IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 34, NO. 10, OCTOBER 1998 1835 Time-Varying Beam Quality Factor and Mode Evolution in TEA CO Laser Pulses F. Encinas-Sanz, J. Serna, C. Mart´ ınez, R. Mart´ ınez-Herrero, and P. M. Mej´ ıas Abstract— The time evolution of the transversal modes in a TEA CO laser cavity has been investigated from the analysis of the time-varying beam quality factor of the emitted pulses. The experiments reveal a significant change in this parameter during the pulse evolution, which can be translated into an evolution of the modes of the laser cavity to reach a nearly stationary behavior. Attention is focused on both the appearance of a particular mode and the duration of its growing process. Index Terms—Beam quality, laser modes, TEA CO lasers. I. INTRODUCTION I N GENERAL, the spatial profile of a laser pulse cannot be expected a priori to remain constant during the pulse evolution [1]–[4]. To characterize this evolution in a rigorous way, time-resolved spatial parameters were recently introduced [5], [6] on the basis of the intensity moments formalism [7]–[11]. Under certain conditions which are often met in practice, as occurs for the pulses considered in this paper, it was shown that the second-order moments that characterize the instantaneous field profile (time-slice approach) at the input and output planes of an optical system are related by the same propagation law used to describe the propagation of nonvarying (time-integrated) moments. In this paper we are interested in the time evolution of the transversal modes in the laser cavity. More specifically, atten- tion is focused on both the instant (within the pulse length) in which the presence of a particular mode begins to be signifi- cant and the time interval during which such mode grows to reach a quasi-stationary spatial behavior. As we will see in the following, this kind of information can be inferred from both the experimental analysis of the time-varying parameter of the pulse and the transversal mode beating measurements. Thus, in Section II, we describe the experimental setup in detail. In Section III, the experimental results concerning the evolution of the beam quality factor during the pulse are presented, and we discuss a number of conclusions about mode appearance and evolution in Section IV. II. EXPERIMENTAL SETUP We consider in this work the pulses emitted by a TEA CO laser device, with the presence of nitrogen in the gas mixture. Manuscript received March 9, 1998; revised June 11, 1998. This work was supported by the Comisi´ on Interministerial de Ciencia y Tecnolog´ ıa of Spain under Project TAP96-2333-E within the framework of EU-1269 Eureka Project. The authors are with the Departamento de ´ Optica, Facultad de Ciencias F´ ısicas, Universidad Complutense, 28040 Madrid, Spain. Publisher Item Identifier S 0018-9197(98)07163-2. Fig. 1. Experimental setup for the measurement of the factor. We have also installed an intracavity diaphragm to reduce the Fresnel number. The laser cavity is a half-symmetric resonator in which the distance between the curved mirror (radius of curvature 10 m) and the planar output mirror is 112 cm [12]. An intracavity Brewster plate has been introduced to obtain a linearly polarized beam. The beam width has been determined at different planes for time slices whose thickness (10 ns) is typically much shorter than the complete pulse duration s). By repeating this series of measurements during the pulse evolution at time intervals of tens of nanoseconds, we can get the beam quality factor resolved in time. The experimental setup is shown in Fig. 1. The ensem- ble pyroelectric camera (Spiricon PYROCAM I), laser beam analyzer, and computer provides the (squared) beam widths averaged during each time slice. To cut such time slices an electrooptical switching device formed by a CdTe crystal and a polarizer was used, with the transmission axis of the polarizer perpendicular to the polarization of the beam emerging from the laser cavity. A high-voltage pulse (8.48 kV) produces a transverse Pockels effect in the CdTe crystal, which turns the polarization of the linearly polarized laser beam. As a result, the beam is transmitted by the crossed polarizer as long as the high-voltage pulse lasts. The system is fired by the polarizer itself, using a spark gap that collects the rejected beam at the polarizer. The duration of the electronic pulse is given by the length of the coaxial forming cable that links the spark gap and the high-voltage charge resistor, and the relative position of the time slice within the laser pulse is controlled by the length of the delay cable between the spark gap and the switching device. A reference time for each slice was measured by splitting the beam before the electrooptical device in such a way that the complete pulse is collected by a fast photodetector (photon drag, 1-ns rise time), and the 0018–9197/98$10.00  1998 IEEE