Dynamic holography in photorefractive quantum
well heterostructures has opened a wide new range of optical applications
that utilize the ability of the hologram to adapt to environmental
disturbances or to changes in the signal of interest. Examples
of applications include three-dimensional imaging through turbid
media, femtosecond pulse processing and compensation, and adaptive
laser-based ultrasound detection.
1 INTRODUCTION
Holograms that can change in time and adapt to environmental disturbances have interesting and important applications in diverse areas such as ultrafast femtosecond holography and laser-based ultrasound receivers. The key to adaptive performance is the ability of the holographic recording process to track slow changes, such as thermal fluctuations in the optical path, or mechanical vibrations. Low-frequency noise is adaptively compensated by the adapting hologram, while high-frequency signals are passed through to the detector.
A classic example of an incessant problem in optics is the stability
of an interferometer. Great efforts are usually needed to shield
a Michelson interferometer from vibrations and thermal drifts.
For critical situations, the interferometer may need to be actively
stabilized, such as by a feed-back circuit that drives a piezoelectric
mirror to maintain constant phase through the interferometer.
However, no active stabilization is necessary with an adaptive
hologram acting as a beam combiner in the interferometer. Any
changing path lengths are simply compensated by a corresponding
shift in the interference fringes of the hologram.
We have developed and are now applying a versatile and sensitive
class of dynamic holographic materials called photorefractive
quantum wells (PRQW) to several applications [1]. Photorefractive
quantum wells and heterostructures rank among the highest sensitivity
nonlinear optical materials currently known. They can form fully
developed holograms using only microwatts per cm2,
and can adapt to changing intensity patterns at rates no slower
than one kilohertz. These intensities and rates open up wide
possibilities for uses of dynamic holography in optical information
processing.
2 PHYSICS OF PHOTOREFRACTIVE QUANTUM WELLS
The process of photorefractive dynamic holography draws from a cross-section of solid-state phenomena including transport physics, optical physics and defect physics of semiconductors. The photorefractive effect at its simplest level can be described as the transformation of the spatial gradient of a light intensity pattern into a change in the optical properties of the material. Photorefractive materials and effects are ubiquitous. Any high-resistivity material (such as insulators or semiconductors) with an electro-optic effect (all materials have either a first-order or second-order electro-optic effect) that contain high concentrations of deep charge-carrier traps will exhibit photorefractivity.
The process begins with two coherent laser beams that form interference patterns of bright and dark fringes inside a photorefractive medium. The light is absorbed in the bright fringes, generating free charge carriers. These are free to drift or diffuse to the dark fringes where they are trapped at deep level defects. The transfer of charge from the bright fringes to the dark fringes produces a space-charge that generates a space-charge electric field. This electric field then modifies the optical properties of the material through the electro-optic effect. The end result is an optical diffraction grating that has the identical pattern as the light interference pattern. This diffraction grating is the physical hologram.
Even Kodak film can record a hologram, but what makes photorefractive holography special is that the holograms have a response rate determined by the dielectric relaxation of the space-charge. Therefore they can change and track shifting interference patterns up to the relaxation rate of the hologram. This dynamic property gives the photorefractive holograms their adaptability.
Photorefractive quantum wells take advantage of quantum-confined excitons in combination with high carrier mobilities to produce the most sensitive photorefractive material currently known. These devices have been developed over the past 8 years at Purdue. The quantum-confined excitons have excellent electroabsorption properties with strong field-induced absorption changes up to 5000 cm-1. These are accompanied by changes in the refractive index that approach 1%. These strong electro-optic effects produce strong diffraction gratings. There are three basic photorefractive quantum well geometries, depending on the direction of the applied electric field and the orientation of the interference grating vector, shown in Fig. 1. These consist of a transverse transmission geometry [2], a longitudinal transmission geometry [3], and a reflection geometry that relies on volume gratings [4].
The reliance of the photorefractive effect on charge transport
can have unexpected and surprising physical consequences. In
GaAs/AlGaAs multiple quantum well structures there is an effect
that is well-known in semiconductor physics called the Gunn effect.
This arises from electron velocity saturation due to intervalley
scattering from the direct to the indirect conduction band minima.
The Gunn effect can only occur in highly conductive materials.
