The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of four practical three-dimensional systems confined towards one dimension, particularly their observed large increases in ground state binding energy. The true 1D atom is in principle restored when the short distance a tends to zero but it is sometimes claimed that the solutions obtained by the limiting procedure differ from those obtained by solution of the basic Schrödinger equation without any cut-off in the potential. The treatment of the singularity by a limiting procedure for applications to practical systems is endorsed.

We present a classical linear response theory for a magneto-dielectric material and determine the polariton dispersion relations. The electromagnetic field fluctuation spectra are obtained and polariton sum rules for their optical parameters are presented. The electromagnetic field for systems with multiple polariton branches is quantised in 3 dimensions and field operators are converted to 1-dimensional forms appropriate for parallel light beams. We show that the field-operator commutation relations agree with previous calculations that ignored polariton effects. The Abraham (kinetic) and Minkowski (canonical) momentum operators are introduced and their corresponding single-photon momenta are identified. The commutation relations of these and of their angular analogues support the identification, in particular, of the Minkowski momentum with the canonical momentum of the light. We exploit the Heaviside-Larmor symmetry of Maxwell's equations to obtain, very directly, the Einsetin-Laub force density for action on a magneto-dielectric. The surface and bulk contributions to the radiation pressure are calculated for the passage of an optical pulse into a semi-infinite sample.

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.

The name of Poynting is universally recognized for his development of the well-known expression for the flow of electromagnetic energy. Not so well known is Poynting's series of papers on radiation pressure, with 2011 marking the centenary of the last of his 15 publications on this topic. This paper reviews and assesses his radiation-pressure work, with a level of coverage aimed at the reader familiar with the Maxwell electromagnetic theory and interested in the current understanding of radiation pressure. We begin with brief details of Poynting's life, followed by accounts of the relevant publications by others before and during his period of activity in the field from 1903 to 1911. His contributions to the understanding of radiation-pressure effects in the solar system, and the linear and angular momenta of light are discussed, with evaluations from a modern perspective.

Nonlinear dynamics of an optically-injected tunable three-section semiconductor laser have been investigated numerically. For the first time, to the best of our knowledge, we present stability maps, showing different types of the nonlinear behavior versus optical injection parameters, for different points of the tuning curve. Areas of stable locking, limit-cycle, and chaos change in a periodic manner as the lasing frequency undergoes staircase-shaped tuning controlled by the index of the distributed Bragg reflector section. Physical explanation relating this behavior to that of the relaxation oscillation frequency and damping factor is provided. These phenomena suggest that tuning can be an effective way to control laser stability properties.

We review the magnitudes of the photon momenta in free space, derived by Maxwell and Einstein, and those in homogeneous, dispersionless and lossless dielectrics, associated with Abraham and Minkowski. These momenta determine the forces exerted by light beams on material objects, as measured in radiation pressure experiments. It is shown that conservation conditions for components of the electromagnetic energy-momentum tensors derived by Abraham and Minkowski, also by Einstein and Laub, are equivalent relations simply derived from Maxwell's equations. The challenge for theory is the reliable interpretation of experimental momentum transfers from light to matter, which requires extensions of the basic theory to include material dispersion and surface effects. The main experiments are reviewed, together with details of a Lorentz-force theory that accounts for them. It is shown that the Abraham kinetic momentum is associated with the overall motion of a dielectric sample, while the Minkowski canonical momentum applies to the motion of bodies embedded in the dielectric.

The properties of a linear optical amplifier or attenuator in which the input light is coupled to a collection of non-saturable atoms are considered. The photon-number factorial moments and probability distribution of the amplifier output are derived for arbitrary input statistics. Relations are obtained between the output and input variances in photon number, phase-angle cosine, and electric-field magnitude. The effects of amplification and attenuation on signal-to-noise ratio are obtained for both direct and homodyne detection. Particular attention is paid to the extents to which the non-classical properties of photon antibunching and squeezing are preserved by amplification and attenuation. It is found that both properties can at best survive only twofold intensity amplification.

