requirement for circular polarization of an electromagnetic wave, its electric vector needs two equal components E and on exit of the retarder. 

If such a retarder is placed with its optic axis aligned exactly with the x or y directions, however, no change in the polarisation is induced, i.e. linearly polarised light stays linearly polarised. A combination of linear polariser and quarter wave plate can therefore be used to create any state of polarisation by proper orientation of their relative azimuths. 

The optical system used to assess flow-induced birefringence consisted of a 2-mW polarized He-Ne laser focused by a condenser lens on the center of the flow field. The birefringence patterns are observed between crossed polars by using a quarter wave (X/4) retardation plate as a Senarmont compensator. The polarized laser has an extinction ratio of 100 1 the polarizer and analyzer are Carl Zeiss components with extinction ratios of approximately 10... 

There are a considerable number of ways to constract the apparatus shown in Fig. 1 [24,25]. In many cases, PSA consists of a controllable retarder and fixed linear polarizer (RRFP), often with a quarter-wave plate as the retarder. In the case A > 4, the controllable retarder is rotated continuously and data reduction assumes Fourier transformable detector signal. In the case of A < 4, the controllable retarder has four or less fixed orientations. 

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