Self-Focusing of TE01and TM01Light Beams: Influence of Longitudinal Field Components

The self-focusing (SF) of T${\mathrm{E}}_{01}$ and T${\mathrm{M}}_{01}$ ruby-laser pulses in C${\mathrm{S}}_2$ was studied experimentally and theoretically. The T${\mathrm{E}}_{01}$ and T${\mathrm{M}}_{01}$ modes are characterized by strictly transverse circularly electric and magnetic fields, respectively. Rotational symmetry and, in the case of T${\mathrm{E}}_{01}$, absence of longitudinal field components allow computational predictions on the selffocusing which are valid even close to a "catastrophic" focus where scalar approximations become problematic. Comparison between the critical powers of T${\mathrm{E}}_{01}$ and T${\mathrm{M}}_{01}$ yields information on the induced birefringence selectively from the focal zone. The difference in critical powers depends on the convergence of the light beam incident on the nonlinear medium and disappears for parallel incidence. These theoretical predictions are supported by our experimental findings: giant pulses (∼70 nsec, ∼300-kW peak) and mode-locked pulse trains (∼1 nsec, ≥1-MW peak) in the T${\mathrm{E}}_{01}$ mode were obtained from a $Q$-switched ruby laser by an appropriate mode selection. These pulses could be easily converted into T${\mathrm{M}}_{01}$ by rotating the electric field by 90°. Little difference in critical power of the two modes was seen with singlemode pulses; but at 1-nsec duration a distinct difference in threshold developed with increasing convergence. This finding is clear evidence for the influence of longitudinal field components (of T${\mathrm{M}}_{01}$) on nonlinear light propagation—a phenomenon which, to our knowledge, has never been observed before. Interestingly, the experimental results are closest to the theoretical values for electrostriction and not to the ones attributed to the optical Kerr effect. Although a restraint in conclusions is necessary in view of the well-known complications of the SF process, it may tentatively be concluded that electrostriction plays an important role in the focal zone even at pulse durations as short as 1 nsec—which in turn provides an estimate for the size of the focus.