C. L. Tang

Saturation and Spectral Characteristics of the Stokes Emission in the Stimulated Brillouin Process

An analysis is given of the saturation effect in the stimulated Brillouin scattering of coherent light waves. It is shown that the three coupled nonlinear wave equations describing the complex amplitudes of the forward‐traveling primary and acoustic waves and the backward‐traveling Stokes wave can be replaced for room‐temperature situations by two coupled first‐order nonlinear equations for the intensities of the primary and Stokes waves. These resulting equations are solved exactly and the solutions describe completely the process of photoelastic amplification of the coherent Stokes wave via stimulated Brillouin scattering in both the linear and the nonlinear saturated regimes. The results also give a more realistic estimate of the intensity of the hypersonic wave generated in the process than that made on the basis of either the Manley‐Rowe relationship, which does not take into account the losses, or the usual linear theories, which do not take into account the saturation effect. It is believed that th...

Transition Probabilities for some Ar II Laser Lines

In the Ar II system transition probabilities are being calculated between states arising from the 3p44p and 3p44s configurations and between states of the 3p44s and 3p5 configurations. We compare these calculations with previous theoretical and experimental work relating to the above‐mentioned transitions as well as to laser data. It is found that the various observed laser transition thresholds between the considered configurations are in reasonable agreement with the calculations. It appears that the various upper maser states are being pumped nonuniformly. It is also found that laser action should persist to rather high current densities. We estimate that, in 2‐mm‐diam tubes, output powers of at least 10 W/cm3 of gas should be obtainable.

Transition Probabilities between Laser States in Carbon Dioxide

Radiative transition probabilities were investigated between certain vibrational levels of carbon dioxide. The number of levels studied was restricted to those that are directly or indirectly involved in the observed laser action. Vibrational wavefunctions were determined by diagonalizing large Hamiltonian matrices (up to 30×30). In the Hamiltonian, nonlinear forces were included and the potential energy contained terms up to fourth order in the normal coordinates. The dipole moment as a function of the normal coordinates was determined by comparing certain observed and calculated absorption coefficients. Reasonable agreement is obtained between theory and experiment for most transitions where experimental information is available. The radiative lifetimes of most vibrational levels were calculated to be rather long. Thus, radiative processes cannot account for relaxation times observed in laser action. Relaxation probably takes place during collisions with other molecules or light atoms. From gain measure...

Spectroscopic Studies of the Ar+ Laser

The spontaneous intensities of all the laser transitions as well as the important cascade transitions into the upper laser states of a typical cw Ar+ laser have been measured. In addition, we give here the calculated Einstein A coefficients and the radiative lifetimes of all the upper states of all these Ar+ transitions. From these results, we have also obtained the population densities and the various pumping rates of all the laser states and those states which contribute significantly to the upper laser states through cascade transitions. On the basis of these and other related data, a number of conclusions on the physical processes taking place in the Ar+ discharge can be reached. Furthermore, some of the previous suggestions and speculations on these processes can now be evaluated on a more quantitative basis; some of these are discussed here.

Phase‐Locking of Laser Oscillators by Injected Signal

The condition for frequency locking of a laser oscillator by an externally injected signal is derived. The results allow one to estimate the minimum‐frequency separation in rotation sensing ring lasers as a function of scattering in the beam path. The formula may also be used as a design criterion in phase‐locking arrays of laser oscillators.

Problem of Spike Elimination in Lasers

We have investigated theoretically and experimentally the conditions under which spiking in the laser output can be completely suppressed. It is predicted that a nonlinear absorber in the cavity producing greater loss at the higher power levels, and vice versa, should be highly effective. Experimental work was carried out with a single‐mode traveling‐wave laser, since in this case the predictions can be most easily checked. Instead of using a nonlinear absorber, a Kerr cell controlled by a feedback circuit was used. It was found, in agreement with theory, that the time delay between the build‐up of the electromagnetic energy in the cavity and the corrective action of the Kerr cell is a rather important parameter. Spike suppression can only be obtained when this time delay is short as compared to the duration of one oscillation pulse.

