Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
Nanoplasmonic metamaterials are an exciting new class of engineered media that promise a range of important applications, such as subwavelength focusing, cloaking, and slowing/stopping of light. At optical frequencies, using gain to overcome potentially not insignificant losses has recently emerged as a viable solution to ultra-low-loss operation that may lead to next-generation active metamaterials. Maxwell-Bloch models for active nanoplasmonic metamaterials are able to describe the coherent spatiotemporal and nonlinear gain-plasmon dynamics. Here, we extend the Maxwell-Bloch theory to a Maxwell-Bloch Langevin approach-a spatially resolved model that describes the light field and noise dynamics in gain-enhanced nanoplasmonic structures. Using the example of an optically pumped nanofishnet metamaterial with an embedded laser dye (four-level) medium exhibiting a negative refractive index, we demonstrate the transition from loss-compensation to amplification and to nanolasing. We observe ultrafast relaxation oscillations of the bright negative-index mode with frequencies just below the THz regime. The influence of noise on mode competition and the onset and magnitude of the relaxation oscillations is elucidated, and the dynamics and spectra of the emitted light indicate that coherent amplification and lasing are maintained even in the presence of noise and amplified spontaneous emission.
The study of optical effects in active media is rich with unexpected consequences. For instance, one may imagine that absorption and amplification in a dielectric medium will exhibit some sort of symmetry because both are related to the same imaginary part of the dielectric constant, except for a sign change. It turns out that such a symmetry does not exist [1]. This issue has also been investigated in detail for random or disordered gain media, with varying viewpoints [2]. Traditionally, much of the research on amplifying media has considered the interaction of light within the entire volume of such a medium. Recent interest in metamaterials and other esoteric structures in which plasmons are used to manipulate optical signals has brought attention to the role of surface waves in active dielectrics [3, 4]. From a fundamental perspective, the main difference between active and passive media is that spontaneous emission cannot be avoided in gain media. As a result, a rigorous analysis of gain media demands a quantum-mechanical treatment. Spontaneous emission in a gain medium depends not only on the material properties of that medium but also on the optical modes supported by the structure containing that material [5]. By a clever design of this structure (e.g., photonic crystals or microdisk resonators with a metallic cladding), it is possible to control the local density of optical modes and the spontaneous emission process itself. In Chapter 4, we discuss how to model a gain medium under such conditions by deploying optical Bloch equations.
Surface plasmon polaritons (SPPs) lasing requires population inversion, it is inefficient and possesses poor spectral properties. We develop an inversion-less concept for a quantum plasmonic waveguide that exploits unidirectional superradiant SPP (SSPP) emission of radiation to produce intense coherent surface plasmon beams. Our scheme includes a resonantly driven cold atomic medium in a lossless dielectric situated above an ultra-low loss negative index metamaterial (NIMM) layer. We propose generating unidirectional superradiant radiation of the plasmonic field within an atomic medium and a NIMM layer interface and achieve amplified SPPs by introducing phase-match between the superradiant SPP wave and coupled laser fields. We also establish a parametric resonance between the weak modulated plasmonic field and the collective oscillations of the atomic ensemble, thereby suppressing decoherence of the stably amplified directional polaritonic mode. Our method incorporates the quantum gain of the atomic medium to obtain sufficient conditions for coherent amplification of superradiant SPP waves, and we explore this method to quantum dynamics of the atomic medium being coupled with the weak polaritonic waves. Our waveguide configuration acts as a surface plasmon laser and quantum plasmonic transistor and opens prospects for designing controllable nano-scale lasers for quantum and nano-photonic applications.
