This chapter provides an overview of a class terahertz quantum cascade lasers based upon amplifying electromagnetic metasurfaces. The metasurface comprises two-dimensional arrays of sub-wavelength surface radiating antenna elements, in which the antennas are loaded with the quantum cascade laser gain material. Several types devices are described: (a) vertical-external-cavity surface-emitting-lasers (VECSELs) in which the amplifying metasurface is paired with external optics to form a laser cavity; (b) monolithic metasurface lasers in which the metasurface array self-oscillates in a coherent supermode; and (c) metasurfaces which operate below threshold as free-space terahertz amplifiers. The metasurface approach allows the realization of large-area radiating apertures while preserving the sub-wavelength sized of the individual metallic waveguide antenna elements. This has resulted in significantly improved performance and functionality in many categories, including lasers with high-quality beam patterns, high-efficiency lasers with scalable output powers, broadband spectral tunability of single-mode emission, and free-space amplification of terahertz beams.

Quantum cascade lasers (QCLs) emitting in the 4-10 micron wavelength range are treated with emphasis on key issues not covered in previous books on QCLs. The foremost issue discussed: what does it take to achieve continuous-wave (CW) operation to multi-watt powers in a highly efficient manner, is of interest to a wide range of applications. A comprehensive review of the temperature dependence of the electro-optical characteristics of QCLs is presented by including elastic scattering and carrier-leakage triggered by elastic and inelastic scattering, thus accounting for all mechanisms behind the device internal efficiency. Maximizing the CW wall-plug efficiency via conduction-band and elastic-scattering engineering, and photon-induced carrier transport is treated in detail. Then coherent-power scaling is discussed for both one- and two-dimensional (2-D) structures with emphasis on the optimal solution: high-index-contrast (HC) photonic-crystal (PC) lasers. Grating-coupled surface-emitting lasers are also treated with emphasis on those needed for 2-D HC-PC lasers; that is, devices most likely to operate in diffraction-limited, single-lobe beam pattern to multi-watt CW output powers

Laser spectroscopy in the mid-infrared (IR) and terahertz (THz) spectral regions is of particular interest since it gives access to the fundamental rovibrational bands of many molecules as well as to molecular rotational bands and lattice vibrations in solid-state samples. Among all modern laser technologies, optical frequency combs have emerged as the most promising sources for high-resolution spectrometers with broadband spectral coverage. We provide an overview of recent advancements in electrically pumped quantum- and interband-cascade-laser (QCL and ICL) frequency combs operating in the mid-IR and THz regions as an important step towards field applications with truly integrated and scalable frequency-comb technology. We also discuss dual-comb spectroscopy techniques that offers fast chemical sensing without the need for optomechanical tuning or dispersive spectrometers, and provide an overview of the spectroscopic capabilities provided by QCL and ICL dual-comb spectrometers. Measurement approaches and recent experimental implementations of mid-IR and THz dual-comb spectroscopy of chemicals by various research groups using QCL and ICL frequency-comb technology are discussed

The chapter reviews long wavelength mid-infrared quantum cascade lasers (QCLs) emitting between 15 and 28 μm. Historically, 15 μm was a border wavelength above which the QCL performances dramatically degraded, which was partly due to an increase in optical losses in the devices with approaching the Reststrahlen band. This intrinsic limitation caused by multi-phonon absorption sets forbidden or favorable spectral areas depending on the employed materials. The chapter considers specific properties of long wavelength mid-infrared QCLs based on different materials, as well as more general issues related to the QCL design in this long-wavelength frontier of the mid-infrared. The discussed results are presented in the chronological order for each QCL material system, which allows the reader to follow the advances in the field.

Chapter devoted to the basic quantum properties of entanglement and separability. Introduces the Schmidt decomposition for pure states and the positive partial transpose criterion for mixed states as entanglement witnesses. Introduces the famous Einstein–Podolsky–Rosen paradox and its implementation in terms of qubits, then the Bell inequality, quickly reviewing the experimental demonstrations that quantum mechanics violates this inequality. Gives examples of the use of entanglement in a quantum algorithm to accelerate an information task, namely a database search (Grover algorithm) and the possibility of teleportation of a quantum state.

This chapter presents the theoretical framework that allows us to describe evolutions in the general case using Kraus operators as the main tool. It considers in detail the phenomenon of decoherence and gives examples of such maps. It shows that any evolution can be considered as unitary by going in a larger Hilbert space. The Lindblad equation for the evolution of the density matrix appears as a particular case of evolution in the short memory or Markov approximation. Up-jumps and down-jumps are also described within this framework using cavity damping, spontaneous emission, and the shelving technique as examples.

