A silicon micro-lens is proposed and analyzed when it is integrated into the photodiode for the application of a backside illuminated (BSI) image sensor (Pixel size is around 1 um). Due to the small dimension of the BSI pixel, each pixel of the image sensor receives from its adjacent pixels cross-talk (x-talk) due to large light incident angle and light diffraction, resulting in reduced sensor MTF and possible color artifacts. A silicon ulens formed between the photodiode and RGB color filter works as an inner lens to improve the focus of the light and guide it into its corresponding pixel, thus decreasing optical x-talk and reducing noise. Since the silicon ulens is integrated into the photodiode and could be doped as part of the photodiode, this design would eliminate any internal reflection caused by traditional inner micro lens solutions (made of Si oxide, Si nitride or polymer). ‘By color' anti-reflection coatings (ARC) on top of the silicon ulens can work as a versatile optical filter to compensate the light spectrum and angular mismatch. Our design and analysis provide a solution to improve the quantum efficiency (QE) and x-talk of the BSI image sensor and the QE enhancement for each pixel are discussed in detail.

We generate and measure the versatile vortex linear light bullet, which combines a high-order Bessel beam and an Airy pulse. This three-dimensional optical wave packet propagates without distortion in any medium, while carrying an orbital angular momentum. Its non-varying feature in linear propagation is verified by a three dimensional measurement. Such a novel versatile linear light bullet can be useful in various applications such as micromachining.

Han Li, Xin Huang, Qian Cao, Yun Zhao, Peiyun Li, Chenchen Wan, and Andy Chong* Department of Electro-Optics and Photonics, University of Dayton, Dayton, OH, 45469, USA Department of Physics, University of Dayton, Dayton, OH 45469, USA Image Sensor Group, ON Semiconductor, San Jose, CA 95134, USA Center for Free-Electron Laser Science, Hamburg 22607, Germany Deutsches-Elektronen Synchrotron (DESY), Hamburg 22607, Germany Department of Physics, University of Hamburg, Hamburg 22761, Germany Intelligent Robot System Department, SIASUN Robot & Automation Co., Ltd., Shenyang 110168, China *Corresponding author: achong1@udayton.edu Received December 1, 2016; accepted January 23, 2017; posted online February 17, 2017

Under nondepleted pump assumption, third harmonic generation (THG) generated by obliquely incident fundamental frequency (FF) waves in a nonlinear multilayer structure is derived analytically by a recursive transfer matrix method (RTMM). This method is useful for determining THG conversion efficiency inside and outside the structure.

Generalization of the transfer matrix method is developed to analyze Type I second-harmonic generation in linear–nonlinear multilayer one-dimensional photonic bandgap structures for oblique incidence of a nondepleted fundamental. The advantage of the transfer matrix method is that it takes into account reflections and interferences between all forward and backward propagating fundamental and second-harmonic waves. The conversion efficiency is calculated as a function of the incident angle of the fundamental and the thicknesses of the linear and nonlinear layers. Specific incident angles and thicknesses may generate relatively high conversion efficiency inside nonlinear material. Our analytical and numerical analyses show that the conversion efficiency of second-harmonic generation depends on the fundamental pump power, second-order susceptibility, and field enhancement in the photonic bandgap structure. Upper bounds on pump intensity can be found for a given incidence angle and sample thickness where the nondepleted pump approximation can be used to model such a nonlinear structure.

We demonstrate a versatile vortex linear light bullet as a vortex Airy-Bessel wave packet for the first time. Its non-varying three-dimensional (3D) vortex field in linear propagation is verified by 3D measurements.

Second harmonic generation generated by an obliquely incident fundamental wave in a nonlinear photonic bandgap structure is analyzed by applying the transfer matrix method, where multiple reflection and interference effects are taken into account. The radiation of fundamental and second harmonic waves from the exit plane of the nonlinear photonic bandgap structure, and the distribution of the fields within the structure are discussed. Under the non-depleted pump wave assumption, the conversion efficiency of the second harmonic wave versus the incident angle of the fundamental is studied in detail.

In recent years, multilayer photonic bandgap structures comprising stacks of alternating layers of positive and negative index have been proposed for a variety of applications, such as perfect imaging, filters, sensors, coatings for tailored emittance, absorptance, etc. Following a brief review of the history of negative index materials, the performance of such stacks is reviewed, with emphasis on analysis of plane wave and beam propagation, and possible applications in sensing. First, the use of the transfer matrix method to analyze plane wave propagation in such structures to determine the transmittance and reflectance is developed. Examples of cases where the Bragg bandgap and the so-called zero <;\(n \) > gap can be used for possible applications in sensing are illustrated. Next, the transfer matrix approach is extended to simulate the spatial evolution of a collection of propagating and nonpropagating TE and TM plane waves (or plane wave spectra) incident on such multilayer structures. The use of the complex Poynting theorem in checking the computations, as well as monitoring powers and the stored electric or magnetic energy in any section of the multilayer stack, is illustrated, along with its use in designing alternating positive and negative index structures with optimal gain to compensate for losses in the negative index material. Finally, the robustness of PIM-NIM stacks with respect to randomness in the dimensions of the PIM-NIM structure is examined. This should be useful in determining the performance of such structures when they are physically fabricated.

The transfer matrix method (TMM) has been used to analyze plane wave and beam propagation through linear photonic bandgap structures. Here, we apply TMM to determine the exact spatial behavior of TE and TM waves in periodic refractive index structures of arbitrary thickness. First, we extend the TMM approach to analyze plane wave propagation through Kerr type nonlinear media. Secondly, we analyze second harmonic fields in a 1D nonlinear photonic crystal for arbitrary angle of incidence of the fundamental plane wave. This allows us to construct the overall transfer matrix of nonlinear waves for the whole nonlinear optical structure from all the individual layer transfer matrices. We extend this method to analyze the effect of second order nonlinearity to beam propagation by applying TMM to the angular spectral components of the beam(s).

The development of electromagnetic (EM) metamaterials for perfect lensing and optical cloaking has given rise to novel multilayer bandgap structures using stacks of positive and negative index materials. Propagation of a collection of TE or TM plane waves, comprising the angular plane wave spectrum, through such structures is analyzed by using the transfer matrix method (TMM) on every plane wave component. Results obtained from this TMM approach for a Gaussian spectrum are compared with those using standard FEM techniques.