Development of spatial turbulence from boundary-controlled patterns in class-B lasers

We report time-resolved measurements of transverse dynamics in a pulsed custom-made Nd:YAG (yttrium aluminum garnet) broad-area laser, where a dynamic transition from order to turbulentlike patterns appears, without the modification of the Fresnel number. To our knowledge, it is the first time this dynamical transition is observed in a class-B laser. Higher values of the pumping and a higher ratio between the electric field and the inversion population decay rates diminish the time at which the transition takes place. A theoretical model based on the adiabatic approximation allows us to explain the main features of the observed dynamics and to compare the results with those previously seen, especially in broad-area $\mathrm{C}{\mathrm{O}}_2$ lasers.

Figure 1

(Color online) (Top) Experimental setup to measure the instantaneous intensity pattern of our broad-area Nd:YAG laser. FL, flash-lamps; F, fans for air cooled system; HV PS, high voltage power supply; C, capacitor $100\mu \mathrm{F}$; RH, Rodowsky Hall; M1, concave ($10\mathrm{m}$ radius); total reflector; M2, plane output couple (70% reflectivity); BS, beam splitter, NF, filter to avoid overexposure of the camera; IR CCD, camera; D, diffusor; PD, photodiode; O, oscilloscope. (Bottom) Signals recorded in the transient programmable digitizer: (a) pump time profile, (b) output intensity, (c) internal shutter of the camera.

Figure 2

(Color online) Experimental instantaneous intensity patterns (resolution time $9\mathrm{ns}$) for a pumping 2.7 times above threshold. (a) and (b) for $4\mu \mathrm{s}$ of time delay from the beginning of the pulse, (c) for $8\mu \mathrm{s}$ of delay, and (d) for $40\mu \mathrm{s}$ of delay. Pattern size $6\times 6\mathrm{mm}$.

Figure 3

(Color online) Experimental instantaneous intensity patterns (resolution time $9\mathrm{ns}$) for a pumping 2.7 times above threshold. (a) for $77\mu \mathrm{s}$ of time delay from the beginning of the pulse and (b) for $83\mu \mathrm{s}$ of delay. Pattern size $6\times 6\mathrm{mm}$.

Figure 4

(Color online) Experimental instantaneous intensity patterns (resolution time $3\mathrm{ns}$) for a pumping 4 times above threshold. (a), (b), and (c) for $8\mu \mathrm{s}$ of time delay from the beginning of the pulse. Pattern size $6\times 6\mathrm{mm}$. (d) Transverse pattern calculated by using Eq. (3) in Ref. 20, ${\mid {\psi }_{11}(x,y;3\pi ∕4)+{\psi }_{11}^{*}(x,y;3\pi ∕4)\mid }^2$.

Figure 5

(Color online) Experimental instantaneous intensity patterns (resolution time $3\mathrm{ns}$) for a pumping 4 times above threshold. (a) for $23\mu \mathrm{s}$ of time delay from the beginning of the pulse and (b) for $25\mu \mathrm{s}$. Pattern size $6\times 6\mathrm{mm}$.

Figure 6

(Color online) Simulated intensity patterns corresponding to different times along the laser pulse: at the beginning of the pulse (a) for $3\mu \mathrm{s}$, (b) for $5\mu \mathrm{s}$, and in the middle of the pulse (c) for $50\mu \mathrm{s}$. Those patterns were obtained for a pumping value of (a) 2 times above threshold, and (b),(c) 5 times above threshold.

Figure 7

(Color online) Simulated instantaneous patterns showing the evolution of the spatial intensity profile along the pulse for different values of $\gamma ={\gamma }_{\Vert }∕\kappa$. (Top) $\gamma ={10}^{-4}$ (closer to the case of Nd:YAG lasers). (Bottom) $\gamma ={10}^{-2}$ (closer to the case of $\mathrm{C}{\mathrm{O}}_2$ lasers).

Figure 8

(Color online) Simulated instantaneous patterns showing the transition to disorder in a broad area $\mathrm{C}{\mathrm{O}}_2$ laser. (a) for $40\mathrm{ns}$ and (b) for $145\mathrm{ns}$.