Stability Condition of a Haken-Lorentz Equation with Self-Feedback Light Field

A Haken-Lorentz equation with self-feedback light field as well as its stability condition were gained through a series of mathematic process, and the stability judgements of the equation under 6 groups of parameters were gained using the stability condition, then a MATLAB simulation was carried out on the equation and the movement orbits of the equation were gained. It shows that when the stability condition gives a stable judgement, the movement orbit in the mathematic simulation is a single helix ends in a stable point, which shows that the simulation results are stable too; when the stability condition gives an unstable judgement, the movement orbits in the mathematic simulation are two chaotic helixes, which shows that the simulation results are unstable too. The judgements which result from the stability condition are consistent with the MATLAB simulation judgements, which shows that this stability condition can be a criterion of the Haken-Lorentz equation with self-feedback light field in some parameter ranges.

Quasi-Common-Path Laser Feedback Interferometers for Precision Measurement of Non-Cooperative Targets

In this paper, we report a novel quasi-common-path laser feedback interferometer (QLFI) for highly stable, high-resolution and non-contact displacement measurement. QLFI measures the displacement of the target by measuring the phase of feedback light. In addition to the target-generated feedback light (frequency shifted by 2#), a reference mirror generates a reference feedback light which is frequency shifted by #. The phase variations of both feedback lights are measured by heterodyne detection simultaneously and their difference offers the phase variations caused only by target displacement. When the optical path lengths of the reference and measuring feedback light are nearly the same, the phase fluctuations caused by the environment and laser instability are effectively removed. The heat-induced deformation of a He-Ne laser tube is successfully in-line measured using QLFI.