Amplitude, Competition, Self-Locking, Beat Frequency, and Time Development in a Three-Mode Gas Laser

Abstract

The unabbreviated Lamb semiclassical equations for the case of three interacting modes are numerically solved for a variety of laser parameters. Steady-state solutions are obtained for the amplitudes, beat frequencies, and time development of the modes by using the Kutta-Merson method of integration. It is found that for some solutions the relative phase angle g becomes constant, and so it is clear under what conditions self-locking is possible. When the modes are unlocked, the value of g varies with time even after the steady-state amplitudes have been achieved. Comparison is made with the locking criteria predicted by approaches to the theory where approximations have been made. A physical interpretation is given for the presence or absence of self-locking in terms of competition and of the ratio 4/AvD. Some general rules are established for the behavior. of the rise time and delay of the onset of oscillation of the three modes.

The generation of ultrashort laser pulses

“…The dynamics of the SML process were first studied theoretically by Lamb (1964) and subsequently by numerous other authors (Uchida 1967, Sargent 1968, Bambini and Burlamacchi 1968, Jones 1968, Jones et a1 1969, Sayers and Allen 1970, Allen and Jones 1971). Lamb's theory, which is based on the self-consistency equations (equations (A1.10) and ( A l -l l ) ) , is extremely difficult to apply when more than two or three modes are oscillating (see Sargent et a1 (1974) for an excellent pedagogical presentation).…”

“…However, this simple theory is inadequate in the case of inhomogeneous broadening and, in fact, o is always negative for x = y when the theory is suitably generalised (Statz et al 1967). Since the MEP is itself open to question, numerous authors have studied the spontaneous mode-locking problem starting from Lamb's self-consistent equations (Lamb 1964, Uchida 1967, Sargent 1968, Bambini and Burlamacchi 1968, Jones 1968, Jones et a f 1969, Sayers and Allen 1970; see Allen and Jones (1971) for an extensive discussion).…”

Active mode-coupling phenomena in pulsed and continuous lasers

“…Self-mode-locking in lasers Many gas and some solid-state lasers will spontaneously 'self-mode-lock' without the use of any modulator or other mode-locking element, although this behaviour usually occurs rather precariously and only over special limited ranges of cavity length, pumping level, and cavity loss. Much theoretical and some experimental attention continues to be given to these phenomena [21][22][23][24][25][26][27][28][29][30]. However, this form of mode-locking does not seem to be sufficiently stable or reliable to be employed in any practical laser system.…”

Frequency stabilized three mode HeNe laser using nonlinear optical phenomena

“…In this paper, we use a semiclassical model of the three mode laser [14,15,16] to describe a frequency stabilization scheme using an intrinsic mixed mode signal. The instrinsic mixed mode signal is directly correlated to the absolute frequency because of nonlinear interactions between adjacent modes.…”