Self‐Locking of Modes in Lasers

We investigated phase‐locking effects between longitudinal modes in lasers. In order to show the general trend to be expected for a large number of oscillating modes, we treat three‐, four‐, and five‐mode oscillations. The expected phases depend in a complicated manner upon the relaxation times T1 and T2 of the medium, on the degree of inhomogeneous broadening, the mode separation and location of the medium in the cavity. Simple formation of sharp output spikes at the fundamental frequency are expected where crystals like ruby or YAG are placed near the edges of the cavity. Sharp spikes at twice the fundamental frequency are expected when these solids are placed in the center of a cavity. Certain filters, when placed near the edge or center of the cavity are expected to cause similar locking effects. Gases and solids are expected to act quite differently. The calculations are based on the maximum‐emission principle. This principle will be discussed in a later publication. Some experimental results are also presented.We investigated phase‐locking effects between longitudinal modes in lasers. In order to show the general trend to be expected for a large number of oscillating modes, we treat three‐, four‐, and five‐mode oscillations. The expected phases depend in a complicated manner upon the relaxation times T1 and T2 of the medium, on the degree of inhomogeneous broadening, the mode separation and location of the medium in the cavity. Simple formation of sharp output spikes at the fundamental frequency are expected where crystals like ruby or YAG are placed near the edges of the cavity. Sharp spikes at twice the fundamental frequency are expected when these solids are placed in the center of a cavity. Certain filters, when placed near the edge or center of the cavity are expected to cause similar locking effects. Gases and solids are expected to act quite differently. The calculations are based on the maximum‐emission principle. This principle will be discussed in a later publication. Some experimental results are als...

Maximum‐Emission Principle and Phase Locking in Multimode Lasers

In this paper the phase relationships between self‐locked modes in lasers are investigated. The calculations are based on a self‐consistency condition. The electric field in the cavity produces in the medium nonlinear polarization terms. These polarization terms may then be considered acting as source terms onto which the mode oscillations lock. The self‐consistency condition imposed on the phases arises from the fact that the phase‐locked modes must reproduce the originally assumed electric field. We find the calculated phase relationships in essential agreement with earlier predictions based on the maximum‐emission principle. The latter principle assumes that the phase relations which maximize the total rate of‐stimulated emission should grow most rapidly and should be the ones that establish themselves in lasers. The present paper gives additional evidence for the validity of the maximum‐emission principle. In either calculation the basic physical mechanism that is responsible for the phase‐locking eff...

Large‐Signal Effects in Self‐Locked Lasers

Most past studies of mode locking are concerned with conditions near laser threshold. In this paper we use numerical analysis to study large‐signal conditions. Specifically, we restrict ourselves to a traveling wave cavity, a homogeneously broadened line, and a small spatial extent of the medium. The density matrix equations characterizing the medium and Maxwells equations are solved by computer. It is found for small pump power that mode locking and spike formation occur as previously predicted by the small‐signal theory. As the pump intensity is increased, the spike amplitude increases to a certain critical level and then upon further increasing the pump power, the spike repetition frequency increases discontinuously to twice, three times, four times, etc., its original value. The critical spike amplitudes are not simply related to 180° pulses.

Rotational Transition of CO2 Molecule by Collisions

The quantum‐mechanical method of distorted waves for calculating the rotational relaxation rates in H2 as developed by Brout is used here to calculate the relaxation time for the ΔJ=±2 rotational transitions of linear polyatomic CO2 by taking into account the higher partial wave contributions. The intermolecular potential used consists of a spherical part and a nonspherical part with a constant parameter to characterize the deviation of the potential from spherical symmetry. The results obtained indicate that the collision number Z (and hence the relaxation time τ) is a monotonically decreasing function of the temperature T for a given J and is a monotonically increasing function of J for a given T. Except for small values of J, Z and τ for a given T are both approximately proportional to exp(aJ), where a is a constant. Detailed numerical results are also obtained and compared with known experimental results. It is shown that the method used here is not valid when the temperature is too high or whenever Z...