Photorefractive Phase Shift Research Articles

The impact of electron and hole trapping coefficient on nonlinear phenomena in photorefractive multiple quantum well structures

Semiconductor photorefractive quantum wells belong to materials with strong optical nonlinearity. One of the parameters that may affect the course of nonlinear phenomena in these materials is the electron and hole trapping coefficient. We present the results of a numerical analysis aimed to find out, how electric field-dependent trapping coefficients affect the process of space-charge field formation in multiple quantum wells in the phenomenon of photorefractive two-wave mixing. Full Text: PDF ReferencesQ. Wang, R. M. Brubaker, D. D. Nolte and M. R. Melloch, "Photorefractive quantum wells: transverse Franz-Keldysh geometry," J. Opt. Soc. Am. B 9, 1626 (1992) CrossRef D.D. Nolte and M.R. Melloch, in: Photorefractive effects and Materials, Chap.6, ed. by D. D. Nolte (Kluwer Academic, Boston, 1995) CrossRef D.D. Nolte, "Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications"", J. Appl. Phys. 85, 6259 (1999) CrossRef Q.Wang, R. M. Brubaker and D. D. Nolte, "Photorefractive phase shift induced by hot-electron transport: Multiple-quantum-well structures", J. Opt. Soc. Am. B 9 (1994) 1773. CrossRef V. Ya. Prinz, S. N. Rechkunov, "Influence of a Strong Electric Field on the Carrier Capture by nonradiative Deep-Level Centers in GaAs", Phys. Stat. Sol. (b) 118, 159 (1983) CrossRef S.M. Sze, Physics of Semiconductors Devices, second ed., Wiley, New York, 1981 (Chapter 10) DirectLink B. Jablonski, "Impact of donor compensation ratio on photorefractive two-wave mixing dynamics in multiple quantum wells structures", JNOPM 23, 1450029 (2014) CrossRef

Impact of proton implantation parameters on the photoconductivity of photorefractive multiple quantum wells

Semi-insulating GaAs/AlGaAs multiple quantum wells are photorefractive materials with high sensitivity and a short response time. Semi-insulation of these structures is commonly obtained by proton implantation. We present the measurements of photoconductivity in the samples with different proton doses. The results were compared to the theoretically predicted relationship between photoconductivity and the donor to acceptor concentration ratio. This allows to estimate the impact of proton dose on deep donor concentration. Full Text: PDF References D.D. Nolte, "Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications", J. Appl. Phys. 85, 6259 (1999). CrossRef D.D. Nolte, M.R. Melloch, in Photorefractive effects and Materials, ed. D.D. Nolte (Kluwer, Dordrecht, 1995). CrossRef Q. Wang, R.M. Brubaker, D.D. Nolte, M.R. Meloch, "Photorefractive quantum wells: transverse Franz–Keldysh geometry", J. Opt. Soc. Am. B 9, 1626 (1992). CrossRef Q. Wang, RM. Brubaker, D.D. Nolte, "Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures", J. Opt. Soc. Am. B 11, 1773 (1994). CrossRef M. Wichtowski, A. Ziolkowski, E. Weinert-Rączka, "A general approach to the space?charge field solution in photorefractive materials in a TWM geometry", J. Opt. 12, 065201 (2010). CrossRef A. Ziółkowski, "Self-bending of light in photorefractive semiconductors with hot-electron effect", Opt. Expr. 22, 4599 (2014). CrossRef K. Seeger, Semiconductors Physics, fifth ed., Chapter 1 (Springer-Verlag, Berlin, 1991). CrossRef S.M. Sze, Physics of Semiconductors Devices, Second ed., Chapter 1 (Wiley, New York, 1981). S. Balasubramanian, I. Lahiri, Y. Ding, M.R. Melloch, D.D. Nolte, "Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings", Appl. Phys. B 68, 863 (1999). CrossRef P. Yeh in Introduction to Photorefractive Nonlinear Optics, (Wiley, New York, 1993). CrossRef

On the mobility-lifetime products in photorefractive GaAs-AlGaAs quantum wells structures determined by moving grating technique measurements

