Optical path length difference

Since there are a large number of different experimental laser and detection systems that can be used for time-resolved resonance Raman experiments, we shall only focus our attention here on two common types of methods that are typically used to investigate chemical reactions. We shall first describe typical nanosecond TR spectroscopy instrumentation that can obtain spectra of intermediates from several nanoseconds to millisecond time scales by employing electronic control of the pnmp and probe laser systems to vary the time-delay between the pnmp and probe pnlses. We then describe typical ultrafast TR spectroscopy instrumentation that can be used to examine intermediates from the picosecond to several nanosecond time scales by controlling the optical path length difference between the pump and probe laser pulses. In some reaction systems, it is useful to utilize both types of laser systems to study the chemical reaction and intermediates of interest from the picosecond to the microsecond or millisecond time-scales. 

The subsequent thermal processes201 give rise to diffusion of the polycarbonate substrate into the dye layer, decomposition of the dye, and mechanical deformation of the film due to thermal contraction. Each of these processes can contribute to a reduction in the optical path length of the low-intensity readout beam. The optics within the detector are designed such that phase differences due to the optical path length differences cause the light intensity falling on the detector to be reduced when the beam passes over a recorded mark .196... 

The arrangement employed for the VPC experiment is described in Reference 4. A cw argon-ion laser at 488 nm was used in a standard DFWM geometry. The s-polarized output beam was first split by a beam-splitter to provide the pump and the probe beams. The transmitted beam from the beam-splitter was then divided into the two s-polarized pump beams each with a power of approximately 0.35 mW. The reflected beam from the beamsplitter was used as the probe beam, whose intensity was about 7% of the total intensity in both pump beams. The forward pump beam and the probe, which constituted writing beams, were overlapped at the sample. Their optical path length difference was much smaller than the laser coherence length, so that they were coherent at the sample. The backward pump beam was... 

Equation (5.4) is extremely useful for practical measurements, because it allows a very precise tracking of the moveable mirror. In fact, all modem FT-IR and FT Raman spectrometers use the interference pattern of the monochromatic light of a He-Ne laser (iue-Ne — 633 nm or f = 15800 cm ) in order to control the change in optical path length difference. To emphasize this the reference inter-... 

Equation (5.9) shows that in order to measure the complete spectrum, we would have to scan the moving mirror of the interferometer an infinitely long distance, with (5 varying between -oo and +cx) centimeters. In practice, the optical path length difference is finite. By restricting the maximum retardation to /, we are effectively multiplying the complete interferogram by the boxcar truncation function (see Fig. 5.3a left)... 

The optical thickness of the dielectric spacer of refractive index, n, is chosen such that it is half the desired wavelength of maximum transmission. As can be seen from Figure 2, the components of the transmitted beam will be in phase if the optical path length difference is an integral number of wavelengths or when eqn [1]... 

Using the relation Z = /nds to find the optical path length , the following equation is derived in terms of the difference between the object and reference path for high relative accuracy ... 

Figure 20.2. Schematic outline of typical pump-probe-detect experiments with femtosecond pulses, a molecular beam source, and mass spectrometric detection of transient species. Computer control and data processing instruments, as well as various optical components, are not shown. The time separation Af between pump and probe pulses is dictated by the difference in optical path lengths. Ad, traversed by the two components of the original pulse.

The refractive index, n, may be measured using an optical microscope [1,2,23,27,34]. Phase contrast increases the contrast due to differences in n and allows a more accurate determination. Interference contrast in transmission gives the optical path length and the average refractive index through the specimen thickness [1], The Becke line method gives the surface refractive index [1],... 

To introduce phase-differences, small mica plates have been used. Buerger (1951) cut small plates from the same uniform cleavage sheet, and placed one over each hole, suitably tilted to give the appropriate increase in optical path-length. Hanson, Taylor, and Lipson (1951) used mica plates to control both amplitude and phase the reciprocal lattice was represented by an array of equal holes, and placed between crossed polarizers a mica plate over each hole was rotated to some position between the two extinction positions to give the correct amplitude different signs were obtained by rotating the plate either clockwise or anti-clockwise. 

Optical interference. We assume that the light is coupled perpendicular into the thin film (a = 90°). Case 1 1 < ni < n2. The phase shift due to a difference in optical path length between the beams reflected at the two interfaces 1 and 2 is n 2d. The reflection at the interface between air and ni leads to a phase shift of 7r, as well as the reflection at the interface between n and n2. Thus, it is identical for both beams. The condition for the first minimum to occur (destructive interference) is that the total phase shift between 1 and 2 should be A/2. Thus we get ... 

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