title: Visibility oscillation in a multimode laser interferometer signal and its use in optimizing path lengths.
abstract: 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 Z(S) between the probe and reference beam optical path lengths and the spectral separation k(S) between the center of the laser gain profile and the nearest laser mode of higher frequency. k(S) has a significant effect on V for a given Z(S). 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 Z(S) (for the purpose of reducing it, say). However, the difference to sum ratio of the maximum and minimum V due to variations in k(S) for a given Z(S) 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(Z(S)) 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 Z(S)values for a laser with an unknown gain profile in a (heterodyned) interferometer whose interference signal oscillates between maximum and minimum intensity at 80 MHz due to the reference beam's optical frequency being acousto-optically upshifted by that amount, while k(S) spontaneously varies on an acoustic time scale. A single high-bandwidth waveform record for each Z(S), 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.
authors.affiliation: Air Force Research Laboratory, Directed Energy Directorate, Kirtland AFB, New Mexico 87117-5776, USA.
authors.forename: E L
authors.initials: EL
authors.lastname: Ruden
authors.forename: J F
authors.initials: JF
authors.lastname: Camacho
authors.forename: A G
authors.initials: AG
authors.lastname: Lynn