This paper has two purposes: 1) to clarify the relationship between the quantum theory of radiation, where the electromagnetic field-expansion coefficients satisfy commutation relations, and the semiclassical theory, where the electromagnetic field is considered as a definite function of time rather than as an operator; and 2) to apply some of the results in a study of amplitude and frequency stability in a molecular beam maser. In 1), it is shown that the semiclassical theory, when extended te take into account both the effect of the field on the molecules and the effect of the molecules on the field, reproduces almost quantitatively the same laws of energy exchange and coherence properties as the quantized field theory, even in the limit of one or a few quanta in the field mode. In particular, the semiclassical theory is shown to lead to a prediction of spontaneous emission, with the same decay rate as given by quantum electrodynamics, described by the Einstein A coefficients. In 2), the semiclassical theory is applied to the molecular beam maser. Equilibrium amplitude and frequency of oscillation are obtained for an arbitrary velocity distribution of focused molecules, generalizing the results obtained previously by Gordon, Zeiger, and Townes for a singel-velocity beam, and by Lamb and Helmer for a Maxwellian beam. A somewhat surprising result is obtained; which is that the measurable properties of the maser, such as starting current, effective molecular Q, etc., depend mostly on the slowest 5 to 10 per cent of the molecules. Next we calculate the effect of amplitude and frequency of oscillation, of small systematic perturbations. We obtain a prediction that stability can be improved by adjusting the system so that the molecules emit all their energy h Ω to the field, then reabsorb part of it, before leaving the cavity. In general, the most stable operation is obtained when the molecules are in the process of absorbing energy from the radiation as they leave the cavity, most unstable when they are still emitting energy at that time. Finally, we consider the response of an oscillating maser to randomly time-varying perturbations. Graphs are given showing predicted response to a small superimposed signal of a frequency near the oscillation frequency. The existence of "noise enhancing" and "noise quieting" modes of operation found here is a general property of any oscillating system in which amplitude is limited by nonlinearity.

Comparison of quantum and semiclassical radiation theories with application to the beam maser

Hybrid plasmonic waveguides are described that employ a high-gain semiconductor nanostructure functioning as a gain medium that is separated from a metal substrate surface by a nanoscale thickness thick low-index gap. The waveguides are capable of efficient generation of sub-wavelength high intensity light and have the potential for large modulation bandwidth >1 THz.

/pdf/plasmon-lasers-at-deep-subwavelength-scale-luevvk8jie.pdf

Plasmon lasers at deep subwavelength scale

A simple, rigorous geometrical representation for the Schrodinger equation is developed to describe the behavior of an ensemble of two quantum‐level, noninteracting systems which are under the influence of a perturbation. In this case the Schrodinger equation may be written, after a suitable transformation, in the form of the real three‐dimensional vector equation dr/dt=ω×r, where the components of the vector r uniquely determine ψ of a given system and the components of ω represent the perturbation. When magnetic interaction with a spin ½ system is under consideration, ``r'' space reduces to physical space. By analogy the techniques developed for analyzing the magnetic resonance precession model can be adapted for use in any two‐level problems. The quantum‐mechanical behavior of the state of a system under various different conditions is easily visualized by simply observing how r varies under the action of different types of ω. Such a picture can be used to advantage in analyzing various MASER‐type devi...

Geometrical Representation of the Schrödinger Equation for Solving Maser Problems

This self-contained, comprehensive book describes the fundamental properties of soft x-rays and extreme ultraviolet (EUV) radiation and discusses their applications in a wide variety of fields, including EUV lithography for semiconductor chip manufacture and soft x-ray biomicroscopy. The author begins by presenting the relevant basic principles such as radiation and scattering, wave propagation, diffraction, and coherence. He then goes on to examine a broad range of phenomena and applications. The topics covered include EUV lithography, biomicroscopy, spectromicroscopy, EUV astronomy, synchrotron radiation, and soft x-ray lasers. He also provides a great deal of useful reference material such as electron binding energies, characteristic emission lines and photo-absorption cross-sections. The book will be of great interest to graduate students and researchers in engineering, physics, chemistry, and the life sciences. It will also appeal to practicing engineers involved in semiconductor fabrication and materials science.

X-Rays and Extreme Ultraviolet Radiation: Principles and Applications

The dynamical complexity of optically injected semiconductor lasers

A type of device is described which can be used as a microwave amplifier, spectrometer, or oscillator. Experimental results are given. When operated as a spectrometer, the device has good sensitivity, and, by eliminating the usual Doppler broadening, a resolution of 7 kc/sec has been achieved. Operated as an oscillator, the device produced a frequency stable to at least 4 parts in ${10}^{12}$ in times of the order of a second, and stable over periods of an hour or more to at least a part in ${10}^{10}$. The device is examined theoretically, and results are given for the expected sensitivity of the spectrometer, the stability and purity of the oscillation, and the noise figure of the amplifier. Under certain conditions a noise figure approaching the theoretical limit of unity, along with reasonably high gain, should be attainable.

https://link.aps.org/pdf/10.1103/PhysRev.99.1264

The Maser—New Type of Microwave Amplifier, Frequency Standard, and Spectrometer

https://link.aps.org/pdf/10.1103/PhysRev.95.282

Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of N H 3

PAPER 3 – Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of NH3†*

Structure of HNCS from Microwave Spectra

The molecular beam magnetic resonance method has been used to investigate the spectra of Tl${\mathrm{Cl}}^{35}$ and Tl${\mathrm{Cl}}^{37}$ at zero field. A splitting of the quadrupole line for both isotopes is observed and is attributed to a cosine coupling of the form ${c}_{a}\mathbf{I}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{J}$, between the chlorine spin ${\mathbf{I}}_{a}$ and the rotational angular momentum of the molecule J.

H. J. Zeiger

Papers

The Maser—New Type of Microwave Amplifier, Frequency Standard, and Spectrometer

Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of N H 3

PAPER 3 – Molecular Microwave Oscillator and New Hyperfine Structure in the Microwave Spectrum of NH3†*

Structure of HNCS from Microwave Spectra

MOLECULAR BEAM MAGNETIC RESONANCE SPECTRA OF TlCl$sup 35$ AND TlCl$sup 37$ AT ZERO FIELD