J. M. Hickmann

Fast light, slow light, and phase singularities: a connection to generalized weak values.

We demonstrate that Aharonov-Albert-Vaidman weak values have a direct relationship with the response function of a system, and have a much wider range of applicability in both the classical and quantum domains than previously thought. Using this idea, we have built an optical system, based on a birefringent photonic crystal, with an infinite number of weak values. In this system, the propagation speed of a polarized light pulse displays both superluminal and slow light behavior with a sharp transition between the two regimes. We show that this systems response possesses two-dimensional, vortex-antivortex phase singularities. Important consequences for optical signal processing are discussed.

Photonic crystal polarizers and polarizing beam splitters

We have experimentally demonstrated polarizers and polarizing beam splitters based on microwave-scale two-dimensional photonic crystals. Using polarized microwaves within certain frequency bands, we have observed a squared-sinusoid (Malus) transmission law when using the photonic crystal as a polarizer. The photonic crystal also functions as a polarizing beamsplitter; in this configuration it can be engineered to split incident polarizations in either order and in any direction, making it more versatile than conventional, Brewster-angle beamsplitters.

Experimental demonstration of photonic crystal waveplates

We have constructed and experimentally tested a microwave half-waveplate using the dispersive birefringent properties of a bulk, two-dimensional, photonic crystal away from its band gap. Our waveplate device exhibited a 200:1 polarization contrast, limited by our experimental resolution. We anticipate that photonic crystal waveplates will have important practical applications in several areas, including integrated photonic circuits.

Demonstration of Superluminal Effects in an Absorptionless, Nonreflective System

We present an experimental and theoretical study of a simple, passive system consisting of a birefringent, two-dimensional photonic crystal and a polarizer in series, and show that superluminal dispersive effects can arise even though no incident radiation is absorbed or reflected. We demonstrate that a vector formulation of the Kramers-Kronig dispersion relations facilitates an understanding of these counterintuitive effects.

Microwave measurements of the photonic band gap in a two-dimensional photonic crystal slab

We have measured the photonic band gap in the transmission of microwaves through a two-dimensional photonic crystal slab. The structure was constructed by cementing acrylic rods in a hexagonal array to form rectangular stacks. We find a band gap centered at approximately 11 GHz, whose depth, width, and center frequency vary with the number of layers in the slab, angle of incidence, and microwave polarization.

Birefringence in two-dimensional bulk photonic crystals applied to the construction of quarter waveplates

We have experimentally measured the birefringence in bulk two-dimensional hexagonal photonic crystals in transparent spectral regions above and below the fundamental band gap. Data is presented for structures with different numbers of layers and two different air-filling fractions. We have used these data to design a photonic crystal quarter waveplate and provide independent experimental demonstrations of its operation.

Experimental observation of superluminal group velocities in bulk two-dimensional photonic bandgap crystals

The authors have experimentally observed superluminal, negative, and infinite group velocities in bulk hexagonal two-dimensional photonic bandgap crystals with bandgaps in the microwave region. The group velocities depend on the polarization of the incident radiation and the air-filling fraction of the crystal.

Faster-than-light effects and negative group delays in optics and electronics, and their applications

Recent manifestations of apparently faster-than-light effects confirmed our predictions that the group velocity in transparent optical media can exceed c. Special relativity is not violated by these phenomena. Moreover, in the electronic domain, the causality principle does not forbid negative group delays of analytic signals in electronic circuits, in which the peak of an output pulse leaves the exit port of a circuit before the peak of the input pulse enters the input port. Furthermore, pulse distortion for these superluminal analytic signal scan be negligible in both the optical and electronic domains. Here we suggest an extension of these ideas to the microelectronic domain. The underlying principle is that negative feedback can be used to produce negative group delays. Such negative group delay scan be used to cancel out the positive group delays due to transistor latency as well as the propagation delays due to the interconnects between transistors. Using this principle, it is possible to speed up computer systems.

Faster-than-light propagations and their applications

Recent experiments have confirmed our predictions that the group velocity of light pulses propagating in transparent optical media can exceed c. In electronics, the causality principle does not forbid negative group delays of analytic signals in electronic circuits, in which the peak of an output pulse leaves the exit port of a circuit before the peak of the input pulse enters the input port. In condensed matter physics, negative transmission times of atoms are possible through superfluid helium slabs and through atomic BECs. Relativity is not violated by these phenomena.

Experimental demonstration of "fast light" in an absorptionless, non-reflective system using the birefringence of a photonic crystal

This study investigates the first experimental observation of faster-than-c group velocities in a passive system with neither absorption nor reflection. The investigation shows that superluminal and even negative group velocities can exist because of interference, instead of absorption or reflection. Results suggest that causal superluminal propagation can potentially be observed in any system in which input energy can escape into other modes. These results also demonstrate a particularly unusual application of the amplitude-phase Kramers-Kronig (K-K) relations; for the system being described, an infinitesimal adjustment of parameters radically affects the validity of the K-K transformation between amplitude and phase.