Search

We construct an analog computer based on light interference to encode the hyperbolic function f({\zeta}) = 1/{\zeta} into a sequence of skewed curlicue functions. The resulting interferogram when scaled appropriately allows us to find the prime number decompositions of integers. We implement this idea exploiting polychromatic optical interference in a multipath interferometer and factor seven-digit numbers. We give an estimate for the largest number that can be factored by this scheme., Comment: 4 pages, 2 figures

Picosecond phase conjugation and two-wave coupling in cerium-doped strontium barium niobate at 778 nm were studied. The phase conjugation reflectivity at 778 nm was measured to be R pc = 58%. It is close to that pumped by a continuous-wave pump source. The temporal width t pc and spectral width δγpc of the phase conjugate pulse were measured to be the same as that of the pump pulse. The intensity coupling gain of two-wave coupling as a function of time delay τD between two beams was also studied.

A high reflectivity broad-band SBN : Ce phase conjugator with an external ring cavity in the near infrared wavelength region, 706 to 830 nm, is reported. Phase conjugation reflectivity was measured to be greater than 60% in the wavelength region, 706-820 nm, and as high as 67% at 716 nm. To our knowledge, this is the highest phase conjugation reflectivity by a SBN : Ce self-pumped phase conjugator. Both c.w. and square-wave pump sources were used. No significant changes of the phase conjugation reflectivity were observed when the pump source was changed from c.w. to a square wave at each different wavelength. The wave form of the phase conjugate wave follows the pump square wave. The build-up time of the phase conjugate wave under a square-wave pump was found to be twice that under a c.w. pump when the peak power of the square wave was the same as the power of the c.w. beam.

Using an undoped BaTiO 3 crystal, the reflectivities of the self-pumped phase-conjugate mirror operated in total internal-reflection geometry (TIR) at near infrared wavelengths from 706 to 850 nm were measured. The phase conjugation reflectivities R pc > 50% at 706 to 760 nm, R pc =40% at 816 nm, and R pc =20% at 850 nm were observed. The two-wave coupling exponential gain coefficient Γ and the photorefractive index grating formation rate τ -1 PR as a function of wavelength from 706 to 850 nm were studied. The exponential gain coefficients Γ=11.1 cm -1 at 706 nm and Γ=7.6 cm -1 at 850 nm were obtained. It was also found that the absorption coefficient α in the near infrared wavelengths is much smaller than that in the visible region.

A new method for measuring electrooptic coefficients of nonlinear crystals has been developed and used to obtain an accurate measurement of r33 and r13 for Strontium Barium Niobate (SBN). An electrooptic modulator was used with a Michelson interferometer for ac modulation (sub-Hz to MHz). By observing the appearance and symmetrical shape of the second harmonic of the ac modulation, the electrooptic coefficients r33 and r13 of SBN were measured with higher accuracy. The unclamped electrooptic coefficients of poled of SrxBa1-xNb2O6 single crystal are: r33=237±3 pm/V and r13=37±1 pm/V, at λ=632.8 nm and T=21°C. In addition the piezoelectric coefficient d23 has been measured with d23=25±5pm/V.

In this paper, we will describe a new factorization algorithm based on the continuous representation of Gauss sums, generalizable to orders j>2. Such an algorithm allows one, for the first time, to find all the factors of a number N in a single run without precalculating the ratio N/l, where l are all the possible trial factors. Continuous truncated exponential sums turn out to be a powerful tool for distinguishing factors from non-factors (we also suggest, with regard to this topic, to read an interesting paper by S. Woelk et al. also published in this issue [Woelk, Feiler, Schleich, J. Mod. Opt. in press]) and factorizing different numbers at the same time. We will also describe two possible M-path optical interferometers, which can be used to experimentally realize this algorithm: a liquid crystal grating and a generalized symmetric Michelson interferometer., 8 pages, 5 figures