John W. Y. Lit

Focal depth of a transmitting axicon

The transmitting axicon is examined for the axial field distribution of a regular axicon when the incident wave is plane and uniform, and when it has a gaussian irradiance distribution. In the microwave region, the focal depth of an axicon does not differ very much from that of a perfect lens. In the visible region, the axicon possesses a much greater focal depth, which can be greatly changed by changing the curvature of the slanting side of the axicon. For an axicon with a straight slanting side and small height, when a gaussian incident wave is used, the irradiance at the principal focus varies inversely with the focal length.

Boundary-Diffraction-Wave Theory of Cascaded-Apertures Diffraction*

Systems of cascaded circular apertures may be built to focus electromagnetic waves if the difference (d) between the Fresnel numbers of any two apertures pertaining to two points (A and B) is an even number. With a point source at A, the spherical incident wave will be focused to B. In general, the irradiance at B (principal focus) is roughly proportional to (n±1)2 where n is the number of apertures; the plus sign is used when the Fresnel numbers are odd integers, and minus when even. A system of a few apertures with d = 0 can focus waves over a wide range of frequencies, though the actual irradiance at the principal focus is a function of frequency. A condition to maximize the irradiance at the principal focus has been found. Theoretically such systems have been analyzed by the boundary-diffraction-wave theory generalized by Miyamoto and Wolf. Analytical expressions for the diffraction wave amplitude have been obtained for axial and off-axial points. when the iteration method of Fox and Li is also applicable, the two theoretical results agree very well with each other. Experimental data obtained agree well with the theoretical results.

Measurement of surface roughness using dichromatic speckle

Abstract The dependence on the surface roughness of the structural difference of two normalized intensity distributions in a dichromatic speckle pattern is studied theoretically. It is shown that the difference of two speckle intensity distributions increases with increase of the object surface roughness. Using this proportional relationship, a new method for measuring surface roughness is proposed. The effective measuring range can be changed by varying the two wavelengths of the illuminating light. Some computer simulation studies are conducted to verify the theoretical results.

Surface roughness measurement using dichromatic speckle pattern: an experimental study

Surface roughness is studied experimentally by making use of the statistical properties of dichromatic speckle patterns. The rms intensity difference between two speckle patterns produced by two argon laser lines are analyzed in the far field as functions of the object surface roughness and the difference in the two wavenumbers of the illuminating light. By applying previously derived formulas, the rms surface roughness is obtained from rms intensity differences. Glass and metal rough surfaces are used. Other than the scattering arrangement, the experimental setup has a simple spectrometric system and an electronic analyzing circuit.

Diffracted waves in the shadow boundary region

The boundary-diffraction-wave theory is used to calculate the diffracted field in the shadow boundary region. Discussions are based on expressions derived for a Gaussian beam incident on a circular aperture.

Effects of a Half-Wave Filter in a Portion of the Aperture of a Perfect Lens

The aperture of a perfect lens is divided into several concentric circular zones. The effects of the different zones having different phase retardations are studied. The following conditions are found by a straightforward consideration: When the aperture is divided into two zones, with the inner zone having a phase retardation of π rad with respect to the outer zone, the diffraction pattern in the focal plane of the lens has the smallest central bright spot; this assumes that the same irradiance is always produced at the focus. Conversely, for a given radius of the central bright spot in the diffraction pattern, the greatest irradiance at the focus of the lens is produced when the lens aperture is divided into two concentric circular zones, with the inner zone having a phase retardation of π rad. Such a lens also possesses the same advantages over a perfect lens with a circular stop in its center. It may also possess an effective focal depth greater than that of the latter. It may have one or two foci depending on the value of the radius of the circle that divides its aperture.

Edge-On Diffraction of a Gaussian Laser Beam by a Semi-Infinite Plane

A He-Ne laser beam is used here to illuminate a razor blade at edge-on incidence. The incident light is found to be scattered into a single straight cone of circular cross section. The tip of this cone of diffracted light lies at the point of incidence, its axis coincides with the prolongation of the razor edge, and its halfangle is equal to the angle of incidence. Such cones formed by a family of diffracted rays are basic to the so-called geometrical theory of diffraction. However, the properties and geometrical laws associated with the diffracted rays are derived analytically here by application of the boundary diffraction wave theory. The experimental results are in agreement with theoretical predictions.

Multiaperture Focusing Technique

A method of focusing electromagnetic waves by diffraction alone is proposed. An incident beam is diffracted by a series of circular apertures which have their diffracting edges falling on a surface of revolution. A geometrical consideration of the principle involved is presented, followed by a series of experimental results.

Radius of uncladded optical fiber from back-scattered radiation pattern*

The back-scattered pattern produced by a plane-polarized beam incident normally on a large uncladded optical fiber can be used to determine the refractive index and the radius of the fiber. The geometric-optics method is used to analyze the pattern. A new procedure to find the radius of the fiber is proposed. The procedure can make use of nearly the whole of the back-scattered pattern, without need to measure exactly the positions of all of the individual fringes. Special attention is given to the limits of accuracy.

Effects of a thin overlying film on optical waveguides and couplers

The effects of a thin film on the propagation of waves inside an optical waveguide are examined. The cases considered are planar guides, rectangular embedded guides, and rectangular ridged guides. Couplers formed by such guides are also studied. Analytical results together with some numerical and experimental results are presented.