Slow light in photonic crystals

The problem of slowing down light by orders of magnitude has been extensively discussed in the literature. Such a possibility can be useful in a variety of optical and microwave applications. Many qualitatively different approaches have been explored. Here we discuss how this goal can be achieved in linear dispersive media, such as photonic crystals. The existence of slowly propagating electromagnetic waves in photonic crystals is quite obvious and well known. The main problem, though, has been how to convert the input radiation into the slow mode without loosing a significant portion of the incident light energy to absorption, reflection, etc. We show that the so-called frozen mode regime offers a unique solution to the above problem. Under the frozen mode regime, the incident light enters the photonic crystal with little reflection and, subsequently, is completely converted into the frozen mode with huge amplitude and almost zero group velocity. The linearity of the above effect allows to slow light regardless of its intensity. An additional advantage of photonic crystals over other methods of slowing down light is that photonic crystals can preserve both time and space coherence of the input electromagnetic wave.Comment: 96 pages, 12 figure

Limits of slow-light in photonic crystals

While ideal photonic crystals would support modes with a vanishing group velocity, state-of-the art structures have still only provided a slow-down by roughly two orders of magnitude. We find that the induced density of states caused by lifetime broadening of the electromagnetic modes results in the group velocity acquiring a finite value above zero at the band gap edges, while attaining superluminal values within the band gap. Simple scalings of the minimum and maximum group velocities with the imaginary part of the dielectric function or, equivalently, the linewidth of the broadened states, are presented. The results obtained are entirely general and may be applied to any effect which results in a broadening of the electromagnetic states, such as loss, disorder, finite-size effects, etc. This significantly limits the reduction in group velocity attainable via photonic crystals.Comment: 5 pages, 3 figures, accepted for Physical Review

Slow light in photonic crystals with loss or gain

We develop a perturbation theory for slow-light photonic-crystal waveguides engineered to suppress group-velocity dispersion, and predict that weak material loss (gain) is enhanced proportionally to the slow-down factor, whereas the attenuation (amplification) rate saturates for loss (gain) exceeding a certain threshold. This happens due to hybridization of propagating and evanescent modes which allows significant intensity enhancement observed in our numerical simulations for photonic crystal waveguides even under strong material losses

Enhanced spectral sensitivity of a chip-scale photonic-crystal slow-light interferometer

We experimentally demonstrate that the spectral sensitivity of a Mach-Zehnder (MZ) interferometer can be enhanced through structural slow light. We observe a 20 times enhancement by placing a dispersion-engineered-slow-light photonic-crystal waveguide in one arm of a fibre-based MZ interferometer. The spectral sensitivity of the interferometer increases roughly linearly with the group index, and we have quantified the resolution in terms of the spectral density of interference fringes. These results show promise for the use of slow-light methods for developing novel tools for optical metrology and, specifically, for compact high-resolution spectrometers

Time reversal constraint limits unidirectional photon emission in slow-light photonic crystals

Photonic crystal waveguides are known to support C-points - point-like polarisation singularities with local chirality. Such points can couple with dipole-like emitters to produce highly directional emission, from which spin-photon entanglers can be built. Much is made of the promise of using slow-light modes to enhance this light-matter coupling. Here we explore the transition from travelling to standing waves for two different photonic crystal waveguide designs. We find that time-reversal symmetry and the reciprocal nature of light places constraints on using C-points in the slow-light regime. We observe two distinctly different mechanisms through which this condition is satisfied in the two waveguides. In the waveguide designs we consider, a modest group-velocity of $v_g \approx c/10$ is found to be the optimum for slow-light coupling to the C-points.Comment: 16 pages, 4 figure

Silicon-on-insulator photonic crystal miniature devices with slow light enhanced third-order nonlinearities

The effects of the slow-down factor on third-order nonlinear effects in silicon-on-insulator photonic crystal channel waveguides were investigated. In the slow light regime, with a group index equal to 99, these nonlinear effects are enhanced but the enhancement produced depends on the input peak power level. Simulations indicate the possibility of soliton-like propagation of 1 ps pulses at an input peak power level of 50 mW inside such a photonic crystal waveguide. The increase in the induced phase shift produced by lower group velocities can be used to decrease the size and power requirements needed to operate devices such as optical switches, logic gates, and wavelength translators

Four-wave mixing in slow light photonic crystal waveguides with very high group index

This work was supported by the EPSRC - UK Silicon Photonics consortium.We report efficient four-wave mixing in dispersion engineered slow light silicon photonic crystal waveguides with a flat band group index of n(g) = 60. Using only 15 mW continuous wave coupled input power, we observe a conversion efficiency of -28 dB. This efficiency represents a 30 dB enhancement compared to a silicon nanowire of the same length. At higher powers, thermal redshifting due to linear absorption was found to detune the slow light regime preventing the expected improvement in efficiency. We then overcome this thermal limitation by using oxide-clad waveguides, which we demonstrate for group indices of n(g) = 30. Higher group indices may be achieved with oxide clad-waveguides, and we predict conversion efficiencies approaching -10 dB, which is equivalent to that already achieved in silicon nanowires but for a 50x shorter length.Publisher PDFPeer reviewe

Semi-analytic method for slow light photonic crystal waveguide design

We present a semi-analytic method to calculate the dispersion curves and the group velocity of photonic crystal waveguide modes in two-dimensional geometries. We model the waveguide as a homogenous strip, surrounded by photonic crystal acting as diffracting mirrors. Following conventional guided-wave optics, the properties of the photonic crystal waveguide may be calculated from the phase upon propagation over the strip and the phase upon reflection. The cases of interest require a theory including the specular order and one other diffracted reflected order. The computational advantages let us scan a large parameter space, allowing us to find novel types of solutions.Comment: Accepted by Photonics and Nanostructures - Fundamentals and Application

Non-trivial scaling of self-phase modulation and three-photon absorption in III-V photonic crystal waveguides

We investigate the nonlinear response of photonic crystal waveguides with suppressed two-photon absorption. A moderate decrease of the group velocity (~ c/6 to c/15, a factor of 2.5) results in a dramatic (30x) enhancement of three-photon absorption well beyond the expected scaling, proportional to 1/(vg)^3. This non-trivial scaling of the effective nonlinear coefficients results from pulse compression, which further enhances the optical field beyond that of purely slow-group velocity interactions. These observations are enabled in mm-long slow-light photonic crystal waveguides owing to the strong anomalous group-velocity dispersion and positive chirp. Our numerical physical model matches measurements remarkably.Comment: 10 pages, 4 figure