Phase preservation of orbital angular momentum of light in multiple scattering environment

Abstract

Recent advancements in wavefront shaping techniques have facilitated the study of complex structured light's propagation with orbital angular momentum (OAM) within various media. The introduction of spiral phase modulation to the Laguerre-Gaussian (LG) beam during its paraxial propagation is facilitated by the negative gradient of the medium's refractive index change over time, leading to a notable increase in the rate of phase twist, effectively observed as phase retardation of the OAM. This approach attains remarkable sensitivity to even the slightest variations in the medium's refractive index (∼10^-6). The phase memory of OAM is revealed as the ability of twisted light to preserve the initial helical phase even propagating through the turbid tissue-like multiple scattering medium. The results confirm fascinating opportunities for exploiting OAM light in biomedical applications, e.g. such as non-invasive trans-cutaneous glucose diagnosis and optical communication through biological tissues and other optically dense media.

Fig. 1. Twist of OAM induced by gradual change of the medium refractive index.

a Schematic representation of the central part of the Mach–Zehnder interferometer experiment: the LG beam, carrying OAM imparted by a spatial light modulator (SLM), traverses a cuvette containing the probed medium; interference between the transmitted LG beam and a reference plane wave (an initially expanded Gaussian beam) is then analyzed for intensity and/or retrieved phase distributions. b Spiral modulation of the intensity of $L{G}_0^5$ beam observed experimentally (left) during the gradual increase of the medium’s refractive index, alongside the prediction from theoretical modeling^, (right); blue line corresponds to an increased rate of twist of OAM light along LG beam propagation in the medium. The inset (left) depicts the relative phase twist ($\Theta =\frac{\Psi }{\ell }$) of the OAM of $L{G}_0^5$ beam during gradual increase of the medium refractive index ($\mathrm{\Delta }n=3.69\times {10}^{-4}$). c Relative phase twist of OAM of $L{G}_0^3$ (circles) and $L{G}_0^5$ (squares) beams during the gradual increase of medium refractive index within a range of $2\times {10}^{-5}$; Highlighted colored areas $\mathrm{\Delta }n=5\times {10}^{-6}$) feature corresponding twist of OAM for $L{G}_0^3$ and $L{G}_0^5$ beams, respectively

Fig. 2. Phase memory of OAM of light in multiple scattering.

a Phase distribution (speckle patterns) observed experimentally for the $L{G}_0^3$ beam propagated through the low (d/l∗ = 2) scattering (left) and multiple (d/l∗ = 9.6) scattering (right) media. The axial annular zone (embossed by contours) corresponds to the $L{G}_0^3$ beam as if it were passing through a medium devoid of scattering. b Phase variations manifest at the single speckle grain within a deliberately chosen sector of the $L{G}_0^3$ axial annular area for low scattering (indicated by black circles) and multiple-scattering (represented by red squares) media. The observed phase changes are contingent upon the initial phase configuration $(-3\pi /10\le \mathrm{\Psi }\le 3\pi /10$) established at SLM (schematically shown in inset). c The ensuing alterations in the phase mapping of the speckle pattern within the designated areas (150 × 150 µm) highlighted in the $L{G}_0^3$ axial annular domain (see a), aligning with the prescribed initial phase configuration established at the SLM ($-3\pi /10\le \mathrm{\Psi }\le 3\pi /10$). The upper and lower rows present, respectively, scenarios for low and multiple scattering environments; the scale bar corresponds to 150 µm. Video 1 presents the speckle pattern phase dynamics corresponding to the phase twist at the SLM

Fig. 3. Polarization and phase evolution upon propagation of LG beam through a multiple scattering environment.

a The spiral-like photon trajectories, schematically depicted in Cartesian coordinates, for the scalar linearly x-polarized $L{G}_0^3$ beam as if it were passing from the SLM to the axial annular zone (embossed by contours) at the detector through a medium devoid of scattering. b Radial distribution of the degree of polarization (P) and relative phase shift (ΔΨ) occurring along the open channel as propagated through a multiple scattering medium (d/l^∗ ∼ 10) with the characteristic length of depolarization (ξ_L). The colorful background represents the longitudinal profile of the intensity of the beam along the radial component (ρ)

Fig. 4. Experimental setup.

LD laser diode, P polarizer, FM fiber mount, BC beam collimator, SLM spatial light modulator, M1, M2 mirrors, L1, L2, L3, L4 lenses, PH pinhole, PBS polarizing beam splitter, HWP half-wave plate, S cuvette filled with the sample liquid, BS beam splitter, NF neutral filter, O objective, and CCD camera. A detailed description of the optical setup is presented in the main article text

Fig. 5. Analysis of the LG beam interference patterns.

Schematic presentation of a main steps and principles for determining the relative twist of petals in the on-axis regime; b main steps and principles for the phase retrieval procedure in the off-axis regime