Holography is the only truly three-dimensional imaging method available, and MATLAB has become the programming language of choice for engineering and physics students. Whereas most books solely address the theory behind these 3D imaging techniques, this monograph concentrates on the exact code needed to perform complex mathematical and physical operations. The text and the included CD-ROM spare students and researchers from the tedium of programming complex equations so that they can focus on their experiments instead. Topics include a brief introduction to the history, types, and materials of holography; the basic principles of analog and digital holography; a detailed explanation of famous fringe-deciphering techniques for holographic interferometry; holographic and non-holographic 3D display technologies; and cutting-edge concepts such as compressive, coherence, nonlinear, and polarization holography.
The transfer matrix method is used to analyze induced reflection gratings in photorefractive iron doped lithium niobate in a self-pumped configuration. The optical field distribution and the induced refractive index distributions inside the material are computed, and the overall transmission and reflection are determined for different orientations of the c-axis. Numerical simulations are compared with experimental results.
In earlier work, the transfer matrix method (TMM) and the angular plane wave spectrum method (APWS) have
been used to analyze plane wave and beam propagation in a multilayer structure consisting of positive index and
negative index materials. In this paper, we demonstrate the use the complex Poynting theorem (CPT) to validate
numerical calculations by the TMM and APWS methods. Application of CPT also gives physical insight into
the power balance inside such structures which may possess complex permittivities and permeabilities, and have
propagating and nonpropagating waves.
The transfer matrix method (TMM) has been used to analyze plane wave and beam propagation through linear
photonic bandgap structures. Here, we apply TMM to determine the exact spatial behavior of TE and TM waves
in periodic refractive index structures of arbitrary thickness. First, we extend the TMM approach to analyze
plane wave propagation through Kerr type nonlinear media. Secondly, we analyze second harmonic fields in a
1D nonlinear photonic crystal for arbitrary angle of incidence of the fundamental plane wave. This allows us to
construct the overall transfer matrix of nonlinear waves for the whole nonlinear optical structure from all the
individual layer transfer matrices. We extend this method to analyze the effect of second order nonlinearity to
beam propagation by applying TMM to the angular spectral components of the beam(s).
Metamaterials exhibiting a negative index of refraction in the visible are of recent interest due to many possible
applications including cloaking and perfect lensing. Nanoparticle dispersed metamaterials have been researched due to
their flexibility in operating frequency, electronic tunability, ease of fabrication and low cost. We propose sputtered
binary polaritronic-plasmonic nanoparticles as candidates for metamaterials. Specifically, we show that co-sputtered SiC
and Ag nanoparticles are used to obtain a negative index in the visible. Experimental verification of the negative
refractive index include the z-scan technique for measurement of the linear refractive index, phase and group velocity
measurements using a double Michelson interferometer, and surface plasmon resonance measurements for s and p
polarizations for finding the effective permeability and permittivity. Through numerical simulations, we show that our
nanoparticle mixture can yield near-field super-resolution for both TE and TM polarizations.
The development of electromagnetic (EM) metamaterials for perfect lensing and optical cloaking has given rise to
novel multilayer bandgap structures using stacks of positive and negative index materials. Propagation of a
collection of TE or TM plane waves, comprising the angular plane wave spectrum, through such structures is
analyzed by using the transfer matrix method (TMM) on every plane wave component. Results obtained from this
TMM approach for a Gaussian spectrum are compared with those using standard FEM techniques.
We propose tunable single-layer and multi-layer (periodic and with defect) structures comprising nanoparticle dispersed
metamaterials in suitable hosts, including adaptive coded aperture constructs, for possible Adaptive Coded Aperture
Imaging (ACAI) applications such as in microbolometry, pressure/temperature sensors, and directed energy transfer,
over a wide frequency range, from visible to terahertz. These structures are easy to fabricate, are low-cost and tunable,
and offer enhanced functionality, such as perfect absorption (in the case of bolometry) and low cross-talk (for sensors).
Properties of the nanoparticle dispersed metamaterial are determined using effective medium theory.
