Lossless Cavity Research Articles

Line structure of radiation emitted from a molecular or atomic gas interacting with one-mode photon states; theory with implications for lasers

We treat the interactions between a molecular (or atomic) gas and a strong one-mode radiational field in an ideal lossless cavity. Our system is perturbed by a very large number of weak collisions which lead to the dephasing of the molecular dipoles. In our system we neglect noise due to spontaneous emission, cavity losses, and relaxation to other molecular levels, and obtain the line profile of the spectral line due to weak collisions and power broadening. A comparison is made between the present effect of power broadening and other works which treat the power spectrum scattered by the two-level system. We find that for real lasers the power broadening should be small relative to the broadening of the laser line by noise effects (like spontaneous emission, imperfections in the cavity and losses), described in other works. In the present work theoretical quantum mechanical methods are developed for treating the interactions between a two-level system and a one-mode radiational field in the presence of weak collisions. The radiational field with the characteristics of an oscillator and the molecular system with the characteristics of a two-level system are described in the present work on the same basis, by the use of the Liouville space formalism. Previous methods for treating collisions in a molecular gas are generalized, and the use of the Liouville space formalism for gaseous lasers is discussed. We find a mathematical description for the oscillatory coupling which exists in a gaseous laser between the radiational oscillator and the two-level molecular gas in the presence of weak collisions.

Progress in Weyl's problem achieved by computational methods

The smoothed eigenvalue distribution for the scalar, and the electromagnetic vector, wave equations are studied for large, but finite wavenumbers k by counting the first 10 6 eigenvalues for various shapes of the domain. The results have implications on the Fermi-gas model of nuclear matter, the electron gas as well as the long-wave acoustic vibration modes in small crystals, the laws of black-body radiation, the acoustics of complicated resonators, and the thermodynamics of perfect gases in a finite volume. The relevance of the computational procedure is compared to that of the analytical methods yielding asymptotic expansions for the eigenvalue distribution which are valid in the limit of infinite k. As an illustrative example for the computational procedure, we present the calculation of the electromagnetic mode density in a lossless cavity resonator with the shape of a circular cylinder. This calculation comprehends the computation of the first 10 4 zeros of the Bessel functions.

Transient behavior of a cavity

An expression for the transient electric field setup in a lossless cylindrical cavity by a short pulse of electrons has been derived by means of the Laplace transformation. It is found that longitudinal and radial fields are set up in the cavity. Expressions for the electric field have been evaluated as a function of time for several different points within a representative cavity.

On the interaction of harmonic oscillators with the radiation field

The radiation of charged harmonic oscillators is investigated. Detailed classification of states of oscillators from the point of view of their radiation is given. The super-radiant behaviour of certain states is derived. The exact solution to the problem of interaction with one mode in the lossless cavity is discussed.

Effect of Non-Uniformity in the Disk-Loaded Waveguides of Electron Linear Accelerators

The effect of incrementing dimensions of a cell in a periodic lossless cavity chain is shown to be represented by series reactances and shunt susceptances loaded on a uniform transmission line. Expressions for the reactances and susceptances are given in terms of the fields in the perturbed regions of the particular cell concerned. The treatment is then applied to the disk-loaded waveguides of electron linear accelerators and a numerical example is given. Some discussions are made on the effect of imperfections of one cell on the frequency of a resonant cavity formed by several cells including the imperfect one, on the mismatches inherent in gradient structures and on the implication of “tuning” of individual cells comprised in a fabricated guide.

Quantum Theory of Radiation. II. Statistical Aspects of Laser Light

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

Quantum Theory of Laser Radiation. II. Statistical Aspects of Laser Light

We have solved a master equation to obtain the diagonal elements of the density matrix for laser light. The master equation represents a generalization of a master equation derived earlier for a single radiation mode interacting with $N$ stationary two-level atoms. The generalization takes into account the pumping scheme which characterizes a three-level laser. For positive temperatures and a lossless cavity, the equilibrium solution of the master equation gives the correct statistical-mechanical description of the atoms and radiation. For negative temperatures, the distribution function for the number of photons in the mode is either exponential or peaked, depending on whether the laser is operating below or above threshold. The calculated intensity fluctuations are in good agreement with semiclassical results for lasers operating slightly above threshold.