Appendix J: mechanical effects of light on matter. The appendix first derives the two forces exerted by a light beam on an atom: the radiation pressure force and the dipole force. Appropriate combinations of beams lead to a friction force that slows the atoms (Doppler cooling), and to a trapping force in the so-called magneto-optics trap (MOT). One then considers the forces exerted on ions, leading to trapping in a suitable geometry of electrodes and fields. Two configurations are used, named Paul and Penning traps. In addition, it is possible to cool the ions to their ground motional state using sideband cooling. It is also possible to trap and cool macroscopic nano-objects, such as microdiscs, membranes, toroids, etc. in a resonant optical cavity.

This chapter focuses on the propagation of vortex beams inside a GRIN medium. After an overview in Section 8.1 of polarization-related topics such as the Stokes vector and the Poincare sphere, the concept of a phase singularity is discussed in Section 8.2. This concept is used to form specific combinations of the modes that act as vortices with different state of polarizations. In Section 8.3, we discuss the techniques used for generating different types of vortex beams. Section 8.4 shows that a vortex beam also exhibits the self-imaging property during its propagation inside a GRIN medium. The impact of random mode coupling is also discussed in this section. Vortex-based applications of GRIN fibers are covered in Section 8.5.

This chapter provides an introduction to the subject known as gradient-index optics. In Section 1.1, we present a historical perspective on this subject before introducing the essential concepts needed in later chapters. Section 1.2 is devoted to various types of refractive-index profiles employed for making gradient index devices, with particular emphasis to the parabolic index profile because of its practical importance. In Section 1.3, we discuss the relevant properties of such devices such as optical losses, chromatic dispersion, and intensity dependence of the refractive index occurring at high power levels. The focus of Section 1.4 is on the materials and the techniques used for fabricating gradient-index devices in the form of a rod or a thin fiber

This chapter focuses on the effects of loss or gain in a graded-index (GRIN) medium. In Section 6.1, we discuss the impact of losses on the modes of such a medium. Section 6.2 considers the mechanisms used for providing optical gain inside a GRIN medium. Section 6.3 is devoted to Raman amplifiers and Raman lasers, built with GRIN fibers and pumped suitably to provide optical gain. Parametric amplifiers are discussed in Section 6.4, together with the phase matching required for four-wave mixing to occur. The focus of Section 6.5 is on amplifiers and lasers made by doping a GRIN fiber with rare-earth ions. Section 6.6 includes the nonlinear effects and describes the formation of spatial solitons and similaritons inside an active GRIN medium.

This chapter is devoted to the study of dispersive effects that affect short pulses inside a graded-index fiber. An equation governing the evolution of optical pulses inside a GRIN medium is found in Section 4.1. The dispersion parameters appearing in this equation change, depending on which mode is being considered. Section 4.2 focuses on the distortion of optical pulses resulting from differential group delay and group velocity dispersion. Section 4.3 deals with the effects of linear coupling among the modes, occurring because of random variations in the core’s shape and size along a fiber’s length. A non-modal approach is developed in Section 4.4 for the propagation of short optical pulses inside a GRIN medium. The focus of Section 4.5 is on the applications where optical pulses are sent through a GRIN rod or fiber

Appendix H: treats the interaction between a light beam and a linear optical medium. This first part considers the propagation of a light beam in a sample of two-level atoms using a semiclassical approach, calculates the index of refraction of the medium and its gain when there is population inversion, and losses when the ground state is populated. It then treats in a full quantum way linear attenuation or amplification, for which the "3dB penalty" on the signal-to-noise ratio is derived from basic quantum principles. Finally, it considers the input–output relation for the two input modes of a linear beamplitter, an important example of a symplectic map.

This chapter focuses on the impact of partial coherence on the propagation of optical beams inside a GRIN medium. Section 11.1 introduces the basic coherence-related concepts needed to understand the later material. Section 11.2 uses the evolution of cross-spectral density to study whether periodic self-imaging, an intrinsic property of a GRIN medium, is affected by partial coherence of an incoming beam. Section 11.3 employs the Gaussian-Schell model to discuss how the optical spectrum, the spectral intensity, and the degree of coherence associated with a Gaussian beam change with the beam’s propagation inside a GRIN medium. The focus of Section 11.4 is on Gaussian beams that are only partially polarized. The concept of the polarization matrix is used to study how the degree of polarization evolves when such a partially coherent Gaussian beam is transmitted through a GRIN medium