PHYSICAL REVIEW A VOLUME 44, NUMBER 1 Type-III intermittency of a laser 1 JULY 1991 D. Y. Tang, J. Pujol, * and C. O. Weiss Physikalisch Tec-hnische Bundesanstait, D 3300 -Braunschweig, Federal Republic of Germany (Received 31 January 1991) We observe transitions to chaos by type-III intermittency of a laser. A family of transitions is found in which the onset of intermittency is preceded by subharmonic period-N states. The laser used is an optically pumped far-infrared ring laser. In dissipative systems making a transition to chaos, three "routes" have been predominantly found: the per- iod-doubling route [1, 2], the quasiperiodicity route [3], and the intermittency route [4-6]. Of the latter, three variations exist. Type-I intermittency is associated with a tangent bifurcation; type-II, with a Hopf bifurcation; and type-III, with a subharmonic bifurcation. No type-III intermittency transition to chaos has yet been observed from optical systems, even though a the- oretical prediction exists [7]. We show here that this type of transition to chaos occurs in lasers, from observations on a NH3 far-infrared (FIR) undirectional ring laser, which was recently found to exhibit the dynamics of the Lorenz model in great detail [8-10]. We found not only one but a family of type-III intermittent transitions to chaos which diA'er in the order of the subharmonic state preceding the onset of intermittency. The experimental setup used is a ring laser, which is de- I (a) scribed in [2], designed to fulfill the conditions of a single-mode traveling-wave operation. The active medi- um is NH3, the aR(7, 7) rotational transition in the Uq =1 vibrational state of ' NH3 is the laser transition. It is op- tically pumped with the P(13) line of the N20 laser via the vibrational ag(8, 7) transition. The backward laser emission at 81-pm wavelength is detected by a Schottky- barrier diode. The pump intensity and the resonator tun- ing are utilized as control parameters. Figure 1 gives the route to chaos that we observe at a ' NH3 gas pressure of 40 pbar and a fixed resonator tun- ing while increasing the pump strength. At low pump in- tensity, the FIR emission pulses periodically. As the pump intensity is increased, a period doubling appears. Increasing the pump intensity further, a second period doubling does not take place as in the usual period- doubling route to chaos [1, 2]; instead, new dynamics, as shown in Fig. 1(c), appear. This time evolution has the characteristics of type-III intermittency. It is clearly seen that the intensity of one component of the period-2 pulses grows while the intensity of the other component de- sjijjit UJJJUUJJiUUULiijjjjiUIUJ~LIJUUI444J~IijiujjjiU~UU44iJJ~IUUJUJ (a) iIUJLILILiuju4UJL i IL ill iUJ Ili I Ijjj it iUIUIII L IL4UiUIUIUIIJI OUI (c) iililllliilillllllillllljili lil)IIII llll I illlllli Ililllil, 'IIII)ll I lll)I IIIIIII IIII (b) uinaialaalisLLUJUallaaI)a, aaan4» igasaa~sle (~) UI] C (L) C I (c) I U. LIIIII~UUi414 &III&slj&i LI I~(A UIN I IUIliiL Ijug IU~I I I I I I 20 40 60 Time ( ps ) 80 FIG. 1. Time dependence of the FIR laser output as the pump intensity is varied. Gas pressure is 40 pbar. (a) Stable oscillatory state. Pump intensity is 4 W/cm2. (b) Period- doubled state. Pump intensity is 6 W/cm'. (c) Type-III inter- mittency. Pump intensity is 7 W/cm . (d) Chaotic state. Pump intensity is 9 W/cm~. 40 60 Time ( ps ) 80 FIG. 2. Intermittency preceded by a period-3 state. Gas pressure is 50 @bar. Pump intensity is 7 W/cm'. From (a) to (c) the resonator detuning is decreased. M4 R35 @1991The American Physical Society