Experimental results of beam coupling in semi-insulating GaAs are presented, and the signs of dominant charge carriers and the density of photorefractive species are estimated from beam coupling gain. Yariv, “Photorefringent beam coupling in semi-insulating undoped and Cr-doped GaAs: identification of dominant photocarrier signatures and deep level densities and temperature dependence of two-beam coupling gain,” unpublished.
CHAPTER
Introduction
This means that no radiation pressure and torque are supplied to the PCM because linear momentum is conserved by reflection among all the waves involved in the generation of the phase conjugate wave in the PCM (i.e. the phase matching condition is satisfied) and Ape = Ain [1 ,4,5]. By double passing through the medium, the distortions can be corrected, provided that e(r) of the medium is Hermitian, i.e. the distortions are mutual.
DPCM
This thesis describes the theory and applications of modal scattering of information and wave mixing in photorefractive crystals for vector phase conjugation and real-time information processing. The experimental demonstration of this method is given, and the experimental results of the reliability of phase conjugation are also compared with the theory.
TWO The Photorefractive Effect
In the following two subsections the two solutions for the lowest Fourier component K of the space charge field are given: one for a species and one. These will be used for evaluating the space charge field enhancement (and thus the two-beam coupling gain) in semi-insulating GaAs in Chapter 3.
THREE Beam Coupling
Beam 1
3.2) where c is the speed of light in vacuum, 1 the second order linear dielectric tensor, a. the second-order conductivity tensor, and PNL the nonlinear polarization given by Eq. 2.30), all measured in the beam propagation coordinate system. This interference pattern creates the space-charge electric field in the photorefractive crystal [3.53], whereby PNL in Eq. We note that, for the most common case where the two input waves are arbitrarily polarized, at least six waves and three photorefractive gratings are involved in the beam coupling process.
These coupled wave equations can be directly obtained by considering the symmetry of the following result. The present treatment is, however, complete for the case of anisotropic crystals without a unidirectional electric field and the two special cases described in the next section. Some of the elements in the above matrices include modulation indices m1 and m2. • The set of coupled wave equations is therefore nonlinear and the general solutions of Eq. 3.5) is difficult to solve exactly.
- Beam coupling experiments in semi-insulating GaAs .1 Elecrooptic semiconductors as photorefractive materials
- Photorefractive species in semi-insulating GaAs
- Identification of the signs of dominant photocarriers and deep level densities by scalar two-beam coupling
These include enhancing the coupling gain of the two beams by means of an applied alternating electric field [3. In the following two subsections, we present our photorefractive beam coupling experiment in SI-doped and Cr-doped GaAs [3.54] for the above purpose. On the other hand, the optical and electronic parameters of SI GaAs (e.g., density of deep levels and sign of dominant photocarriers) can be estimated from the beam coupling experiment described below.
The absorption spectra of the two SI GaAs samples at room temperature are shown in Fig. showed. If Ii(O)~ I2(O), i.e. the non-depleted pumping approximation is satisfied, the two-beam coupling gain coefficient is obtained from Eq. 3.28). Figures 3.10 and 3.11 show the experimental results of the r dependence on lattice period in the undoped and Cr-doped SI GaAs samples.
3.12(a), it is seen that r increases as the DC electric field increases, but its amplification effect is less effective than the other two methods. This is because the application of the DC electric field induces additional phase shifts in the space charge field such that the phase shift deviates from ±1r/2. Furthermore, in long transport length materials such as GaAs and BSO, the actual DC electric field inside the crystal tends to be lower than the applied DC electric field due to the migration of charge carriers to the electrodes.
With both the AC electric field method and the moving edge method, r can be larger than 1 cm-1, potentially leading to the generation of self-pumped phase conjugation. This is at least 100 times faster than the response time in ferroelectric oxides such as BaTiO3 and SBN.
Grating Period (µm)
An experiment on the temperature and intensity dependence of the two-beam coupling gain in Cr-doped SI GaAs was previously reported by Cheng and Partovi [3.73]. They observed a strong temperature dependence of the gain over a relatively narrow temperature range (295K–386K) and concluded that this dependence could be attributed to the competing effects of the dark and photoconductivity. To better understand this effect and to optimize two-beam coupling conditions, we discuss in this subsection the temperature dependence of the relevant photorefractive parameters in SI GaAs, in particular the mobility (µe), the recombination coefficient be), the number density of EL2 (NEL2+) and the thermal ionization rate (.Be) [3,54].
Numerical evaluations of the temperature dependence of the two-beam coupling gain in undoped SI GaAs are made using equations (A2), (A4), (A6) and (A12) given in Appendix A. We therefore expect that the competing effect of the dark and photoconductivities, which are related to the parameter .Be/Se, play a major role in the temperature dependence of the two-beam coupling gain. In the diffusion dominant case (Eo=O), it is found that . {3.31) where a is constant, and En and EtT are the deep level energy of the neutral deep level (e.g. the EL2° level) and the thermal activation energy of the trapping cross section of the ionized deep level (e.g. the EL2+ level), respectively (see Appendix Lx A).
