Abstract-We present a simple electronic circuit which provides negative group delays for band-limited, base-band pulses. It is shown that large time advancement comparable to the pulse width can be achieved with appropriate cascading of negative-delay circuits but eventually the out-of-band gain limits the number of cascading. The relations to superluminality and causality are also discussed.Index Terms-negative group delay, superluminal propagation, group velocity, filter, causality I. IBrillouin and Sommerfeld showed that in the region of anomalous dispersion, which is inside of the absorption band, the group velocity can exceed c, the light speed in a vacuum, or even be negative [1], [2]. Recently, it was shown that for a gain medium, superluminal propagation is possible at the outside of the gain resonance. Superluminal effects are also predicted in terms of quantum tunneling or evanescent waves [3], [4], [5]. Superluminal group velocities have been confirmed experimentally in various systems, and most controversies over this counterintuitive phenomenon have settled down. However, there seem a several questions remain open; for example, "How far we can speed up the wave packets," "Is it really nothing to do with information transmission," "What kind of applications are possible," and so on. In this paper we will try to solve some of these problems by utilizing a simple circuit model for negative group delays.Negative delay in lumped systems such as electronic circuits is very helpful to understand various aspects of superluminal group velocity. Mitchell and Chiao [6], [7] constructed a bandpass amplifier with an LC resonator and an operational amplifier. An arbitrary waveform generator is used to generate a gaussian pulse by which a carrier is modulated. The circuit basically emulates an optical gain medium which shows anomalous dispersion in off-resonant region. Wang et al. [8] extended this circuit by using two LC resonators which correspond to the two Raman gain lines [9], [10]. At the middle of two gain peaks the frequency dependence of amplitude response is compensated and the pulse distortion can be minimized. The present authors [11] used an operational amplifier with an RC feedback circuit. It provides negative delays for baseband pulses. In previous experiments, optical or electronic, a carrier frequency (ω 0 ) is modulated by a pulse which varies slowly compared with the carrier oscillation and the displacement of the envelopes is measured. Without carriers (ω 0 = 0), the system becomes much more simple. The amplitude response symmetric with respect to zero frequency is helpful to reduce the distortion. The baseband pulse is simply derived from a rectangular pulse generator and a series of lowpass filters.The time constants can easily be set at the order of seconds and we can actually observe that the output LED (light-emitting diode) is lit earlier than the input LED. In addition to the usefulness as a demonstration tool, this circuit turned out to be very convenient to look into the e...

We present a simple electronic circuit which produces negative group delays for base-band pulses. When a band-limited pulse is applied as the input, a forwarded pulse appears at the output. The negative group delays in lumped systems share the same mechanism with the superluminal light propagation, which is recently demonstrated in an absorption-free, anomalous dispersive medium [Wang et al., Nature 406, 277 (2000)]. In this circuit, the advance time more than twenty percent of the pulse width can easily be achieved. The time constants, which can be in the order of seconds, is slow enough to be observed with the naked eye by looking at the lamps driven by the pulses.

We investigate the mechanism of weak measurement by using an interferometric framework. In order to appropriately elucidate the interference effect that occurs in weak measurement, we introduce an interferometer for particles with internal degrees of freedom. It serves as a framework common to quantum eraser and weak measurement. We demonstrate that the geometric phase, particularly the Pancharatnam phase, results from the post-selection of the internal state, and thereby the interference pattern is changed. It is revealed that the extraordinary displacement of the probe wavepackets in weak measurement is achieved owing to the Pancharatnam phase associated with post-selection.

We study the dispersion relation of a metamaterial composed of metallic disks and bars arranged to have kagomé symmetry and find that a plasmonic flat band is formed by the topological nature of the kagomé lattice. To confirm the flat-band formation, we fabricate the metamaterial and make transmission measurements in the terahertz regime. Two bands formed by transmission minima that depend on the polarization of the incident terahertz beams are observed. One of the bands corresponds to the flat band, as confirmed by the fact that the resonant frequency is almost independent of the incident angle.