Sinusoidal grating

By an interesting application of the conception of sinusoidal gratings" and of the correspondence principle" Epstein and Ehrenfest2 have extended this theory and have calculated the probability of the deflection of a quantum in the direction given by Equations (1). When a very large number of quanta strike the diffracting system, this probability represents the intensity of the radiation deflected in the said direction. The theory... 

Fig. 32 Reflectivity (upper plot) and phase (lower plot) as a function of the angle of incidence for four different depths of a metallic sinusoidal grating and TM polarization. Conflguration gold (sm = - 25 + 1.44i), water (n = 1.329), wavelength 800 nm, grating period 540 nm, angle of incidence taken in air. Reflectivity and phase of the TE polarization are shown for comparison...

Problem 3.10. A light beam of wavelength A = 590 nm falls from a vacuum onto a metal surface with a sinusoidal grating of period d = 1.77 pm. The dielectric function of the metal is e(A) = —9. Find all possible angles of incidence at which light will excite surface plasmon polaritons, provided that the plane of incidence is perpendicular to the grating ruling. 

Optical density is shown as open circles the calculated spectra is fit to a sinusoidal grating with a An of 0.059 and thickness of 10.4 and is shown as a solid line. 

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

Figure 15. Amplitude -time plots obtained from AFM measurements for the decay of sinusoidal 1-D gratings with the periods indieated on the surface of a silicate glass(Corning 1737) annealed in air at827C.[42], The exponential decay constant scales approximately as q as expected for a viscous flow controlled process[l].

The thermal healing has been studied most extensively for one-dimensional gratings. Above roughening, the gratings acquire, for small amplitude to wavelength ratios, a sinusoidal form, as predicted by the classical continuum theory of Mullins and confirmed by experimenf-s and Monte Carlo simulations. - The decay of the amplitude is, asymptotically, exponential in time. This is true for both evaporation dynamics and (experimentally more relevant) surface diffusion. 

Figure 5. Profiles z(x, f) of a grating below the roughening transition temperature, at increasing time, of the standard SOS model with 80 x 320 sites and a miscut of a few lattice spacings, using evaportion kinetics in Monte Carlo simulations (full symbols). For comparison, a sinusoid is shown (open symbols). The initial amplitude of the grating is five lattice spacings.

If the retardation of the temperature grating is neglected for the moment, which is valid if A t > T, a sinusoidal amplitude modulation of the optical grating translates directly into a sinusoidal amplitude modulation of the temperature grating with amplitude 5 T = % al0 (pc ) 1 according to Eq. (16) ... 

From an experimental point of view, a sinusoidal amplitude modulation of the optical grating can be achieved with the setup shown in Fig. 23 in one of the writing beams. 

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

Figure 1 Formation of a holographic grating. Crossed laser beams create a sinusoidal intensity pattern recorded in the film through photochemical processes.

---