(b) Write out the equations for the time dependence of ρ11, ρ22, ρ12 and ρ21 assuming that a light field interaction V = -μ12Ee iωt + c.c. couples only levels |1> and |2>, and that the excited levels exhibit spontaneous decay. (8 marks) (c) Under steady-state conditions, find the ratio of populations in states |2> and |3>. (3 marks) (d) Find the slowly varying amplitude ̃ ρ 12 of the polarization ρ12 = ̃ ρ 12e iωt . (6 marks) (e) In the limiting case that no decay is possible from intermediate level |3>, what is the ground state population ρ11(∞)? (2 marks) 2. (15 marks total) In a 2-level atom system subjected to a strong field, dressed states are created in the form |D1(n)> = sin θ |1,n> + cos θ |2,n-1> |D2(n)> = cos θ |1,n> sin θ |2,n-1>

The Quantum Theory of Light

BACKGROUND Singularities are critical points for which the behavior of a mathematical model governing a physical system is of a fundamentally different nature compared to the neighboring points. Exceptional points are spectral singularities in the parameter space of a system in which two or more eigenvalues, and their corresponding eigenvectors, simultaneously coalesce. Such degeneracies are peculiar features of nonconservative systems that exchange energy with their surrounding environment. In the past two decades, there has been a growing interest in investigating such nonconservative systems, particularly in connection with the quantum mechanics notions of parity-time symmetry, after the realization that some non-Hermitian Hamiltonians exhibit entirely real spectra. Lately, non-Hermitian systems have raised considerable attention in photonics, given that optical gain and loss can be integrated as nonconservative ingredients to create artificial materials and structures with altogether new optical properties. ADVANCES As we introduce gain and loss in a nanophotonic system, the emergence of exceptional point singularities dramatically alters the overall response, leading to a range of exotic functionalities associated with abrupt phase transitions in the eigenvalue spectrum. Even though such a peculiar effect has been known theoretically for several years, its controllable realization has not been made possible until recently and with advances in exploiting gain and loss in guided-wave photonic systems. As shown in a range of recent theoretical and experimental works, this property creates opportunities for ultrasensitive measurements and for manipulating the modal content of multimode lasers. In addition, adiabatic parametric evolution around exceptional points provides interesting schemes for topological energy transfer and designing mode and polarization converters in photonics. Lately, non-Hermitian degeneracies have also been exploited for the design of laser systems, new nonlinear optics phenomena, and exotic scattering features in open systems. OUTLOOK Thus far, non-Hermitian systems have been largely disregarded owing to the dominance of the Hermitian theories in most areas of physics. Recent advances in the theory of non-Hermitian systems in connection with exceptional point singularities has revolutionized our understanding of such complex systems. In the context of optics and photonics, in particular, this topic is highly important because of the ubiquity of nonconservative elements of gain and loss. In this regard, the theoretical developments in the field of non-Hermitian physics have allowed us to revisit some of the well-established platforms with a new angle of utilizing gain and loss as new degrees of freedom, in stark contrast with the traditional approach of avoiding these elements. On the experimental front, progress in fabrication technologies has allowed for harnessing gain and loss in chip-scale photonic systems. These theoretical and experimental developments have put forward new schemes for controlling the functionality of micro- and nanophotonic devices. This is mainly based on the anomalous parameter dependence in the response of non-Hermitian systems when operating around exceptional point singularities. Such effects can have important ramifications in controlling light in new nanophotonic device designs, which are fundamentally based on engineering the interplay of coupling and dissipation and amplification mechanisms in multimode systems. Potential applications of such designs reside in coupled-cavity laser sources with better coherence properties, coupled nonlinear resonators with engineered dispersion, compact polarization and spatial mode converters, and highly efficient reconfigurable diffraction surfaces. In addition, the notion of the exceptional point provides opportunities to take advantage of the inevitable dissipation in environments such as plasmonic and semiconductor materials, which play a key role in optoelectronics. Finally, emerging platforms such as optomechanical cavities provide opportunities to investigate exceptional points and their associated phenomena in multiphysics systems.

Exceptional points in optics and photonics.

