266 research outputs found
Associative memories based on message-bearing optical modes in phase-conjugate resonators
We describe in generic terms a class of associative memory that is based on (1) an oscillating message-bearing optical mode in a resonator containing a multimessage hologram, (2) image-selective (discriminatory) amplification of the desired picture in a photorefractive crystal, and (3) phase-conjugate reflection
Theory of laser oscillation in resonators with photorefractive gain
A theory for oscillation in an optical resonator with photorefractive gain was formulated. The threshold conditions for the oscillation were also obtained. The result, applicable to a whole class of new devices, is a prediction for an oscillation frequency different from that of the pump beam
Determinantal and eigenvalue inequalities for matrices with numerical ranges in a sector
Let A = \pmatrix A_{11} & A_{12} \cr A_{21} & A_{22}\cr\pmatrix \in M_n,
where with , be such that the numerical range of
lies in the set \{e^{i\varphi} z \in \IC: |\Im z| \le (\Re z) \tan
\alpha\}, for some and . We
obtain the optimal containment region for the generalized eigenvalue
satisfying \lambda \pmatrix A_{11} & 0 \cr 0 & A_{22}\cr\pmatrix x = \pmatrix
0 & A_{12} \cr A_{21} & 0\cr\pmatrix x \quad \hbox{for some nonzero} x \in
\IC^n, and the optimal eigenvalue containment region of the matrix in case and are
invertible. From this result, one can show . In particular, if is a accretive-dissipative
matrix, then . These affirm some
conjectures of Drury and Lin.Comment: 6 pages, to appear in Journal of Mathematical Analysi
Canonical forms, higher rank numerical range, convexity, totally isotropic subspace, matrix equations
Results on matrix canonical forms are used to give a complete description of
the higher rank numerical range of matrices arising from the study of quantum
error correction. It is shown that the set can be obtained as the intersection
of closed half planes (of complex numbers). As a result, it is always a convex
set in . Moreover, the higher rank numerical range of a normal
matrix is a convex polygon determined by the eigenvalues. These two
consequences confirm the conjectures of Choi et al. on the subject. In
addition, the results are used to derive a formula for the optimal upper bound
for the dimension of a totally isotropic subspace of a square matrix, and
verify the solvability of certain matrix equations.Comment: 10 pages. To appear in Proceedings of the American Mathematical
Societ
Optical tracking filter using transient energy coupling
Transient energy coupling between two coherent beams occurs in dynamic holographic media with local and noninstantaneous responses. The physical origin of the effect is described, and an optical tracking filter based on the effect is demonstrated in a photorefractive Bi12SiO20 crystal
Real time image subtraction and "exclusive or" operation using a self-pumped phase conjugate mirror
Real time "exclusive or" operation with an interferometer using a self-pumped phase conjugate mirror is reported. Also, results of image subtraction and intensity inversion are shown
Conversion of optical path length to frequency by an interferometer using photorefractive oscillation
Frequency detuning effects in photorefractive oscillators are used in a new type of (passive) interferometry which converts optical path length changes to frequency shifts. Such an interferometer is potentially more accurate than conventional interferometers which convert optical path length changes to phase or intensity changes
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