Theory of quarter-wave-stack dielectric mirrors used in a thin fabry-perot filter

I present a new derivation of the analytic form for the phase shift near resonance and the optical penetration length upon reflection from a distributed dielectric mirror consisting of a quarter-wave stack. The requirement of proper termination to achieve high reflectivity is suspended to investigate large optical penetration depths. Separate equations, derived for N and N + 1/2 layer pairs, are convenient for the design of tunable Fabry-Perot filters with a specified tuning range. The analysis is also applicable to distributed Bragg reflectors, vertical-cavity surface-emitting lasers, and resonant photodiodes. I show that the penetration length can sharply reduce the overly broad free spectral range of an ultrathin Fabry-Perot filter that might be useful in applications such as tunable wavelength filters for wavelength division multiplexing applications. The results also demonstrate regimes of zero dispersion and of superluminal reflection in the dielectric mirrors, which are of particular interest in photonic bandgap structures.     

Tandem triple-pass Fabry-Perot interferometer for applications in the near infrared

A standard tandem triple-pass scanning Fabry-Perot interferometer of the Vernier type for applications in the near infrared is described. The Fabry-Perot etalons have been coated with a specially designed dielectric multilayer stack with low loss factors and a uniform reflectivity of (92.5 +/- 1.0)% between 730 and 860 nm. The performances of the instrument, such as resolution, total transmission, and contrast, are equivalent to conventional tandem Fabry-Perot spectrometers but over the whole near-infrared wavelength range. Applications of the system to Brillouin scattering on semiconductors in the transparent wavelength regime and high-resolution spectroscopy of vertical cavity surface-emitting lasers are given.     

Phase Shift Effects in Fabry-Perot Interferometry

A method is demonstrated for utilizing in Fabry-Perot interferometry the data on reflection phase shift dispersion obtained from fringes of equal chromatic order. Unknown wavelengths can be calculated from the Fabry-Perot patterns obtained with a large etalon spacing, even without prior knowledge of the phase shift of the reflecting surfaces. When the theoretical phase shift as a function of wavelength is known approximately, then the correct orders of interference can be determined for both the Fabry-Perot fringes and fringes of equal chromatic order. From the wavelengths of the latter the phase shift dispersion can be measured to an accuracy of about 10 A. The method is especially useful for reflectors with large dispersion of phase shift, such as multilayers. Results in the visible spectrum are reported for aluminum films and a pair of dielectric 15-layer broadband reflectors.     

Dispersion-free, multiple-beam interferometer

A two-mirror Fabry-Perot interferometer is described haivng a dependence of transmission T? (ω) on frequency that is very different from the dependence T? (l) on the distance l between the mirrors. This feature is due to resonant dielectric mirrors in which the reflection phase and amplitude depend sharply on ω. The function T? (ω) can have several extrema ?T? /?ω = 0. At these points the interferometer becomes insensitive to a frequency change, whereas the dependence on l remains. Interferometer parameters are defined and some examples are considered. The dispersion-free interferometer can be used for measuring very small mechanical displacements with a light source with poor frequency stability. The applications to gravitational wave detectors and sensitive seismometers can be suggested if the small distance between the mirrors is acceptable.     

Phase-stepped gauge block interferometry using a frequency-tunable visible laser diode

Frequency changes induced by bias or temperature modulation of injection diode lasers can provide an economical and effective method of applying phase-stepping interferometry to optical metrology. However, the intrinsic frequency instability of these devices limits their use in gauge block interferometry where precise and repeatable phase steps must be maintained simultaneously on two discontinuous surfaces and over relatively long path lengths. We demonstrate a method using a visible injection diode laser, the frequency of which is locked by using a Fabry-Perot interferometer. Small changes to the length of the Fabry-Perot interferometer shift the frequency of the laser producing proportional and repeatable phase steps to the gauge block interferogram. This method has been successfully implemented with a Fizeau-type gauge block interferometer with a phase measurement resolution of 0.005 lambda. The phase data are then processed to map the surface form of gauge blocks up to 100 mm in length and to objectively assess surface shape parameters.     

Experimental study of the phase-shift miscalibration error in phase-shifting interferometry: use of a spectrally resolved white-light interferometer

The white-light interferogram in a spectrally resolved white-light interferometer is decomposed in its constituent spectral components by a spectrometer and displayed along its chromaticity axis. A piezoelectric transducer phase shifter in such an interferometer can give a desired phase shift of pi/2 only at one wavelength. The phase shift varies continuously at all other wavelengths along the chromaticity axis. This situation is ideal for an experimental study of the phase error due to the phase-shift error in the phase-shifting technique, as it will be shown in this paper.     