Optically-injected semiconductor lasers have been investigated for many years. The attention has nowadays shifted towards multi-section lasers as they provide new kinds of applications. Recently, an improved travelling-wave (TW) method for simulation of multi-section lasers was presented in which spatio-temporal effects were included. An automated analysis tool was presented for the simulated data to distinguish between different states of dynamics outside the locking bandwidth as this was not possible before. Here, a three-section tunable laser, with and without optical injection, is simulated with the improved TW method and two new results are found. Firstly, the penetration depth of the optical power inside the DBR section of a solitary three-section laser strongly depends on its position on the tuning characteristic curve. It is shown that even with a small variation of the carrier density in the tuning region a large variation of the penetration depth can be observed and, hence, the optical power emitted out of the grating section changes significantly. Secondly, the dynamics of an optically-injected tunable laser for middle and high injection strengths are presented and it is demonstrated that the locking bandwidth becomes symmetric around zero detuning and new regions of higher-order instabilities appear outside the locking region.

It is 100 years since Minkowski and Abraham first gave rival expressions for the momentum of light in a material medium. At the single-photon level, these correspond, respectively, either to multiplying or dividing the free-space value (symbol:see text) by the refractive index (n). The debate that this work started has continued till the present day, punctuated by the occasional publication of 'decisive' experimental demonstrations supporting one or other of these values. We review the compelling arguments made in support of the Minkowski and Abraham forms and are led to the conclusion that both momenta are correct. We explain why two distinct momenta are needed to describe light in a medium and why each appears as the natural, and experimentally observed, momentum in appropriate situations.

Multi-section tunable lasers with optical injection are simulated using the travelling wave approach. By investigating the trajectory of the system the dynamical state can be obtained. The locking bandwidth for a large injection regime and the dynamics outside the locking bandwidth for small injection strengths are presented. It can be seen that the locking bandwidth becomes symmetric around zero detuning for high injection strengths. The dynamics outside the locking bandwidth for small injection strengths are comparable to a single-section single-mode semiconductor laser and it is shown that the stability map exhibits similar patterns.

The travelling-wave method was used to investigate nonlinear spatio-temporal dynamics of a tunable laser under both weak and strong external optical injection. The results suggest effective methods of controlling laser dynamics in network applications.

A new automated analysis of the Poincare map is suggested to perform a complete stability investigation of optically-injected lasers simulated with the travelling wave approach.

Modifications have been introduced to the Fabry-Perot (FP) and the rate equation methods to improve the accuracy of the analysis of the nonlinear dynamics of a laser with external optical injection. Comparison between the modified methods and the more accurate transmission-line laser model (TLLM) shows good agreement, while the computational time of the latter is larger by two or three orders of magnitude. In the FP method, the stimulated recombination term in the carrier density evolution equation is modified to include the backward propagating wave and the exponential longitudinal dependence of the electromagnetic field. In the rate equation method, the optical injection term is modified to account for the contribution of the amplification and losses of the injected light inside the cavity to the average photon density. The derivation explaining the validity of these changes and the mathematical relationship between the two methods is presented. Improved stability maps for different values of the injected optical power and frequency detuning are demonstrated and compared with those obtained by the TLLM. The gain compression effect is included in the FP model, and its effect on the stability properties is discussed.

The frequency spectrum and the power output of a weakly optically-injected semiconductor laser in a period-one state are investigated. It is found that the oscillations in the power output consist of three components each caused by different physical effects, namely the relaxation oscillation frequency, the detuning between master and the slave laser frequency and the photon roundtrip time. For each set of parameters the spatio-temporal dynamics are obtained and the same internal oscillations occur.

Complete pictures of the nonlinear behavior of three optically-injected DFB lasers with different products of coupling coefficient and cavity length described by the travelling wave method are obtained by using a new stability analysis approach.

Different expressions for the linear polarizability of a two-level atom with radiative corrections have been derived recently. We show that an expression said to differ from that obtained by the present authors is in fact consistent with it. The same-sign and opposite-sign prescriptions for linewidths are revisited with respect to the polarizability, the scattering amplitude, and the optical theorem. Both prescriptions represent approximations to more general expressions in the two-level case, and neither is correct for transitions between excited atomic states, as we demonstrate by calculating the linear polarizability of a three-level atom.