John O. Schenk

Picosecond scale experimental verification of a globally convergent algorithm for a coefficient inverse problem

A globally convergent algorithm by the first and third authors for a 3D hyperbolic coefficient inverse problem is verified on experimental data measured in the picosecond scale regime. Quantifiable images of dielectric abnormalities are obtained. The total measurement timing of a 100 ps pulse for one detector location was 1.2 ns with 20 ps (=0.02 ns) time step between two consecutive readings. Blind tests have consistently demonstrated an accurate imaging of refractive indexes of dielectric abnormalities. At the same time, it is shown that a modified gradient method is inapplicable to this kind of experimental data. This inverse algorithm is also applicable to other types of imaging modalities, e.g. acoustics. Potential applications are in airport security, imaging of land mines, imaging of defects in non-distractive testing, etc.

THIRD ORDER NONLINEAR EFFECT NEAR A DEGENERATE BAND EDGE

We describe the properties of a 1D anisotropic periodic structure, designed to have a band edge with fourth order degeneracy, called a degenerate band edge (DBE). A giant field resonance at the transmission peak frequency closest to this band edge has been verified by rigorous numerical calculation and is supported by experimental evidence. Simulations are presented of the consequences of a χ3 nonlinear index change at a DBE resonant frequency which can provide all-optical switching and transmission self-limiting.

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.

Form birefringent anisotropic photonic crystal exhibiting external field anomalies.

A strongly anisotropic photonic crystal structure was made exploiting form birefringence. It was designed to have a low group velocity close to a degenerate band edge (DBE) which is also associated with large field enhancements proportional to the fourth power of the number of periods. Numerical results are presented illustrating the expected properties and these are compared with experimental data. There are interesting discrepancies in behavior and possible reasons are discussed which include the nature of the anisotropy and fabrication-related structural disorder. At microwave frequencies, unexpected field enhancements at specific frequencies and locations outside the structure have been observed which have potential applications

Revisiting the perfect lens with loss

We reconsider the refraction of evanescent waves at an interface between air and a negative index medium under the assumption that the negative index medium is necessarily dispersive and lossy. We show that all evanescent waves in air will be refracted into decaying propagating waves inside the negative index medium, with different spatial frequency components having different propagation directions and separated both in time and space; hence no refocus of these evanescent waves is possible. Accordingly, all information encoded by evanescent waves will be lost in the image making sub-diffraction-limited imaging impossible.

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.

Split Band Edge Structures and Negative Index

Highly anisotropic periodic waveguide structures show gigantic field enhancements near a split band-edge due to low group velocities. An effective negative index regime is observed, leading to strong but localized field emission around the waveguide.

Energy Velocity in Negative Group Index Structures

Energy velocity in negative group index structures is investigated. It is shown that the negative group index phenomenon is an exhibition of effective negative index-of-refraction while the group velocity still equals the energy velocity.

ANISOTROPIC METAMATERIALS FOR FIELD ENHANCEMENT AND NEGATIVE INDEX APPLICATIONS

1D highly anisotropic periodic structures can exhibit very large internal field enhancements and positive spectral phase slopes. The field enhancement can lead to significant external fields radiating from the structure close to frequencies at which the spectral phase slope changes sign and where an effective negative index regime can occur.

Design and experimental verification of a novel anisotropic photonic crystal band edge device

We have been studying a novel 1D anisotropic photonic crystal structure which can be designed to have a strong resonant effect, a very low group velocity over a specific bandwidth. The structure requires two anisotropic layers and one isotropic layer per period and was first introduced by Figotin and Vitebskiy. By the careful design of the parameters of the structure, we can find a special band edge point which has fourth order degeneracy, and is called degenerate band edge (D.B.E). It was predicted that in the case of a transmission resonance in the vicinity of the D.B.E, the resonant field intensity increases as N4, where N is the total number of periods, while in the case of a regular band edge, the field intensity is proportional to N2. By making a comparison among different anisotropic materials, we have found that the giant resonant effects in the vicinity of the D.B.E also need a large anisotropy of the materials. However, materials with the required anisotropy at optical wavelengths are difficult to find and so we use equivalent form-birefringence layer to replace the anisotropic layer in our photonic crystal structure design. In order to verify our design, we make a real device for use at microwave frequencies using a rapid-prototyping tool. Our measurement results show that using form-birefringence to design this novel device is feasible and can push this novel photonic crystal structure to a lot of potential applications.