PARAMETRIC PROCESS DUE TO NONLINEAR INTERACTION OF LASER BEAMS WITH UNIAXIAL CRYSTALS

Abstract

Parametric amplification and oscillation due to nonlinear interaction of laser beams with uniaxial crystals have been known for sometime. Technical data required for the design of these devices are still wanting. The scope of this thesis concerns with the formulation and evaluation of Design Data of Mechanically Tuned Parametric Amplifiers and Optical Generators. Design data on parametric amplifiers and tunable oscillators using the three types of nonlinear uniaxial crystals, KDP, ADP and LifJb03, were calculated by digital o o computer. Five laser frequencies from 3164 I to 5761 A are taken for calculation of the phase-matching angles in KDP and ADP crystals, both at the degenerate frequencies and when ^(«Aw/w0) changes from 0 to 0.4 • Phase matching angles have also been calculated for LiNb03 corresponding to four laser pump frequencies from 6300 I to 11,523 A, The refractive index data of KDP and ADP used were derived by the computer from the equations by Zernike. These data were then used by the computer to derive the phase match angles from the equation ne(9* =n° [l+(r2-l)sin2ft] .. Ho attempt was made to approximate the equation, which may rosult in difference between theoretical prediction and experimental results* The curves between «0 and >p ore concave in shape showing a minimum at about the middle of the range for >p considered. This indicates that employing pump sources of shorter wave-lengths are preferable* Because of larger variation in refractive indices, LiBbQg, especially in shorter wave lengths show greater angular spread A9 for a given &h. Prom the plotted graphs for aach of these eases, one can determine the phase matching angles corresponding to any pump frequency and any eignal~to*idler frequency ratio* Design Tuning curves are given from which one can readily find the ^/^ ratio (or /) as the crystal is rotated away from the degenerate angle #0* The mismatch gradients (dk/d9) are derived wherefrom the power changes caused by divergence of laser beams can be readily estimated* User beams are essentially Gaussian in the trans versal direction* The simpler theories of parametric processes originated by plane waves are extended to Gaussian distribution by adopting a simplified concept. Stationary modes of pulsed oscillations are considered in Febry-Perot resonators with plana parallel mirrors having mirror loss~eoeffieionts ranging from 0*01 to 0.1 • The Q-values of resonators with cavity length JL«lcm are obtained for different valuea of >. and im These q-values are used to estimate the coefficient P of dielectric modulation m and consequently the threshold of pump power required to excite oscillation in these resonators, from Equations m>2/(QtQi)* EpaanJn°/2/ All these are programmed seriatim in digital computer. A set of computed values are given for R«0.99(l percent loss coefficient) of plane parallel mirrors spaced 1 cm apart. For a KDP crystal at the degenerate wavelength Xo«1.06 u and beam radius w^wl mm of plane waves, (3 * 4*449 x 106 o m » 4*496 x lG7 8 a 12.66 KVcm1 Ip • 0.317 MWcm2 Pp * 10 KW The pump threshold increases as one tunes off the degenerate frequency. Graphical plots are given from which one can readily find out the single-pass parametric gain of amplifiers consisting of KDP, ADP and LiNbOg for any intensity Ip of the exciting laser pump source and any ratio of the signal and idler —1 frequency. As an illustration, the g values with E^lOO KVcm in UNb03 (corresponding to I«30 MWcm2) range from 3.46 Np cm at xai#06 u to 1.16 Np cm1 at A «2.3 u. The corresponding signal-power gain are 24 and 4.7 db. The g values reduce with tuning off the degenerate frequency. CW oscillations caused by well-defined pump beams from CW gas lasers are considered in the lowest modes of confocal type resonators containing LiNbQg crystals in the focal region. Beam radii at the beam waist are calculated from the equation Js^oN/2*11© for tw0 typical values of confocal parameter bQ=l and 5 cm at five laser frequencies. These are then utilized to estimating the power required of x»" the pump source* At the degenerate frequency P P ^irh&o^fP' As an illustration, the pump power required of an Argon-ion (5145 X) laser in order to commence parametric oscillation in a confocal resonator with b0»l cm and containing LiNbOg crystal 1»1 cm, is 5*27 mW at the degenerate wavelength > *1*03 u*-The threshold level rises to 8*87 mW at V «0*4 • In cw parametric amplifiers much smaller gains in Idler modes are available* If bo«10 cm, the beam radii are w^«7*33 x105 cm2 at X8«0*936 uand w|«3.66 x3/55 cm2 for i «0.1 and >q*1*03 u* With a pump power of 10 mW <>3*5145 X), the idler-to-slgnal power ratio t±(!)/?,<©) is 2.15 x lO5 in a1=1 cm long crystal. The corresponding ratio for oscillator is 7.73 x l5. The threshold pump power, power gain and other useful design data for mechanically tuned CW oscillator/ amplifier with LiNbOg crystal are evaluated by computer at five pump frequencies and given in Tabular form. MKS system of units is used in this Thesis*