Determining spatial modes of lasers with spatial coherence measurements

Abstract

We explain a technique that extracts both the structure and the modal weights of spatial modes of lasers by analyzing the spatial coherence of the beam. This is the first time, to our knowledge, that an experimental method is being used to measure arbitrary forms of the spatial modes. We applied this method to an edge-emitting Fabry-Perot semiconductor laser with a stripe width of 5 mum and extracted fundamental and first-order lateral modes with relative power weights of 96.2% and 3.8%. There was a single transverse mode.

Improved Modal Reconstruction for Spatially and Spectrally Resolved Imaging $({\rm S}^{2})$

“…For N interfering modes (4) has to be extended with a summation and generalizes to (5) As a direct consequence solution and are related to the intensity distribution of the th mode and the incoherent superposition of all other modes that interfered with the th mode. Therefore, the allocation uncertainty mentioned before depends not longer on the intensity ratio of two single modes but on one single mode and the incoherent superposition of all other modes.…”

“…For anexplicit modal decomposition the relative phase of the modes has to be retrieved. The phase can be retrieved by employing a phase retrieval algorithm applied to near and far field intensity images of the same beam [5]- [8]. Another approach utilizes the orthogonally of modes by employing a computer generated hologram (CGH) to detect the modal content [9].…”

Mode-matched phase diffractive optical element for detecting laser modes with spiral phases

“…Typically, the modal distribution is estimated by visual inspection, but such inspection is inadequate for most applications that involve sensitive optical sensors [8,9], feedback loops in adaptive optics, and diagnostics of temperature induced changes in high power lasers, as well as for laser beam characterization [7,10]. Other far field image processing techniques for extracting modal composition suffer from nonlinearities, have limited dynamic range, and involve complicated time consuming digital processing [11,12]. Still other techniques involve high quality computer generated diffractive optical elements (DOEs), designed by efficient iterative or cell oriented procedures for converting a complex transmittance function into a phase function (encoding) [4,6,7,10,[13][14][15][16][17].…”

Resolving spatial modes of lasers via matrix completion

“…Previously this was solved by using a Jacobian method [16], which is an alternating projection method that alternates between maintaining the orthogonality of modes and a leastsquares fit to the measured data. Still, whatever method is used to collect the data, it would be beneficial to reduce the amount of data needed to successfully retrieve the modes.…”

“…The parameter ϵ is a regularization parameter and is usually set proportional to the noise level. Once the whole mutual intensity matrix is recovered, the modes and power weights of the spatial modes are then found by performing SVD on the recovered complete matrix V. We comment on the difference between the MC method and the Jacobian method [16]. Unlike the Jacobian method, the MC method does not require one to specify the number of modes a priori.…”