Kenro Miyamoto

Bio: Kenro Miyamoto is an academic researcher from University of Rochester. The author has contributed to research in topics: Green's theorem & Position (vector). The author has an hindex of 4, co-authored 5 publications receiving 429 citations.

Generalization of the maggi-rubinowicz theory of the boundary diffraction wave part I

Abstract: As a first step towards a generalization of the Maggi-Rubinowicz theory of the boundary diffraction wave, a new vector potential W(Q,P) is associated with any monochromatic scalar wavefield U(P). This potential has the property that the normal component of its curl, taken with respect to the coordinates of any point Q on a closed surface S surrounding a field point P, is equal to the integrand of the Helmholtz-Kirchhoff integral; that is, curlQW(Q,P)·n=14π{U(Q)∂∂n(exp(iks)s)−exp(iks)s∂∂nU(Q)}.where s is the distance QP and ∂/∂n denotes the differentiation along the inward unit normal n to S.Further it is shown that the vector potential always has singularities at some points Q on S and that the field at P may be rigorously expressed as the sum of disturbances propagated from these points alone.A closed expression for the vector potential associated with any given monochromatic wavefield that obeys the Sommerfeld radiation condition at infinity is derived and it is shown that in the special case when U is a spherical wave, this expression reduces to that found by G. A. Maggi and A. Rubinowicz in their researches on the boundary diffraction wave.

The Phase Fresnel Lens

Abstract: In order to deform the wave surface passing through an optical system by the amount ϕ(u,v), it is suggested that a phase Fresnel lens be inserted in the pupil of the optical system. Assuming 0⩽ϕ(u,v)

On Gabor’s Expansion Theorem*

Abstract: As a generalization for optics of the well-known sampling theorem of information theory, D. Gabor proposed an expansion theorem. It relates to the number of independent solutions of the wave equation in a region defined by the object and by the aperture of an optical system.A proof of this theorem presents formidable difficulties. In this paper, a proof relating to important cases is established, and a more accurate estimate for the number of the independent solutions in the general case is given.

On the Design of Optical Systems with an Aspheric Surface

Abstract: This short article is concerned with the problem of designing a correcting aspherical surface which is situated in an arbitrary position within an optical system. The method requires the solution of two first-order differential equations and seems more suitable for the use with an electronic computer than methods previously proposed by other authors. It can be considered as a differential form of a method previously proposed by E. Wolf.

Metalenses: Versatile multifunctional photonic components

Abstract: BACKGROUND Future high-performance portable and wearable optical devices and systems with small footprints and low weights will require components with small form factors and enhanced functionality. Planar components based on diffractive optics (e.g., gratings, Fresnel lenses) and thin-film optics (e.g., dielectric filters, Bragg reflectors) have been around for decades; however, their limited functionality and difficulty of integration have been key incentives to search for better alternatives. Owing to its potential for vertical integration and marked design flexibility, metasurface-based flat optics provides a rare opportunity to overcome these challenges. The building blocks (BBs) of metasurfaces are subwavelength-spaced scatterers. By suitably adjusting their shape, size, position, and orientation with high spatial resolution, one can control the basic properties of light (phase, amplitude, polarization) and thus engineer its wavefront at will. This possibility greatly expands the frontiers of optical design by enabling multifunctional components with attendant reduction of thickness, size, and complexity. ADVANCES Recent progress in fabrication techniques and in the theory and design of metasurfaces holds promise for this new optical platform (metaoptics) to replace or complement conventional components in many applications. One major advance has been the migration to all-dielectric metasurfaces. Here, we discuss the key advantages of using dielectric phase-shifting elements with low optical loss and strong light confinement in the visible and near-infrared regions as BBs of flat lenses (metalenses). High–numerical aperture metalenses that are free of spherical aberrations have been implemented to achieve diffraction-limited focusing with subwavelength resolution, without requiring the complex shapes of aspherical lenses. Achromatic metalenses at discrete wavelengths and over a bandwidth have been realized by dispersion engineering of the phase shifters. By suitably adjusting the geometrical parameters of the latter, one can impart polarization- and wavelength-dependent phases to realize multifunctional metalenses with only one ultrathin layer. For example, polarization-sensitive flat lenses for chiral imaging and circular dichroism spectroscopy with high resolution have been realized, and off-axis metalenses with large engineered angular dispersion have been used to demonstrate miniature spectrometers. The fabrication of metalenses is straightforward and often requires one-step lithography, which can be based on high-throughput techniques such as deep-ultraviolet and nanoimprint lithography. OUTLOOK In the near future, the ability to fabricate metalenses and other metaoptical components with a planar process using the same lithographic tools for manufacturing integrated circuits (ICs) will have far-reaching implications. We envision that camera modules widely employed in cell phones, laptops, and myriad applications will become thinner and easier to optically align and package, with metalenses and the complementary metal-oxide semiconductor–compatible sensor manufactured by the same foundries. The unprecedented design freedom of metalenses and other metasurface optical components will greatly expand the range of applications of micro-optics and integrated optics. We foresee a rapidly increasing density of nanoscale optical elements on metasurface-based chips, with attendant marked increases in performance and number of functionalities. Such digital optics will probably follow a Moore-like law, similar to that governing the scaling of ICs, leading to a wide range of high-volume applications.

