Modes of step-index multimode fibers

Scattering media were the first type of "complex media" for which wavefront shaping techniques were applied. Quickly, applications were developed for multimode fibers as well. One can consider multimode fiber as a complex media; because of its inherent modal dispersion (different modes travel at different speeds) and also because of the possible coupling between modes, the output field of the fiber does not resemble its input one. Wavefront shaping in multimode fibers has had a fast development because of its applications in biomedical endoscopic imaging and for telecommunications, where the exploitation of the spatial modes in multimode fibers offers a promising way to increase data rates compared to single-mode fibers. 

I present here quickly the expression of the modes of a step-index multimode fiber and the so-called linearly polarized modes, that are convenient for manipulation using shaping techniques.

How to use a binary amplitude Deformable Miror Device (DMD) as a phase modulator: The "superpixel" method

I previously presented a technique based on the Lee hologram that allows to use a binary amplitude modulator (like a DLP chip you find in standard projectors) to perform a phase modulation (or amplitude and phase modulation). Recently, a new technique was introduced in [S.A. Goorden et al., Opt. Express (2014)] that allows an accurate complex modulation with less loss in term of spatial resolution. This post is more a highlight on this paper than a proper tutorial. In a nutshell, while the Lee hologram only takes advantage of one dimension to encode the amplitude and phase in fringes, this technique exploits both dimensions of the pixel array using superpixels.

Off-axis holography

Off-axis holography is a popular technique to reconstruct a hologram. It allows retrieving the amplitude and the phase of a field pattern by measuring only one image with a digital camera. It relies on an intereferometric setup with a non-zero angle between the reference beam and the signal beam and requires to numerically filter the spatial frequencies. I provida Matlab and Python example codes.

How to use a binary amplitude Deformable Mirror Device (DMD) as a phase modulator: The Lee hologram method

The optical field measured at the output of a complex medium (multimode waveguide, multimode cavity, scattering medium...) is the result of the interference of the many paths taken by the light. Most of the applications of wavefront shaping techniques in these media rely on taking advantage of these interference effects to force the medium to perform a desired function. For this reason, the phases of the controlled segments of the input wavefront are usually the most important degrees of freedom to control. Common phase-only Spatial Light Modulators (SLMs) have a limited refresh rate (~100 Hz) due to the liquid crystal technology. This limits the applications in media with a low decorrelation time (like biological tissues) or for experiments for which a long optimization process is needed. Although a new class of phase-only SLMs based on deformable mirrors allows high-speed modulations (>30 kHz), these devices are currently very expensive compared to liquid crystal technology and have a limited resolution (~1000 pixels maximum). On the other hand, fast binary-amplitude modulators with high resolutions are widespread and affordable since the technology is the same one as used in commercial digital projectors. In a recent publication, [D.B. Conkey et al., Opt. Express (2012)] introduced a method to use such a binary-amplitude Deformable Mirror Device (DMD) for phase modulation. This technique allows a fast phase modulation (up to 23 kHz) at the cost of a loss of resolution.