Técnicas e instrum entos de recolección de datos 1 Técnicas

3.2 An overview of nonlinear optical materials for use in the UV 3.3 Selection of the optical parametric oscillator gain medium 3.4 Lithium triborate (LBO) crystal

References

Recently new developments in nonlinear optical materials such as the discovery and

development of KNbOg (KN), KTiOPO# (KTP), (3-BaB204 (BBO), LiBgOg (LBO)

etc, have given investigators much choice in selecting a nonlinear optical material for their applications. This has greatly invigorated the field of nonlinear optics in general,

and optical parametric oscillator in particular. However, these nonlinear materials have

many different features such that some are better suited to a particular application than others. The task of the optical designer is to strike a balance between the physical limitations of the crystal and the demands of the application.

3.1 Figure of merit of a material

In attempting to classify the many materials available for specially designed

applications it is imperative that materials be compared with well defined terms of reference. Defining a figure of merit based on relevant nonlinear optical parameters is a convenient method for choosing a material. This allows a semi-quantitative comparison to be made of the gain available from different crystals, without resort to complicated calculations. General considerations of figures of merit have normally been based on frequency conversion efficiency in SHG, where we have T|shg ^ M (figure of merit), and

have been discussed by many authorsll]. The actual form most commonly used is

CHAPTER 3 Nonlinear optical materials

However, this figure of merit formula does not address all the issues. In addition to the effective nonlinear coefficient, the following parameters are also important in comparing crystals, normally the crystal damage power threshold, the available maximum crystal length and the double refractive walkoff angle etc. In some cases, comprehensively considering these parameters together and stressing a particular

parameter is very useful. Based on the above considerations we have defined three

different figures of merit and we now discuss there.

In the last chapter we mentioned that if the pump power is high enough, so that

focusing is not required, then theoretically we can use the plane wave approximation. In this case the parametric gain coefficient can be written as

nin2n3£oc3

= (— ) ( Ip) 3 -2

£oC ninansAiAa

If we further assume that the available pump intensity is high enough, so as to approach the crystal damage threshold, then using Id to represent this parameter, the second part

of the light hand side of formula (3-2) can be used to defined a crystal damage limited figure of merit, which is

M (figures of merit) = — Id 3 - 3

niUingAiAi

Where L represent the available crystal length. In this case a crystal with a high optical damage threshold is generally considered to be superior. However, the material's figure of merit as defined above does not depend on this parameter only. For example, LBO

has a high damage threshold (~10 GW/cm^) which is twice that of BBO's (-5 GW/cm^), but, if we consider both crystals used under similar conditions, due to BBO's larger effective nonlinear coefficient, the figure of merit of BBC is larger than LBO's (please see table (3-1)).

If we take into account the effect of walkoff, then using the simple relations given by

A = TtWo^

3 - 4

Wo« pL ,

the figure of merit formula (3-3) can be rewritten as

M (figures of merit) - — Pp , 3 -5

7cp2nin2n3X,iX<2

where Pp is assumed to be the available pump power. The formula (3-5) is the walkoff limited figure of merit. In this case the crystal length for a given pump beam radius is restricted by the walkoff angle of the crystal. Further comparison of the properties of BBO and LBO crystals under similar conditions to above, and assuming that the pump power is limited so as not to approach the crystal damage threshold, then we can see that due to the larger walkoff angle of BBO the figure of merit given by formula (3-5) is then a few times smaller than that of LBO.

Actually Gaussian beams are usually used in frequency conversion processes. In this case, according to the Boyd and Kleinman theory[2], the parametric gain can be written as

2(0iC02deff^L 7cnin2n3eoC-

EqC n in 2 A iA 2 ^ 3

where the parameters have been defined in Chapter 2. Under optimised conditions and in the absence of walkoff effects, the focusing factor h(^,B) has a maximum value (h(2.84, 0) = 1.068[2]), and the figure of merit formula can hence be written as

M (figures of merit) = Pp 3 -7

0102^ 1X2^3

The figure of merit defined by (3-7) is called the crystal length limited figure of merit. It

is clear that under given conditions, a longer crystal length can compensate for a poorer nonlinear coefficient. However, when walkoff effects are taken into account in the

presence of a Gaussian beam, formula (3-6) becomes more complicated due to the variation in the parameter h(B,%). However, it has been shown that the conditions when the birefringence walkoff aperture length is greater than the crystal length (La= Tt^/^Wo/p > L), and the focusing parameter ^ < 1, the gain in the parametric interaction process can be approximated by[2]

CHAPTER 3 Nonlinear optical materials