Quarter-waveplate

A RIKES experunent is essentially identical to that of CW CARS, except the probe laser need not be tunable. The probe beam is linearly polarized at 0° (—>), while the polarization of the tunable pump beam is controlled by a linear polarizer and a quarter waveplate. The pump and probe beams, whose frequency difference must match the Raman frequency, are overlapped in the sample (just as in CARS). The strong pump beam propagating tlirough a nonlinear medium induces an anisotropic change in the refractive mdices seen by tlie weaker probe wave, which alters the polarization of a probe beam [96]. The signal field is polarized orthogonally to the probe laser and any altered polarization may be detected as an increase in intensity transmitted tlirough a crossed polarizer. When the pump beam is Imearly polarized at 45° y), contributions... 

Figure 9.9 Simulated normalized line shapes of -polarized (a-c) and p-polarized (if-/) second-harmonic signals for quarter waveplate measurements (a) and (if) hypothetical achiral surface (hs = 0.5 fp = 0.75, gp = —0.5), (b) and (if) hypothetical chiral surface with in-phase chiral coefficient (fs = 0.75, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25), (c) and (/) hypothetical chiral surface with out-of-phase chiral coefficient ( fs = 0.75 0.25i, hs = 0.5 fp = 0.75, gp = —0.5, hp = 0.25z). Upper (solid line) and lower (dashed line) sign in expansion coefficients correspond to two enantiomers. Rotation angles of 45° and 225° (135° and 315°) correspond to right-hand (left-hand) circularly polarized light and are indicated for one of enantiomers with open and filled circles, respectively.

To determine /, g, and h the second-harmonic intensity is measured as a function of the angle of the quarter waveplate for different experimental geometries. The experimental setup is shown in Figure 9.12. A thin film is irradiated with an infrared Nd YAG laser (1064 nm, 50 Hz, 8 ns). The polarization of the input beam (p polarized) is continuously varied with a quarter waveplate... 

Figure 9.13 (a) and (b) Examples of polarization patterns obtained from quarter waveplate... 

Figure 9.15 Second-harmonic intensity as function of rotation angle of quarter waveplate. (a) Transmitted -polarized SH signal, (b) transmitted p-polarized SH signal, (c) reflected -polarized SH signal, and (d) reflected p-polarized SH signal. Left- and right-hand circularly polarized input light is indicated with open and filled circles, respectively.

The problem is that one can never know whether a fitting routine has found the physical solution or one of the other solutions. Of course, once the parameter values are determined from the fit to the quarter waveplate data curve, then the physical solution is known and should be recognizable from the four sets of parameter values found to fit the half waveplate data curve. We have done this and give in Table 9.4 the physically correct parameter values that fit the half waveplate data curve. The solid-line curves in Figures 9.15 and 9.16 are plots of Eqs. 42 and 43, respectively, using the parameter values given in Table 9.4. One can see that the solid-line curves provide an excellent fit to the data curves. 

We anticipate that, regardless of the detuning from an optical resonance used, the parameters f, g, and h will always be determinable from measurements of SHG as a function of the rotation angle of a quarter waveplate used to set the polarization state of the incident fundamental light. The amount of SHG-CD can be calculated from the parameters or, of course, read directly... 

Figure 9.18 Eight measured second-harmonic signals. Waveplate rotation angle of 0° corresponds to p-polarized fundamental field. Dots are experimental data and lines fit to Eq. 42 with polarization control by quarter waveplate. (a-d) Film-side incidence, (e-h) glass-side incidence (a) and (e) transmitted -polarized (b) and (/) transmitted p-polarized (c) and (g) reflected -polarized (if) and (h) reflected p-polarized.

The nonlinearity of the sample was analyzed using the experimental procedure described in Section 3.3 The polarization of the fundamental beam of a YAG laser was continuously varied by means of a quarter waveplate, and the intensity of the second-harmonic signal was measured as a function of the rotation angle of the quarter waveplate. The obtained polarization pattern were then fitted to Eq. (42), which yields the relative values of the expansion coefficients /, g, and h. The experimental results for the transmitted, glass-side-incidence, s-polarizcd signal are shown in Figure 9.20. 

Figure 9.20 Intensity of s-polarized second-harmonic signal generated in transmitted direction for glass-side incidence as function of rotation angle of quarter waveplate. Note significant difference in response for right- (45° and 225°) and left-hand (135° and 315°) circularly polarized light. Points represent experimental data, solid line fit to the model described in Section 3 with nonvanishing g, and the dashed line the fit with vanishing g.

Figure 1. Schematic diagrams of TEB and LLS instrumentation. P, pinholes L, lenses B, polarizers C, cell Q, quarter wave plate PMT, photomultiplier tube HVG, high voltage generator MP, microprocessor TR, transient recorder CL, correlator CT, counter 6, scattering angle. For the TEB setup polarizers B-, B2 have polarization axis oriented at tt/4 with respect to the x-axis, as shown in (a). After the light beam passed through the cell with electric field in the x-direction containing a suspension of anisotropic particles and the quarter waveplate with its fast axis oriented at tt/4 with respect to the x-axis, the transmitted light beam is polarized in the direction of 71/4 + 6/2, as shown in (b). Analyzer B has polarization axis oriented at 3t/4 + a as shown in (c).

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]. 

Jaffe and Jaffe (26) have described another technique of measuring ultraviolet and visible dichroism by obtaining a single absorption spectrum. Their method makes use of a single polarizer and a quarter waveplate placed ahead of the sample. The precise state of polarization seen by the sample will depend on the relative retardation, R(A), introduced by the waveplate. Specifically... 

Zero order quarter waveplate (WPQ05M-488, Thorlabs, USA)... 

---