Embedded fiber-optic Fabry-Perot ultrasound sensor

A fiber-optic ultrasound sensor is presented. The sensor consists of a continuous length of single-mode optical fiber with a built-in Fabry-Perot interferometer. The acoustic pressure produces changes in the index of refraction along the interferometer cavity through the strain-optic effect, thus modulating the reflected power of the light propagating in the fiber. The dielectric internal mirrors that form the interferometer are fabricated by joining a fiber coating with a TiO(2) film at one end to an uncoated fiber by electric arc fusion splicing. Experimental results have been obtained for sensors embedded in plastic and graphite composite materials, using ultrasound waves in the range from 100 kHz to 5 MHz. Values for the optical phase shift amplitude as large as 0.5 rad were obtained at an acoustic frequency of 200 kHz for a 1.1-cm-long interferometer embedded in plastic.     

Optical coating without phase dispersion for a Fabry-Perot interferometer

Phase dispersion induced by coatings can be a critical phenomenon in interferometry. We are interested in special mirrors intended for a Fabry-Perot interferometer with a high reflectance region and a low reflectance region in which phase dispersion on reflection must be avoided. We describe how a classical approach that uses the concepts of admittance and symmetrical multilayers allows the design of simple solutions.     

Spatiospectral transmission of a plane-mirror Fabry-Perot interferometer with nonuniform finite-size diffraction beam illuminations

The transmission of a plane-mirror Fabry-Perot (PFP) interferometer is theoretically modeled and investigated by treating the spatial and spectral features in a unified manner. A spatiospectral transfer function is formulated and utilized to describe the beam propagation and the multiple-beam interference occurring in an ideal one-dimensional strip PFP interferometer with no diffraction loss. The spatial-frequency filtration of a finite-size beam input not only determines the transmitted spatial beam profile but also plays a crucial role in affecting the overall spectral transmittance. The inherent deviations of the spectral transmittance from what we know as the standard Airy's formula are revealed in diverse aspects, including the less-than-unity peak transmittance, the displacement of a resonance peak frequency, and the asymmetric detuning profile. Our theoretical analysis extends to the misaligned PFP interferometers, such as the cases in which non-normal-incidence beams or wedge-aligned mirrors are used that could severely degrade the effective interferometer finesse.     

High spectral resolution lidar to measure optical scattering properties of atmospheric aerosols. 1: theory and instrumentation

A high spectral resolution lidar technique to measure optical scattering properties of atmospheric aerosols is described. Light backscattered by the atmosphere from a narrowband optically pumped oscillator-amplifier dye laser is separated into its Doppler broadened molecular and elastically scattered aerosol components by a two-channel Fabry-Perot polyetalon interferometer. Aerosol optical properties, such as the backscatter ratio, optical depth, extinction cross section, scattering cross section, and the backscatter phase function, are derived from the two-channel measurements.     

Resonant frequencies of Fabry-Perot interferometers with ultrathin mirror spacings

Fabry-Perot interferometers (FPIs) with multilayer dielectric mirrors and mirror spacings as low as 0.7% of the operating wavelength are studied. It is shown how these low-order FPIs are affected by the phase dispersion characteristics of multilayer dielectric mirrors. Because experimental results in the optical regime are extremely difficult to obtain, radio frequency experiments are performed with coaxial cable FPI structures. Experimental results show excellent agreement with theory. These phase effects in FPIs with ultrathin mirror spacings are of great interest in the design of tunable microcavities with possible applications in optical communications.     

Oxygen 630.0- and 557.7-nm line source for thermospheric dynamics studies

A novel design of a rf afterglow source of the oxygen forbidden lines at 630.0 and 557.7 nm for use in thermospheric dynamics studies is presented. With a repetitive discharge-afterglow excitation cycle, the source yields adequate afterglow intensities of the OI lines that are sufficiently free of background continuum for use in Fabry-Perot interferometer measurements of spectral line profiles. These lines provide accurate zero-velocity references in Fabry-Perot determinations of Doppler shifts in the OI thermospheric lines. The design considerations for the rf source are described, together with its preparation and filling by an ultrahigh-vacuum gas-handling system. Examples are given of the source's output spectrum, as measured by a grating spectrometer, and its spectral line profiles, as determined by a Fabry-Perot interferometer. Comparative interferometry between the OI afterglow source lines and nearby (within approximately 0.01-0.02-nm) lines from hollow-cathode sources illustrates the means of establishing secondary reference sources in cases in which the primary OI afterglow source is not available.     

