Takagi-Taupin Description of X-ray Dynamical Diffraction from Diffractive Optics with Large Numerical Aperture

We present a formalism of x-ray dynamical diffraction from volume diffractive optics with large numerical aperture and high aspect ratio, in an analogy to the Takagi-Taupin equations for strained single crystals. We derive a set of basic equations for dynamical diffraction from volume diffractive optics, which enable us to study the focusing property of these optics with various grating profiles. We study volume diffractive optics that satisfy the Bragg condition to various degrees, namely flat, tilted and wedged geometries, and derive the curved geometries required for ultimate focusing. We show that the curved geometries satisfy the Bragg condition everywhere and phase requirement for point focusing, and effectively focus hard x-rays to a scale close to the wavelength.Comment: 18 pages, 12 figure

Diffractive optics approach towards subwavelength pixels

Pixel size in cameras and other refractive imaging devices is typically limited by the free-space diffraction. However, a vast majority of semiconductor-based detectors are based on materials with substantially high refractive index. We demonstrate that diffractive optics can be used to take advantage of this high refractive index to reduce effective pixel size of the sensors below free-space diffraction limit. At the same time, diffractive systems encode both amplitude and phase information about the incoming beam into multiple pixels, offering the platform for noise-tolerant imaging with dynamical refocusing. We explore the opportunities opened by high index diffractive optics to reduce sensor size and increase signal-to-noise ratio of imaging structures.Comment: submitted to SPIE-DCS 201

Diffractive Optics for Gravitational Wave Detectors

All-reflective interferometry based on nano-structured diffraction gratings offers new possibilities for gravitational wave detection. We investigate an all-reflective Fabry-Perot interferometer concept in 2nd order Littrow mount. The input-output relations for such a resonator are derived treating the grating coupler by means of a scattering matrix formalism. A low loss dielectric reflection grating has been designed and manufactured to test the properties of such a grating cavity

Diffractive optics fabricated by direct write methods with an electron beam

State-of-the-art diffractive optics are fabricated using e-beam lithography and dry etching techniques to achieve multilevel phase elements with very high diffraction efficiencies. One of the major challenges encountered in fabricating diffractive optics is the small feature size (e.g. for diffractive lenses with small f-number). It is not only the e-beam system which dictates the feature size limitations, but also the alignment systems (mask aligner) and the materials (e-beam and photo resists). In order to allow diffractive optics to be used in new optoelectronic systems, it is necessary not only to fabricate elements with small feature sizes but also to do so in an economical fashion. Since price of a multilevel diffractive optical element is closely related to the e-beam writing time and the number of etching steps, we need to decrease the writing time and etching steps without affecting the quality of the element. To do this one has to utilize the full potentials of the e-beam writing system. In this paper, we will present three diffractive optics fabrication techniques which will reduce the number of process steps, the writing time, and the overall fabrication time for multilevel phase diffractive optics

Multiplication and division of the orbital angular momentum of light with diffractive transformation optics

We present a method to efficiently multiply or divide the orbital angular momentum (OAM) of light beams using a sequence of two optical elements. The key-element is represented by an optical transformation mapping the azimuthal phase gradient of the input OAM beam onto a circular sector. By combining multiple circular-sector transformations into a single optical element, it is possible to perform the multiplication of the value of the input OAM state by splitting and mapping the phase onto complementary circular sectors. Conversely, by combining multiple inverse transformations, the division of the initial OAM value is achievable, by mapping distinct complementary circular sectors of the input beam into an equal number of circular phase gradients. The optical elements have been fabricated in the form of phase-only diffractive optics with high-resolution electron-beam lithography. Optical tests confirm the capability of the multiplier optics to perform integer multiplication of the input OAM, while the designed dividers are demonstrated to correctly split up the input beam into a complementary set of OAM beams. These elements can find applications for the multiplicative generation of higher-order OAM modes, optical information processing based on OAM-beams transmission, and optical routing/switching in telecom.Comment: 28 pages, 10 figure

Very High Resolution Solar X-ray Imaging Using Diffractive Optics

This paper describes the development of X-ray diffractive optics for imaging solar flares with better than 0.1 arcsec angular resolution. X-ray images with this resolution of the \geq10 MK plasma in solar active regions and solar flares would allow the cross-sectional area of magnetic loops to be resolved and the coronal flare energy release region itself to be probed. The objective of this work is to obtain X-ray images in the iron-line complex at 6.7 keV observed during solar flares with an angular resolution as fine as 0.1 arcsec - over an order of magnitude finer than is now possible. This line emission is from highly ionized iron atoms, primarily Fe xxv, in the hottest flare plasma at temperatures in excess of \approx10 MK. It provides information on the flare morphology, the iron abundance, and the distribution of the hot plasma. Studying how this plasma is heated to such high temperatures in such short times during solar flares is of critical importance in understanding these powerful transient events, one of the major objectives of solar physics. We describe the design, fabrication, and testing of phase zone plate X-ray lenses with focal lengths of \approx100 m at these energies that would be capable of achieving these objectives. We show how such lenses could be included on a two-spacecraft formation-flying mission with the lenses on the spacecraft closest to the Sun and an X-ray imaging array on the second spacecraft in the focal plane \approx100 m away. High resolution X-ray images could be obtained when the two spacecraft are aligned with the region of interest on the Sun. Requirements and constraints for the control of the two spacecraft are discussed together with the overall feasibility of such a formation-flying mission