We report the results of a Snell's law experiment on a negative index of refraction material in free space from 12.6 to 13.2 GHz. Numerical simulations using Maxwell's equations solvers show good agreement with the experimental results, confirming the existence of negative index of refraction materials. The index of refraction is a function of frequency. At 12.6 GHz we measure and compute the real part of the index of refraction to be -1.05. The measurements and simulations of the electromagnetic field profiles were performed at distances of 14lambda and 28lambda from the sample; the fields were also computed at 100lambda.

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We propose and implement a quantum procedure for enhancing the sensitivity with which one can determine the phase shift experienced by a weak light beam possessing thermal statistics in passing through an interferometer. Our procedure entails subtracting exactly one (which can be generalized to m) photons from the light field exiting an interferometer containing a phase-shifting element in one of its arms. As a consequence of the process of photon subtraction, and somewhat surprisingly, the mean photon number and signal-to-noise ratio of the resulting light field are thereby increased, leading to enhanced interferometry. This method can be used to increase measurement sensitivity in a variety of practical applications, including that of forming the image of an object illuminated only by weak thermal light.Interferometry is the technique of choice for many of the most sensitive physical measurements to date [1]. It underlies many monumental discoveries in physics, such as Young's double slit experiment, the Michelson-Morley experiment that established the special theory of relativity, and recently and spectacularly in gravitational wave detection [1]. Apart from these foundational contributions, interferometry also plays an important role in many applications in optical metrology and imaging of astronomical objects, e.g. in stellar Michelson interferometry [2,3]. These applications often deal with sources of light that possess thermal statistics. The fluctuations in the number of photons of a thermal state is given by n(n + 1) wheren is the average number of photons contained in the field. For a dim source of thermal light, the magnitude of these fluctuations becomes comparable or even larger thann, overwhelming interferometric signals which are obtained by averaging the number of photons.Ever since the advent of modern quantum optics, strategies have been developed to harness the quantum nature of light in order to enhance the accuracy of interferometric measurements [4][5][6][7][8][9]. These proposals use exotic quantum states of light, e.g. squeezed states or entangled states, to probe the physical process of interest [4,[10][11][12][13][14][15][16]. Unfortunately such an arrangement is infeasible when the object of interest is a remote source of light that possesses thermal statistics. Thus, it remains highly desirable to establish a protocol for increasing the sensitivity of interferometry by distilling the statistical information already contained in the collected light, rather than changing the nature of illumination.Here we describe a means to enhance the phase sensitivity of interferometry based on the use of photonsubtracted thermal states, which are quantum states obtained by removing a fixed number of photons from a light field that possesses thermal statistics [17]. Photonsubtracted states have recently attracted interest because of their applications in quantum communication, quantum computation, and quantum metrology [17][18][19][20][21][22][23][24][25]. In contrast with the conventional approach i...

Negative index of refraction materials have been postulated for many years but have only recently been realized in practice. In the microwave region these materials are constructed of rings and wires deposited on a dielectric substrate to form a unit cell. We have constructed, experimentally characterized and simulated several of these structures operating in the 10 - 15 GHz range. Our simulations using Maxwell's Equations solvers have included wire arrays, ring arrays and assemblies of unit cells comprised of rings and wires. We find good agreement between the numerical simulations and experimental measurements of the scattering parameters and index of refraction. The procedure was to first model ring and wire structures on the unit cell level to obtain scattering parameters from which effective å, ì and n were retrieved. Next an assembled array of unit cells forming a 12 degrees wedge was used for the Snell's Law determination of the negative index of refraction. For the structure examined the computed value of n is within 20% of the one experimentally measured in the Snell's Law experiment from 13.6 to 14.8 GHz.