External mode locking with feedback from a self‐pumped phase‐conjugator BaTiO<sub>3</sub> crystal

Abstract

An external mode locking technique using RF modulation by an acousto-optic modulator and feedback from a phase-conjugate mirror is presented. A photorefractive BaTiO3 crystal is arranged in self- pumped phase-conjugator geometry. The setup is completely self- aligning and subnanosecond pulses are easily observed for He-Ne (632.8 nm), Ar 1 (514.5 nm), and He-Cd (442 nm) lasers. © 1996 Society of Photo-Optical Instrumentation Engineers. 15 years. 1 The discovery of the single-beam method for producing a phase-conjugate beam ~PCB!, self-pumped phase conjugator 2 ~SPPC!, has greatly enhanced the poten- tial use of OPC in practical applications. Many of these applications are related to interferometry and real-time im- age processing. In this paper we discuss mode locking of multimode, low to moderate power continuous wave ~cw! lasers, yet another interferometric application, using OPC with a BaTiO3 crystal in an SPPC arrangement. In order to produce mode locking, it is necessary that the phases of the various longitudinal modes of a multimode cw laser be coupled with each other. This is usually achieved by placing an active or passive frequency-shifting element inside or outside the laser cavity. However, in some cases the additional loss in the cavity due to a modu- lator may not be desirable, since it may suppress the lasting action ~specially for low-gain blue UV wavelengths! .I n such cases one can still obtain a pulsed laser by externally modulating the laser beam in amplitude or frequency. In this case laser modes are modulated by the free spectral range ~FSR! of the laser and injected, through the output coupler, into the cavity, causing the coupling of the adja- cent modes. 3-6 Consider a laser beam that is propagating through an acousto-optic modulator ~AOM! whose driving frequency is half of the free spectral range of the laser. The AOM diffracts most of the light into the first order with a fre- quency shift equal to that of the acoustic wave frequency. This beam is subsequently reflected by the SPPC mirror onto its original path, resulting in a phase-conjugate beam with a total frequency change equal to the longitudinal mode separation of the laser. This means that a portion of the light from one mode returns into the cavity that has the frequency of its adjacent mode. In other words, the frequency-shifted portion of the laser beam is delayed by a roundtrip cavity transit time. Different longitudinal modes of the injected PCB that have the frequency of their neigh- boring modes are recombined with their neighboring modes in the cavity. With every pass through the AOM and reflec- tion by the SPPC, adjacent longitudinal modes are locked together in their phases, thus forcing all the modes into a fixed-phase relation. This results in a characteristic, peri- odic pulsation of a mode-locked multimode laser. Assume each laser mode is expressed by a complex am- plitude field and the total field ofN11 axial modes is given by: