Uncertainty principle forms a crucial part of quantum theory and wave optics. By using the propagation of a scalar, 3-D wave packet with and without dispersion as a heuristic device, we examine different aspects of the principle as it applies to transverse and longitudinal dispersion, and to time-dependent and stationary states.
It is well known that the intensity interferometry of Hanbury Brown and Twiss measures the square of the absolute value of the normalized coherence function and that the phase of the function is lost. We show that the cosine and the sine of the phase can be determined using triple- and quadruple-intensity correlations. This information is used to derive the intensity distribution of the object. The procedure for the phase reconstruction described depends on the starting values of the phase function for the least separation of the mirrors or for the nearest neighbors in the two perpendicular directions of the array of mirrors. These starting values are determined by means of an amplitude correlation experiment, such as the Young's two-slit type. The procedure of intensity correlations is then used for all other separations throughout the array. Computer simulation of the proposed procedure and a simple example of reconstruction of object intensity distribution are shown.
The mechanical torque exerted by a beam of polarized light on a half waveplate that alters the state of polarization is calculated for several laser wavelengths and intensities using electromagnetic theory. The second-order torque that arises through the nonlinear interaction is formulated, and the numerical values are obtained for the 42m crystal class. The experiment used to detect the existence of the torque is reviewed and a demonstration experiment is suggested.
Second-, third-, and fourth-order intensity correlations measured in the field in the pupil plane are used to construct the amplitude and phase of the two-dimensional mutual coherence function. Information about the noncoherent object is derived by a two-dimensional spatial Fourier transform of the mutual coherence function. A computer simulation of the Fourier domain laser speckle patterns is used to provide data from which the expected second-, third-, and fourth-order intensity correlations are computed. These correlations are used in the program for the explicit reconstruction of the phase. In addition, the signal-to-noise ratio (SNR) is discussed with reference to the measured integrated intensity, ?0TI(t)dt, as compared to the theoretically assumed instantaneous intensity,I(t). The study of the SNR for the second-, third-, and fourth-order intensity correlations involves higher-order intensity correlations. With the assumed Gaussian statistics of the wave amplitude, the analytical expressions for the higher-order correlations are algebraically complex. The SNR for the third-order case is discussed. For further development, symbolic manipulation programs (e.g., DERIVE, MATHEMATICA, or MACSYMA) will be used. The discussion of the signal-to-noise ratio applies to intensity correlation interferometry (low light levels) for which the integration time, T, is large compared to the coherence time, ?c, that is, T >> ?c. We will consider the case for laser speckle interferometry for which ?c » T in our follow-up work.