Laser amplification kicks off with just a few photons in the cavity, a regime where standard additive Langevin noise cannot capture the real fluctuations. To understand how this amplification begins, we map out a single-mode photon-carrier model that links macroscopic lasers directly into nanolasers. Stationary rate equations reveal that stimulated emission takes over across a tight pump window. In nanolasers, however, spontaneous processes coexist across a much broader range. Because steady-state averages miss the individual events that lead to the macroscopic photon number, we frame the stochastic dynamics around the actual discrete transitions, deriving a state-dependent diffusion approximation. The destruction of an excited carrier concurrent with the generation of a photon creates a negative photon-carrier cross-correlation. This unavoidably leads to a correlated, multiplicative Gaussian-noise framework. We track the resulting discrete dynamics with an established, event-based Laser Markov Chain (LMC) which stochastically samples pump, relaxation, emission, and cavity-loss events keeping all physical quantities as non-negative integers. Comparing its predictions to those of our multiplicative model proves that the latter reproduces excellently well the statistical behavior of photons and carrier, as long as a continuous diffusion description holds. Once the emission drops into the few-photon regime, however, the discrete model becomes indispensable. On the other hand, at large photon counts relative fluctuations shrink to a level where the state-dependence of the diffusion matrix can be ignored, to leading order, thus returning to the classic Langevin description of the system's stochastic dynamics.
Optical materials exhibit significant losses over the resonance frequency of their constituent atoms and so they are practically implemented at frequencies far from resonances. Electromagnetically induced transparency (EIT) provides a method for effective suppression of optical loss in a narrow window over the resonance, where the medium exhibits significant dispersion but at the expense of zero susceptibility. The classical or plasmonic analogs of the EIT effect are introduced and widely used in the context of electromagnetic or optical metamaterials (MMs). In another interesting phenomenon in quantum optics known as enhancement of index of refraction (EIR), the optical loss of the medium can be zero or even negative at the region of maximal susceptibility and negligible dispersion. This condition is interesting for applications where a strong electromagnetic response of the medium with negligible loss is required, such as zero- or negative-index metamaterials (MMs). Here we introduce a plasmonic analog of the EIR which allows for coherent control over the polarizability and absorption of plasmonic nanoantennas. It can open up the way for loss-compensated propagation of optical waves in zero-index to high-refractive-index plasmonic MMs. The scheme also offers an approach to all-optical switching and coherent control of transmission, diffraction, and polarization conversion properties of plasmonic nanostructures, as well as propagation properties of surface plasmon polaritons on metasurfaces.
The extremely large speed of light is a tremendous asset but also makes it challenging to control, store or shrink beyond its wavelength. Particularly, reducing the speed of light down to zero is of fundamental scientific interest that could usher in a host of important photonic applications, some of which are hitherto fundamentally inaccessible. These include cavity-free, low-threshold nanolasers, novel solar-cell designs for efficient harvesting of light, nanoscale quantum information processing (owing to the enhanced density of states), as well as enhanced biomolecular sensing. We shall here present nanoplasmonic-based schemes where timedependent sources excite “complex-frequency” modes in uniform (plasmonic) heterostructures, enabling complete and dispersion-free stopping of light pulses, resilient to realistic levels of dissipative, radiative and surface-roughness losses. Our theoretical and computational results demonstrate extraordinary large lightdeceleration factors (of the order of 15,000,000) in integrated nanophotonic media, comparable only to those attainable with ultracold atomic vapours or with quantum coherence effects, such as coherent population oscillations, in ruby crystals.
We demonstrate a new class of "coherent" metamaterials, where narrow band EIT-like transmission/reflection resonances correspond to a truly collective response of the entire ordered metamaterial array. The resonances appear as a result of coherent excitations of strongly interacting ordered meta-molecules and are controlled by the size of the array. Coherent maetamaterials provide a promising platform for various intriguing applications including slow-light and polarization controlling devices and the "lasing spaser", which we illustrate in a number of microwave, THz and optical experiments. Also, for the first time we experimentally show that resonant properties and losses in a photonic version of the metamaterial can be controlled through optical gain medium. (from session titled: Metamaterials - from modelling and fabrication to application).