Self-focusing and continuum generation in gases

This book attests to the fact continuum generation has become both technically and conceptually important. Discovered in 1970 (Alfano and Shapiro, 1970a, 1970b), continuum generation is a ubiquitous response of transparent materials (liquids, solids, and gases) to high-power, ultrashort-pulse radiation. This chapter highlights some of these aspects while presenting the sometimes unique characteristics of continuum generation in gases. In addition, we introduce some related results that reflect on the light-atom interaction at high intensities. Gases are ideal media in which to study nonlinear phenomena, such as continuum generation. The choice of low-density rare gases makes the nonlinearity simple since the susceptibility will be purely electronic in nature. Experimentally, the strength of the nonlinearity can be precisely controlled by varying the gas pressure. Gases are ideal in another way. There is a strong conceptual link between the susceptibility and the transition probability. Since there is a lot of emphasis, at present, on understanding multiphoton ionization in rare gases,* concepts being developed in this area can provide a framework for further advances of nonlinear optics in general and continuum generation in particular. In gases, the lowest-order contribution to the nonlinear susceptibility is \u3c7(3). The magnitude of the nonresonant \u3c7(3) for the rare gases (Lehmeier et al., 1985) and for many molecular gases is well known. For xenon \u3b72 = (3\u3c7(31111 (3)/\u3b70 = 2.4 7 10 -25m2/V2atm, where the refractive index \u3b7 is given by \u3b7 = \u3b70 + \u3b72E2 + . . . , E being the rms electric field. \u3c7(3) is proportional to the gas pressure. This chapter is organized around the pressure-dependent strength of the nonlinearity. Much of the content originates from six experimental papers (Corkum et al., 1986a, 1986b; Corkum and Rolland, 1987, 1988a, 1988b; Chin et al., 1988) describing related work at the National Research Council of Canada. Section 2 discusses the aspects of the experiment that are common to all parts of the chapter. Section 3 describes the interaction of ultrashort pulses with very lowpressure gases. Low pressure ensures that nonlinear optics plays no role in the interaction (Corkum and Rolland, 1988a; Chin et al., 1988). This allows the ionization properties of xenon to be established. We will see that relatively high intensities are required to ionize gases with ultrashort pulses (~100fs). In this way, we establish an upper intensity limit for the nonlinear interaction in a purely atomic system. Section 3 also introduces the concept of transient resonances. Although transient resonances are a characteristic of the interaction of ultrashort pulses with matter in the intensity and wavelength range discussed in this chapter, their role in multiphoton ionization depends on the pulse duration. As the gas pressure is increased, we enter the traditional realm of nonlinear optics. If the intensity for the production of significant plasma is not exceeded, changes to the spectrum of the pulse can be investigated under conditions where self-phase modulation is the dominant mechanism. We will see in Section 4 that high-order nonlinear terms must contribute to the spectral bandwidth if the laser intensity reaches 1013 W/cm 2 or higher (Corkum and Rolland, 1988b). A qualitative explanation of why high-order terms must contribute to selfphase modulation is given in Section 5. At still higher pressures the region of continuum generation (Corkum et al., 1986a, 1986b) and self-focusing (Corkum and Rolland, 1988b) is reached. Section 6.1 describes the spectral aspects of continua in gases. In particular, it shows that the spectra are similar for condensed media and for gases. The spatial characteristics of continuum generation are particularly striking (Corkum and Rolland, 1988b). These are described in Section 6.2 with special emphasis on the role of self-focusing in continuum generation. There is a wide range of conditions over which continua are produced with virtually the same beam divergence as the incident diffraction-limited beam (Corkum and Rolland, 1987, 1988b). As the intensity or the gas pressure is increased, conical emission is observed.Peer reviewed: YesNRC publication: Ye