Slow axis

Relative to specimens examined under the microscope, the a or fast axis corresponds to the direction of the minimum refractive index, the minimum dielectric constant, and the maximum velocity. The y or slow axis corresponds to the maximum refractive index, the maximum dielectric constant, and the minimum velocity. Occasionally, a (3 axis is recognized with intermediate properties between a and y. When working with elongated bireffingent structures, birefringence usually is taken as positive when the y axis is parallel to the longitudinal axis. 

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°.

Polarization modulation The cross section of the optical fiber has a fast axis and a slow axis that are mutually perpendicular. Two light waves individually polarized about each of these axes will not usually interfere with each other and their intensity can be separately measured using polarizing filters. External stimuli such as pressure or twisting of the fiber may induce transfer between the two polarized modes, which may be quantified and used for measurement. 

Figure 2 Schematic representation of the orientation of the optical components (as viewed from the photomultiplier). E, electric field P, polarizer and laser A and A, two alternative orientations ( a) of the analyzer A/4, slow axis of quarter-wave plate, (a) Standard orientation detects birefringence together with turbidity (if it occurs), (b) Detection of turbidity only. (Reprinted with permission from Ref. 6. Copyright 1989 American Chemical Society)...

The polarization of a light beam can be changed into any other polarization state by using a proper birefringent film. If the incident light is linearly polarized along the x axis and the uniaxial birefringent film is a quarter plate with its slow axis (the uniaxial axis) at 45° with... 

When light propagates through films in which the slow and fast axes as well as the refractive indices are a function of position z, the Jones matrix method can still be used as an approximation method as long as the the refractive indices do not change much in one wavelength. We divide the film into N slabs as shown in Figure 3.2. When the thickness Ah = hIN of the slabs is sufficiently small, then within each slab, the slow axis can be considered fixed. 

For layer j, the angle of the slow axis with respect to the x axis is Pj and the phase retardation is Tj = l7t[ne z=j h)-no z=jish)]ishlX. In the lab frame, the Jones vector of the incident... 

Figure 3.2 Schematic diagram showing the propagation of hght through a hirefringent film with varying slow axis.

For a retarder with retardation angle F = InAnh/X and the slow axis along x axis... 

The Mueller matrix of a retarder, whose slow axis makes the angle with the x axis is... 

We consider how the three-component Stokes vector S evolves on the Poincare sphere under the action of retardation films. The Mueller matrix of a uniform uniaxial retarder with the retardation angle F and the slow axis making the angle (p with the x axis is given by (from Equations (3.77) and (3.78))... 

From Equation (3.93), we can see that the effect of the retarder is to rotate S around the axis represented by Q with the rotation angle of dT, as shown in Figure 3.7. From Equation (3.94), it can be seen that the rotation axis is on the equator and makes an angle of 2 with the Si axis, which is twice the angle of the slow axis (with respect to the x axis) of the retarder (in the xy frame). 

Derive the Mueller matrix given by Equation (3.77) of a retarder whose retardation is F and its slow axis makes the angle (p with respect to the x axis. 

Use the Jones matrix method and the Berreman matrix method separately to calculate the transmittance pattern in the following two cases as a function the polar and azimuthal angles 0 and tp of the incident light. A uniaxial bireffingent film is sandwiched between two crossed polarizers. The transmission axis of the polarizer at the entrance plane is along the x axis. (1) an a plate has the retardation And = A and its slow axis makes the... 

Figure 18.14(a) shows a schematic of the electrostatically driven mirror with two directions of deflection. The fast moving mirror is fixed by torsion springs at a gimbal and is excited to oscUlate by an electrostatic drive, realized by stacked comb electrodes. The gimbal itself is also fixed by torsion springs to the MEMS chip and is excited to oscillate more slowly to perform the vertical sweep. In one of the test designs realized in the author s lab, the mirror has a diameter of 0.9 mm and oscillates in resonance with 32 kHz as fast axis frequency and with 0.6 kHz as slow axis frequency. 

Incident light linearly polarized in the x-direction (a = 0°) becomes, after transmission through a A/4 polarizer with its slow axis in the x-direction... 

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