In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched eigenproblems: for a given structure, find the incident wavefronts and frequencies which are not partially reflected, but are instead transmitted through the scatterer, or dissipated within it. We analyze the relevant symmetry properties, and find that they support exceptional points (EPs) which can be directly probed with steady-state excitation. We study degenerate coherent perfect absorption (CPA EP), which is a specific example of the new kind of EP mentioned above. We show that the CPA EP is chiral in a ring resonator, and use this to design a resonator which predominantly absorbs or reflects light, depending on the direction of incidence. We extend CPA from cavities with a linear dielectric response to include the saturating nonlinearity and dispersion of a two-level absorbing medium. We show that the SALT algorithm in the single-mode regime can also be used to find the saturable CPA modes through a simple mapping. We also clarify the bad-cavity limit of dispersive but linear CPA, identifying new modes that are hybrids of the cavity and atomic degrees of freedom. We present and solve the general problem of scattering from an arbitrary cavity with a saturable two-level amplifying or absorbing medium, generalizing the known phenomenology of bistability that has mainly been studied in structures with little or no spatial complexity. We carefully analyze the validity of approximations used for isolated resonances, and find that the previously used inverse single-pole approximation requires some modification for the case of scattering.
In this thesis we address a series of new problems in non-hermitian optical scattering with increasing degrees of complexity. We develop the theory of reflectionless scattering modes, introducing a novel and broad class of impedance-matched eigenproblems: for a given structure, find the incident wavefronts and frequencies which are not partially reflected, but are instead transmitted through the scatterer, or dissipated within it. We analyze the relevant symmetry properties, and find that they support exceptional points (EPs) which can be directly probed with steady-state excitation. We study degenerate coherent perfect absorption (CPA EP), which is a specific example of the new kind of EP mentioned above. We show that the CPA EP is chiral in a ring resonator, and use this to design a resonator which predominantly absorbs or reflects light, depending on the direction of incidence. We extend CPA from cavities with a linear dielectric response to include the saturating nonlinearity and dispersion of a two-level absorbing medium. We show that the SALT algorithm in the single-mode regime can also be used to find the saturable CPA modes through a simple mapping. We also clarify the bad-cavity limit of dispersive but linear CPA, identifying new modes that are hybrids of the cavity and atomic degrees of freedom. We present and solve the general problem of scattering from an arbitrary cavity with a saturable two-level amplifying or absorbing medium, generalizing the known phenomenology of bistability that has mainly been studied in structures with little or no spatial complexity. We carefully analyze the validity of approximations used for isolated resonances, and find that the previously used inverse single-pole approximation requires some modification for the case of scattering.
Open photonic systems provide a versatile platform for non-Hermitian physics, enabling control over complex spectra, transport, and light-matter interactions. Exceptional points (EPs), at which eigenvalues and eigenvectors coalesce and the governing operator becomes defective, play a central role because they combine branch-point spectral topology, nonanalytic perturbative response, and controllable eigenstate conversion. This Review provides a unified framework for EP photonics by systematically distinguishing exceptional degeneracies according to the underlying operator, spectral variable, boundary conditions, and experimentally accessible observables. We discuss Hamiltonian EPs, absorbing EPs associated with scattering zeros, real-frequency scattering-matrix and Jones-matrix EPs, Bloch and Floquet EPs, and Liouvillian EPs in open quantum systems. We review their spectral topology, static and dynamical encircling, higher-order exceptional structures, and coexistence with bound states in the continuum, together with applications in sensing, lasing, coherent absorption, directional scattering, polarization and wavefront control, nonlinear optics, optical storage, nonreciprocal photonics, and quantum photonics. We also critically assess the current limitations, practical challenges, and future perspectives of EP-based photonic technologies, with particular attention to robustness, noise, scalability, and experimentally measurable performance.
Recent works [Chong et al., Phys. Rev. Lett. 105, 053901 (2010); Wan et al., Science 331, 889 (2011)] have shown that the time-reversed process of lasing at threshold realizes a coherent perfect absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific degree of dissipation, equal in modulus to the gain of the lasing medium, can perfectly absorb coherent optical waves at discrete frequencies that are the time-reversed counterpart of the lasing modes. Here the concepts of time reversal of lasing and CPA are extended for optical radiation emitted by a laser operated in an arbitrary regime, i.e., for transient, chaotic, or periodic coherent optical fields. We prove that any electromagnetic signal E(t) generated by a laser system S operated in an arbitrary regime can be perfectly absorbed by a CPA device ${S}^{\ensuremath{'}}$ which is simply realized by placing inside S a broadband linear absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA devices that perfectly absorb a chaotic laser signal and a frequency-modulated optical wave.
