Harmonic generation is one of the nonlinear optical phenomena and a very useful method for generating coherent light in the short wavelength region. Since the research on harmonic generation has begun in 1961, many efforts have been devoted to increase the conversion efficiency and measure the nonlinear properties of the various media. Until now, many nonlinear media which are phase matchable and have high nonlinearity are introduced and their nonlinear properties are investigated in detail. Experimental phase matching techniques are also much developed, however, it is still a difficult subject to find out the phase matching condition. The present work deals with the theoretical phase matching condition in harmonic generation and experimental realization of the condition.
$KH_2PO_4$ (KDP) single crystals are grown by solution growing method. Laue spots are observed in X-ray back scattering crystallographic method, and conoscopic figure is obtained in the grown KDP crystal. From these results, the KDP crystals are proved to be sufficiently well grown single crystals.
Second harmonic wave (wavelength 0.53 um) is generated in type-1 (oo-e interaction type) and type-2 (eo-e interaction type) cuts of KDP crystal by using neodymium-glass laser beam (wavelength 1.06 um) as a fundamental wave, and the third harmonic wave (wavelength 0.3533 um) is generated by summing the second harmonic wave with the fundamental wave in type-2 cut KDP crystal.
Angular full width at half maximum (FWHM) of the second harmonic conversion efficiencies of the both types of phase matching are measured first by goniometric method. Second harmonic wave is generated by using diverging fundamental beam and the diverging output pattern of the second harmonic wave is recorded on the photographic emulsion. By measuring the periods of second harmonic output pattern, angular FWHM of second harmonic conversion efficiencies are calculated and compared with the results of the goniometric method. Angular FWHM of conversion efficiencies are 0.136 ± 0.006 deg. for the 7.1mm thick type-1 cut KDP crystal and 0.272 ± 0.005 deg. for the 7.25 mm thick type-2 cut KDP crystal. Type-2 phase matching is convenient for angle tuning because it has wider acceptance angle and tight focusing is available for increasing the conversion efficiency.
Thermo-optic and electro-optic effects for phase matching conditions are accurately investigated using diverging beam technique. Temperature of the type1 and type-2 KDP crystal is increased from room temperature to 110℃. Electric field is applied to the both types of KDP crystals. The shifts of the diverging second harmonic output pattern are recorded on the photographic film. Least-squares-fit linear regression is used to calculate the thermo-optic and electro-optic tuning sensitivities. The measured thermo-optic tuning sensitivities are $0.00546 ± 4 x 10^{-5} deg./℃$ for type-1 and $0.0143 ± 4 x 10^{-4} deg./℃$ for type-2, and the measured electro-optic tuning sensitivities are $0.00437 ± 3 x 10^{-5} deg./kV-cm$ for type1 and zero for type-2.
Since the thermal conductivity of the KDP crystal is not good, thermo-optic tuning requires usually longer time for thermal equilibrium. Electro-optic tuning has the fast response time. Particularly in electro-optic tuning with type-1 phase matching, the direction of phase matching angle variation can be reversed simply by reversing the polarity of the electric field. For type-2 phase matching system, electro-optic tuning can not be used and thermo-optic tuning is only useful.
By using the diverging beam technique, the error due to the power fluctuation of the laser beam is eliminated. Mechanical errors are also eliminated because it has no moving part. Narrow and small variations in phase matching angles can be precisely measured without expensive and bulky equipments. Diverging beam technique is found to be very useful for the measurement of the angular FWHM of conversion efficiency and that of the tuning sensitivity of various nonlinear crystals in harmonic generation.
