George Nehmetallah

Fully automated, high speed, tomographic phase object reconstruction using the transport of intensity equation in transmission and reflection configurations

While traditional transport of intensity equation (TIE) based phase retrieval of a phase object is performed through axial translation of the CCD, in this work a tunable lens TIE is employed in both transmission and reflection configurations. These configurations are extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by a custom fabricated rotating assembly of the phase object. Synchronization circuitry is developed to control the CCD camera and the Arduino board, which in its turn controls the tunable lens and the stepper motor to automate the tomographic reconstruction process. Finally, a MATLAB based user friendly graphical user interface is developed to control the whole system and perform tomographic reconstruction using both multiplicative and inverse radon based techniques.

Co-sputtered SiC + Ag nanomixtures as visible wavelength negative index metamaterials

The fabrication and characterization of a novel metamaterial that shows negative index in the visible (blue) is reported. The real part of the negative index of this metamaterial at 405 nm, comprising co-sputtered SiC + Ag nanoparticle mixture on a glass substrate, is deduced from results of double Michelson interferometry setup which shows a negative phase delay. It is numerically verified that this metamaterial can yield near-field super-resolution imaging for both TE and TM polarizations.

Accurate quantitative phase digital holographic microscopy with single- and multiple-wavelength telecentric and nontelecentric configurations.

In this work, we investigate, both theoretically and experimentally, single-wavelength and multiwavelength digital holographic microscopy (DHM) using telecentric and nontelecentric configurations in transmission and reflection modes. A single-wavelength telecentric imaging system in DHM was originally proposed to circumvent the residual parabolic phase distortion due to the microscope objective (MO) in standard nontelecentric DHM configurations. However, telecentric configurations cannot compensate for higher order phase aberrations. As an extension to the telecentric and nontelecentric arrangements in single-wavelength DHM (SW-DHM), we propose multiple-wavelength telecentric DHM (MW-TDHM) in reflection and transmission modes. The advantages of MW-TDHM configurations are to extend the vertical measurement range without phase ambiguity and optically remove the parabolic phase distortion caused by the MO in traditional MW-DHM. These configurations eliminate the need for a second reference hologram to subtract the two-phase maps and make digital automatic aberration compensation easier to apply compared to nontelecentric configurations. We also discuss a reconstruction algorithm that eliminates the zero-order and virtual images using spatial filtering and another algorithm that minimizes the intensity of fluctuations using apodization. In addition, we employ two polynomial models using 2D surface fitting to compensate digitally for chromatic aberration (in the multiwavelength case) and for higher order phase aberrations. A custom-developed user-friendly graphical user interface is employed to automate the reconstruction processes for all configurations. Finally, TDHM is used to visualize cells from the highly invasive MDA-MB-231 cultured breast cancer cells.

Holographic Volume Displacement Calculations via Multiwavelength Digital Holography

In this work multiwavelength digital holography is applied to calculate the volume displacement of various topographic surface features. To accurately measure the volume displacement of macroscopic features, long synthetic wavelengths up to several millimeters are generated using tunable IR laser sources. Practical methods of implementation are considered, including geometric effects of both Michelson and Mach-Zehnder recording configurations and error due to wavelength selection.

Spatial and spatiotemporal solitary waves and their stabilization in nonlinear negative index materials

Starting from a simple dispersion relation for negative index materials and a heuristic nonlinear Klein-Gordon-type extension, we derive the evolution equations for the envelopes of beams and spatiotemporal pulses in nonlinear dispersive negative index media. Using existing numerical methods, based on fast Fourier-Bessel transforms, we study the stability of the solitary wave solutions. Nonlinearity and dispersion management are then incorporated to find stable solutions of the underlying partial differential equations.

Noninterferometric tomographic reconstruction of 3D static and dynamic phase and amplitude objects

Non-interferometric intensity based methods of phase retrieval such as the transport of intensity (TI) employs a simple experimental technique for amplitude and phase reconstruction of a static object by capturing several diffraction patterns at different observation planes. The purpose of this work is to numerically and experimentally extend this technique to moving phase and amplitude objects. The simulation part is done based on solving the TI equation (TIE) using the Fast Fourier Transform (FFT) method, and the amplitude and the calculated phase in the detection plane is numerically back-propagated to the object plane using the paraxial transfer function. Furthermore, we illustrate how a static 3D phase and/or amplitude object can also be reconstructed tomographically by illuminating it at multiple angles. For illustration purposes, the object is mounted on a rotating stage and multiple diffraction patterns are captured for different angles and at different observation planes. The reconstructed optical fields are tomographically recomposed to yield the final 3D shape using a simple multiplicative technique. The tomographic technique can be generalized for the case of 3D moving objects. Finally, we have used TIE to determine the phase induced in a liquid due to heating by a focused laser beam, which causes self-phase modulation of the beam.

Stabilization of a (D+1)-dimensional dispersion-managed solitons in Kerr media by an alternating dispersion structure

We study the propagation of chirped (D+1)-dimensional optical pulses in bulk media with periodic dispersion, analytically by using the variational approach and numerically by using a new, to our knowledge, numerical technique relying on the adaptive fast Hankel split-step method using cylindrical and spherical symmetries for two and three dimensions, respectively. Stability criteria for (2+1)- and (3+1)-dimensional solitons are identified, and the long-term dynamics of the solitons are studied with the averaged equations obtained using the Kapitza approach. Also, the slow dynamics of the solitons around the fixed points for the width and the chirp are studied. The importance of this research is in generating dispersion-managed optical solitons in optical communication. Also, this research is applied to the stabilization of the Bose-Einstein condensate in (2+1)- and (3+1)-dimensional optical lattices. We compare results of the new numerical technique with those obtained using the fast Fourier split-step technique.

Perturbed multilayered structures of positive and negative index materials

In this work, we study the influence of disorder on the omnidirectional bandgap in a one dimensional stack of alternating positive and dispersive negative index materials. We achieve this through using the transfer matrix method to study wave propagation properties. In the case where the number of periods becomes infinitely large, the limit of the transmittance is derived from the trace of the matrix, and thus reducing the calculation complexity. The origin of the transmission resonances and their relation with the field localization for random systems are analyzed and compared with that of the periodic case. Our result shows that the zero average refractive index bandgap is not affected by small disorders in layer thickness or refractive index, and thus the multilayer stack is robust against fabrication. The finding is expected to achieve potential applications in optoelectronic sensor devices such as omnidirectional reflectors in airplane radomes. We also show that a random mixture of positive and dispersive negative index materials in an equal ratio always possesses a zero average refractive index bandgap.

Application of the transfer matrix method to reflection gratings in positive and negative index materials

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).

Adaptive defect and pattern detection in amplitude and phase structures via photorefractive four-wave mixing.

This work comprises the theoretical and numerical validations of experimental work on pattern and defect detection of periodic amplitude and phase structures using four-wave mixing in photorefractive materials. The four-wave mixing optical processor uses intensity filtering in the Fourier domain. Specifically, the nonlinear transfer function describing four-wave mixing is modeled, and the theory for detection of amplitude and phase defects and dislocations are developed. Furthermore, numerical simulations are performed for these cases. The results show that this technique successfully detects the slightest defects clearly even with no prior enhancement. This technique should prove to be useful in quality control systems, production-line defect inspection, and e-beam lithography.