Analysis of an interferometer with acoustic surface waves on one mirror.
It has been demonstrated that surface waves propagating on one mirror of an interferometer form an optical diffraction grating. Experimentally confirmed analyses of an interferomet er with 95.5% reflectivity mirrors now indicate that a surface wave power density of 0.028 mW/mm.MHz is required to diffract 1% of transmitted light into the first order beam. This power can be diminished by a factor of more than 20 by increasing the mirror reflectivity to 99%.
Signal processing with surface waves via the double acousto‐optic interaction
Optical diffraction by two successive surface acoustic waves was used to achieve various signal‐processing operations. Expressions were derived for the frequency spectrum and bilinearity factor associated with this double interaction and these formulas were verified experimentally using Fabry‐Perot interferometry. An aperture function formalism was used to demonstrate that the doubly diffracted field corresponds in form to that required for real‐time convolution. The addition of a simple lens system extended the capability of this technique to a full range of processing functions. The following operations were demonstrated for pulses of the order of 1 μs: squaring convolution, squaring correlation, variable time expansion, variable time compression, time inversion, and image scanning. This processor is characterized by large bandwidth since the diffraction takes place in the Raman‐Nath limit up to GHz frequencies.
The Invariance of the Vacuum is the Invariance of the World
The following theorem is demonstrated: If the vacuum is invariant under the group generated by the space integral of the time component of a local vector current, then the Hamiltonian is invariant also. A similar theorem holds for the group generated by the space integral of a space component of a local axial-vector current.