Focusing of light within and beyond a strong scattering disordered medium via wavefront shaping (WFS) using a spatial light modulator (SLM) has been demonstrated for speckle-sized target regions over a decade ago, and has since been explored extensively with potential applications for imaging, phototherapy, communications and cryptography. The intensity enhancement scales linearly with the number, M1, of SLM pixels and is unaffected by any correlations in the speckle field of transmitted or reflected light. However, a fundamental question of great importance for applications is the possibility of focusing to regions much larger than a single speckle, where neglect of correlations would predict a decrease in the enhancement as 1/M2, where M2 is the number of speckles in the target region.
It has been known for many years that speckle patterns from highly scattering media have long-range field correlations. We have developed a quantitative theory of the effect of these correlations on large scale focusing and demonstrated excellent agreement between the theory and experiments on the transmission of light through ZnO nanoparticles. The correlations between speckles allows much greater control via WFS of focusing to larger target regions than the simple prediction above. Specifically, for a given sample, each set of experimental illumination conditions defines a measurable dimensionless number, g, which controls focusing efficiency. When the dimensionless size of the target region, M2 > g, significantly enhanced focusing through WFS is possible due to correlations, with the maximal enhancement increasing by M2/g compared to the result in the absence of correlations.
By controlling the many degrees of freedom in the incident wavefront, one can manipulate wave propagation in complex structures. Such wavefront-shaping methods have been used extensively for controlling light transmitted into wavelength-scale regions (speckles), a property that is insensitive to correlations in the speckle pattern. Extending coherent control to larger regions is of great interest both scientifically and for applications such as optical communications, photothermal therapy, and the imaging of large objects within or behind a diffusive medium. However, waves diffusing through a disordered medium are known to exhibit non-local intensity correlations, and their effect on coherent control has not been fully understood. Here, we demonstrate the effects of correlations with wavefront-shaping experiments on a scattering sample of zinc oxide microparticles. Long-range correlations substantially increase the dynamic range of coherent control over light transmitted onto larger target regions, far beyond what would be achievable if correlations were negligible. This and other effects of correlations emerge when the number of speckles targeted, M2, exceeds the dimensionless conductance g. Using a filtered random matrix ensemble appropriate for describing coherent diffusion and the lateral spreading in an open geometry, we show analytically that M2/g appears as the controlling parameter in universal scaling laws for several statistical properties of interest---predictions that we quantitatively confirm with experimental data. Our work elucidates the roles of speckle correlations and provides a general theoretical framework for modeling open systems in wavefront-shaping experiments.
Visible lasers have a wide range of applications in imaging, spectroscopy and displays. Unfortunately, they suffer from coherent artifacts such as speckle. Various compounding techniques have been developed to remove speckle, but these methods usually involve mechanically moving parts and require long acquisition times. A different approach to prevent speckle formation is developing lasers with low spatial coherence. A careful design of the laser cavity can facilitate lasing in many spatial modes with distinct emission pattern. The total emission from those mutually incoherent lasing modes has low spatial coherence. To date, several types of such lasers have been developed, but most of them have emission beyond the visible spectrum, making them unsuitable for imaging or display applications that require visible light.
An alternative way of making visible sources, especially of green color, is frequency doubling of infrared (IR) lasers. We develop a green light source with low spatial coherence via intracavity frequency doubling of a solid-state degenerate laser. The second harmonic emission is distributed over a few thousands independent transverse modes, and exhibits low spatial coherence. A strong suppression of speckle formation is demonstrated for both fundamental and second harmonic beams. Using the green emission for fluorescence excitation, we show the coherent artifacts are removed from the full-field fluorescence images. The achievable high power, low spatial coherence, and good directionality make the green degenerate laser an attractive illumination source for parallel imaging and projection display.
Anderson localization, also known as strong localization, is the absence of diffusion in turbid media resulting from wave interference. The effect was originally predicted for electron motion, and is widely known to exist in systems of less than 3 dimensions. However, Anderson localization of optical photons in 3 dimensional systems remains an elusive and controversial topic. Random Raman lasing offers the unique combination of large gain and virtually zero absorption. The lack of absorption makes long path length, localized modes preferred. The presence of gain offsets what little absorption is present, and preferentially amplifies localized modes due to their large Q factors compared with typical low Q modes present in complex media. Random Raman lasers exhibit several experimentally measured properties that diverge from classical, particle-like, diffusion. First, the temporal width of the emission being 1 to a few nanoseconds in duration when it is pumped with a 50 ps laser is a full order of magnitude longer than is predicted by Monte Carlo simulations. Second, the random Raman laser emission is highly multi-mode, consisting of hundreds of simultaneous lasing modes. This is in contrast to early theoretical results and back of the envelope arguments that both suggest that only a few modes should be present. We will present the evidence that suggests a divergence from classical diffusion theory. One likely explanation, that is consistent with all of these anomalies, is the presence of high-Q localized modes consistent with Anderson localization.
Spectrometers are widely used tools in chemical and biological sensing, material analysis, and light source
characterization. The development of a high-resolution on-chip spectrometer could enable compact, low-cost
spectroscopy for portable sensing as well as increasing lab-on-a-chip functionality. However, the spectral resolution of
traditional grating-based spectrometers scales with the optical pathlength, which translates to the linear dimension or
footprint of the system, which is limited on-chip. In this work, we utilize multiple scattering in a random photonic
structure fabricated on a silicon chip to fold the optical path, making the effective pathlength much longer than the linear
dimension of the system and enabling high spectral resolution with a small footprint. Of course, the random spectrometer
also requires a different operating paradigm, since different wavelengths are not spatially separated by the random
structure, as they would be by a grating. Instead, light transmitted through the random structure produces a wavelengthdependent
speckle pattern which can be used as a fingerprint to identify the input spectra after calibration. In practice,
these wavelength-dependent speckle patterns are experimentally measured and stored in a transmission matrix, which
describes the spectral-to-spatial mapping of the spectrometer. After calibrating the transmission matrix, an arbitrary
input spectrum can be reconstructed from its speckle pattern. We achieved sub-nm resolution with 25 nm bandwidth at a
wavelength of 1500 nm using a scattering medium with largest dimension of merely 50 μm.
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