An experimental work [W. J. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, Science 331, 889 (2011)] showed that a resonator that contains a loss medium instead of a gain medium enables coherent perfect absorption (CPA) by interference. Here, we propose an alternative approach to realize such a CPA and coherent perfect transmission (CPT) as well as the switching between CPA and CPT in a cavity quantum electrodynamics (CQED) system by applying an external magnetic field. The proposed CPA and CPT scheme is based on the magnetically induced transparency (MIT) configuration, instead of the conventional electromagnetically induced transparency configuration, which offers a sensitive method to tune CPA and CPT and also is conducive to the flexible control of the CPA and CPT scheme. Under the linear and nonlinear excitation regimes, we derive the approximate analytical solutions of the cavity-output power and the CPA criteria of the CQED system, and find that the CPA can occur at different frequencies in both regimes. In the nonlinear excitation regime, the relationship between the cavity-output power and the cavity-input power can show a bistable characteristic by the control of the static magnetic field, and the CPA point is near the turning point of the cavity-input power on the bistable return hysteresis curve. Furthermore, the line shape and the threshold value for optical bistability can be flexibly controlled by varying the magnetic field under experimentally accessible conditions, thus the magnetic field can well tune the CPA. Also, we compare the analytical and numerical results of the cavity-output power in the nonlinear excitation regime, and they are in good agreement. Our results show that the CQED system based on the MIT configuration can be used as a perfect absorber or nearly perfect transmitter, which may have practical applications in optical logic and optical communication devices.
This paper presents new results for the steady states of a detuned ring laser with a saturable absorber. We employ a semiclassical model which assumes homogeneously broadened two-level atoms. We proceed by solving the Maxwell-Bloch equations for the longitudinal dependence of the steady states of this system, and then simplify our solution by use of the uniform-field approximation. We present uniform-field results for squared electric field versus operating frequency, and for each of these versus cavity tuning and laser excitation. Various cavity linewidths and both resonant and nonresonant amplifier and absorber line-center frequencies are considered. The most notable finding is that cavity detuning breaks the degeneracies found in the steady-state solutions of the fully tuned case. This leads to the prediction that an actual system will bifurcate from the zero-intensity solution to a steady-state solution as laser excitation increases from zero, rather than to the small-amplitude pulsations found for the model with exactly resonant tuning of the cavity and the media line centers. Other phenomena suggested by the steady-state results include tuning-dependent hysteresis and bistability, and instability in both intensity and frequency due to the appearance of one or more new steady-state solutions as tuning is varied. These effects of detuning are being tested by a linearized stability analysis whose results will be reported separately.
When two identical (coherent) beams are injected at a semi-infinite non-Hermitian medium from left and right, we show that both reflection (rL,rR) and transmission (tL,tR) amplitudes are nonreciprocal. In a parametric domain, there exists spectral singularity (SS) at a real energy E=E∗=k∗2 and the determinant of the time-reversed two port scattering matrix, i.e., $|det(S(\ensuremath{-}k))|=|{t}_{L}(\ensuremath{-}k){t}_{R}(\ensuremath{-}k)\ensuremath{-}{r}_{L}(\ensuremath{-}k){r}_{R}(\ensuremath{-}k)|$, vanishes sharply at k=k∗, displaying the phenomenon of coherent perfect absorption (CPA). In the complementary parametric domain, the potential becomes either left or right reflectionless at E=Ez. We rule out the existence of invisibility despite rR(Ei)=0 and tR(Ei)=1 but $T({E}_{i})\ensuremath{\ne}1$, in this avenue. We present two simple exactly solvable models where expressions for E∗, Ez, Ei, and parametric conditions on the potential have been obtained in explicit and simple forms. Earlier, the phenomena of SS and CPA have been found to occur only in the scattering complex potentials which are spatially localized (vanish asymptotically) and have tL=tR.
The ancient laws developed by Snell, Bouguer, Lambert, Fresnel, and Beer, describing the reflection, absorption, and transmission of light by a plane slab of absorbing materials, are applicable only at low irradiances. We have developed new laws that apply at irradiances sufficiently high to produce partial optical saturation of the chromophoric atoms, ions, or molecules of the slab. The radiation field is treated in accordance with the characteristic matrix method of Abelès, based upon Maxwell’s equations. The chromophores are treated in accordance with the optical analogs to the Bloch equations, based upon quantum-statistical mechanics. Our results are presented in the form of an algorithm, by means of which the optical properties are initially estimated assuming no saturation. These properties are then used to compute the field intensities within the medium, and these field intensities are employed in the computation of estimates for the saturated properties. Successive iterations of this procedure are used until the calcuated fields and properties are self-consistent. We show for the first time how to calculate the influence of optical saturation upon the reflectance and angle of refraction of an absorbing sample, and how the method of characteristic matrices can be employed in a problem in nonlinear optics. In addition, the effects of the divergence and finite width of the incident beam, of the cell windows, and the interaction of the forward- and backward-traveling waves to produce a spatial variation in the saturation within the sample, are all treated correctly. The results may therefore be of use to those who wish to design a practical optical memory for a computer, using bistable saturable Fabry-Perot interferometers.