Abstract

Several ultralast all-optical switching devices as nonlinear Mach-Zehnder interferometers (MZI), nonlinear loop mirrors and phase rotators are based on a nonlinear induced phase shift of π or π/2 (antisymmetric MZI). Traditionally, materials exhibiting a cubic nonlinearity have been used lor this purpose. Apart from the large power requirements they have another disadvantage, namely the dependence of the phase modulation on the instantaneous power of the pulse. Thus the phase shift is not homogeneous across the pulse which is equivalent to a strong chirp. This feature leads to a serious degradation of the switching contrast. On the other hand, in recent years it was rediscovered that the cascaded process of fundamental frequency (FF) up- and subsequent down-conversion of the SH wave in a quadratic nonlinear medium can produce a large phase modulation of the FF wave as well. In contrast to the cubic process cascading has two essential peculiarities, namely the unavoidable coexistence of amplitude and phase modulation and the feasibility of the existence of large plateaus in the phase shift in dependence on the power [1]. Two parameters of the cascading process arc crucial for the character of the amplitude and phase modulation. These arc the wavevector mismatch, which can be controlled by quasi-phase matching, and the imbalance of the two FF wave components, controllable by the angle of polarization, if the crystal orientation is such that these both components are excited (vectorial interaction). It is well-known that for large mismatch the results familiar from the cubic scenario are essentially reestablished, i.e. the generation of a strong chirp. The plateaus in the phase shift appear only for small or zero mismatch. Other control parameters as the SH seed intensity and the initial phase shift affect the actual character of the modulation too. By using a fully analytical approach [2,3] we can identify various situation which generate a homogeneous phase shift of π or π/2 across the pulse and where the effect of the detrimental amplitude modulation can be almost excluded. We show that switching characteristics in a quadratic environment can be superior to that known from cubic nonlinearities. For example, we assume we study the case where two slightly unbalanced FF wave components are excited and phase matching holds. It can be shown [2,3] that only the phase of the weaker wave changes by π at that points where this wave is completely depleted and remains constant over a whole period. This phase shift can be used for switching in phase sensitive devices or polarization rotation by π/2. As far as the pulsed input is concerned the portion of the weaker FF pulse exceeding some threshold power acquires the π-phase shift but the wings (about 10% of the total pulse power) remain unshifted. The pulse shape is only slightly affected by the amplitude modulation. The switching contrast can be improved if additionally a SH seed is input. Then the relative phase of all participating waves comes into play. The initial conditions can be adjusted properly to obtain the depletion of the weaker FF wave directly at the beginning of the process. Thus the homogeneous phase shift can be obtained for the entire pulse. Moreover the power necessary to switch the signal is about four times less [3] than in the previous configuration [4]. We show that a π-phase shift mostly required can be only obtained after one period (minimum power) if there is a SH seed. If the phase matched interaction is left the estimation of the phase evolution is less trivial but can nevertheless be described analytically in terms of elliptic functions [2,3]. Based on these analytical results we present various detailed studies of the switching contrast and the power requirements for phase sensitive switching devices by using picosecond pulses. The effect of the pulse walk-off is estimated too and suggestions for its avoidance are put forward.

© 1996 IEEE