Metamaterials — transparent materials containing tiny metallic inclusions of various shapes and arrangements — cause light to propagate in unusual ways. Now a new, theoretical metamaterial architecture is proposed, with the potential to bring light to a complete standstill. In contrast to previous methods of decelerating and storing light, this scheme simultaneously allows both high in-coupling efficiency and broadband, room-temperature operation. At a critical point a light ray is prevented from propagating; each frequency component (or colour) of the wave stops at a slightly different place, leading to the formation of a 'trapped rainbow'. This work bridges the gap between two important contemporary realms of science, metamaterials and slow light, and may lead to applications in optical data processing and storage or the realization of quantum optical memories. Light usually propagates inside transparent materials in well known ways1. However, recent research2,3,4,5,6 has examined the possibility of modifying the way the light travels by taking a normal transparent dielectric and inserting tiny metallic inclusions of various shapes and arrangements. As light passes through these structures, oscillating electric currents are set up that generate electromagnetic field moments; these can lead to dramatic effects on the light propagation, such as negative refraction. Possible applications include lenses that break traditional diffraction limits3,4 and ‘invisibility cloaks’ (refs 5, 6). Significantly less research has focused on the potential of such structures for slowing, trapping and releasing light signals. Here we demonstrate theoretically that an axially varying heterostructure with a metamaterial core of negative refractive index can be used to efficiently and coherently bring light to a complete standstill. In contrast to previous approaches for decelerating and storing light7,8,9,10,11,12,13, the present scheme simultaneously allows for high in-coupling efficiencies and broadband, room-temperature operation. Surprisingly, our analysis reveals a critical point at which the effective thickness of the waveguide is reduced to zero, preventing the light wave from propagating further. At this point, the light ray is permanently trapped, its trajectory forming a double light-cone that we call an ‘optical clepsydra’. Each frequency component of the wave packet is stopped at a different guide thickness, leading to the spatial separation of its spectrum and the formation of a ‘trapped rainbow’. Our results bridge the gap between two important contemporary realms of science—metamaterials and slow light. Combined investigations may lead to applications in optical data processing and storage or the realization of quantum optical memories.

‘Trapped rainbow’ storage of light in metamaterials

Metamaterials have a tremendous potential for applications from biophotonics to optical circuits, although progress has been hampered by intrinsic metal losses. This Review discusses the progress in countering such losses through the use of gain media to realize devices such as nanoplasmonic lasers or improved metamaterials for imaging and nonlinear optical applications.

Active nanoplasmonic metamaterials

1. Semiconductor Laser Diodes 2. Basic Concepts 3. Free-Carrier Theory 4. Coulomb Effects 5. Many-Body Gain 6. Band Mixing and Strain in Quantum Wells 7. Semiclassical laser Theory 8. Multimode Operation 9. Quantum Theory of the Laser 10. Propagation Effects 11. Beyond Quasiequilibrium Theory, Appendices A-e, Index

Semiconductor-Laser Physics

On the basis of a full-vectorial three-dimensional Maxwell-Bloch approach we investigate the possibility of using gain to overcome losses in a negative refractive index fishnet metamaterial. We show that appropriate placing of optically pumped laser dyes (gain) into the metamaterial structure results in a frequency band where the nonbianisotropic metamaterial becomes amplifying. In that region both the real and the imaginary part of the effective refractive index become simultaneously negative and the figure of merit diverges at two distinct frequency points.

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Overcoming Losses with Gain in a Negative Refractive Index Metamaterial

This paper presents a selection of recent advances on two-section passively mode-locked InGaAs-based quantum-dot laser diodes. Pulse generation is demonstrated for repetition rates ranging from 310 MHz to 240 GHz, and with pulse durations ranging from the picosecond to the sub-400 fs regime. Mode-locking trends in these devices are discussed, and device performance improvements in terms of pulse duration, output power, and noise properties are presented. Design rules for reducing the pulse duration, increasing the output power, and improving noise performance are outlined. Implementation of tapered waveguide structures yields significant performance improvements, allowing the simultaneous achievement of ultrashort, Fourier-limited pulse generation with low amplitude noise, low timing jitter, and narrow RF linewidths.