On the degrees of freedom of scattered fields

Abstract: Starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities, the degrees of freedom of the scattered field are introduced and then computed. The degrees of freedom are shown to be practically equal to the Nyquist number appropriate to the effective (spatial) bandwidth of the scattered field and to the extension of the observation domain. Accordingly, a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error. It is also shown that the field representation can be made in terms of field values and simple sampling functions, provided that a marginal increase in the approximation error is tolerated. The results not only completely justify the use of sampling interpolation for representing scattering fields, but also demonstrate that such representation is practically an optimal one. An algorithm for the reconstruction of scattered fields, given the maximum allowed error, is then produced. >

Optical Systems with Resolving Powers Exceeding the Classical Limit. II

Abstract: The fundamental invariant of an optical system is the number N of degrees of freedom of the message it can transmit. The spatial bandwidth of the system can be increased over the classical limit by reducing one of the other constituent factors of N. As examples of this invariance theorem N=const. established in Part I of this series [ J. Opt. Soc. Am.56, 1463 ( 1966)], we discuss (a) a system whose spatial-bandwidth increase is achieved by a proportional reduction of its temporal bandwidth, and (b) the airborne synthetic-aperture, terrain-mapping radar, whose spatial resolution comes from exploitation of the temporal degrees of freedom of the received signal. The increase of the spatial bandwidth beyond the classical limit is, however, limited by the appearance of evanescent waves.The number of degrees of freedom of the object wave field stored in a hologram is discussed. The storage capacity of the photographic plate, which is proportional to its size times its spatial cutoff frequency, is fully exploited only by single-sideband Fraunhofer but not by single-sideband Fresnel holograms.

A review of dielectric optical metasurfaces for wavefront control

Abstract: During the past few years, metasurfaces have been used to demonstrate optical elements and systems with capabilities that surpass those of conventional diffractive optics. Here, we review some of these recent developments, with a focus on dielectric structures for shaping optical wavefronts. We discuss the mechanisms for achieving steep phase gradients with high efficiency, simultaneous polarization and phase control, controlling the chromatic dispersion, and controlling the angular response. Then, we review applications in imaging, conformal optics, tunable devices, and optical systems. We conclude with an outlook on future potentials and challenges that need to be overcome.

Phase zone plates for x rays and the extreme uv

Abstract: Phase-reversal zone plates can be designed even for regions of the electromagnetic spectrum where the index of refraction is complex, with a real part close to 1.0. These devices are superior to Fresnel zone plates both in their light collection, and in their signal-to-noise characteristics. Materials with suitable optical and mechanical properties exist throughout most of the 1–800-A wavelength range for their construction. Imperfections in fabrication, such as incorrect plate thickness, sloping zone edges, or an error in the width of alternate zones result in only moderate deterioration in optical performance.