H. Statz

Spectral Output of Semiconductor Lasers

This paper investigates problems associated with multimode oscillations in semiconductor lasers. In particular, even in semiconductors there can exist a spatially nonuniform distribution of excess electrons and holes because a given mode de‐excites electrons most strongly at antinodes and not at all at nodes of the electric vector. This nonuniform distribution encourages the oscillation of other modes which have a different distribution of the electric field vector and which, in particular, have finite electric fields at nodes of the first oscillating mode. Diffusion of electrons and holes tends to wipe out nonuniform carrier distributions. For low temperatures, this diffusion is relatively slow, and for current densities only moderately above the threshold, several modes may oscillate simultaneously. At higher temperatures the suppression of additional modes is much more effective. Because of the complexity of the calculations, the present work had to be restricted to Fabry‐Perot type modes and relativel...

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...

Phase Locking of Modes in Lasers

An investigation is made of the phase‐locking effects in lasers. It is shown that the phases of the simultaneously oscillating modes of lasers are not independent variables as sometimes thought. The calculations have been limited to three modes and homogeneously broadened lines. It is found that the sum of the phases of the low‐ and high‐frequency modes as measured relative to the phase of the center mode assumes a definite value, which depends in turn upon the location of the active medium within the cavity. This phase relationship has a profound effect on experiments conducted with multimode lasers. For example, it is found that there should be essentially no fundamental‐frequency beat note as observed by a square‐law detector when a small laser crystal is placed in the center of an optical cavity.

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.

Multimode Oscillations in Solid‐State Masers

Previous work by the authors on the effects of slow spatial cross relaxation is extended in two directions. First, off‐axis modes are included in the calculations, and thus it becomes possible to calculate the number of oscillating off‐axis modes as a function of the various laser parameters. In this way the expected beam angle of a laser can be predicted. Second, a more detailed analysis of the spiking behavior is given; both regular and irregular spiking trains may be obtained depending upon the laser parameters and the pump power.

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...

Problem of Mode Deformation in Optical Masers

Fox and Li first calculated mode shapes in Fabry‐Perot‐type oscillators assuming a passive homogeneous medium between the mirrors. In laser oscillators the gain is strongly depressed by saturation in regions where the amplitude of the mode is large, thus giving a nonuniform gain distribution in the cavity. In addition, nonuniformities in the excitation may lead to gain variations. Through numerical solutions it is found that even with nonuniform gain distribution in the transverse direction, the lower order optical modes as originally calculated represent the electromagnetic fields in the cavity rather accurately. The present work justifies earlier calculations of the number of oscillating off‐axis modes in lasers.

Chromium Ion Pair Interactions in the Paramagnetic Resonance Spectrum of Ruby

The paramagnetic resonance spectrum of Cr3+ pairs in ruby which interact via exchange and dipolar forces have been studied at 15.74 kMc in the temperature range 1.2° to 700°K. Theoretical analysis predicts and experiments confirm that relatively distant neighbors with negligible exchange coupling give rise to resonance lines which cluster around isolated Cr3+ ion lines. Spin pairs coupled through exchange forces large as compared to the Zeeman or crystalline field energies give rise to lines that cluster around magnetic field values different from those for isolated Cr3+ lines. Exact calculations on an IBM 704 computer are used to assign lines in a given cluster to various neighbor pairs. This assignment together with the temperature dependence of the line intensities are used to determine the exchange forces. For nearest neighbors the exchange constant is 390±50 cm−1 while the 3rd through 11th neighbor shells have exchange interactions of order 1 cm−1. Spin-lattice relaxation is discussed for pairs coupl...