Apparatus for providing an optical analog intensity that is approximately proportional to the value of a polynomial function expressible in the form ##STR4## wherein p(x) is a function of x,
- x is any variable,
- n is any positive integer, the cooefficients, a.sub.i, are any constants, variables, or constants and variables;
- comprising:
- an electrooptic planar waveguide;
- a plurality, n+1, of integrated optical modules in the waveguide, each module comprising at its input end a modulator for receiving light travelling in a predetermined input direction and transmitting a controlled proportion thereof further in a predetermined output direction to the output end, and a beam combiner for receiving the light from the modulator and transmitting a predetermined proportion thereof further in the predetermined output direction and on through the output end of the module;
- the modulator comprising electrooptic diffractive means comprising a pair of electrodes for forming a Bragg grating therebetween, positioned with a direction of Bragg incidence approximately in the predetermined input direction, the first electrode comprising a first set of substantially straight and parallel, thin, elongate, electrically conductive members connected together at one end, and the second electrode comprising a second set of substantially straight and parallel, thin, elongate, electrically conductive members, interleaved with the first set, insulated therefrom, and connected together at the opposite end, so that when a first electrical potential is applied to the first electrode and a second electrical potential is applied to the second electrode the controlled portion of input light transmitted through the modulator is provided by a Bragg diffraction thereof in the predetermined output direction and has an intensity approximately proportional to a known function of the difference between the first and second electrical potentials;
- and the beam combiner comprising a fixed surface grating;
- diode laser means and collimating means for directing input light of intensity approximately proportional to the coefficient a.sub.n to the input end of the nth optical module;
- means for applying across the electrodes of the modulator, while the light is passing through the modulator, a potential difference approximately proportional to a function of x such that the intensity of the output light from the modulator is approximately proportional to a.sub.n x;
- diode laser means and collimating means for directing input light of intensity approximately proportional to the coefficient a.sub.n-1, via the beam combiner, to the output end of the optical module, to combine with the output light from the modulator so that the intensity of the output light from the nth optical module is approximately proportional to a.sub.n x+a.sub.n-1 ;
- the (n-1)th optical module being positioned to receive the output light from the nth optical module in the predetermined input direction of the (n-1)th module;
- means for applying across the electrodes of the modulator in the (n-1)th optical module, while the light received from the nth module is passing through the modulator, a potential difference approximately proportional to a function of x such that the intensity of the output light from the modulator is approximately proportional to (a.sub.n x+a.sub.n-1)x;
- diode laser means and collimating means for directing input light of intensity approximately proportional to the coefficient a.sub.n-2, via the beam combiner, to the output end of the optical module, to combine with the output light from the modulator so that the intensity of the output light from the (n-1)th optical module is approximately proportional to (a.sub.n x+a.sub.n-1)x+a.sub.n-2 ;
- and so on, in the same manner, and finally to the zeroth optical module, so that the intensity of the polynomial function output light from the zeroth optical module is approximately proportional to
- ((((a.sub.n x+a.sub.n-1)x+a.sub.n-2)x+ -- -- -- +a.sub.2)x+a.sub.1)x+a.sub.o.