Measurement of superluminal optical tunneling times in double-barrier photonic band gaps

Abstract

Tunneling of optical pulses at 1.5 µm wavelength through double-barrier periodic fiber Bragg gratings is experimentally investigated. Tunneling time measurements as a function of barrier distance show that, far from the resonances of the structure, the transit time is paradoxically short, implying Superluminal propagation, and almost independent of the distance between the barriers. These results are in agreement with theoretical predictions based on phase time analysis and also provide an experimental evidence, in the optical context, of the analogous phenomenon expected in Quantum Mechanics for non-resonant Superluminal tunneling of particles across two successive potential barriers. [Attention is called, in particular, to our last Figure].

Quantum-mechanical analogy and supersymmetry of electromagnetic wave modes in planar waveguides

“…Vice versa, the propagation of light in waveguides can be used for experimental verification of many quantum-mechanical effects, such as quantum tunneling and time of tunneling, Bloch oscillations in periodic structures, quantum chaos. The reviews on this subject can be found in [5][6][7][8]. Note also recent papers [9,10], where the quantum-mechanical analogy was used for investigation of light confinement in waveguide structures and in microtube bottle resonators, respectively.…”

Experimental and Theoretical Studies of a Broadband Superluminality in Fabry-Perot Interferometer

“…The broadband characteristic is similar to that of the doublebarrier tunneling system, which is generally made of periodic photonic crystals [20][21][22][23][24][25][26]. If the double-barrier system is composed by two opaque barriers (R → 1), the first part in (5) part dominates the total group delay.…”

“…Therefore, in the superluminal region, the total transmission of the double-barrier system is extremely small and the group delay does not change with the opaque barrier width and the barrier separation. This characteristic is renowned as the generalized Hartman effect [11,[20][21][22], which can be explained as a special case in (5) with extremely high boundary reflection rate (R → 1). Since the reflection of the boundary in our system is not too high (R = 0.55), the first part in the right hand side of (5) becomes relatively important.…”

“…Moreover, the group delay in the proposed system is linearly proportional to the selected lengths, which indicates that the understanding of the generalized Hartman effect should be further clarified [11,[20][21][22]. A complete equation set derived based on multiple-reflection interference is displayed to elucidate the observed phenomena and to clarify that the generalized Hartmann effect is valid only for the cases of extremely low transmission.…”

“…Such phenomenon called superluminality is generally attributed to steep anomalous dispersion [1][2][3][4][5][6][7][8] and tunneling effect [9][10][11][12][13][14][15][16][17], which have been experimentally demonstrated in the electromagneticallyinduced-absorption [1][2][3][4][5]/ring-resonator [6][7][8] optical systems and the photonic/waveguide [9][10][11][12][13][14][15][16][17] systems, respectively. However, the systems employing the anomalous dispersion usually operate near the steep absorption line, which leads to a narrow superluminal frequency range as well as low transmission (for passive systems), while the systems associated with the tunneling mechanism also suffer from extremely low transmission [16][17][18][19][20][21][22][23][24][25][26]. Therefore, finding a new mechanism that supports both relat...…”