In this article we present a novel approach for determining the electromagnetic modes of photonic multilayer structures. We combine the plane wave expansion method with the method of lines resulting in a fast and accurate computational technique which we named the plane wave admittance method. In addition, we incorporate perfectly matched layers at the boundaries parallel to the multilayer surfaces which allow for easy determination of leaky modes. The convergence of the method is verified for the case of photonic crystal slab showing very good agreement with the results obtained with full three-dimensional plane wave expansion method while the numerical effort is largely reduced. The numerical implementation of the method will be soon available on the web.

We report on experimental evidence of unidirectional transmission of terahertz waves through a pair of metallic gratings with different periods. The gratings are optimized for a broadband transmission in one direction, accompanied with a high extinction rate in the opposite direction. In contrast to previous studies, we show that the zero-order nonreciprocity cannot be achieved. Nonetheless, we confirm that the structure can be used successfully as an asymmetric filter.

We present a closed-form image reconstruction method for single-pixel imaging based on the generalized inverse of the measurement matrix. Its numerical cost scales proportionally with the number of measured samples. Regularization of the inverse problem is obtained by minimizing the norms of the convolution between the reconstructed image and a set of spatial filters. The final reconstruction formula can be expressed in terms of matrix pseudoinverse. At high compression, this approach is an interesting alternative to the methods of compressive sensing based on l1-norm optimization, which are too slow for real-time applications. For instance, we demonstrate experimental single-pixel detection with real-time reconstruction obtained in parallel with measurement at a frame rate of 11 Hz for highly compressive measurements with a resolution of 256 × 256. To this end, we preselect the sampling functions to match the average spectrum obtained with an image database. The sampling functions are selected from the Walsh-Hadamard basis, from the discrete cosine basis, or from a subset of Morlet wavelets convolved with white noise. We show that by incorporating the quadratic criterion into the closed-form reconstruction formula, we can use binary rather than continuous sampling and reach similar reconstruction quality as is obtained by minimizing the total variation. This makes it possible to use cosine- or Morlet-based sampling with digital micromirror devices without advanced binarization methods.

Single-pixel imaging is an indirect imaging technique which utilizes simplified optical hardware and advanced computational methods. It offers novel solutions for hyper-spectral imaging, polarimetric imaging, three-dimensional imaging, holographic imaging, optical encryption and imaging through scattering media. The main limitations for its use come from relatively high measurement and reconstruction times. In this paper we propose to reduce the required signal acquisition time by using a novel sampling scheme based on a random selection of Morlet wavelets convolved with white noise. While such functions exhibit random properties, they are locally determined by Morlet wavelet parameters. The proposed method is equivalent to random sampling of the properly selected part of the feature space, which maps the measured images accurately both in the spatial and spatial frequency domains. We compare both numerically and experimentally the image quality obtained with our sampling protocol against widely-used sampling with Walsh-Hadamard or noiselet functions. The results show considerable improvement over the former methods, enabling single-pixel imaging at low compression rates on the order of a few percent.

The usually reported pixel resolution of single pixel imaging (SPI) varies between 32 × 32 and 256 × 256 pixels falling far below imaging standards with classical methods. Low resolution results from the trade-off between the acceptable compression ratio, the limited DMD modulation frequency, and reasonable reconstruction time, and has not improved significantly during the decade of intensive research on SPI. In this paper we show that image measurement at the full resolution of the DMD, which lasts only a fraction of a second, is possible for sparse images or in a situation when the field of view is limited but is a priori unknown. We propose the sampling and reconstruction strategies that enable us to reconstruct sparse images at the resolution of 1024 × 768 within the time of 0.3s. Non-sparse images are reconstructed with less details. The compression ratio is on the order of 0.4% which corresponds to an acquisition frequency of 7Hz. Sampling is differential, binary, and non-adaptive, and includes information on multiple partitioning of the image which later allows us to determine the actual field of view. Reconstruction is based on the differential Fourier domain regularized inversion (D-FDRI). The proposed SPI framework is an alternative to both adaptive SPI, which is challenging to implement in real time, and to classical compressive sensing image recovery methods, which are very slow at high resolutions.