pm/V using single crystals, though application of the material in a frequency doubled laser was not obtained.

Subsequently, Dunning et al [20] obtained pulsed UV from LFM crystals, using a pulsed dye laser to pump a sealed cell dye laser, whose output was then passed to the LFM crystal.

The phasematching data used by Dunning was taken from Singh's paper, which produced a dispersion formula of the forms

where for the three axes the values of S^ and Xq are as fol1owss

S^ Xq (in microns)

X 0.8415 0.0953

Y 1 . 1 4 1 0 6 0.1183

Z 1.2454 0.12496

This formula was based upon experimental data in the range 460nm to 1060nm, covering only 9 values of wavelength.

The calculation of phasematch angle for any type of matching in the region of 480nm requires the values of refractivity at around 240nm, and we feel that it is not satisfactory to extrapolate the range of (41) by this

degree, particularly as dispersion normally increases at shorter wavelengths. As will be shown in Chapter 3, there is experimental evidence that this belief is justified.

The work of Naito and Inaba, however, uses experimental data over the entire range 350nm to ISOOnm, to produce a

dispersion equation of the forms |

j n2 = A + BX2/<x2_^2) _ q^2 (42) I

where the values of A, B , C and ares

A B C X^fin microns)

X 1.4376 0.4045 0.0005 0.1301 Y 1.6586 0.5006 0.0127 0.1530 Z 1.6714 0.5928 0.0153 0.1592

In this case, extrapolation to a wavelength of 240nm or less must be far more reliable than on the basis of the data of Singh, and we have prepared graphs of the

phasematch angle 0^ for Type I matching, measured with respect to the Z axis, using both (41) and (42) for refractivities and (27) for the value of 0m

Tables of values of 0^^ and the ref ractivi ties from 200nm to SOOnm, based on (42) only, are given in the Appendix 1. The graphs of phasematch angle against wavelength using the two different sets of refractivities are shown in Fig 2-3, where the comparison is for a beam propagating in the ZX plane and polarised along the Y axis. It is seen that for shorter wavelengths the two sets of results are in considerable disagreement, and results using a crystal of

CD o m IT) _o

g

§

s

§

I

I

Fig 2-3: Graphs of phasematching angle, 0^, for the two

dispersion formulae; (a) Naito and Inaba [12],

(b) Singh et al [6]

known orientation tend to support the results of Naito and Inaba rather than those of Singh (see Section 3-2-4).

The choice of Type I or Type II phasematching for LFM is made as follows. Using (42) to provide values of

refractivity for use in (28), we find that for a beam propagating in the ZX plane, Type II is not possible for fundamental wavelengths below about 950nm, and for the ZY plane, the lower limit is about 410nm while the upper is 44Bnm. For Type I, the use of (27) applied to the ZY plane shows that for the entire range of wavelengths above 400nm, the value of sin^O^p) is negative and so the

matching scheme is impossible. However, as shown in Fig 2-3 for Type I in the ZX plane, 0pp is real for all

wavelengths above 400nm, although below about 470nm the SH is significantly absorbed by the crystal.

Thus the choice lies between Type I in the ZX plane and, for the range 410nm to 44Snm only. Type II in the ZY plane. For these cases, the SH polarisations are given from (19) bys

Type I , P^2 = S "*32

Type II s P^2 =

Measurements by Singh et al C63 have shown that d^ 2 is

much greater than d^g , and so even if we let - E ^ , which is often the case, the Type I scheme gives a very much greater SH polarisation where any choice exists, and above 44Bnm, Type I must be used anyway.

Thus the phasematching scheme for LFM around 4B0nm is that of Type I with the fundamental polarised as an ordinary wave Ey in the ZX plane, with the generated SH as an extraordinary wave E^ (Fig 2-4).

2-2-2 Urea

Bauerle et al C23] have made determinations of the

refractivities, absorption and nonlinear coefficients of Urea, based on earlier work by Kurtz and Perry [24] and have also obtained phasematched SHB in single crystals. More recently, Hal bout et al C113 and Cassidy et al [93 have used Urea as a SHG and mixing material, using a

pulsed dye laser and and a CW argon ion laser operating on discrete lines between 488nm and 528nm. None of the

experiments reported has used Urea as an intracavity frequency doubling element.

The variation of refractivity for Urea is given by the following expressions, determined from data in [113g

n^ = 2,1678 + 0.0139/(A? - 0,0207)

n^ « 2,4917 + 0,0141/(A^ - 0,0240)

(43)

(A in microns) The phasematch angle is then determined from (24) or (25) as required. The shortest wavelength at which Type II is possible is 599,9nm and so this type will not be

considered further here. For Type I, the limit is 474nm, and the material is 90% transmitting to well below the SH, Thus for generation of tunable UV down to as low as 240nm,