Demonstration of Superluminal Effects in an Absorptionless, Nonreflective System

Abstract

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 counter-intuitive effects.Superluminal group velocities have been observed in a number of different physical systems. These include passive absorptive [1], passive reflective [2,3], and active transparent [4] media. There have also been numerous theoretical and experimental proposals to observe superluminality in the tunneling of electromagnetic wavepackets [5].Here we report the first experimental observation of superluminal effects in a passive system with neither absorption nor reflection. The effects arise because of a transfer of energy or interference between two modes of the electromagnetic field, in this case two different polarizations of light. We are able to interpret these results using a new vector formulation of the Kramers-Kronig relations.It is widely believed that the Kramers-Kronig (K-K) relations [6] require that passive systems be either absorptive or reflective in order to exhibit superluminal effects. In this paper, we demonstrate that this is not the case; while absorptive and reflective systems are required to have spectral regions of anomalous dispersion, the converse is not necessarily true. In fact, the exchange of energy between modes is a sufficient condition for superluminal propagation in any system. We show that these effects are consistent with causality.Our experimental system consists of a slab of highly birefringent two-dimensional (2D) photonic crystal and a linear polarizer, placed in series. The photonic crystal has fundamental and second-order photonic band gaps in the regions of 10 and 20 GHz, and displays strong birefringence with very high transmission in the frequency range between the two gaps [7]. The crystal itself is an 18-layer hexagonal array of hollow acrylic rods (outer diameter 1/2") with an air-filling fraction (AFF) of 0.60. The crystal was constructed using a method which we have previously described [8].We studied the transmission and dispersive properties of this system between the two band gaps, using an HP 8720A vector network analyzer (VNA). Microwaves were coupled to and from free space with polarization-sensitive horn antennae. The photonic crystal was placed in the far-field of the transmitter horn to ensure that planar wavefronts of a well-defined polarization were incident on it. The receiver horn was positioned immediately behind the photonic crystal on a direct line of sight with the transmitter horn. In addition, the crystal and receiver horn were placed inside a microwave-shielded box with an open square aperture, whose size was chosen to minimize diffraction effects while eliminating signal leakage around the crystal. This method has proven very...

Direct Measurement of Superluminal Group Velocity and Signal Velocity in an Optical Fiber

“…Although these features are usual in their qualitative formulation, we note (as the authors of Ref. [11] did) that the standard Kramers-Kronig relations do not apply: these relations predict that the absorption coefficient ("imaginary part of the index") determines uniquely the index of refraction ("real part"), and viceversa; while in our case, the same absorption is associated to different dispersions. Modified Kramers-Kronig relations have been discussed in [14].…”

“…Then we describe the experiment and present our main results in Figs 4 and 5. We shall conclude by comparing our experiment to a related one [11], and by stressing the differences with other fast-and slowlight techniques. Theoretical analysis.…”

Observation of simultaneous fast and slow light

“…More recently it has also been established that systems where two modes can propagate can also show anomalous dispersion, even in the absence of absorption or reflection [16]. This has been shown in photonic crystals [16,17] and coupled mode systems [18].…”

“…More recently it has also been established that systems where two modes can propagate can also show anomalous dispersion, even in the absence of absorption or reflection [16]. This has been shown in photonic crystals [16,17] and coupled mode systems [18]. Our system combines both approaches, using a coherent linear superposition of two propagating modes where only one of them shows a sharp spectral feature [19,20].…”

Two-stage radio-frequency interferometer sensors

“…Such abnormal electromagnetic properties have been reported in a few other structures and circuits. [11][12][13][14] In RF interferometers, these properties occur around the operating frequency points and are caused by destructive interference of two traveling waves at the output port. The process is similar to that at the dark port of a Mach-Zehnder interferometer.…”