We theoretically explored the feasibility of a tunable metamaterial using binary as well as core-shell nanoparticle dispersed liquid crystal cells in the infrared and optical regimes. Owing to the spatial variation of the permittivity of the liquid crystal host upon the application of a bias voltage, the host was decomposed into a layered medium and the effective refractive index recalculated for each layer due to the distribution of polaritonic and plasmonic nanoparticles. The scattering, extinction, and absorption of such a nanoparticle dispersed liquid crystal cell were also found. Depending on the applied voltage bias across the liquid crystal host, the types of nanoparticles used, and their radii and volume-filling fractions in the liquid crystal host, near-zero as well as negative index of refraction can be obtained over a range of frequencies, according to the effective medium theory.
Propagation of a monochromatic Gaussian beam through a stack of alternating layers of positive-refractive-index
dielectrics and negative-refractive-index metamaterials is analyzed using paraxial ray-optics approach.
Expressions for the change of the spot-size of the Gaussian beam are derived. Sensors for measuring parameters
that affect the thickness or refractive index of the metamaterials can be developed based on the change of the
spot-size.
Metamaterials with tunable properties are of great importance due to potential applications in super-resolution lensing
and sensors. In this paper we study the feasibility of the fabrication of a metamaterial using binary nanoparticle-dispersed
liquid crystal cell (NDLCC). Depending on the angle between the director axis of the LCC and the incident
beam, types, radii, and volume filling fractions of the nanoparticles, a negative index of refraction cell is obtained in a
certain range of frequencies. The effective index of refraction is calculated using the effective medium theory. The
scattering, extinction, and absorption of such a NDLCC cell is also found. Finally, the influence of the various
parameters to obtain such a negative index metamaterial has been investigated.
Transmission and reflection spectra of periodic and random stacks comprising positive index materials and
metamaterials have been extensively studied. In this paper we investigate the effectiveness of periodic stacks of
PIM/NIM for use as a sensor. The transfer matrix method is used to find the transmittance and reflectance.
Differences between the zero average refractive index bandgap and Bragg bandgap are illustrated. It is shown how
these bandgaps can be used as the basis for designing sensors with minimal cross-sensitivity.
In this work, we illustrate a framework that can model propagation through a dispersive, homogeneous periodic/quasiperiodic/
randomly perturbed, layer lengths in a multilayered structure of positive and negative index materials. We
achieve this by using a transfer matrix-based multilayered approach. In the quasi-periodic case the layers lengths vary
according to a predetermined function like a sinusoidal function for example. In the random case we use zero mean
random variables as the perturbation around a nominal layer length of positive and negative index materials. We also
use the trace of the transfer matrix to determine the limiting case of the transmittance when the number of periods
become infinitely large, and determine the locations of the bandgaps in the multi-layered structure. This helps in
reducing the calculations since only one unit cell is needed. Plane wave propagation is investigated, and aggregated
transmittivity is calculated in the different cases. Finally we study wave localization in the randomly perturbed
structure and compare it with the periodic case.
Metamaterials, which maybe the answer to "perfect lensing", are often fabricated as a periodic array of elements which
exhibit negative refractive index or negative permeability/permittivity. In this work, we outline and illustrate a
framework that can model propagation through a homogeneous and random mixture of positive and negative index
materials. We achieve this by using a matrix-based multilayered approach, and a random sequence of positive and
negative index materials, and by incorporating all possible combinations of such layers. Plane wave propagation is
investigated, and aggregated transmittivity is calculated. We show that near-zero net refractive index maybe achieved
through a random homogeneous mixture of positive and negative index materials.
In this work we theoretically model continuous and pulse wave propagation using the underlying dispersion relations. We also derive the dispersion relations of the underlying wave equations based on the real and imaginary parts of the propagation constant which are related through Hilbert transformation to ensure causality. Also, in this paper we show that by using a model of photorefractive two wave coupling, we can derive the dispersion relation for pulsed propagation and coupling in a diffusion dominated photorefractive material. We note that the dispersion relation we have found in photorefractive material also obeys the Hilbert transform property. Finally, we show that the group velocity of light can be slowed down by means of phase coupling in the photorefractive two-wave mixing
process.
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