Rayleigh, Brillouin and Raman scatterings in fibers result from the interaction of photons with local material characteristic features like density, temperature and strain. For example an acoustic/mechanical wave generates a dynamic density variation; such a variation may be affected by local temperature, strain, vibration and birefringence. By detecting changes in the amplitude, frequency and phase of light scattered along a fiber, one can realize a distributed fiber sensor for measuring localized temperature, strain, vibration and birefringence over lengths ranging from meters to one hundred kilometers. Such a measurement can be made in the time domain or frequency domain to resolve location information. With coherent detection of the scattered light one can observe changes in birefringence and beat length for fibers and devices. The progress on state of the art technology for sensing performance, in terms of spatial resolution and limitations on sensing length is reviewed. These distributed sensors can be used for disaster prevention in the civil structural monitoring of pipelines, bridges, dams and railroads. A sensor with centimeter spatial resolution and high precision measurement of temperature, strain, vibration and birefringence can find applications in aerospace smart structures, material processing, and the characterization of optical materials and devices.

Recent progress in distributed fiber optic sensors.

Review of thermal conductivity in composites: Mechanisms, parameters and theory

Since the introduction of optical fiber technology in the field of sensor based on the technique of surface plasmon resonance (SPR), fiber-optic SPR sensors have witnessed a lot of advancements. This paper reports on the past, present, and future scope of fiber-optic SPR sensors in the field of sensing of different chemical, physical, and biochemical parameters. A detailed mechanism of the SPR technique for sensing purposes has been discussed. Different new techniques and models in this area that have been introduced are discussed in quite a detail. We have tried to put the different advancements in the order of their chronological evolution. The content of the review article may be of great importance for the research community who are to take the field of fiber-optic SPR sensors as its research endeavors.

Fiber-Optic Sensors Based on Surface Plasmon Resonance: A Comprehensive Review

1. Introduction 2. Basic optics 3. The optical fiber 4. Ray analysis of planar optical waveguide 5. Graded index optical fibers 6. Material dispersion 7. Planar waveguides 8. Characteristics of a step-index fiber 9. Graded Index fibers 10. Waveguide dispersion and design considerations 11. Sources for optical fiber communication 12. Detectors for optical fiber and communication 13. Fiber optic communication system design 14. Optical fiber Amplifiers 15. Dispersion compensation and chirping phenomenon 16. Optical solitons 17. Single-mode fiber optic components 18. Single mode optical fiber sensors 19. Measurement methods in optical fiber: I 20. Measurement methods in optical fibers: II 21. Periodic interactions in waveguides 22. Ray equation in Cartesian coordinates 23. Ray paths 24. Leaky modes.

An Introduction to Fiber Optics

A new method for tracing rays through graded-index media is presented. The method essentially consists of transforming the ray equation into a convenient form and solving the resulting equation using a standard numerical technique. A detailed comparison of this method with existing methods has also been made, and it is shown that for obtaining a desired accuracy this method requires much less computational effort.

Tracing rays through graded-index media: a new method

We present here a simple matrix method for obtaining propagation characteristics, including losses for various modes of an arbitrarily graded planar waveguide structure which may have media of complex refractive indices. We show the applicability of the method for obtaining leakage losses and absorption losses, as well as for calculating beat length in directional couplers. The method involves straightforward 2 × 2 matrix multiplications, and does not require the solutions of any transcendental or differential equations.

Numerical analysis of planar optical waveguides using matrix approach

We report the exact solution of the scalar-wave equation for a rectangular-core waveguide structure and develop a perturbation analysis for evaluating accurately the propagation characteristics of practical integrated-optical structures. We show that the present method gives results that are more accurate than other analytical methods reported earlier.

Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach

The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc Extreme conditions of matter are encountered both in nature and iq the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where temperatures of IO'K and pressures of several million atmospheres can be achieved) A sound knowledge of the equation of state is a prerequisite to an understanding of processes at very high temperatures and pressures

Ajoy Ghatak

Papers

An Introduction to Fiber Optics

Tracing rays through graded-index media: a new method

Numerical analysis of planar optical waveguides using matrix approach

Analysis of rectangular-core dielectric waveguides: an accurate perturbation approach

An Introduction to Equations of State: Theory and Applications