Anomalously wide continuous tuning range of the emission frequency of an injection laser with an external selective resonator

Abstract

By using the Lewis-Riesenfeld quantum invariant theory and properly choosing Hermitian invariant operator, a closed solution of the Schrödinger equation is derived for two forced quantum oscillators with mixing of two modes, and the quantum fluctuations in the output fields are evaluated. For the initial two-mode squeezed number or squeezed coherent state, in some particular conditions, the time evolution of the oscillators can not only preserve the initial two-mode squeezing, but also produce squeezing in the individual modes; and exhibit a periodical squeezing behaviour. For the initial two-mode number state or coherent state, there is no squeezing in the individual and mutual quadrature phases of the two-mode fields. Furthermore, regardless of which state above being initially considered, the quantum fluctuations of all the quadrature phases in the output fields are all independent of the driving parameters. In particular, for the initial two-mode coherent state, the variances of the output fields are also independent of other parameters in the Hamiltonian, and always preserve their initial values 1/4.

The complex way to laser diode spectra: example of an external cavity laser strong optical feedback

“…The purpose of the present paper is to perform a detailed theoretical investigation of the effect of mode coupling, due to four-wave mixing (FWM), on the stability properties of the longitudinal modes of the ECL composite cavity. This "self-stabilization" effect was analyzed in [3], [8], [10]- [13]. We show that a stability analysis of each longitudinal mode of the ECL can be easily performed in the frequency domain, and we support our claim through the use of complex frequency diagrams which show how stability is affected by bias current and mode detuning from the frequency of the peak of the external reflectivity.…”

“…Finally, if the unstable mode is moved to even lower frequencies along the locus curve, it simply makes a mode hop to its neighboring mode [3]. This behavior is shown in Fig.…”

“…The stabilizing effect of mode coupling was first studied by Bogatov et al [10], and it has since been analyzed in a number of articles [3], [8], [11]- [13]. In the recent work by Godard et al [8], it was shown that mode coupling gives a tuning range versus output power similar to Fig.…”

“…The expression for the right reflectivity derives directly from the scattering matrix for a Fabry-Pérot etalon (3) where is the round-trip time in the external cavity.…”

“…If we disregard the work on mode-locking, there have been surprisingly few papers addressing the dynamics of laser diodes with strong and filtered optical feedback and with an external cavity that is much longer than the active region. The papers [3]- [9] are some of the exceptions. The ECL with short external cavity operates in much the same way as a DBR laser on which there is a comprehensive Manuscript received July 21, 2004; revised September 21, 2004.…”