We discovered the semi-insulating consequence of the Gunn effect
in the photorefractive quantum wells. Through experiments by
Qingnan Wang and later by Robert Brubaker [5, 6], we discovered
that the velocity saturation caused a spatial shift of the photorefractive
gratings relative to the interference pattern. In extreme cases
(high applied electric fields and short fringe spacings) the spatial
shift can be one quarter of a fringe spacing. This shift has
important consequences, allowing one of the laser beams to gain
energy at the expense of the other in a process of nonreciprocal
energy transfer. This is one of the rare instances in physics
of optical amplification without stimulated emission.
3. APPLIED PHYSICS
One of the most exciting aspects of this research are the growing
number of diverse applications. Three of the most promising applications
are optical holography to perform 3-D imaging through turbid media,
ultrafast femtosecond pulse shaping and compensation, and adaptive
laser-based
Fig. 1 The three photorefractive quantum well geometries defined
by the direction of the applied electric field (Franz-Keldysh
effect or Stark effect) and by the orientation of the grating
vector (in the plane or perpendicular to the plane).
ultrasound sensing. Although these applications are quite different,
they all are based on dynamic holography and require a highly
sensitive and dynamic holographic film. The special ability of
the holograms to change and adapt to the optical system and its
environment make these applications qualitatively different than
most other holographic applications.
3.1 Three-Dimensional Biomedical Imaging with Light
The first of the three applications has potential for biomedical imaging. The use of light at optical frequencies has been a long-standing goal for biomedical imaging. Optical photons are non-ionizing, and therefore have always represented an attractive alternative to x-ray imaging. In addition, optical wavelengths are near one micron, providing excellent spatial resolution. Unfortunately, biological tissues are turbid media that strongly scatter light, preventing penetration by more than one or two mean free scattering lengths.
An important new development in optical imaging through tissue is called optical coherence tomography (OCT). This technique uses optical coherence as a means to differentiate between scattered light and light that has propagated unimpeded through the tissue. The unimpeded light remains coherent with the incident light. Therefore, in a simple interferometer with a reference beam, the signal buried in scattered light can be extracted by detecting interference fringes. A difficulty with OCT is the need to scan the interferometer over a specimen position by position.
We have taken a related approach that can acquire a full video
frame, imaging into a turbid medium without the need to scan spatially.
We do this by allowing the unimpeded light to form a hologram
with the reference beam. The hologram is only written by the
light that bears the image, while the scattered light writes no
hologram. When the hologram is read out by a read laser beam,
the image can be seen without scattered background and recorded
directly to video. We have already demonstrated the ability to
acquire full-frame images at a depth of 13 mean free paths (compared
with the usual one to two for direct visual inspection) [7], and
project that with refinements we should be able to image as deep
as 22 mean free paths. This imaging depth would be sufficient
to fully image through human skin tissue as well as into the walls
of the esophagus and colon to allow subsurface detection of carcinomas
that are invisible to visual inspection. This work is being pursued
in our collaboration with researchers at the Imperial College
of Science and Medicine in London.
3.2 Optical Manipulation of Time at Picosecond Scales
Time is perhaps the most fundamental of all physical coordinates. It is the only coordinate that can have only one direction of motion -- into the future. But time also is a concept that enters symmetrically into the Fourier description of wave propagation. This may be a mathematical artifact that does not actually allow time to go backwards, but it can be used to perform interesting operations on time associated with an optical pulse.
Ultrafast optical pulses with durations of only 100 femtoseconds are routinely generated using mode-locked Ti:Sapphire lasers. Pulses of this duration have approximately 10 nm bandwidths, which are easily accessible to spectroscopic investigation and manipulation. A device called a femtosecond pulse shaper [8] is a simple spectrometer that decomposes a pulse into its spectral components, manipulates the phase and amplitude of the components, then puts them back together again into a shaped pulse. Nearly arbitrary pulse shapes are possible, limited only by details of the spectral resolution of the spectrometer and the spectral width of the incident pulse. This device performs as a femtosecond function generator. A variation on this concept uses a dynamic holographic material to record the holographic spectrum of the original pulse. This spectral hologram contains all the spectral phase information associated with the pulse. In the spectral domain of a fast optical pulse, time is imprinted on the pulse spectrum as simply a linear phase dependence. If the pulse is delayed in time, then the hologram records a linear phase dependence that is proportional to the delay time.
A well-known aspect of holographic gratings is the presence of conjugate gratings that generate a phase-conjugate optical signal. This phase-conjugate signal carries all the information of the original pulse, but with the conjugate phase. By diffracting a time-delayed pulse off the recorded hologram into the conjugate diffraction order, the linear phase is exactly compensated. When the pulse is reconstructed out of its spectral components, it has no delay.
