CThE4 2005 Conference on Lasers & Electro-Optics (CLEO)

Optimizing Two-Wave Mixing Efficiency inPhotorefractive Quantum Wells by Selective Angle

TuningM. Gramlich, S. Balasubramanian, and P. Yu

Department ofPhysics andAstronomy, University ofMissouri-Columbia, Columbia, MO 65211mwzy63(&,mizzoui.edu

D. D. NolteDepartment ofPhysics, Purdue University, West Lafayette, IN 47907-1396

M. R. MellochDepartment ofElectrical Engineering, Purdue University, West Lafayette, IN 47907-1396

Abstract: We observe that the two-wave mixing efficiency in photorefractiveAlGaAs/GaAs quantum wells (PRQW) can be controlled by rotating the sample to gofrom Raman-Nath to the Bragg regime. This has applications in PRQWs likeInGaAs/GaAs.OCIS Codes: (090.2880) Holographic interferometry; (190.5970) Semiconductor nonlinear optics includingMQW

Fringe spacing plays an important role in holographic optical coherence imaging (OCI) based onphotorefractive multiple quantum well (PRQW) devices. Holographic OCI has showed potentialapplications in biomedical imaging and ultrasound detection. Recent experiments demonstrated that theholographic OCI can be used to record full-frame depth-resolved images through tumor tissue, withoutcomputed tomography, allowing real-time video "fly-through" under interactive control of an operator[1,2]. In the holographic OCI system, two beams, one from the signal and another from the reference, writefringes on the device to produce wave mixing. Different fringe spacing can be selected by adjusting thecross angle between the two beams. The fringe spacing has several impacts on the holographic coherencedomain imaging. One is the limitation of lateral resolution. To increase the lateral resolution very smallerfringe spacing is desired for the system. Another is speckle reduction where the fringe spacing is requiredto be smaller than the speckle size. In addition to the improvement of resolution and speckle reduction,small fringe spacing can also influence the diffraction efficiency.In PRQW structures, the diffraction grating is finite in the growth direction due to the limited thickness ofthe device, and the fringe spacing is typically larger than the film thickness [3]. The resulting diffractionfrom this fringe spacing is in the Raman-Nath regime. However, if the fringe spacing is comparable orsmaller than the film thickness while the incident beams are tilted to the normal direction of the devicesurface, Bragg diffraction may occur and diffraction efficient will be enhanced at several incident angles.Determination of the diffraction regime for particular fringe spacing can be described by the equation:

27rALQ= 2 (1)nA~

where A is the wavelength, n is the refractive index, L is the film thickness, and A is the fringe spacing[4,5]. For Q<1 the device operates in the Raman-Nath regime while for Q>l the device is within the Braggregime [3]. When the two waves were tuned to the excitonic transition and mixing on the PRQW, there is anon-reciprocal energy transfer so that one beam gains energy from the other. This energy transfer isexplained by the equation:

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CThE4 2005 Conference on Lasers & Electro-Optics (CLEO)

r=1+ 9 (4iaLSftUp+ am,L cosqO) 2I+13 AcOS,s9 pcOs,' (2)

where a,,, is the relative absorption grating, na is the relative refractive index grating, ,B is the mixed tounmixed intensity ratio, 69 is the internal angle, and o is the photorefractive phase shift.

In this paper we report how the diffraction efficiency gets enhanced by adjusting the sample angle to tunethe system from Raman-Nath to Bragg regime. Degenerate two-wave mixing experiments were carried outin a modified Michelson interferometer configuration. The main components of the setup include the laserdiode source (Hitachi HL8325G), the PRQW, beam splitters, ND filters, and a source to provide anexternal transverse modulated electric field to the PRQW. The laser diode is temperature tuned through theexcitonic resonance of the quantum wells. We used a photorefractive AlGaAs/GaAs semi-insulatingquantum wells that is identical to the one used in reference 3. The non-reciprocal energy transfer is detectedby chopping the signal beam and detecting on the reference beam using a photodiode (ThorLabs DET 110)and a lock-in amplifier. Based on the non-reciprocal energy transfer equation (2), a beam intensity ratio (f3= ISigna,/IReference) of 1:10 is chosen for optimum mixing efficiency. Excessive joule heating is avoided bysuitably modulating the applied electric field. A transverse electric field of 1OkV/cm at a 40% duty cycleapplied in the positive direction minimized the joule heating in our sample without reducing mixingefficiency. The sample is mounted so that the sample angle, defined as the angle made by the in-planegrating vector to the optic axis, can be selected to probe different fringe spacings, coupled with the rangeavailable from the incoming beam separations. The mixing experiments discussed here were done at twodifferent sample angles of 30° and 45°. For each sample angle, different fringe spacings were achieved withdifferent angular separations between the mixing beams ranging from 5.710 to 38.75°. With a sample angleof 300 the fringe spacing probed ranged from 3.58 gm to 0.45 pm and with 450 the fringe spacing probedranged from 2.92pm to 0.37um.

Figure 1 shows two-wave mixing efficiency as a function of fringe spacing for the two incident angles. Bychanging the fringe spacing one can obtain several maximum diffraction efficiencies. This is because byquasi-Bragg matching the grating vector in the sample plane to the incident beams, optimum two-beamcoupling is achieved. The diffraction efficiency of a large incident angle (dashed line in figure 1) is smallerthan the one of smaller incident angle (solid line in figure 1) at the cross angle between 5 to 25 degree.When the cross angle is larger than 30 degree, the diffraction efficiency reverses between the two curves.This is especially useful to optimize mixing efficiency of the PRQW device for the holographic OCIapplications. An example is to apply this result to InGaAs/GaAs PRQW where inherent strain effects limitthe efficiency.

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CThE4 2005 Conference on Lasers & Electro-Optics (CLEO)

O._.

. )

aj)

0.14

0.12

0.10

0.08

0.06

0.04

0.02

0.000 10 20 30 40 50

Angle between two beams (degree)

Figure 1. Two wave mixing as a finction of fringe spacing for two incident angles.References:1. P. Yu, M. Mustata, J. J. Turek, P. M. W. French, M. R. Melloch, and D. D. Nolte, "Holographic Optical Coherence Imaging of

Tumor Spheroids", App. Phys. Lett., vol. 83, 575, 2003.2. P. Yu, L. Peng, D. D. Nolte, and M. R. Melloch, "Ultrasound detection through turbid media", Opt. Lette., vol.28, 819, 2003.3. D. D. Nolte, "Semi-insulating semiconductor heterostructures: Optoelectronic properties and applications," J. Appl. Phys., vol.

85, 6259, 1999.4. M. Chang and N. George, "Holographic Dielectric Grating: Theory and Practice", Appl. Opt., vol. 9, 713, 1 970.5. M. G. Moharam and L. Young, "Criterion for Bragg and Raman-Nath diffraction regimes", Appl. Opt., vol. 17, 1757, 1978.

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