InGaAs Quantum-Dot Mode-Locked Laser Diodes

We present a mesoscopic theory for the spatiotemporal carrier and light-field dynamics in quantum-dot lasers. Quantum-dot Maxwell-Bloch equations have been set up that mesoscopically describe the spatiotemporal light-field and interlevel/intralevel carrier dynamics in each quantum dot (QD) of a typical QD ensemble in quantum-dot lasers. In particular, this includes spontaneous luminescence, counterpropagation of amplified spontaneous emission, and induced recombination as well as carrier diffusion in the wetting layer (quantum-well media) of the quantum-dot laser. Intradot scattering via emission and absorption of phonons, as well as scattering with the carriers and phonons of the surrounding wetting layer are dynamically included on a mesoscopic level. The spatiotemporal light-field dynamics reveals a characteristic interplay of spontaneous and stimulated emission in quantum-dot lasers that depends on typical spatial fluctuations in size and energy levels of the quantum dots and irregularities in the spatial distribution of the quantum dots in the active layer. Those effects are simulated via statistical methods. They are shown to directly affect the propagation of an ultrashort pulse in a quantum-dot waveguide. The strong influence of the localized carrier dynamics is seen in the selective depletion and refilling of quantum-dot energy levels.

Mesoscopic spatiotemporal theory for quantum-dot lasers

We present a comparative study of numerical simulations and experiments on the spatiotemporal dynamics and emission characteristics of quantum-well and quantum-dot lasers of identical structure. They show that, in the quantum-dot laser, the strong localization of carrier inversion and the small amplitude-phase coupling enable a significant improvement of beam quality compared to quantum-well lasers of identical geometry. Near-field profiles and beam quality (M-2) parameters calculated on the basis of time-dependent effective Maxwell-Bloch equations into which the physical properties of the active media are included via space-dependent material parameters, effective time constants, and matrix elements are fully confirmed by experimental measurements. Together they indicate that, in the quantum-dot laser, the strong localization of carrier inversion and the small amplitude-phase coupling enable a significant improvement of beam quality compared with quantum-well lasers of identical geometry. (C) 2004 American Institute of Physics.

Dynamic Filamentation and Beam Quality of Quantum-Dot Lasers

Introduction.- Advanced Semiconductor Lasers.- Semiconductor Laser Theory.- Spatio-Temporal Dynamics of In-Plane Lasers.- Polarization Dynamics of Vertical-Cavity Surface-Emitting Lasers.- Master-Oscillator Power-Amplifier Systems.- Conclusion.- References.- Subject Index.

Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers

We present theoretical and experimental results on the propagation of ultrashort pulses in quantum-dot (QD) laser amplifiers. The propagation time of the light pulses is controlled by the pulse itself (self-induced speed control) or by injection of a second pump pulse (external speed control). Our simulations on the basis of spatially and temporally resolved QD Maxwell-Bloch equations reveal that the excitation and relaxation dynamics induced by the propagating pulse or a pump pulse within the active charge carrier system leads to a complex gain and index dynamics that may either speed up or slow down the propagating light pulse. The physical effects allowing for the dynamic speed control could be ascribed to complex (coherent and incoherent) level dynamics leading to dynamic gain saturation and index dispersion. The dependence of the propagation time on injection current density and pulse energy is discussed. The numerical results of pulse reshaping and propagation times in the gain and absorptions regime are compared to experimental results

Dynamic Spatiotemporal Speed Control of Ultrashort Pulses in Quantum-Dot SOAs

We present a theoretical model for the description of carrier and light dynamics in a quantum dot semiconductor optical amplifier that includes the inhomogeneous broadening of the quantum dots (QDs) via a spatially resolved statistical approach. The model is based on Maxwell-Bloch equations and takes into account the scattering of charge carriers between 2-D wetting layer states and bound quantum dot states, the amplification, and the wave-guiding of the light fields in the optical cavity. Simulations allow the analysis of the occupation probability of the quantum dot levels at steady state and during optical excitation by a femtosecond pulse. The influence of homogeneously and inhomogeneously broadened quantum dot media on spatial and spectral hole burning is revealed and discussed. It is shown that spatially varying dot properties lead to the reshaping of the optical pulse in the active medium.

Edeltraud Gehrig

Papers

Mesoscopic spatiotemporal theory for quantum-dot lasers

Dynamic Filamentation and Beam Quality of Quantum-Dot Lasers

Spatio-Temporal Dynamics and Quantum Fluctuations in Semiconductor Lasers

Dynamic Spatiotemporal Speed Control of Ultrashort Pulses in Quantum-Dot SOAs

Pulse Amplification and Spatio-Spectral Hole-Burning in Inhomogeneously Broadened Quantum-Dot Semiconductor Optical Amplifiers