Quasi-phasematching

Biréfringent phasematching has been successfully demonstrated cotmtless times, for the generation of a vast range of wavelengths from many varieties of nonlinear device. However, the fact that it relies on a physical propeity, namely, refractive index, means that it is limited and not viable for every application. This is particulaiiy true for the generation of mid-infrared wavelengths; there are very few materials that are both transparent and phasematchable beyond 4 pm.

Ideally, researchers would like to be able to tailor nonlinear materials to fît any application. In effect, this means introducing some extra element into the wave vector mismatch equation to maintain AA = 0 for any required combination of wavelengths. Happily, there is a way to do this - quasi-phasematching. This technique was originally suggested before that of biréfringent phasematching, by Armstrong et al [14] in 1962, although they did not refer to it by that name.

Consider an OPO in which the pump, signal and idler propagate collinearly, but the interaction is not phasematched, so that AA 9^ 0. The waves slip out of phase and interact less strongly as they propagate through the crystal. Back conversion occurs until eventually the phase relation favours forward conversion again, and the process repeats itself. Over the length of a crystal the overall conversion efficiency is negligible, and no useful light is generated. The propagation distance after which the gain is reduced by half is referred to as the coherence length, 4, given by

^ JC

^ A., - A, - A; AA

This detrimental process can be compensated for, however. If the sign of the nonlinear coefficient can be reversed after each coherence length (and is therefore modulated with a period equal to twice the coherence length), the interaction is brought back into phase, and continues to build up through the whole crystal length. This is the process of quasi-phasematching.

The sign reversal of the nonlinearity can be achieved by stacking plates of a nonlinear material in opposing orientations, but this is difficult to engineer on a small enough scale. A more useful technique is the periodic poling of ferroelectric ciystals, whereby an electric field is applied to a crystal to periodically reverse the polarity, and hence the nonlinearity. This is discussed further in Section 6.4. Reliable fabrication methods for poled crystals are relatively new, so that the use of quasi- phasematching is only now becoming widespread, despite being based on an idea almost four decades old.

The modulation of the nonlinearity is referred to as a grating, so the period of the modulation is the grating period. A, where

^ (2.25)

It is the grating period that makes up the extra parameter required to balance the wave-vector mismatch, so that, for an OPO,

&kQ = k j , - k , - ki - k„

(

,

)

, 27m

Ki=^—7 -

^ (2.27)

and m is the order of the quasi-phasematched process, such that m = 1, 3, 5... m = \ is refeiTed to as a first order process, and so on. The appropriate grating period can therefore be chosen to produce phasematching.

Quasi-phasematching calculations can be caiTied out in the same way as for biréfringent phasematching, provided that the grating vector is accounted for. The conservation of momentum condition for first order quasi-phasematching in an OPO is therefore given by

^ (2.28) while the conservation of energy condition of Equation 2.20 remains unchanged.

The advantages of quasi-phasematching over biréfringent phasematching aie manifold. The creation of a grating means that a nonlinear crystal can be tailored to phasematch any desired combination of wavelengths within the transparency range of a material, thus overcoming the limitations placed by biréfringent properties. The lack of dependence on birefringence means that any propagation direction and polarisation combination can be used. Hence, beams can always be propagated along a ciystal axis to avoid the problems caused by Poynting vector walk-off, outlined in the previous section. Also, larger nonlinearities can be accessed, leading to higher gain. The polarisation combinations imposed by biréfringent phasematching mean that frequently the largest nonlinear coefficient in a crystal is not exploited, whereas a quasi-phasematched arrangement allows the use of the polarisations which access the largest coefficient. The effective nonlinearity of a quasi-phasematched process is given by

‘ (2.29)

where dg/fis the nonlinearity for the equivalent process in the absence of a grating, if such a process were phasematchable. Thus, a first order process is the most efficient.

All these reasons have contributed to the current meteoric rise in the popularity of quasi-phasematching, since the recent introduction of high quality poled crystals.

This section has described the three principal methods of phasematching; critical and noncritical biréfringent phasematching, and quasi-phasematching. Experimental examples of each of these techniques are presented in subsequent chapters of this thesis. Chapter 4 describes a noncritically phasematched OPO based on RbTiOAs0 4; Chapter 5 discusses the use of noncollinear propagation to overcome walk-off in a critically phasematched KTi0As0 4 OPO; and a quasi- phasematched OPO based on periodically poled lithium niobate is presented in Chapter 5.