Quarter-wave phase plate

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... 

This is not the same as circularly polarized light which is obtained by passing linearly polarized light through a quarter-wave plate [53]. The plate produces a superposition of x and y components which are 90° out of phase, i.e. 

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. 

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 ... 

An equally accurate measurement of the phase difference is obtained when a quarter wave plate is introduced between rotor unit and analyzer in the usual way (extinguished between the crossed polarizing prisms). As is well-known, this quarter wave plate transforms the ellipticity of the light-wave emerged from the rotor unit into a rotation according to the simple relation ... 

Fig. 6.8. A Principle of frequency-multiplexed CARS microspectroscopy A narrow-bandwidth pump pulse determines the inherent spectral resolution, while a broad-bandwidth Stokes pulse allows simultaneous detection over a wide range of Raman shifts. The multiplex CARS spectra shown originate from a 70 mM solution of cholesterol in CCI4 (solid line) and the nonresonant background of coverglass (dashed line) at a Raman shift centered at 2900 cm-1. B Energy level diagram for a multiplex CARS process. C Schematic of the multiplex CARS microscope (P polarizer HWP/QWP half/quarter-wave plate BC dichroic beam combiner Obj objective lens F filter A analyzer FM flip mirror L lens D detector S sample). D Measured normalized CARS spectrum of the cholesterol solution. E Maximum entropy method (MEM) phase spectrum (solid line) retrieved from (D) and the error background phase (dashed line) determined by a polynomial fit to those spectral regions without vibrational resonances. F Retrieved Raman response (solid line) calculated from the spectra shown in (E), directly reproducing the independently measured spontaneous Raman response (dashed line) of the same cholesterol sample...

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,... 

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. ... 

With an angle of incidence of 30° and a beam waist w = 6A, it is possible to achieve d/w 0.02 for a quarter-wave plate, which we will take as a practical specification. The portion of the phase-shifted beam in the fundamental mode of Eq. (96) may be used to calculate the polariza-... 

In order to calculate the bandwidth of the PTR, we need to calculate the phase error introduced in the phase-shifted portion of the output beam as A varies. For a PTR operated as a quarter-wave plate, we write... 

We should emphasize that by using thick but still transparent IsoSm films, we can obtain huge phase delay even for moderate values. For instance, the maximum value of the photoinduced birefringence shown in Figure 5.15 (curve 1) was measured for a 24-pm-thick film and corresponds to the phase delay value AO = -245°, i.e., close to the three-quarter-wave plate. 

When a quarter-wave rotating phase plate is used in a polarization modulator, it is possible to measure parameters of linear and eireular polarization simultaneously, but the aeeuraey of determining Q and U parameters is half that of parameter V. When a PSP with a phase shift of A = 126.52° is used, the accuracy of measurements of all three Stokes parameters is idenrieal. When 92= 0, the formula for right modulation beeomes... 

Far-Field Nanoscopic Measuring Technique, Fig. 1 Schematic of a typical STED system setup. L , L2, Lj, L4, and L optical lenses, PH and PH2 pinholes, WPj and WP2 wave plate (WPj half wave plate, WP2 quarter wave plate), Pol light polarization direction, DMi and DM2 dichroic mirrors, PP phase plate (vortex mode), APD avalanche photon detector, MF multimode... 

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