DESCRIPCION Y DATOS PSICOMÉTRICOS DE LA ESCALA

2.7.1 Introduction

A photorefractive material like BaTiC^, can be used in many different configurations to operate as a phase conjugate mirror. The difference between the configurations is the way in which the beams are brought together to produce the FWM interaction and the temporal coherence relationships between them (Cronin-Golomb et al 1984 [12], Fischer et al 1989 [25]). The configuration which is used will simply depend on the constraints determined by the application of the phase conjugate mirror. In our application a form of double phase conjugate mirror (DPCM) [82], known as the semilinear phase conjugate mirror (SLPCM) [11], has proven to be the most suitable. The reasons for this will be discussed in chapter six of this thesis.

2.7.2 The Double Phase Conjugate Mirror

The DPCM is one the easier photorefractive phase conjugate mirrors to realize experimentally (Wiess et al 1987 [82]). In this phase conjugate mirror, two temporally incoherent input beams enter the photorefractive material, and the phase conjugate of each input beam is produced. A schematic diagram of this phase conjugate mirror is shown in figure 2.8.

Barium Titanate Crystal

Figure 2.8. A schematic diagram of the DPCM. The thick arrows represent the two input beams, while the thin arrows represents the scatter of each beam.

As the two input beams are temporally incoherent with respect to one another a grating cannot be formed between them. However, a weak grating can form between an input beam and that part of the same input beam scattered off crystal imperfections as it enters the photorefractive material. If the light scattered by one of the input beams counter-propagates with respect to the other input beam and vice versa, then two gratings are formed which exactly overlap. As a result the two gratings reinforce one another producing an overall grating which has an amplitude greater than each of the constituent gratings. This reinforcement leads to an increase in the amount of energy diffracted from each input beam because of the increased diffraction efficiency of the

grating. Therefore, as the diffraction of one input beam off the grating produces the phase conjugate of the other input beam, and vice versa, substantial phase conjugate reflectivities for each input beam are obtained.

The exact value of the phase conjugate reflectivity for each input beam of the DPCM can be evaluated using the solution to the FWM interaction as described in section 2.6. From those equations it is evident that the phase conjugate reflectivity will depend on y, which is the coupling strength per unit length of the photorefractive material, and the boundary conditions that apply. In the case of the DPCM these boundary conditions can be expressed as;

I1(0)=1.0; I2(0) = I4(d) = 0.0; I3(d) = x

Using these conditions the phase conjugate reflectivity for the second input beam, which is defined as I2(d)/I3(d) from the notation of figure 2.8, can be evaluated as a function of the ratio of input beam intensities, x. Figure 2.9 shows the phase conjugate reflectivity for the second input beam as a function of x for various coupling strengths (this is the product of the coupling strength per unit length and the interaction length).

This diagram shows that for a range of input beam ratios that the phase conjugate reflectivity for the second input beam is greater than unity. In this regime the phase conjugate mirror is acting as a combination of a mirror and a source of gain for that input beam. Therefore it is possible to remove the source of the second input beam and replace it by an ordinary mirror. Oscillations will then be initiated by a noise field that exists in this oscillator. This photorefractive oscillator has been experimentally realized and is known as the semilinear phase conjugate mirror (SLPCM) (Cronin-Golomb et al

INPUT BEAM INTENSITY RATIO (x)

Figure 2.9. Phase conjugate reflectivity (PCR) as a function of the input beam intensity

ratio, x, for three different values of coupling strength a) yd = 3.0; b) yd = 3.5; c) yd =

4.0. The dark solid line indicates the region above which the PCR is greater than unity.

2.7.3 The Semilinear Phase Conjugate Mirror

A schematic diagram of the FWM interaction that occurs in a SLPCM is shown in figure 2.10. Essentially the SLPCM comprises an oscillator formed between the phase conjugate mirror and a conventional mirror. Unlike a conventional oscillator though, the counter-propagating beams that oscillate in the cavity, are always phase conjugates of one another, regardless of what phase aberrating object is placed in the cavity. Therefore, if the radiation at the ordinary mirror side of the oscillator is constrained to some particular spatial distribution, then the beam 'reflected' by the phase

Barium Titanate Crystal

Input Beam

Ordinary Mirror

Phase conjugate of beam 1

Figure 2.10. A schematic diagram o f the semilinear phase conjugate mirror

conjugate mirror will always have that same spatial distribution when it reaches the ordinary mirror. This will occur regardless of what phase distortion is produced in the rest of the cavity. Consequently it is possible to place a multi-mode optic fibre in the cavity of a SLPCM and maintain oscillations with the radiation constrained to a single transverse mode at the ordinary mirror. A diagram of this is shown in figure 2.11.

Multimode fibre

Figure 2.11. A diagram o f one o f the possible ways that the SLPCM is to be employed to obtain single mode output from multi-mode fibres.

If the ordinary mirror is chosen such that it is partially transmitting, then some of this single mode radiation can leave the system. In this way single mode radiation can be obtained from the output end of a multi-mode fibre. The exact amount of power that can be transferred from the input to the output of the system will depend on the reflectivity of the ordinary mirror and the properties of the photorefractive material. Importantly though, it will be independent of the amount of phase distortion introduced by the multi-mode fibre.

We have experimentally realised this system [38], the details of which will be described in the following chapters, as will the behaviour of the system.