Visibility oscillation in a multimode laser interferometer signal and its use in optimizing path lengths

摘要

The interference signal visibility V (difference to sum ratio of intensities at maximum and minimum interference) of an interferometer that uses a multimode laser is here derived for a given laser gain profile and spectral mode separation as a function of the difference ZS between the probe and reference beam optical path lengths and the spectral separation kS between the center of the laser gain profile and the nearest laser mode of higher frequency. kS has a significant effect on V for a given ZS. This parameter, in lasers where it sweeps freely across the gain profile, and other effects, such as various misalignments and optical coupling inefficiencies, render V alone an unreliable parameter for quantifying ZS (for the purpose of reducing it, say). However, the difference to sum ratio of the maximum and minimum V due to variations in kS for a given ZS is an intrinsic property of the laser insensitive to configurational details. Parameter W so defined, therefore, proves very useful for balancing path lengths. This is of particular importance for systems where probe and/or reference beams are transmitted via long single mode optical fibers, so this application is detailed. Optical path lengths within such fibers often cannot be measured to sufficient accuracy by spatial path length measurements due to fiber nonuniformity resulting in variations in the mode's group velocity (needed to convert to optical path length). Two examples are provided using different makes and models of 0.633 μm HeNe lasers with similar specifications. In the first case, the function W(ZS) is calculated directly from the laser's published gain profile and mode separation. In the second case, W is determined empirically for a range of ZS values for a laser with an unknown gain profile in a (heterodyned) interferometer whose interference signal oscillates between maximum and minimum int- nsity at 80 MHz due to the reference beam's optical frequency being acousto-optically upshifted by that amount, while kS spontaneously varies on an acoustic time scale. A single high-bandwidth waveform record for each ZS, therefore, provides all the information needed to determine W. Despite the second laser's gain profile apparently differing in detail, qualitative agreement is achieved between the two methods sufficient to validate the technique.