Memory in Nonlinear Ionization of Transparent Solids P. P. Rajeev, 1 M. Gertsvolf, 1,2 E. Simova, 1 C. Hnatovsky, 1 R. S. Taylor, 1 V. R. Bhardwaj, 2 D. M. Rayner, 1, * and P.B. Corkum 1,† 1 National Research Council of Canada, Ottawa, Canada, K1A 0R6 2 Department of Physics, University of Ottawa, Ottawa, Canada, K1N 6N5 (Received 12 September 2006; published 18 December 2006) We demonstrate a shot-to-shot reduction in the threshold laser intensity for ionization of bulk glasses illuminated by intense femtosecond pulses. For SiO 2 the threshold change serves as positive feedback reenforcing the process that produced it. This constitutes a memory in nonlinear ionization of the material. The threshold change saturates with the number of pulses incident at a given spot. Irrespective of the pulse energy, the magnitude of the saturated threshold change is constant ( 20%). However, the number of shots required to reach saturation does depend on the pulse energy. Recognition of a memory in ionization is vital to understand multishot optical or electrical breakdown phenomena in dielectrics. DOI: 10.1103/PhysRevLett.97.253001 PACS numbers: 33.80.Rv, 61.80.Ba, 73.20.Mf, 81.16.Rf Intense, nonresonant femtosecond light pulses will io- nize bulk atomic [1] or molecular gases [2], transparent liquids [3] or solids [4], when focused inside them, through nonlinear interaction with the material. However, solids are unique in that the material in the focal volume remains in place between laser shots. Any nonlinear laser-induced chemical changes will accumulate and the laser-modified material constitutes a feedback mechanism, or a nonlinear memory in the system. Current models of intense light interaction with dielectrics [4 – 6] do not take this memory effect into account, yet it can be very important. If chemi- cal changes lower the ionization threshold, then the feed- back on the ionization process is positive and any plasma nonuniformities will be reinforced. Such a mechanism has been proposed [7] to play a pivotal role in the formation of ordered nanostructures in fused silica following femtosec- ond laser irradiation [8,9]. Feedback must influence the interaction and evolution of any nonlinear phenomena developing over multiple shots. We demonstrate the existence of such a feedback by measuring the transmission of the ionizing pulse through the material. We find that the ionization threshold reduces if the material has been previously ionized. The change, which appears to be permanent, is not caused by scattering or resonant absorption since transmission in the low inten- sity linear regime remains unchanged. We measure that the ionization threshold for fused silica is 1:2  10 13 W=cm 2 on the first shot and that the threshold reduces on each laser shot until it reaches a saturation value that is 20% lower. We show that the saturated threshold is independent of the peak pulse energy. However, we find that the rate at which the threshold approaches the saturated value depends on the free carrier density in the focal region and therefore on the pulse energy. In a multiphoton context, a 20% reduction in the thresh- old is large. Because of the nonlinear interaction it corre- sponds to a large local difference in absorption. Thus our results show a new kind of nonlinearity where chemical change provides feedback that can drive a shot-to-shot nonlinear interaction. No laser-induced breakdown process in dielectrics will be free of this nonlinearity. Our work is related to experiments that have observed incubation effects on damage thresholds for light interact- ing with dielectric surfaces and bulk glass [10 –13]. The causes of these incubation effects are not well established due to the complexity of the damage process. As ionization is the first step in this process it is likely that nonlinear memory is important here too. For our experiment we used 40 fs, 800 nm pulses from a Ti:sapphire laser operating at 400 Hz. The pulses are focused inside the glass samples mounted on precision X, Y stages, using a 0.25 NA microscope objective. A combi- nation of a half-wave plate and a polarizer controls the intensity of incident light. The input beam is prechirped to compensate for material dispersion. We use integrating spheres to monitor both the incoming light fluctuations and the transmitted light. This ensures that the transmitted beam is collected completely, even if scattered or defocused by the plasma formed by ionization. The transmission is measured on a shot-to-shot basis using a computer-controlled data acquisition system. Figure 1 illustrates some of the main characteristics of the nonlinear memory in SiO 2 . With the laser firing at 400 Hz the transmission was measured on a shot by shot basis while the pulse energy was ramped up to 100 nJ and then back down again without moving the focal spot. The figure emphasizes four major features of the interaction. (a) The transmission drops monotonically from unity with the initiation of ionization; it defines an ionization thresh- old. Beyond this threshold, the transmission is reduced with an increase in pulse energy. (b) The transmission curve does not retrace when energy is decreased, indicating a memory induced in the material by the previous laser shots. Since the focus is fixed, the total number of shots incident at the spot increases continuously during the experiment. (c) The ionization threshold is indeed reduced with a previous history of ionization. (d) There is no change in transmission at low energies: the memory can PRL 97, 253001 (2006) PHYSICAL REVIEW LETTERS week ending 22 DECEMBER 2006 0031-9007= 06=97(25)=253001(4) 253001-1  2006 The American Physical Society