Temperature (K)
This is because the response time is expressed as Tde/(roe,T"Ee,Toe,TJe) [see Eq. (2.17a)] and its behavior is mainly determined by Tde, which is inversely proportional to the dark conductance O' d, and thus decreases rapidly as T increases in the range (T > 300 K). In this subsection, we discussed the temperature dependence of the two-beam coupling gain coefficient and the response time. From the numerical results, it is concluded that it is better to work with undoped SI GaAs at higher temperatures (T ~ 350 K) in order to achieve a higher gain coefficient and faster response time.
We have also found that, although semiconductors have narrower bandgaps and shallower deep levels (due to infrared response) than ferroelectric oxides, such as BaTiO3 and SBN, the effect of temp. Finally, we speculate that the strong temperature dependence of the two-beam coupling gain (even a change of its sign at one temperature) can be seen in Cr-doped SI GaAs having simultaneous electron and hole transport . This effect can be modeled by including the temperature dependence of N EL20 /N EL 2 + and N cr2+ /N Cr3.
APPENDIX
Temperature Dependence of Photorefractive Parameters
Since EL2 is considered an impurity donor, NEL2+ is obtained by means of the usual theoretical treatment seen in basic solid state physics textbooks, i.e. by considering the Fermi-Dirac statistics or "the so-called maximum likelihood method. The result was given by where go and g1 are the degeneracy factors for the EL2+ and EL2° levels respectively, and EF and En are the Fermi energy and the energy respectively of the EL2° level, measured from the conduction band.
We also assume that the Fermi energy is greater than kB T, which is appropriate in SI GaAs. We note that when multiple photorefractive gratings exist in the crystal (e.g. the case shown in Fig. 3.3), the treatment of the space charge electric field generation should include the effect of multiple interference patterns (i.e. multiple spatial Fourier components of intensity variations).
FOUR Four-wave Mixing
This has recently been verified by quantitative measurements of the phase shifts of reflection from an externally pumped PCM, [4.34]. In particular, we measured the phase shifts of reflected conjugate waves from a SPPCM with two (coherent) input beams as a function of a uniform phase change of one of the inputs. The sign of the phase shift was determined by the direction of the edge movement.
It is seen that the phase of Ef) follows the phase modulation of the input. PHASE INJURY OF E~l (rad) . Figure 4.8 Phase shift of the conjugate beam E!1) as a function of a uniform phase change of the input Ei1) presented by the PZT mirror. It is seen that the accumulated phase shifts of E!1) and E111) increase almost linearly with increasing phase of.
FIVE Applications of Photorefractive
When the intensities of the input beam become stationary during the time t » r, the index grating catches up with the change in the interference pattern of the light. In the drift regime to form a photorefractive grating, it can be written as [see Eq. The beam L, which carries the image information of the letter O from the transparency, is shown in fig.
The contrast of the output image can be improved by increasing the intensity difference between the two input beams. The need for equal reflectivities and/or losses in the two arms of the phase conjugate interferometer is eliminated by this method. One of the two beams leaving the beam splitter BS2 was converted into an orthogonal (vertical) polarization by the A/2 plate.
SIX Polarization and Spatial
Theory
- Polarization recovery
In the analysis of the polarization properties of conjugate fields, the modal average over the phase mismatch fields after phase conjugation is used. After propagation and strong intermodal coupling in the fiber, the left-shift field forms the output field E(4) at the input end of the fiber. Next, we examine the properties of the distribution matrices and express the fields E(2.
Since the distribution of the total power between the x and y polarization components in the E(2) field is of interest, each element Ji~~) (i,j = x,y) in Eq. The X-polarized ith fiber guided mode, which is initially excited at the input plane of the fiber, is coupled to all fiber guided modes at the output in the forward direction. 6.2(b) the remaining paths in the backward direction are random and different from those in the forward direction.
In this case, we can ignore such noise contributions Vin Eq. 6.29), and the detected part of the field E(4) can be a true phase-conjugated replica of the input field E(1). In this case, the noise terms in Eq. 6.30) can be expressed by submatrices. In the above expressions of Eq. 6.32a) corresponds to the noise power of the x-polarized ,-th fiber guided mode of the field E( 4).
Equation (6.33a) corresponds to the interference between the true phase-conjugate field and the noise field at the ith fiber conduction mode of the x-polarization. The ratio of this noise power to the true phase-conjugate beam power per mode is of the order of Mo/N (Mo is the number of fiber-guided modes initially excited). We are now in a position to quantitatively evaluate the polarization recovery of the input field E(l) as a function of input beam N.A.'s.
