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Physical Review Letters

Nonlinear nonreciprocity and directional bistability in a ring resonator with a quadratic nonlinear medium

Armin Gasch, D. Jäger

Published Nov 9, 1987• 5 citations
Publisher

Abstract

The mutual interaction of counterpropagating waves in a ring resonator containing a medium with second-order dispersive nonlinearity is studied. The theoretical treatment of nonreciprocal propagation is based upon the novel coupling of counterpropagating and mode-locked first- and second-harmonic waves. The experimentally observed transfer characteristics of a high-frequency model system reveal a directionally asymmetric bistability. This nonreciprocity can also be attributed in the time domain to the occurrence of dissipative structures, i.e., to solitons traveling within the resonator.

DOI
10.1103/physrevlett.59.2145

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The mutual interaction of counterpropagating waves in a ring resonator containing a medium with second-order dispersive nonlinearity is studied. The theoretical treatment of nonreciprocal propagation is based upon the novel coupling of counterpropagating and mode-locked first- and second-harmonic waves. The experimentally observed transfer characteristics of a high-frequency model system reveal a directionally asymmetric bistability. This nonreciprocity can also be attributed in the time domain to the occurrence of dissipative structures, i.e., to solitons traveling within the resonator.
In our recent research1, it was suggested that counter-propagating laser beams in a Kerr-nonlinear medium can induce intensity-dependent nonreciprocity which consists in different changes of refractive indecies for both of the waves. Under some conditions, this can result in such directionally asymmetrical effects as (i) directional bistability in a nonlinear ring resonator which allows one to switch the direction of propagation of a dominant mode and (ii) enhancement of the Sagnac effect in a rotating ring resonator.
A substantial enhancement (by orders of magnitude) of the Sagnac effect in a passive ring resonator can be attained by using a nonreciprocal feedback. This feedback is based on the nonreciprocal element controlled by the signal proportional to the difference between intensities of counterpropagating waves, and is an optoelectronic analog of nonlinear nonreciprocity proposed by us earlier. Under some critical conditions, this system can exhibit directional bistability and directional switching of the counterpropagating waves.
Abstract : A substantial enhancement (by orders of magnitude) of the Sagnac effect in a passive ring resonator can be attained by using a nonreciprocal feedback. This feedback is based on the nonreciprocal element controlled by the signal proportional to the difference between intensities of counterpropagating waves, and is an opto-electronic analog of nonlinear nonreciprocity proposed by us early. Under some critical conditions, this system can exhibit directional bistability and directional switching of the counterpropagating waves. (Author)
Two input beams at the same frequency excite the counter-propagating modes of a bidirectional ring cavity. These modes are coupled in the presence of a homogeneously broadened nonlinear medium and the optical device acts as two bistable switches whose characteristics can be mutually controlled. After a proper account of interference between the forward and backward waves, new features of optical bistability in a bidirectional ring cavity are discussed. It is found that when the intensity of one of the incident beams is held fixed in a critical range, the device switches on but never switches off as the intensity of the other beam is first increased and then decreased to zero.