Polarization-dependent bandwidth in low-index plasmonic metamaterials.

We investigate the visible range, less-than-one index bandwidth, n(λ)<1, of an optical metamaterial structure composed of plasmonic gold nanoparticles, and show that it is highly dependent on the polarization of incident light. The full-wave finite element method is used to obtain the spectral characteristics of the structure. We have found spectral bands over which the structure shows the desired low index. Further, a possible increase of the bandwidth by as much as 270% is demonstrated by a change in the incident polarization that extends the low-index bandwidth range (503-600 nm) asymmetrically into a wider range (485-750 nm) covering longer wavelengths close to near infrared. This asymmetric overlap might have the potential for new optical applications.

Selective field localization in random structured media.

We have introduced a method to find optimized structured media exhibiting large internal electric field amplitudes. The method is based on a genetic algorithm in which a spatial fitness function according to the computed field distribution in the interior of media is defined and maximized. The main feature of our method is that it enables localization of light at a desired layer (or more) within the structure. The enhancements are demonstrated to be up to about 70-fold in |E|(2) by use of only seven layers. The results are interesting for nonlinear and sensor applications, which due to compact size and few number of structure layers, are also desirable for fabrication purposes.

Internal field distribution measurement in 1-D strongly anisotropic sub-wavelength periodic structures of finite length.

We report measurements of the internal field intensity distribution in finite length one dimensional strongly anisotropic sub-wavelength periodic structures in the vicinity of the photonic band gap (PBG) edge. The strong in-plane anisotropy of more than 10% index contrast is obtained via form birefringent sub-wavelength gratings. The structures have a period of less than half the wavelength. Depending on the excitation frequency, both standing wave and evanescent Bloch modes can be identified and observed experimentally. The field enhancement near the PBG edge is confirmed also but at a significantly reduced strength attributed to the small but finite material loss.

Combined image-processing algorithms for improved optical coherence tomography of prostate nerves.

Cavernous nerves course along the surface of the prostate gland and are responsible for erectile function. These nerves are at risk of injury during surgical removal of a cancerous prostate gland. In this work, a combination of segmentation, denoising, and edge detection algorithms are applied to time-domain optical coherence tomography (OCT) images of rat prostate to improve identification of cavernous nerves. First, OCT images of the prostate are segmented to differentiate the cavernous nerves from the prostate gland. Then, a locally adaptive denoising algorithm using a dual-tree complex wavelet transform is applied to reduce speckle noise. Finally, edge detection is used to provide deeper imaging of the prostate gland. Combined application of these three algorithms results in improved signal-to-noise ratio, imaging depth, and automatic identification of the cavernous nerves, which may be of direct benefit for use in laparoscopic and robotic nerve-sparing prostate cancer surgery.

Resolution enhancement of imaging small-scale portions in a compactly supported function.

The ambiguity involved in reconstructing an image from limited Fourier data is removed using a new technique that incorporates prior knowledge of the location of regions containing small-scale features of interest. The prior discrete Fourier transform (PDFT) method for image reconstruction incorporates prior knowledge of the support, and perhaps general shape, of the object function being reconstructed through the use of a weight function. The new approach extends the PDFT by allowing different weight functions to modulate the different spatial frequency components of the reconstructed image. The effectiveness of the new method is tested on one- and two-dimensional simulations.

Tunable negative group index in metamaterial structures with large form birefringence.

We experimentally verify the anomalous phase behavior in metamaterial structures with birefringent materials predicted by Mandatori, et. al. using form birefringent structures. Large birefringence as much as Deltan/n = 0.7 has been achieved by surface-treated form birefringent discs, making compact single layer Mandatori structures viable. With a reduced model of a single layer birefringent structure, the relationship between design parameters (thickness and orientation angle) and device operation and performance parameters (such as the center operation frequency, bandwidth, effective negative index, negative group index of refraction, and the transmission throughput) are derived and verified experimentally. Tunable group index of refraction from strong slow light of ng = 29.6 to fast light of ng = -1.1 are measured experimentally.

