Speckle Engineering through Singular Value Decomposition of the Transmission Matrix

Velocities of transmission eigenchannels and diffusion

The diffusion model is used to calculate both the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered samples, such as a layer of paint or a tissue sample, the flux transmitted through the sample may be dramatically enhanced or suppressed relative to predictions of diffusion theory when the sample is excited by a waveform corresponding to a transmission eigenchannel. Even so, it is widely assumed that the velocity of waves is irretrievably randomized in scattering media. Here we demonstrate in microwave measurements and numerical simulations that the statistics of velocity of different transmission eigenchannels are distinct and remains so on all length scales and are identical on the incident and output surfaces. The interplay between eigenchannel velocities and transmission eigenvalues determines the energy density within the medium, the diffusion coefficient, and the dynamics of propagation. The diffusion coefficient and all scattering parameters, including the scattering mean free path, oscillate with the width of the sample as the number and shape of the propagating channels in the medium change.

Compact high-resolution FBG strain interrogator based on laser-written 3D scattering structure in flat optical fiber

We demonstrate a fiber Bragg grating (FBG) strain interrogator based on a scattering medium to generate stable and deterministic speckle patterns, calibrated with applied strain, which are highly dependent on the FBG back-reflection spectral components. The strong wavelength-dependency of speckle patterns was previously used for high resolution wavemeters where scattering effectively folds the optical path, but instability makes practical realization of such devices difficult. Here, a new approach is demonstrated by utilizing femtosecond laser-written scatterers inside flat optical fiber, to enhance mechanical stability. By inscribing 15 planes of pseudo-randomized nanovoids (714 [Formula: see text] 500 voids per plane) as a 3D array in a 1 [Formula: see text] 0.7 [Formula: see text] 0.16 mm volume, the intrinsic stability and compactness of the device was improved. Operating as a wavemeter, it remained stable for at least 60 h with 45 pm resolution over the wavelength range of 1040-1056 nm. As a reflection mode FBG interrogator, after calibrating speckle patterns by applying tensile strain to the FBG, the device is capable of detecting microstrain changes in the range of 0-200 [Formula: see text] with a standard error of 4 [Formula: see text], limited by the translation stage step size. All these characteristics make it an interesting technology for filling the niche of low-cost, high-resolution wavemeters and interrogators which offer the best available trade-off between resolution, compactness, price and stability.

Tailoring 3D Speckle Statistics

We experimentally generate three-dimensional speckles with customized intensity statistics. By appropriately modulating the phase front of a laser beam, the far-field speckles can maintain a desired intensity probability density function upon axial propagation: while evolving into different spatial patterns. We also demonstrate how to design speckle patterns that obtain distinct tailored intensity statistics on multiple designated axial planes. The ability to design 3D speckle statistics opens many possibilities: three-dimensional imaging and sensing, optical trapping, and manipulation.

Multiscale and local engineering of speckle morphology through disordered media

In this Letter, we prompt a novel, to the best of our knowledge, method based on transmission matrix decomposition with wavelets to engineer the speckle morphology behind disordered media. By analyzing the speckles in multiscale spaces, we experimentally realized multiscale and localized control on the speckle size, position-dependent spatial frequency, and global morphology by operating on the decomposition coefficients using different masks. Speckles with contrasting features in different parts of the fields can be generated in one step. Our experimental results demonstrate a high degree of flexibility in manipulating light in a customizable manner. This technique has stimulating prospects in correlation control and imaging under scattering conditions.