The method to determine mobility-lifetime products of photoexcited electrons and holes in semi-insulating GaAs-AlGaAs quantum wells structures is proposed. The method is based on measurements of a photoconductivity and optical investigations of a photorefractive material response in wave-mixing setup using the running grating technique. Full Text: PDF References L. Solymar, D.J. Webb, A. Grunnet-Jepsen, The physics and applications of photorefractive materials (Clarendon Press: Oxford 1996). D.D. Nolte, M.R. Melloch, Photorefractive effects and Materials, ed. by D.D.Nolte (Kluwer, Dordrecht, 1995). S. Balasubramanian, I. Lahiri, Y. Ding, M.R. Melloch, D.D. Nolte, "Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings", Appl. Phys. B 68, 863 (1999). CrossRef M Wichtowski, "Wave mixing analysis in photorefractive quantum wells in the Franz–Keldysh geometry under a moving grating", Appl. Phys. B 115, 505 (2014). CrossRef Q. Wang, R.M. Brubaker, D.D. Nolte, "Photorefractive phase shift induced by hot-electron transport: multiple-quantum-well structures", J. Opt. Soc. Am. B 9, 1773 (1994). CrossRef M. Shur GaAs devices and circuits (Springer, New York, 1989). D.D. Nolte, "Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications", J. Appl. Phys. 85, 6259 (1999). CrossRef G.C. Valley, H. Rajbenbach, H.J. von Bardeleben, "Mobility?lifetime product of photoexcited electrons in GaAs", Appl. Phys. Lett. 56, 364 (1989). CrossRef A. Ziółkowski, "Temporal analysis of solitons in photorefractive semiconductors", J. Opt. 14, 035202 (2012). CrossRef

Effect of photoconductivity and dielectric constant of the photorefractive materials on two-beam coupling gain and phase-shifts for a single unidirectional photorefractive ring resonator

Photoconductive dependence of two-beam coupling between the pump beam and the signal beam in photorefractive materials have been analyzed in case of non-degenerate wave mixing under the undepleted pump approximation method. During the two-wave mixing in photorefractive materials, steady state amplification of the signal beam and oscillation characteristics of a single unidirectional ring resonator has been studied. The domination of the two-beam coupling gain over the combined absorption and resonator losses such as Fresnel reflections from the crystal and imperfect mirrors builds up unidirectional oscillation. The buildup of such an oscillation leads to a saturation of the gain, which can be explained in terms of the photorefractive phase-shift. The existence of this phase-shift between the photorefractive index grating and the illumination intensity pattern, which is of characteristic of the photorefractive effect, leads to an energy transfer between the two beams. For a single unidirectional ring resonators, the effects of photoconductivity of the materials, two-beam energy coupling coefficient, dielectric constant, crystal thickness, and material's absorption coefficient on amplification of the two-beam coupling gain and photorefractive phase-shifts of the signal beam have also been studied in detail. It has been found that amplification of the signal beam and phase-shift can be enhanced by taking the photorefractive crystal having higher photoconductivity and lower dielectric constant, which improves performance of the resonators.

Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient ( α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (Δ Γ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around Δ Γ=0). But reverse of the case is found for energy coupling coefficient ( γ 0).

Dependence of gain and phase-shift on crystal parameters and pump intensity in unidirectional photorefractive ring resonators

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material’s cavity length (crystal length) and modulation ratio have also been studied.

Dark decay of holograms in photorefractive polymers

The decay of holograms stored in photorefractive polymer composites based on poly(N-vinyl-carbazole) with and without extrinsic deep traps is investigated. The photorefractive phase shift is identified as one of the key parameters determining the dark decay dynamics. This has important implications for all kinds of photorefractive imaging applications including holographic data storage. A trade off will be required between accepting a certain degree of hologram distortion due to two-beam coupling on the one hand and achieving high hologram stability during idle periods in the dark with the external field applied on the other.

Photorefractive properties and applications of polymer composites and fully functionalized polymethacrylates

We have studied the photorefractive properties of (2,4,7-trinitro-9-fluorenylidene)malononitrile (TNFM) sensitized poly( N-vinylcarbazole) (PVK)/ N-ethylcarbazole (ECZ) polymer composites doped with two structurally related chromophores. Characterization included four-wave mixing experiments, two-beam coupling and photoconductivity measurements at a wavelength of 780 nm. At an applied field of 48 V/μm, we have observed complete internal diffraction and gain coefficients exceeding 120 cm −1. A small alteration in the chromophore donor group substituents was used to tune the ionization potential of the dopant dye. This affected the grating build-up time and photorefractive phase shift. As an application, we demonstrate the operation of a photorefractive novelty filter using a 120-μm-thick sample. The performance of the polymer composites is compared to that of three newly synthesized polymethacrylates functionalized with carbazole, a dodecyl chain as an internal plasticizer and three different dyes. Here, we have observed net two-beam coupling gain and a diffraction efficiency of 60% at 58 V/μm.

