Thermal emission is a ubiquitous and fundamental process by which all objects at non-zero temperatures radiate electromagnetic energy. This process is often presented to be incoherent in both space and time, resulting in broadband, omnidirectional light emission toward the far field, with a spectral density related to the emitter temperature by Planck's law. Over the past two decades, there has been considerable progress in engineering the spectrum, directionality, polarization, and temporal response of thermally emitted light using nanostructured materials. This review summarizes the basic physics of thermal emission, lays out various nanophotonic approaches to engineer thermal-emission in the far field, and highlights several relevant applications, including energy harvesting, lighting, and radiative cooling. 2 I: IntroductionEvery hot object emits electromagnetic radiation according to the fundamental principles of statistical mechanics. Examples of this phenomenon-dubbed thermal emission (TE)-include sunlight and the glow of an electric stovetop or embers in a fire. The basic physics behind TE from hot objects has been well understood for over a century, as described by Planck's law 1 , which states that an ideal black body (a fictitious object that perfectly absorbs over the entire electromagnetic spectrum and for all incident angles) emits a broad spectrum of electromagnetic radiation determined by its temperature.Increasing the temperature of a black body results in an increase in emitted intensity, and a skew of the spectral distribution toward shorter wavelengths. A fundamental property of this process is that the thermal emissivity of any object-which quantifies the propensity of that object to generate TE compared to a black body-is determined by its optical absorptivity 1 . The connection between absorption and thermal emission, linked to the time reversibility of microscopic processes, suggests that the temporal and spatial coherence of the TE can be engineered via judicious material selection and patterning.Engineering of TE is of great interest for applications in lighting, thermoregulation, energy harvesting, tagging, and imaging. This review summarizes the basic physics of TE and surveys recent advances in the far-field control of TE via nanophotonic engineering. First, we present the basic formalism that describes TE, and review realizations of narrowband, directional, and dynamically reconfigurable far-field thermal emitters based on nanophotonic structures. Then we review applications of engineered far-field TE, with emphasis on energy and sustainability. II: Theoretical backgroundAt elevated temperatures, the constituents of matter, including electrons and atomic nuclei, possess

Although nanolasers typically have low Q-factors and high lasing thresholds, they have been successfully implemented with various gain media. Intuitively, it seems that an increase in the gain coefficient would improve the characteristics of nanolasers. For a plasmonic nanolaser, in particular, a distributed-feed-back (DFB) laser, we propose a self-consistent model that takes into account both spontaneous emission and the multimode character of laser generation to show that for a given pumping strength, the gain coefficient has an optimal value at which the radiation intensity is at a maximum and the radiation linewidth is at a minimum.

Corresponding authors' emails: melentiev@isan.troitsk.ru (P.M.), balykin@isan.troitsk.ru (V.B.), irodionov@bmstu.ru (I.R.), alexander.lisyansky@qc.cuny.edu (A.A.L.).

We show that net amplification of surface plasmons is achieved in channel in a metal plate due to nonradiative excitation by quantum dots. This makes possible lossless plasmon transmission lines in the channel as well as the amplification and generation of coherent surface plasmons. As an example, a ring channel spaser is considered. In this regard, studies of plasmons propagating along 1D objects such as wires [3], wedges [4,5], and channels [6,7] are of great interest.Losses in metals are the main obstacle to practical applications of plasmonics. It has been suggested that this problem can be overcome by compensating loss in a gain medium [8][9][10][11].This relates nanoplasmonics to quantum optics [1,2]. In particular, a generator of plasmons propagating along a flat surface has been suggested in Refs. [12][13][14]. In this system, periodic surface corrugations produce Bragg mirrors of the resonator cavity. The first quantum nanoplasmonic device which was referred to as spaser (Surface Plasmon Amplification by Stimulated Emission of Radiation) was proposed in Ref. [1]. The spaser consists of a quantum dot (QD) located near a metal nanoparticle (NP). The plasmonic oscillations in the NP play the