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Shortly after their inception, superconducting nanowire single-photon detectors (SNSPDs) became the leading quantum light detection technology. With the capability of detecting single-photons with near-unity efficiency, high time resolution, low dark count rate, and fast recovery time, SNSPDs outperform conventional single-photon detection techniques. However, detecting lower energy single-photons (<0.8 eV) with high efficiency and low timing jitter has remained a challenge. To achieve unity internal efficiency at mid-infrared wavelengths, previous works used amorphous superconducting materials with low energy gaps at the expense of reduced time resolution (close to a nanosecond), and by operating them in complex mK dilution refrigerators. In this work, we provide an alternative approach with SNSPDs fabricated from 5-9.5 nm thick NbTiN superconducting films and devices operated in conventional Gifford-McMahon (GM) cryocoolers. By optimizing the superconducting film deposition process, film thickness and nanowire design, our fiber-coupled devices achieved > 70% system detection efficiency (SDE) at 2 {\mu}m and sub-15 ps timing jitter. Furthermore, detectors from the same batch demonstrated unity internal detection efficiency at 3 {\mu}m and 80% internal efficiency at 4 {\mu}m, paving the road for an efficient mid-infrared single-photon detection technology with unparalleled time resolution and without mK cooling requirements.

Single photon detectors are indispensable tools in optics, from fundamental measurements to quantum information processing. The ability of superconducting nanowire single photon detectors to detect single photons with unprecedented efficiency, short dead time and high time resolution over a large frequency range enabled major advances in quantum optics. However, combining near-unity system detection efficiency with high timing performance remains an outstanding challenge. In this work, we show novel superconducting nanowire single photon detectors fabricated on membranes with 94-99.5 (plus minus 2.07%) system detection efficiency in the wavelength range 1280-1500 nm. The SiO2/Au membrane enables broadband absorption in small SNSPDs, offering high detection efficiency in combination with high timing performance. With low noise cryogenic amplifiers operated in the same cryostat, our efficient detectors reach timing jitter in the range of 15-26 ps. We discuss the prime challenges in optical design, device fabrication as well as accurate and reliable detection efficiency measurements to achieve high performance single-photon detection. As a result, the fast-developing fields of quantum information science, quantum metrology, infrared imaging and quantum networks will greatly benefit from this far-reaching quantum detection technology.

We present a parameter retrieval method which combines ptychography and additional prior knowledge about the object. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of retangule with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cram\'{e}r Rao Lower Bound in both two applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and the correlation of particles in Application 1. For Application 2 the correlation of parameters of the rectangule is discussed.

We investigate the performance of ptychography with noisy data by analyzing the Cram\'{e}r Rao Lower Bound. The lower bound of ptychography is derived and numerically computed for both plane wave and structured illumination. The influence of Poisson noise on the ptychography reconstruction is discussed. The computation result shows that, if the estimator is unbiased, the minimum variance for Poisson noise is mostly determined by the illumination power and the transmission function of the object. Monte Carlo analysis is conducted to validate our calculation results for different photon numbers. The performance of the maximum likelihood method and the approach of amplitude-based cost function minimization is studied in the Monte Carlo analysis also.

In this paper, the design and the characterization of a novel interrogator based on integrated Fourier transform (FT) spectroscopy is presented. To the best of our knowledge, this is the first integrated FT spectrometer used for the interrogation of photonic sensors. It consists of a planar spatial heterodyne spectrometer, which is implemented using an array of Mach-Zehnder interferometers (MZIs) with different optical path differences. Each MZI employs a 3$\times$3 multi-mode interferometer, allowing the retrieval of the complex Fourier coefficients. We derive a system of non-linear equations whose solution, which is obtained numerically from Newton's method, gives the modulation of the sensor's resonances as a function of time. By taking one of the sensors as a reference, to which no external excitation is applied and its temperature is kept constant, about 92$\%$ of the thermal induced phase drift of the integrated MZIs has been compensated. The minimum modulation amplitude that is obtained experimentally is 400 fm, which is more than two orders of magnitude smaller than the FT spectrometer resolution., Comment: 15 pages, 6 figures

The complete characterization of spatial coherence is difficult because the mutual coherence function is a complex-valued function of four independent variables. This difficulty limits the ability of controlling and optimizing spatial coherence in a broad range of key applications. Here we propose a method for measuring the complete mutual coherence function, which does not require any prior knowledge and can be scaled to measure arbitrary coherence properties for any wavelength. Our method can also be used to retrieve objects illuminated by partially coherent beam with unknown coherence properties. This study is particularly useful for coherent diffractive imaging of nanoscale structures in the X-ray or electron regime. Our method is not limited by any assumption about the illumination and hence lays the foundation for a branch of new diffractive imaging algorithms.

We describe a method to control the directional scattering of a high index dielectric nanosphere, which utilizes the unique focusing properties of an azimuthally polarized phase vortex and a radially polarized beam to independently excite insde the nanosphere a spinning magnetic dipole and a linearly polarized electric dipole mode normal to the magnetic dipole. We show that by simply adjusting the phase and amplitude of the field on the exit pupil of the optical system, the scattering of the nanosphere can be tuned to any direction within a plane and the method works over a broad wavelength range.

A high index dielectric nano-sphere can be excited and yet remain radiationless. A method to excite the non-radiating anapole mode of a high index isotropic dielectric nanosphere is presented. With tightly focused radially polarized beam illumination, the main-contributing electric dipole mode and magnetic modes can be zero with only a weak electric quadruple contributing to the total scattering. Further, with a standing wave illumination formed by two counter-propagating focused radially polarized beam under $4\pi$ configuration, the ideal radiationless ananpole can be excited.

The focal field properties of radially/azimuthally polarized Zernike polynomials are studied. A method to design the pupil field in order to shape the focal field of radially or azimuthally polarized phase vortex is introduced. With this method, we are able to obtain a pupil field to achieve a longitudinally polarized hollow spot with a depth of focus up to $12\lambda$ and $0.14\lambda$ lateral resolution for a optical system with numerical aperture 0.99; A pupil field to generate 8 circularly polarized focal spots along the optical axis is also obtained with this method.

We describe and experimentally validate an algorithm to reconstruct an unknown extended object from through-focus measured image intensities blurred by unknown aberrations. It is shown that the method can recover diffraction-limited image quality. The algorithm is a rigorous, computational optics alternative to the conventional adaptive optics which requires additional high end optical devices to measure and to correct the wavefront aberrations. The method can be applied to any optical system that fulfills the condition of incoherent imaging.