Refractive index of a transparent liquid measured with a concave mirror

This paper describes the spherical concave mirror method for measuring the index of refraction of transparent liquids. We derived the refractive index equation using Snell's law and the small-angle approximation. We also verified the validity of this method using the traditional spherical mirror and thin-lens Gaussian equations.Comment: IOPart, 8 pages, 4 figure

Conicoid Mirrors

The first order equation relating object and image location for a mirror of arbitrary conic-sectional shape is derived. It is also shown that the parabolic reflecting surface is the only one free of aberration and only in the limiting case of distant sources.Comment: 9 page

A photonic bandgap resonator to facilitate GHz frequency conductivity experiments in pulsed magnetic fields

We describe instrumentation designed to perform millimeter-wave conductivity measurements in pulsed high magnetic fields at low temperatures. The main component of this system is an entirely non-metallic microwave resonator. The resonator utilizes periodic dielectric arrays (photonic bandgap structures) to confine the radiation, such that the resonant modes have a high Q-factor, and the system possesses sufficient sensitivity to measure small samples within the duration of a magnet pulse. As well as measuring the sample conductivity to probe orbital physics in metallic systems, this technique can detect the sample permittivity and permeability allowing measurement of spin physics in insulating systems. We demonstrate the system performance in pulsed magnetic fields with both electron paramagnetic resonance experiments and conductivity measurements of correlated electron systems.Comment: Submitted to the Review of Scientific instrument

Suspension of the fiber mode-cleaner launcher and measurement of the high extinction-ratio (10^{-9}) ellipsometer for the Q & A experiment

The Q & A experiment, first proposed and started in 1994, provides a feasible way of exploring the quantum vacuum through the detection of vacuum birefringence effect generated by QED loop diagram and the detection of the polarization rotation effect generated by photon-interacting (pseudo-)scalar particles. Three main parts of the experiment are: (1) Optics System (including associated Electronic System) based on a suspended 3.5-m high finesse Fabry-Perot cavity, (2) Ellipsometer using ultra-high extinction-ratio polarizer and analyzer, and (3) Magnetic Field Modulation System for generating the birefringence and the polarization rotation effect. In 2002, the Q & A experiment achieved the Phase I sensitivity goal. During Phase II, we set (i) to improve the control system of the cavity mirrors for suppressing the relative motion noise, (ii) to enhance the birefringence signal by setting-up a 60-cm long 2.3 T transverse permanent magnet rotatable to 10 rev/s, (iii) to reduce geometrical noise by inserting a polarization-maintaining optical fiber (PM fiber) as a mode cleaner, and (iv) to use ultra-high extinction-ratio (10^{-9}) polarizer and analyzer for ellipsometry. Here we report on (iii) & (iv); specifically, we present the properties of the PM-fiber mode-cleaner, the transfer function of its suspension system, and the result of our measurement of high extinction-ratio polarizer and analyzer.Comment: 8 pages, 6 figures, presented in the 6th Edoardo Amaldi Conference on Gravitational Waves, Okinawa, Japan, June 2005, and accepted by "Journal of Physics: Conference Series". Modifications from version 2 were made based on the referees' comments on figures. Ref. [31] were update

Constructing Fresnel reflection coefficients by ruler and compass

A simple and intuitive geometical method to analyze Fresnel formulas is presented. It applies to transparent media and is valid for perpendicular and parallel polarizations. The approach gives a graphical characterization particularly simple of the critical and Brewster angles. It also provides an interpretation of the relation between the reflection coefficients for both basic polarizations as a symmetry in the plane

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 figure

Ultrafast time-resolved spectroscopy of 1D metal-dielectric photonic crystals

We study the all-optical switching behavior of one-dimensional metal-dielectric photonic crystals due to the nonlinearity of the free metal electrons. A polychromatic pump-probe setup is used to determine the wavelength and pump intensity dependence of the ultrafast transmission suppression as well as the dynamics of the process on a subpicosecond timescale. We find ultrafast (sub-picosecond) as well as a slow (millisecond) behavior. We present a model of the ultrafast dynamics and nonlinear response which can fit the measured data well and allows us to separate the thermal and the electronic response of the system.Comment: 7 pages, 5 figure

Transversality of Electromagnetic Waves in the Calculus-Based Introductory Physics Course

Introductory calculus-based physics textbooks state that electromagnetic waves are transverse and list many of their properties, but most such textbooks do not bring forth arguments why this is so. Both physical and theoretical arguments are at a level appropriate for students of courses based on such books, and could be readily used by instructors of such courses. Here, we discuss two physical arguments (based on polarization experiments and on lack of monopole electromagnetic radiation), and the full argument for the transversality of (plane) electromagnetic waves based on the integral Maxwell equations. We also show, at a level appropriate for the introductory course, why the electric and magnetic fields in a wave are in phase and the relation of their magnitudes.Comment: 10 pages, 6 figure

Characterization of porous low-k films using variable angle spectroscopic ellipsometry

doi:10.1063/1.2189018Variable angle spectroscopic ellipsometry (VASE™) is used as a tool to characterize properties such as optical constant, thickness, refractive index depth profile, and pore volume fraction of single and bilayer porous low-k films. The porous films were prepared using sacrificial pore generator (porogen) approach. Two sets of porous films with open- and closed-pore geometries were measured. Three models were used for data analysis: Cauchy, Bruggeman effective medium approximation (BEMA), and graded layer. Cauchy, a well-known model for transparent films, was used to obtain thickness and optical constant, whereas BEMA was utilized to calculate the pore volume fraction from the ellipsometric data. The Cauchy or BEMA models were then modified as graded layers, resulting in a better fit and a better understanding of the porous film. The depth profile of the porous film implied a more porous layer at the substrate-film interface. We found 3%-4% more porosity at the interface compared with the bulk for both films. This work shows that VASE™, a nondestructive measurement tool, can be used to characterize single- and multigraded layer porous films quickly and effectively.The authors would like to acknowledge the financial support of Semiconductor Research Corporation (SRC)