Analytical modeling of two beam coupling during grating translation in photorefractive media

We present two analytical methods of solving the coupled wave equations related to two-wave mixing in a photorefractive medium in the case where the illuminating light pattern is rapidly translated with respect to a stationary photorefractive grating. Both methods lead to the same analytical expressions for the intensities of the transmitted beams and for the initial phase of their temporal oscillations. Our analytical expressions cannot, however, confirm earlier numerical and experimental results obtained by Grunnet-Jepsen et al. [Opt. Lett. 22 (1997) 874] regarding the photorefractive phase shift in photorefractive polymers.

Adaptive beam combining and interferometry with photorefractive quantum wells

We present a comprehensive study of excitonic electroabsorption and two-wave mixing in photorefractive quantum wells. By combining these two measurements, we are able to determine the internal grating writing efficiency for converting an external spatial light modulation into an internal space-charge field. The internal writing efficiency at a fringe spacing Λ=40 µm is found to be a decreasing function of applied field, varying from ξ=0.4 at low fields to 0.2 at 12 kV/cm. The two-wave mixing efficiency in the quantum wells exceeds 40% and is used for adaptive beam combining and laser-based ultrasound detection. The quantum wells balance the hot-electron-induced photorefractive phase shift with excitonic spectral phase to guarantee quadrature in homodyne detection of ultrasound-induced surface displacements. The ability to tune through multiple quadratures is demonstrated here for the first time to our knowledge. We derive a noise-equivalent surface displacement of 1.7×10-6 Å (W/Hz)1/2 at a field of 12 kV/cm and a fringe spacing of Λ=40 µm. This value is within a factor of 7 of the shot-noise limit of an ideal interferometer.

Effect of the chromophore donor group and ferrocene doping on the dynamic range, gain, and phase shift in photorefractive polymers

We have studied the photorefractive performance of poly(N-vinylcarbazole)-based composites doped with various concentrations of two structurally related dipolar chromophores, at 780 nm. The two chromophores had different electron donor groups, N,N-diethylamine and julolidine, respectively. Complete internal diffraction and gain coefficients >130 cm−1 were obtained for polymers doped with these chromophores. The polymers prepared with the chromophore having the strongest electron donor group, the julolidine group, had the largest dynamic range, but proved to be slower and had a smaller photorefractive phase shift.

Influence of the chromophore ionization potential on speed and magnitude of photorefractive effects in poly(N-vinylcarbazole) based polymer composites

We report on the synthesis of three highly polar chromophores and their use as dopants in poly(N-vinylcarbazole) based photorefractive polymer composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile. Small alterations in the amino donor group substituents were used to tune the dye’s ionization potential (IP) by 0.2 eV. At 780 nm, 5 °C above the glass transition temperature (Tg), and with an applied field of 59 V/μm, we observed complete internal diffraction and a gain coefficient of 167 cm−1. In this temperature range, diffraction efficiency, gain coefficient, and photorefractive phase shift were found to correlate with the chromophore IP. At 20 °C below Tg, the contribution from birefringence to the index modulation is insignificant, and the speed of the photorefractive effect correlates well with the chromophore IP. Analysis of the results suggests that the space–charge field is influenced by the chromophore IP.

Effect of plasticizer and temperature on the photorefractive phase shift in fully functionalized polymethacrylates

We have analyzed the evolution of the photorefractive phase shift and the photoconductivity in three fully functionalized photorefractive polymethacrylates with increasing temperature and plasticizer concentration. Apart from a strong increase in refractive index modulation amplitude, the polymers show a larger phase shift and photoconductivity as the measurement temperature is raised. When the measurement temperature is kept at 21 °C, the photorefractive performance can be improved by reducing the glass transition temperature of the polymers by adding an external plasticizer. Two types of plasticizer were used. When doped with 10 or 20 wt% of an inert plasticizer (IP), diffraction efficiencies and gain coefficients are improved substantially. Due to a dilution of the charge transporting groups, however, the photoconductivities and the phase shifts start to decrease when more than 10 wt% of inert plasticizer is added. A detailed analysis of this behaviour is presented. When the carbazole-functionalized copolymers with carbazole as the only charge transporting group are doped with 20 wt% of N-ethylcarbazole, the concentration of the charge transport molecules is increased. Together with the lowering of Tg, this produces a larger phase shift. In all experiments, a good correlation between photoconductivity and photorefractive phase shift was observed.

Nanometer-Au-particle-enhanced photorefractivity in a polymer composite

Doped with nanometer Au particles, a low-Tg photorefractive polymer composite, poly(N-vinylcarbazole):2,4,7-trinitro-9-fluorenone:4-(dicyanovinyl-N,N-diethylaniline), exhibited an effective enhancement on its photorefractivity. Measurements on two-beam coupling (TBC) as well as four-wave mixing were carried out at 633 nm wavelength. At an applied electric field of 118 V/μm, TBC coefficient as high as 206 cm−1 was obtained in the sample doped with Au particles, while only 152 cm−1 in the sample without Au particles. The measurements on the effective electro-optic coefficient and the photorefractive phase shift for two samples with and without doping Au particles were performed, respectively. The observations of distinct difference on the photorefractive phase shift and no difference on the effective electro-optic coefficient implied that enhancement on the photorefractivity was due to the increment of the density of the effective trap center by doping Au particles.

