Slow and fast light in three-beam interferometers: Theory and experiment

Abstract

We demonstrate the generation of slow and fast light (SFL) in a linear and passive three-beam interferometer. Such propagation regimes occur for narrowband pulses with center frequency close to the transmission minima. A model that fully describes SFL effects in this system is developed and an analytical approximate expression for the group delay at the minima is derived. We demonstrate that slow light is not possible if the length difference between adjacent branches of the interferometer is a constant. If a small length detuning (ξ) in one of the branches is introduced, slow light at one of the two minima can be obtained as long as ξ exceeds a critical value. Simultaneously, tunneling, superluminal, or normal regime is sustained at the other minimum, depending on the system's length. A proof-of-model experiment is performed in the radiofrequency range using coaxial cables and 1 × 3 power splitters. The possible realization and performance of such a system in the optical range is also discussed. This system is proposed as a simple alternative to active systems and photonic band-gap structures for sustaining both slow and fast light.

Fast light in unbalanced low-loss Mach-Zehnder interferometers

“…Therefore, fast light is achieved for weak-enough attenuation, while it disappears if it is either zero or too high (> n n−1 ). The fast-light conditions summarized in Table I and the impossibility of getting slow light coincide with those obtained for a three-beam interferometer with constant length difference between adjacent arms [25]. In fact, the exact expression of the group delay at the transmission minima of this latter system is the same as the one derived here if in Eq.…”

“…(6a) lie at phase values β min = (2m + 1)π (for minima) and β max = 2πm (for maxima), where m is an integer number. The position of the minima does not change with attenuation, in contrast to the situation in a three-beam interferometer [25]. A schematic of the two-beam interferometer and its transmission spectrum with and without attenuation are displayed in Fig.…”

“…(14c)], which is useful to transform a device originally designed to operate at a specific frequency range into another operative range. Finally, let us point out that the pulse propagation characteristics described above are equivalent to those derived for a three-beam interferometer [25].…”

“…An analytic expression of the pulse delay, along with relevant figures of merit that quantify fast-light propagation, is determined. A comparison is made to recently reported SFL effects in three-beam interferometers [25]. The model predictions are illustrated with numerical simulations of a silicon-based MZI designed to operate at optical frequencies.…”

“…As an alternative to PBG systems, we recently demonstrated that structural SFL can be generated in multiple-beam interferometers of three or more branches [25,26], which are linear and passive systems not exhibiting photonic band gaps. The simplest interferometer of this kind, with only two branches, is the Mach-Zehnder interferometer.…”