A Model of Interacting Radiation and Matter

We investigate the long-time behavior of a model consisting of N two-level atoms in a lossless cavity. The Hamiltonian of our system contains the radiation oscillators in addition to the matter Hamiltonian and the usual ∫j·Adv interaction term. In order to treat the system perturbatively, it would be necessary to remove the tremendous degeneracy of the system. Since this is prohibitively difficult, and since we are interested in the long-time behavior of the system, we solve the quantum mechanical Liouville equation directly for a wide class of physically important initial distribution functions. We show the effective expansion parameter is γ̃Nγ̃ where γ̃ is a dimensionless atomic dipole moment and N is the number of atoms. In the lowest order we find the self-consistent field approximation. In the next order, particle-field correlations appear. We explicitly solve the equations of motion for the particle-field correlations in terms of the average quantities that appear in the self-consistent field approximation. We show the self-consistent field approximation consists of five first-order differential equations. Next we show the equations of motion for the density matrix of the system correct to order (γ̃Nγ̃)2 are equivalent to eight first-order differential equations. The three additional equations are needed to describe the three second moments of the density matrix of the electromagnetic field that appear in second order. Our lowest-order microscopic equations are equivalent to semiphenomenological theories and our higher-order equations contain only the measurable second-order moments of the electromagnetic field in addition to the variables that appear in semi-phenomenological theories.

Incoherence, Quantum Fluctuations, and Noise

An examination is made of the relationship between the uncertainty principle and minimum amplifier noise. First, the concept of coherence is discussed, and an incoherence parameter is defined in terms of the uncertainty that enters into the uncertainty principle. Harmonic oscillator states are examined for coherence. The concept of noise is then discussed and contrasted with incoherence, noise referring to behavior in time of a single system while incoherence involving comparison among members of an ensemble. It is shown, with illustrations, that the two concepts are different, and that an incoherent field of a cavity mode need not exhibit noise. In particular, the zero-point field in a lossless cavity is not noise. The superposition of many incoherent effects, however, usually leads to noise. Spontaneous emission is examined both for coherence and noise. It is shown that the spontaneous emission field of a single molecule is incoherent but does not exhibit noise; the (low order) spontaneous emission from a molecular beam, however, does constitute noise. Spontaneous emission from complex systems is also discussed. The origin of fundamental noise in an amplifier is investigated and is shown to come from spontaneous emission by the amplification mechanism. It is concluded that fundamental noise cannot be determined by a consideration of quantum fluctuations of---or by the application of the uncertainty principle to---the electromagnetic field only, as has been done in several recent articles. The physical significance of the zero-point field is analyzed, and is shown to lie in a formal contribution to spontaneous emission by the mechanism coupled to the field, provided this mechanism is treated quantum mechanically.

Microwave cavity resonators. Some perturbation effects and their applications

Lagrange's equation is utilized to show the analogy of a lossless microwave cavity resonator with the conventional LC network.A brief discussion on the resonant frequencies of a microwave cavity resonator and the two degenerate companion modes H01 and E11 appearing in a cavity is given.The first order perturbation theory of a small deformation of the wall of a cavity is discussed. The effects of perturbation, such as the change in the resonant frequency and the Q of a cavity, the change in the electromagnetic field configurations and hence mixing of modes are also discussed.An expression for the coupling coefficient between the two degenerate modes H01 and E11 is derived with the help of the field equations. Results indicate that in the absence of perturbation the above two degenerate modes can co-exist without losing their individual identities.Several applications of the perturbation theory, such as the measurement of the dielectric properties of matter, study of ferromagnetic resonance, etc., are described.