Two-wave-mixing dynamics and nonlinear hot-electron transport in transverse-geometry photorefractive quantum wells studied by moving gratings

The photorefractive response to an applied electric field is measured in a photorefractive quantum well, providing evidence in favor of the nonlinear transport in the device due to the hot electrons. The reduced mobility of the hot electrons limits the drift length, and thereby limits fringe overshoot. Thus the nonlinear transport prevents the slowing down of the grating writing rate for increasing fields which is common in bulk photorefractives. The photorefractive phase shift in transverse-field photorefractive quantum wells is measured as a function of the frequency offset between two laser writing beams that generate moving gratings. The two-wave mixing passes through a maximum at an optimum frequency which depends on the magnitude and the sign of the applied dc electric field. The phase shift associated with the moving grating adds or subtracts from the static phase shift induced by hot-electron transport in the semiconductor quantum wells, depending on the sign of the field and the sign of the dominant photocarriers. We observe a linear relationship between the roll-off frequency and the power of the writing beams.

Photorefractive beam coupling between orthogonally polarized light beams by linear dichroism in Cu-doped potassium sodium strontium barium niobate

Two-beam coupling between orthogonally polarized waves is demonstrated by use of linear dichroism in Cu-doped potassium sodium strontium barium niobate. A maximum coupling gain coefficient of approximately 4 cm-1 is obtained at a grating spacing of 1 µm and a wavelength of 514.5 nm, where linear dichroism is moderate. The experimental results are compared with a theoretical model that allows a photorefractive grating to have an arbitrary phase shift with respect to an intensity-interference pattern. Fitting results indicate that the grating is not 90°-phase-shifted under open-circuit conditions. The contribution of the bulk photovoltaic field to the photorefractive phase shift is discussed.

Laser-based ultrasound detection using photorefractive quantum wells

We demonstrate a laser-based adaptive ultrasonic homodyne receiver using dynamic holography in AlGaAs/GaAs photorefractive multiple quantum wells. The dynamic hologram acts as an adaptive beamsplitter that compensates wavefront distortions in the presence of speckle and requires no path-length stabilization. The photorefractive quantum wells have the unique ability to achieve maximum linear homodyne detection regardless of the value of the photorefractive phase shift by tuning the excitonic spectral phase. We achieve a root mean square noise-equivalent surface displacement of 6.7×10−7 Å(W/Hz)1/2.

Measurement of the photorefractive grating phase shift in a polymer by an ac phase-modulation technique

The complex coupling constant of a photorefractive polymer was measured as a function of an applied electric field by use of a modified ac phase modulation technique. We determined that both a photorefractive index grating and a nonphotorefractive absorption grating were present. The electric field dependencies of the amplitude and the phase of the photorefractive gain coefficient were accurately described by standard photorefractive theory. The accuracy of the photorefractive phase shift as measured by this phase-modulation technique was ±1° near phase shifts of 90° and ±3° near phase shifts of 45°.

Off-Bragg analysis of the diffraction efficiency of reflection photorefractive holograms

Formulas are given for the calculation of diffraction efficiency of reflection-type gratings recorded in a photorefractive medium. The analysis incorporates the coupled-wave theory that was developed for photorefractive hologram gratings. This analysis takes into account grating slant with respect to the medium surface, light absorption during reconstruction, any incident angle of the reference beam, and any photorefractive phase shift. General solutions for signal and reference wave functions are given in a closed-form expression by use of a hypergeometric function. The optimum media parameters and recording conditions for high diffraction efficiency are obtained by the derived formulas. The diffraction properties for off-Bragg conditions are also discussed.

Systematics of two-wave mixing in a photorefractive polymer

The high-performance photorefractive polymer composite PVK:PDCST:BBP:C60 is investigated in detail by use of optical two-wave mixing characterization measurements in conjunction with the grating translation technique for determination of the photorefractive phase shift. A large effective trap density of Neff=1.5×1017 cm-3 is estimated from the dependence of the phase shift on the grating spacing and the applied electric field. The theory of orientational enhancement is successfully used to explain the observed photorefractive response, and in this low-glass-transition temperature system the modulation of the refractive index is shown to stem primarily from the spatial modulation of the birefringence.