Sinusoidal Optical Intensity

Consider, for example, an optical intensity function of the form El,)  

This gives rise to an elastic torque term given by 

Writing the wave vector q in terms of the grating constant A.=2-n/q, we have 

From Equation (8.72) we can see that if A J, the orientational relaxation dynamics is dominated by A (i.e., the intermolecular torques) conversely, if A, the (tynam-ics is decided by the boundary elastic torques. 

These influences of the intermolecular and the elastic torques in cw-laser-induced nonlinear diffraction effects in nematic films are reported in the work by Khoo. There it is also noted that the optical nonlinearity associated with nematic director axis reorientation is proportional to the factor AcVAT [see Eq. (8.44)] typical of orientational fluctuations induced by light scattering processes (see Chapter 5). Although both Ae and K are strongly dependent on the temperature, the combination AsV is not. This is because Ae is proportional to the order parameter S, whereas K is proportional to S.  

---

DENSITY AND TEMPERATURE CHANGES INDUCED BY SINUSOIDAL OPTICAL INTENSITY... 

Figure 9.4. Sinusoidal optical intensity profile produced by interference of two co-polarized coherent lasers.

In materials that possess both photoconductive and electro-optic responses, the photo-generation and trapping of charge carriers produces internal fields that modify the refractive index. A sinusoidally varying intensity caused by the... 

The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in amplifier and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148-156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-... 

Figure 10.11—Optical arrangement of a Fourier transform IR spectrometer, a) A 90c Michelson interferometer including the details of the beam splitter (expanded view) b) optical diagram of a single beam spectrometer (based on a Nicolet model). A weak intensity HeNe laser (632.8 nm) is used as an internal standard to measure precisely the position of the moving mirror using an interference method (a simple sinusoidal interferogram caused by the laser is produced within the device). According to the Nyquist theorem, at least two points per period are needed to calculate the wavelength within the given spectrum.

Figure 5. Visible laser stability. The laser power fluctuations using a 488 nm (blue) and 568 nm (red) lasers were determined using a 10x objective and a Chroma red slide. The fluorescence was sequentially measured every 30 sec (400 times) for total time duration of 3.33 hrs. The variation of the peak to peak using 488 nm or 568 nm excitation was approximately 25%. The fluctuating power intensity line suggests that the system scanning and detection devices are yielding large power fluctuations that will affect the illumination of the sample. The Acousto Optical Transmission Filter (AOTF) is probably contributing to this 488-568 nm sinusoidal pattern.

An important aspect of the photorefractive effect is that the optical response of the material is nonlocal. In Figure 7, the position of the space charge field is displaced to the right of the initial excitation, in the direction of the applied electric field. In the case of a sinusoidal intensity pattern the phase shift between the optical excitation of charges and the electric field their movement produces is a parameter characteristic of a photorefractive material. It depends on the balance between the processes of drift and diffusion of mobile charges and on the number density of sites able to capture the mobile charges. 

In order to produce surface-relief electro-optic gratings, Munakata et compared two fabrication methods of SRG inscription. In the first, the SRG was produced with an interference pattern of cw laser, with relatively modest intensities. The gratings so recorded were photo- and thermally erasable, and efficient writing was polarization dependent. In the second method, a phase mask was employed to provide the periodic intensity modulation of a pulsed laser, the 3rd-order harmonic (at 355 nm) of a Nd YAG laser. The SRG was produced with a single laser pulse, allowing a very short fabrication time (less than Is). The direshold for ablation was 500 mj/(em pulse), and the amplitude of the SRG increased with pulse energy. A depth of up to 300 rim could be achieved, leading to a smooth but not sinusoidal surface modulation. 

Figure 2.5. The intensity function or aerial image of a mask is ideally a square wave. However, projection optics operating near their diffraction limit degrade this square wave into a sinusoid with a small direct current dc) term. When this intensity function is imposed on the contrast-enhancement lithographic material, bleaching occurs most rapidly in the high-intensity areas such that the transmitted intensity function that exposes the resist is modified and thus leads to improved contrast.

We noted earlier that when two light beams cross each other, photons in one beam do not affect those in the other beam. This is normally the case, but when the incident light beams are two intense laser beams, the first laser beam will alter the optical behavior of the material so that the second laser beam will behave differently from the first. When two laser beams of the same frequency intersect, they interfere and produce a pattern of light that varies sinusoidally through the crystal. If the crystal is photorefractive, the refractive index of the crystal will also be distorted in a sinusoidal manner (but with a 90 phase shift). As the beams pass through the crystal they may interfere with each other so that one beam, by constructive interference, gains intensity, while the other, by destructive interference, loses it. Effects such as these may provide important technology. 

Interference lithography makes use of the interference pattern which is formed when two or more coherent light waves are superposed. In a t3q>ical optical set-up, a laser is used as a source for UV radiation. The laser beam is spht into two beams. Each of the beams is directed by mirrors towards a substrate coated with photoresist where the beams are superposed after being expanded. Two interfering beams produce a ID grating with a sinusoidal intensity distribution. To this intensity pattern the UV-sensitive photoresist is exposed. After exposure the photoresist plate is developed where exposed or unexposed. Photoresist is removed depending on the type of photoresist. As the intensity profile is sinusoidal continuous microstructure profiles will result in general. 

---