Phase gratings

Deak J, Richard L, Pereira M, Chui H-L and Miller R J D 1994 Picosecond phase grating spectroscopy applications to bioenergetics and protein dynamics Meth. Enzymol. 232 322-60... 

Because the losses tend to be excessive in volume absorption gratings, volume holograms are realized in most cases using index (phase) gratings. 

The spatially periodic temperature distribution produces the corresponding relxactive index distribution, which acts as an optical phase grating for the low-power probing laser beam of the nonabsorbed wavelength in the sample. The thermal diffusivity is determined by detecting the temporal decay of the first-order diffracted probing beam [°o exp(-2t/x)] expressed by... 

The distortions in the aberrated image can be better understood if a weak sinusoidal phase grating is considered [93], described by the object wave ... 

In the next section, we describe two pump-probe approaches and review their use in experiments with MbCO. This places the nonlinear optical techniques of transient phase grating introduced in the subsequent section in their proper context. 

FIGURE 1.9 Schematic representation of the excitation, prohe, signal, and reference beams used for heterodyne detection in transient phase grating experiments. 

One of the widely used methods of analysis of kinetic data is based on extraction of the distribution of relaxation times or, equivalently, enthalpic barrier heights. In this section, we show that this may be done easily by using the distribution function introduced by Raicu (1999 see Equation [1.16] above). To this end, we use the data reported by Walther and coworkers (Walther et al. 2005) from pump-probe as well as the transient phase grating measurements on trehalose-embedded MbCO. Their pump-probe data have been used without modification herein, while the phase grating data (also reproduced in Figure 1.12) have been corrected for thermal diffusion of the grating using the relaxation time reported above, r,, and Equation (1.25). 

FIGURE 1.13 Experimental results (points) obtained from pump-probe (left) and transient phase grating (right) measurements of MbCO recombination as a function of time, t, following photodissociation. Solid lines were computed from equations (26) and (27), and the best-fit parameter values are listed in Table 1.2. (From Walther, M., Raicu, V., Ogilvie, J. R, Phillips, R., Kluger, R., and Miller, R. J. D. 2005. J. Phys. Chem. B 109 20605-11. With permission.)... 

Deak, J., Chiu, H. L., Lewis, C. M., and Miller, R. J. D. 1998. Ultrafast phase grating studies of heme proteins Observation of the low-frequence modes directing functionally important protein motions,/. Phys. Chem. 102 6621-34. 

Refractive index grating and heterodyne detection For a sample transparent at the readout wavelength, a pure refractive index or phase grating builds up, with contributions from both the temperature and the concentration gratings. In analogy to Eqs. (15) and (19), it is expressed as... 

Xr is the readout wavelength and s the sample thickness. Q < 1 indicates thin, Q > 1 thick grating conditions,which are prevalent in the present case with Q 5. An extensive treatment of the diffraction theory of phase gratings has been given by Kogelnik [48]. All experiments discussed here have been conducted within the weak modulation depth limit, where the heterodyne or electric field diffraction efficiency Chet(t) is simply proportional to the refractive index modulation depth ... 

Harrison C, Stafford CM, Zhang WH, Karim A (2004) Sinusoidal phase grating created by a tunably buckled surface. Appl Phys Lett 85 4016—4018... 

For a phase grating of the type illustrated in Fig. 2, the angular and spectral half-peak-efficiency bandwidths can be estimated from the following rules of thumb (6) 2A01/2 A/d, IKXi /X s... 

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