Denoising during optical coherence tomography of the prostate nerves via wavelet shrinkage using dual-tree complex wavelet transform.

The dual-tree complex wavelet transform (CDWT) is a relatively recent enhancement to the discrete wavelet transform (DWT), with important additional properties. It is nearly shift-invariant and directionally selective in two and higher dimensions. In this letter, a locally adaptive denoising algorithm is applied to reduce speckle noise in time-domain optical coherence tomography (OCT) images of the prostate. The algorithm is illustrated using DWT and CDWT. Applying the CDWT provides improved results for speckle noise reduction in OCT images. The cavernous nerve and prostate gland can be separated from discontinuities due to noise, and image quality metrics improvements with a signal-to-noise ratio increase of 14 dB are attained.

Design of generalized invisible scatterers.

A nonlinear signal processing method is applied to the design of strongly scattering objects to realize a defined angular response. Investigated as the complement of inverse scattering problems, k-space design methods are combined with cepstral filtering to obtain a permittivity distribution that scatters with the desired response. Starting with the rigorously computed angular spectrum of the scattering amplitude of an object of simple geometric shape, the corresponding k-space is modified to provide the desired scattering behavior. In order to account for strong scattering, cepstral filtering is applied to map the associated distribution of secondary sources to a unique permittivity distribution. The inversion process results in a structure that exhibits the desired properties and which can be interpreted as a perturbation of the initial structure. Simulation results are presented which illustrate the usefulness of this method. In particular, objects are modified to enhance forward scattering and suppress scattering in all other direction. Results are verified using a rigorous finite-difference frequency-domain scheme to simulate scattering. The method is demonstrated as a novel means for designing invisible objects that act as electromagnetic cloaks.

Accuracy of extrapolated data as a function of prior knowledge and regularization.

The prior discrete Fourier transform (PDFT) is a linear spectral estimator that provides a solution that is both data consistent and of minimum weighted norm through the use of a suitably designed Hilbert space. The PDFT has been successfully used in imaging applications to improve resolution and overcome the nonuniqueness associated with having only finitely many spectral measurements. With the use of an appropriate prior function, the resolution of the reconstructed image can be improved dramatically. We explore the ways in which some significant parameters affect the PDFT estimate. A relationship between estimated spectral values, prior knowledge, and regularization was examined. It allows one to assess the reliability of the estimated spectral values for a given choice of prior estimate and provides a means for optimizing PDFT-based estimators.

Iterative image reconstruction using prior knowledge.

A method is proposed to reconstruct signals from incomplete data. The method, which can be interpreted both as a discrete implementation of the so-called prior discrete Fourier transform (PDFT) spectral estimation technique and as a variant of the algebraic reconstruction technique, allows one to incorporate prior information about the reconstructed signal to improve the resolution of the signal estimated. The context of diffraction tomography and image reconstruction from samples of the far-field scattering amplitude are used to explore the performance of the method. On the basis of numerical computations, the optimum choice of parameters is determined empirically by comparing image reconstructions of the noniterative PDFT algorithm and the proposed iterative scheme.

Image reconstruction: a unifying model for resolution enhancement and data extrapolation. Tutorial.

In reconstructing an object function F(r) from finitely many noisy linear-functional values integral of F(r)Gn(r)dr we face the problem that finite data, noisy or not, are insufficient to specify F(r) uniquely. Estimates based on the finite data may succeed in recovering broad features of F(r), but may fail to resolve important detail. Linear and nonlinear, model-based data extrapolation procedures can be used to improve resolution, but at the cost of sensitivity to noise. To estimate linear-functional values of F(r) that have not been measured from those that have been, we need to employ prior information about the object F(r), such as support information or, more generally, estimates of the overall profile of F(r). One way to do this is through minimum-weighted-norm (MWN) estimation, with the prior information used to determine the weights. The MWN approach extends the Gerchberg-Papoulis band-limited extrapolation method and is closely related to matched-filter linear detection, the approximation of the Wiener filter, and to iterative Shannon-entropy-maximization algorithms. Non-linear versions of the MWN method extend the noniterative, Burg, maximum-entropy spectral-estimation procedure.