Laser operation with output feedback pumping and first-order phase transition analogy

Jerry V. Moloney

Humio Inaba

Valentin Torggler, Ivor Krešić, Ticijana Ban +1 more

Abstract A dilute atomic gas in an optical resonator exhibits a phase transition from a homogeneous density to crystalline order when laser illuminated orthogonal to the resonator axis. We study this well-known self-organization phenomenon for a generalized pumping scheme using a femtosecond pulse train with a frequency spectrum spanning a large bandwidth covering many cavity modes. We show that due to simultaneous scattering into adjacent longitudinal cavity modes the induced light forces and the atomic dynamics becomes nearly translation-invariant along the cavity axis. In addition the laser bandwidth introduces a new correlation length scale within which clustering of the atoms is energetically favorable. Numerical simulations allow us to determine the self-consistent ordering threshold power as function of bandwidth and atomic cloud size. We find strong evidence for a change from a second order to a first order self-ordering phase transition with growing laser bandwidth when the size of the atomic cloud gets bigger than the clustering length. An analysis of the cavity output reveals a corresponding transition from a single to a double pulse traveling within the cavity. This doubles the output pulse repetition rate and creates extra substructures in close analogy to a time crystal formation in the cavity output. Simulations also show that multi-mode operation significantly improves cavity cooling generating lower kinetic temperatures at a much faster cooling rate.

Luigi A. Lugiato

Mansour Mortazavi, Surendra Singh

The equation of motion for the slowly varying field amplitude of the laser containing an intracavity saturable absorber (LSA) is where a is the net gain (pump parameter) and b is a saturation parameter of the laser. In our experiment the absorber saturates faster than the amplifier and the parameter b is positive. q(t) is a complex Gaussian white noise random process representing spontaneous emission noise. From Eq. (1) we obtain for the steady-state probability density of light intensity I = | E |2. From this equation various moments of light intensity can be calculated and compared with experimentally measured quantities. For b > 0 the LSA exhibits bistability and a first order phase transition occurs at a = -3b2/16. For negative values of b there is a continuous transition at a = 0. Experiments were carried out on a He—Ne laser with an intracavity Ne absorber cell. The laser was operated close to the center of the absorption line. Slow drifts of light intensity were controlled by an electronic feedback loop. The parameter b was varied by changing the current in the absorber tube. Pump parameter a was then varied by changing passive losses in the cavity by means of an adjustable knife edge. The main beam from the LSA was allowed to fall on a detector/am- plifier combination. The voltage output from the detector was digitized by a multichannel analyzer and a histogram of voltage amplitudes was built up. Since the voltage output from the detector is directly proportional to the light intensity incident on the detector, voltage histogram is a direct representative of the intensity probability distribution. From the measured histogram moments of light intensity were calculated. These results are compared with the theoretical predictions.

S.T. Dembiński, Andrzej Kossakowski