A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input, i.e., it depends crucially upon the radial variations in the input. Such bistabilities are characterized by much more pronounced changes in transverse profiles than in total transmission. An optical cavity is not required, making such systems good candidates for continuous wave studies of delayed-feedback instabilities which require a round-trip time longer than the medium response time. Trapping bistability and diffraction-free-encoding bistability are two limiting cases of transverse optical bistabilities. Trapping bistability occurs only for a long self-focusing nonlinear medium and arises from self-trapping of a single beam with a single feedback mirror or from cross trapping of two counterpropagating beams. In the diffraction-free-encoding case, diffraction is negligible through the portion of the nonlinear medium performing the encoding, but it is significant through any remaining medium and in the free-space propagation to the mirror and back. This paper is organized as follows: The physics of transverse optical bistabilities is summarized in Section I. Theoretical models are presented in Section II. A thin-sample-encoding (TSE) rings model is defined and shown not only to predict transverse bistability but also to account for the interference rings observed to accompany TSE bistability; it also yields delayed-feedback instabilities with a rich bifurcation sequence. Transverse bistability using a short length of sodium vapor is reported under TSE and DFE conditions in Section III. Recently it was discovered that TSE bistability has been seen only when the feedback beam is displaced from the input by about one beam diameter at the sodium. It remains to be determined just how much the nonconcentric feedback assists the concentric bistability predicted by the TSE rings model. A delayed-feedback instability with a period of twice the round-trip time is also seen.
A transverse optical bistability would not occur with a plane-wave input; it is characterized by pronounced changes in transverse profiles, but not in total transmission.1 The systems studied here consist of a single feedback mirror and a nonlinear medium (Na vapor) sufficiently thin that diffraction is negligible during the nonlinear radially dependent phase encoding. With the input focused beyond (before) the Na and the mirror center of curvature on the input (output) side of the Na, self-defocusing (self-focusing) optical bistability is seen--but only when the feedback is nonconcentric, i.e., the feedback beam is displaced off-axis relative to the input beam. If cylindrical lenses are used to form an elongated focus in the Na, bistability is still seen. This suggests that one-transverse-dimension (ID) theories may be adequate to describe the system's steady-state and transient behavior. ID numerical simulations with nonconcentric feedback are under way.
A transverse optical bistability is defined here as a bistability that would not occur with a plane-wave input; it is characterized by pronounced changes in transverse profiles, but not in total transmission.1-5 In order to use transverse bistabilities to study instabilities of the type first studied by Ikeda6 for a ring cavity, one needs a medium response time τM less than the round-trip time tR between the medium and the feedback mirror. Here instabilities are studied experimentally using a short length of sodium vapor and a far-field mirror (Fig. 1).7,8 This system has advantages over previous9,10 all-optical passive systems for studying instabilities: its input is cw, permitting the study of slowly evolving waveforms; it has little sensitivity to laser frequency shifts, because it has no cavity; its optical nonlinearity arises from a vapor of one-electron atoms, giving hope for a detailed quantitative comparison of experiments and calculations.
Nonlinear optical transverse effects, which arise from the interaction of a Gaussian beam with a nonlinear medium, are discussed. They are cw on-resonance enhancement (CORE), cw off-resonance rings, crosstalk, intracavity phase switching, self-defocusing of a bistable etalon, and thin-sample-encoding (TSE) self-lensing (i.e., self-focusing or self-defocusing) bistability and instabilities. CORE is the enhancement of the on-axis intensity of an on-resonance laser beam in a two-level medium. We report the first observation of CORE using sodium vapor. Cw off-resonance rings, resulting from a pure phase encoding or from simultaneous phase and amplitude encodings, are observed using sodium vapor. These rings have been observed many time before, but we have made the first careful comparison with numerical calculations. Parallel operation and external switching are two crucial themes for the application of bistable optical devices (BODs). For parallel operation, crosstalk between nearby BODs on the same etalon due to diffraction coupling may need to be avoided. Minimum separations needed to ensure independent operation are computed. For external switching, intracavity phase switching using a plane-wave input can switch on (or off) a BOD using an external pulse. The validity of this concept for a Gaussian input is numerically simulated. Self-defocusing effects, resulting in some interesting effects in the transverse bistable loops, are observed using a GaAs-GaAlAs bistable etalon. The results are confirmed by numerical simulations. TSE self-lensing bistability is observed using a short sodium cell and a single mirror. TSE self-lensing bistability results from an enhancement in the feedback via self-lensing of the beam. The lack of an optical resonator and the use of a thin medium make TSE setup a good candidate to study the Ikeda instability. We report the first observation of the Ikeda instability in this all-optical passive system using a cw input. Numerical simulations show a rich bifurcation sequence not yet fully studied experimentally.
Transverse effects are known to play a central role in nonlinear-optical systems.Since experiments are generally performed with lasers with finite transverse dimensions, the transverse nature of the field must be considered.Experimental evidence, for example, indicates that mechanisms in the form of diffusive and diffractive coupling within the medium, free-space diffraction, or some combination of these, can create transverse structures which are important in optical bistability and self-focusing/defocusing.In particular, transverse coupling is attributed to such phenomena as radial dependence of the switch up times of bistable loops, spatial hysteresis, and the formation of solitary waves in passive systems.The dynamical effects of free-space diffraction in a unidirectional ring cavity containing a thin resonant absorber driven by an external coherent signal is considered.Minimal focusing effects exist in this system by incorporating a thin medium whose width is small compared to the cavity length and Raleigh range.There is no restriction on the medium response time relative to the round trip time; i.e. the time-dependent polarization is not adiabatically eliminated from the equations of motion.Free-space diffraction effects are isolated and diffraction and diffusive coupling within the medium is negligible.In this model where free-space diffraction is the dominant mechanism for changing the field profile in the system, shifting, deformation, and radial variation of the bistable loop and spatial hysteresis is attributed to an inherent dispersion induced by the free-space diffraction.
The interaction of two counterpropagating beams in a nonlinear medium leads to many interesting phenomena. One such phenomenon is the occurrence of optical bistability arising from the mutual interaction of the two beams.1 This type of cross-trapping optical bistability is similar to one of those proposed by Kaplan.2 The physics of cross-trapping optical bistability is similar to the self-focusing bistability3 where self-trapping occurs in a single-beam/single-reflector setup. Cross-trapping bistability differs in that it has no external feedback and therefore is the first mirrorless bistability not based on an increasing absorption effect.
A nonlinear oscillator model is used as a prototypical medium for intrinsic optical bistability.1 The phenomenon of intrinsic optical bistability is so named because the medium does not require the optical feedback of a cavity. In this model we retain dispersive effects and introduce a diffractive coupling of the electromagnetic field amplitude. The threshold of the optical bistable device is insensitive to the Fresnel number, which determines the coupling between field amplitudes at different transverse positions.2 This is useful for obtaining reproducible operating characteristics of an array of devices. The medium can be introduced inside a cavity to understand the role of dispersive and diffractive effects in a more fundamental way. The threshold intensity is again insensitive to the Fresnel number. Furthermore, we observe instabilities in the cavity configuration, but no chaotic solutions were found. The periodic instabilities are sensitive functions of the Fresnel number.