Speckles commonly satisfy Rayleigh statistics. However, in many applications, non-Rayleigh speckles with customized intensity statistics are desirable. Here, we present a general method for customizing the intensity statistics of speckle patterns on a target plane. By judiciously modulating the phase front of a monochromatic laser beam, we experimentally generate speckle patterns with arbitrarily tailored intensity probability density functions. Relative to Rayleigh speckles, our customized speckles exhibit radically different topologies yet maintain the same spatial correlation length. The customized speckles are fully developed, ergodic, and stationary&\#x2013;with circular non-Gaussian statistics for the complex field. Propagating away from the target plane, the customized speckles revert back to Rayleigh speckles. This work provides a versatile framework for tailoring speckle patterns with varied applications in microscopy, imaging, and optical manipulation.
We present experimental and numerical studies on principal modes in a multimode fiber with mode coupling. By applying external stress to the fiber and gradually adjusting the stress, we have realized a transition from weak to strong mode coupling, which corresponds to the transition from single scattering to multiple scattering in mode space. Our experiments show that principal modes have distinct spatial and spectral characteristic in the weak and strong mode coupling regimes. We also investigate the bandwidth of the principal modes, in particular, the dependence of the bandwidth on the delay time, and the effects of the mode-dependent loss. By analyzing the path-length distributions, we discover two distinct mechanisms that are responsible for the bandwidth of principal modes in weak and strong mode coupling regimes. Their interplay leads to a non-monotonic transition of the average principal mode bandwidth from weak to strong mode coupling. Taking into account the mode-dependent loss in the fiber, our numerical results are in qualitative agreement with our experimental observations. Our study paves the way for exploring potential applications of principal modes in communication, imaging and spectroscopy.
We designed a high-resolution compact spectrometer based on an evanescently coupled multimode spiral waveguide. Interference between the modes in the waveguide forms a wavelength-dependent speckle pattern, which is used as a fingerprint to identify the input wavelength after calibration. Evanescent coupling between neighboring arms of the spiral results in a non-resonant broadband enhancement of the spectral resolution. Experimentally, we demonstrated a resolution of 0.01 nm at a wavelength of 1520 nm using a 250 &\#x03BC;m radius spiral structure. Spectra containing 40 independent spectral channels are recovered simultaneously, and the operation bandwidth is significantly increased by applying compressive sensing to sparse spectra reconstruction. The ability to achieve such high resolution with low loss in a compact footprint is expected to have a significant impact on low-cost portable sensing and to add functionality to lab-on-a-chip systems.