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Stochastic Gradient Langevin Dynamics (SGLD) have been widely used for Bayesian sampling from certain probability distributions, incorporating derivatives of the log-posterior. With the derivative evaluation of the log-posterior distribution, SGLD methods generate samples from the distribution through performing as a thermostats dynamics that traverses over gradient flows of the log-posterior with certainly controllable perturbation. Even when the density is not known, existing solutions still can first learn the kernel density models from the given datasets, then produce new samples using the SGLD over the kernel density derivatives. In this work, instead of exploring new samples from kernel spaces, a novel SGLD sampler, namely, Randomized Measurement Langevin Dynamics (RMLD) is proposed to sample the high-dimensional sparse representations from the spectral domain of a given dataset. Specifically, given a random measurement matrix for sparse coding, RMLD first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the measurement matrix. The algorithm analysis shows that RMLD indeed projects a given dataset into a high-dimensional Gaussian distribution with Laplacian prior, then draw new sparse representation from the dataset through performing SGLD over the distribution. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of RMLD beyond baseline methods. 

This work investigates the polarization state of light diffracted from uncoated and gold‐coated InP nanowire photonic crystal arrays grown by selective area epitaxy. Experimental data and finite‐difference time‐domain simulations show that both the intensity and the ellipticity of the polarization state of the diffracted light beam can be controlled by the nanowire dimensions and gold coating, while the diffracted angle remains unchanged with respect to variations of these parameters. A nominally 10 nm‐thick gold film deposited around the nanowires enhances the diffraction intensity by plasmonic effects. These results demonstrate that the controlled conversion of incident linearly polarized light to circularly polarized or rotated linearly polarized diffracted light can find applications in photonic integrated circuits. The high sensitivity of the polarization state with respect to alterations of the nanowire dimension opens new prospects in the areas of semiconductor metrology and microchip inspection as well as for submicron particle detection.

 

2D photonic crystal (PhC) lasing from an InP nanowire array still attached to the InP substrate is demonstrated for the first time. The undoped wurtzite InP nanowire array is grown by selective area epitaxy and coated with a 10 nm thick Al₂O₃film to suppress atmospheric oxidation and band‐bending effects. The PhC array displays optically pumped lasing at room temperature at a pulsed threshold fluence of 14 µJ cm⁻². At liquid nitrogen temperature, the array shows lasing under continuous wave excitation at a threshold intensity of 500 W cm⁻². The output power of the single mode laser line reaches values of 470 µW. Rate equation calculations indicate a quality factor ofQ ≈ 1000. Investigations near threshold reveal that lasing starts from isolated islands within the pumped region before coherently merging into a single homogeneous area with increasing excitation power. This field emits a lasing mode with an average off‐normal angle of ≈6°. Single mode lasing with the nanoarray still attached to the InP substrate opens new design opportunities for electrically pumped PhC laser light sources.