This operation is shown in Fig. 2 using photorefractive quantum wells as the holographic medium in the pulse shaper. The input signal pulse is delayed relative to the reference. But at the output, the diffracted signal pulse is temporally coincident with the reference pulse. By simply recording the phase of the delayed pulse, and reading the hologram with an equally delayed pulse, the pulse "jumps forward in time" to exit the pulse shaper at the same time as the reference.
Fig. 2 Time-delay compensation using spectral holography of fsec
pulses. The delayed probe pulse is advanced when its linear phase
is compensated by the dynamic holography.
This "jump forward" can be as much as 30 psec -- a much longer time than the duration of the pulse itself. However, no violation of causality is needed to give a classical explanation of this phenomenon. An analysis of the hologram recording and readout process can identify a change in the path length caused by the linear phase recorded in the hologram.
The importance of this demonstration arises from the adaptability
of the hologram. In practical optical systems, the time delay
can be drifting in time, for instance in a fiber-optic telecommunication
system due to thermal expansion and contraction or fluctuations
of the fiber length. For time-slot communication detection, these
time drifts could limit the data density on the fiber. The photorefractive
hologram in the pulse shaper can adaptively track the changing
time delays, always producing a perfectly timed output pulse.
Other related applications of the photorefractive quantum well
have been demonstrated, such as adaptive dispersion compensation
when fiber dispersion changes and drifts in time. Additional
applications are being pursued.
3.3 Self-Adaptive Laser-Based Ultrasound Detection
One of the simplest and potentially most important of the applications for photorefractive quantum wells is in compensated laser-based ultrasound detection. The adaptability of the photorefractive holograms make them ideal for compensating phase drifts in an interferometer. The basic principal of adaptive interferometric beam combining is shown in Fig. 3. The PRQW device operates in a mode known as two-wave mixing which combines the two beams by diffracting each off the grating into the direction of the other beam. The rules of holographic reconstruction guarantees that the co-propagating wavefronts after the adaptive beam combiner have identical phase. This turns the distorted wavefront into a plane wave in the direction of the reference beam.
In a laser-based ultrasound application, the signal beam reflects
off a specimen that is vibrating at ultrasonic frequencies. The
vibrations are usually induced as a means to perform nondestructive
testing of the specimen. The specimen, however, is typically
not specular and produces a badly speckled and distorted return
signal. In addition, environmental conditions can cause low frequency
drifts of the phase in the interferometer. The adaptive beam
combiner removes all these problems, and allows only the high
frequency ultrasound to co-propagate with the reference beam.
Because of the surface vibration, the signal beam has a phase
Fig. 3 Adaptive beam combining using a photorefractive quantum
well for homodyne receiving of laser-based ultrasound.
modulation that is observed as intensity variations at the photodetector.
A key component of this form of adaptive homodyne receiver is the need to have a linear intensity dependence on phase excursion in the signal beam. This condition is called quadrature. Quadrature only occurs when the signal and reference beams are 90o out of phase. While this condition is often difficult to achieve in traditional interferometers, usually requiring active stabilization, the photorefractive quantum wells provide a mechanism that guarantees the quadrature condition. This is because the real and imaginary parts of the photorefractive grating (the electrorefraction and the electroabsorption) impose an extra phase on the diffracted light. By simply tuning the wavelength of the laser, perfect quadrature can be achieved.
This tuning to quadrature is illustrated in the data in Fig.
4. This graph shows the noise-equivalent surface displacement
(NESD) for which the signal-to-noise ratio is equal to unity for
a specified bandwidth and laser intensity. Small values of NESD
are better. The highest sensitivity occurs at quadrature, which
for this specific photorefractive quantum well is near a wavelength
of 838 nm. The poles in the data and theoretical fit are exactly
out of quadrature, for which no first-harmonic homodyne signal
is detected. Our photorefractive quantum well devices have shown
the highest sensitivity for laser-based adaptive homodyne detection.
Our performance is only a factor of three from the quantum noise
limit for a perfect interferometer. Efforts are under way for
the eventual commercialization of these devices in laser-based
ultrasound systems.
Fig. 4 Noise-equivalent surface displacement for ultrasound detection
using the photorefractive quantum well adaptive beam combiner
[9].
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