Kensuke Ikeda

Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system

Abstract In the stationary situation the transmitted light by a ring cavity containing a homogeneously broadened two level absorber exhibits a multiple-valued response to a constant incident light. The stability of the stationary state is investigated in the fast limit of the atomic relaxation. The stationary state is not always stable even when it belongs to the branch with a positive differential gain. In some cases all the stationary states becomes unstable and the transmitted light exhibits a “chaotic” behavior.

High-dimensional chaotic behavior in systems with time-delayed feedback

Abstract The nature of high-dimensional chaos exhibited by a class of delay-differential equation is investigated by various methods. This delay-differential equation models systems with time delayed feedback such as nonlinear optical resonators. We first describe briefly the bifurcation phenomena exhibited by the system: With an increase in a control parameter representing the energy flow rate, periodic states bi(multi)furcate themselves successively, forming a hierarchy of multistable periodic states with increasing complexities. Finally each branch of multistable periodic states makes transition to chaos. The possibility of applying such a multistability as a memory device for complicated information is discussed. In the chaotic regime each of the bifurcated states, in turn, merge successively into fewer sets of states with larger attractor dimensions, and finally a single developed chaos with a very large attractor dimension is formed. Lyapunov analysis is introduced to study the high-dimensional chaotic states. The Lyapunov vectors as well as Lyapunov spectrum are shown to be very useful to understand the underlying mechanism of the successive merging process mentioned above. Characteristics of developed chaos are investigated by high-pass filtered time series (HFTS). The intermittency characteristics of the HFTS changes markedly at a certain frequency. The Lyapunov analysis reveals that this frequency corresponds to a characteristic Lyapunov mode number. This characteristic number can be looked upon as the dimension of subspace in which active chaotic information is generated and is different from the attractor dimension in the customary sense.

Study of a high-dimensional chaotic attractor

The nature of a very high-dimensional chaotic attractor in an infinite-dimensional phase space is examined for the purpose of studying the relationships between the physical processes occurring in the real space and the characteristics of high-dimensional attractor in the phase space. We introduce two complementary bases from which the attractor is observed, one the Lyapunov basis composed of the Lyapunov vectors and the another the Fourier basis composed of the Fourier modes. We introduce the “exterior” subspaces on the basis of the Lyapunov vectors and observe the chaotic motion projected onto these exteriors. It is shown that a certain statistical property of the projected motion changes markedly as the exterior subspace “goes out” of the attractor. The origin of such a phenomenon is attributed to more fundamental features of our attractor, which become manifest when the attractor is observed from the Lyapunov basis. A counterpart of the phenomenon can be observed also on the Fourier basis because there is a statistical one-to-one correspondence between the Lyapunov vectors and the Fourier modes. In particular, a statistical property of the high-pass filtered time series reflects clearly the difference between the interior and the exterior of the attractor.

Hierarchical multistability and cooperative flip-flop operation in a bistable optical system with distributed nonlinear elements

A bistable optical system with distributed nonlinear elements is proposed. Novel functions are derived from the collective nature of the optical elements. Collective phenomena including spatial period-doubling bifurcations, hierarchical multistabilities, and various types of cooperative all-optical flip-flop operations are predicted to take place in the proposed optical device.

Streak camera investigation of superradiance development

Abstract An evolution of the superradiant pulse has been investigated as a function of atomic number density using a picosecond streak camera. We have observed an evidence that, when the atomic number density is increased, we pass through a pre-superradiant regime before we go to the (true) superradiant regime. The experiment was performed in a coherently two-photon-excited three-level system, however the result discussed here may be regarded as true for two-level systems.

An unstable mode selection rule: Frustrated optical instability due to competing boundary conditions

Abstract Self-oscillation phenomenon which occurs in a system with more than one spatial boundary condition may fall into “frustration” from competition between resonance conditions due to the multiple boundaries. In this paper we study a nonlinear optical instability in a compound resonator which is a typical example of this phenomenon. In this system, for a fixed control parameter the asymptotic behaviour is just oscillation at a single frequency. However, as the rule which determines the oscillation frequency contains chaos, the final oscillation frequency shows a very sensitive dependence on the ratio of lengths of the resonators in the compound cavity. Elementary number-theoretic method is successfully applied to the analysis of this phenomenon and an almost complete selection rule for the oscillating mode is established. The selection rule explains very well the recent experiments. This can be regarded as a typical example of a system in which the final pattern itself is dynamically stable, but the choice of the pattern is unstable with respect to noise in the environment.

Cooperative cascade emission

Abstract An experimental and theoretical study has been performed on the generating process of a cascade emission in a sample three-level system where the ground and the highest excited levels have been initially brought into a coherent superposition state by two-proton excitation. Experimentally the forward and the backward emissions of the upper and the lower transitions of the cascade were observed in Li, and each of the emission lines showed a characteristic growth. In the theoretical analysis it is found that a dephasing in the prepared superposition state is required for the cascade emission as a coupled three level superradiance to grow. Using the concepts of delay time, threshold, lifetime, etc. of the cooperative cascade emission, the general behavior of the experimental results is explained.

Theory of Cooperative Cascade Emission. I. : Linear Stochastic Theory

The time evolution of the cascade omission from an assembly of the three-level atoms excited by two-photon process is investigated under a linear approximation. The propagation effect and the stochastic nature of the quantum noise are fully taken into account. It is found that the time evolution of the emitted radiation shows different behaviors in the three time stages: In the earliest stage a negative feedback mechanism due to the two-photon coherence is important, and the emitted radiation exhibits a characteristic growing behavior peculiar to the cascade system; in the intermediate one this mechanism is destroyed by the dephasing, and a superradiant growth begins; and finally in the latest one this growth is suppressed by the dephasing of the active polarization, and a stationary radiation appears.

T3 in a model of a nonlinear optical resonator

Abstract Oscillations characterized by three incommensurate frequencies (three-dimensional torus of T3) appear in a model of a nonlinear optical resonator driven by a laser beam with transversally inhomogeneous identity distribution. Destruction of T3 leading to chaos occurs when a combination harmonic of two frequencies grows suddenly in the vicinity of the third frequency (and vice versa).

Theory of Cooperative Cascade Emission. II. : Nonlinear Evolution

The characteristics of the cooperative cascade emission is studied by taking into account of the nonlinearity due to depopulation. It is shown that the emitted radiation exhibits considerably different behaviors in three regimes of the atomic number density. In the lowest density regime the radiation is essentially a quasi-stationary amplified spontaneous emission (ASE), in the intermediate one it becomes superradiant, and in the highest one it shows a new cooperative behavior peculiar to the cascade system. By using the present theory the experimental results recently observed in Li vapour is explained. It is also shown that the present theory describes the two-level cooperative emission as a specific limiting case.