Self-mode-locking of cw solid-state lasers with a nonlinear antiresonance ring

Structure of the mode-locking zone of a solid-state laser with an antiresonant ring

“…for Àa2, see Ref. [2]). Such propagation can be described by the generalised Landau^Ginzburg equation [7] da dk 1 where g ln2(1 À R 2 )R 2 is the total gain in the system (deduced ignoring nonlinear bleaching).…”

“…As a rule, self-phase modulation (SPM) of the field and self-focusing are used in these modulators. This modulation is the basis of mode locking with the aid of an additional cavity [1] and an antiresonant ring [2]. The Kerr lens effect is used for self-focusing mode locking [3].…”

“…We shall consider a solid-state laser with an antiresonant ring [2] containing a nonlinear element performing SPM and coupled to the laser cavity by a mirror with a reflection coefficient R. The transmission (in terms of the intensity) T of the modulator based on such an antiresonant ring is…”

“…where I is the laser radiation intensity; ' R 2 (s 1) À 1z is the effective nonlinear coefficient; b is the SPM coefficient; s is a parameter describing the nonreciprocity of the antiresonant ring and equal to the ratio of the transverse sections of the beams propagating in the nonlinear element of length z in opposite directions; d is the difference between the phases of these beams [2]. If the change in the field as a result of a single interaction with the modulator is small, so that 'I ( 1 (when the nonlinear element is vixy Q and the nonreciprocity parameter is s 2, this condition is satisfied right up to intensities of the order of 0.5 GW m ÀP ), the laser radiation field a( k, t) ( k is the serial number of a trip through the cavity and t is the local time) propagates across the active medium with the saturated gain a and through a frequency-selective element with the reciprocal of the pass band t f under conditions of optimal discrimination of the initial fluctuation peaks (i.e.…”

“…The solutions of this equation describe self-oscillations during one cavity period at a frequency which depends on the amplitude and can in general be described by elliptic functions. The nature of these self-oscillations is governed by the properties of the phase space of Eqn (2), and this space has an unstable saddle at a point a 0, daadt 0 and a neutral centre at a point a ( À ga') 1a2 , daadt 0. Generation of ultrashort pulses corresponds to a steady-state solution of Eqn (2), which can be represented in the form a A 0 seh(ta(), where…”