Assessment of a multibeam Fizeau wedge interferometer for Doppler wind lidar

The Fabry-Perot interferometer is the standard instrument for the direct detection Doppler lidar measurement of atmospheric wind speeds. The multibeam Fizeau wedge has some practical advantages over the Fabry-Perot, such as the linear fringe pattern, and is evaluated for this application. The optimal Fizeau must have a resolving power of 10(6) or more. As the multibeam Fizeau wedge is pushed to such high resolving power, the interference fringes of the device become complicated by asymmetry and secondary maxima. A simple condition for the interferometer plate reflectance, optical gap, and wedge angle reveals whether a set of parameters will yield simple, Airy-like fringes or complex Fizeau fringes. Tilting of the Fizeau wedge improves the fringe shape and permits an extension of the regime of Airy-like fringes to higher resolving power. Sufficient resolving power for the wind lidar application is shown to be possible with a large-gap, low-finesse multibeam Fizeau wedge. Liabilities of the multibeam Fizeau wedge in the wind lidar application include a smaller acceptance solid angle and calibration sensitivity to localized deviations of the plates from the ideal.     

Fringe-imaging Mach-Zehnder interferometer as a spectral analyzer for molecular Doppler wind lidar

The theoretical performance of a Mach-Zehnder interferometer used as a spectral analyzer for wind-speed measurement by direct-detection Doppler lidar is presented. The interferometer is optimized for the measurement of wind velocity from the signal that is backscattered by the molecules. In the proposed fringe-imaging Mach-Zehnder (FIMZ) interferometer, a pattern of equally spaced linear fringes is formed and detected by two conventional detector linear arrays. Assuming a pure molecular signal with Gaussian spectral profile, an analytic expression for the standard deviation of the measurement error is obtained and compared with the Cramer-Rao lower bound given by an ideal spectral analyzer (ISA) in the case of shot-noise-limited signal. The FIMZ measurement error is shown to be 2.3 times that of the ISA and is comparable with the error given by previously developed multichannel spectral analyzers that are based on Fabry-Perot interferometers that, in contrast, have the disadvantages of producing unequally spaced circular fringes and requiring dedicated detectors. The optimal path difference for a FIMZ operating at 355 nm is approximately 3 cm. The interferometer is shown to match important lidar beam étendues without significant performance reduction.     

Electro-optically modulated polarizing Fourier-transform spectrometer for plasma spectroscopy applications

A new electro-optically modulated optical solid-state (MOSS) interferometer has been constructed for measurement of quantities related to the low-order spectral moments of line emission from optically thin radiant media such as plasmas. When Doppler broadening is dominant, the spectral moments give the Radon transform of corresponding moments of the velocity distribution function of the radiating species. The instrument, which is based on the principle of the Fourier-transform spectrometer, has high etendue and is rugged and compact. When electro-optical path-length modulation techniques are employed, the spectral information is encoded in the temporal frequency domain at harmonics of the modulation frequency and can be obtained by use of a single photodetector. Specifically, for a plasma in drifting local thermodynamic equilibrium the zeroth moment (brightness) is given by the average signal level, the first moment (shift) by the interferometric phase, and the second moment (linewidth) by the fringe visibility. To illustrate the MOSS performance, I present spectroscopic measurements of the time evolution of the plasma ion temperature and flow velocity for rf-heated discharges in the H-1 heliac, a toroidal plasma magnetic confinement at the Australian National University.     

White-light Fizeau interferometer

A white-light Fizeau interferometer is described. Commonly, white-light fringes can be produced only by using a virtual wedge instrument such as a Michelson interferometer. By use of a series arrangement of a Fabry-Perot interferometer in front of a two-beam Fizeau interferometer, white-light fringes can be produced. For white-light fringes to be obtained, the thickness of the air gap between the Fizeau plates has to be adjusted to the same thickness as the air gap between the Fabry-Perot plates (or in more general terms to a rational multiple of this value). The contrast of the two-beam type of Fizeau fringes depends on the reflectivity of the Fabry-Perot plates.     

Compensation of spacer-thickness variations in a holographic Fabry-Perot filter

The fabrication of a solid, holographically recorded Fabry-Perot interferometer that uses plate glass for the spacer has recently been reported. The component produced sharp, circular Fabry-Perot fringes in spite of its use of a plate-glass spacer. We develop a general theoretical characterization of such a component that accounts for its low sensitivity to spacer-thickness variations. We use the Kogelnik theory of volume holograms to calculate the phase change on reflection from the mirrors. This phase change results from the position of the fringes formed throughout the two holographic media during the recording process. An expression for the wavelength location of the transmission peak versus spacer-thickness variation is derived that agrees with the current experimental information available.     

Ge2Sb2Te5‐Based Tunable Perfect Absorber Cavity with Phase Singularity at Visible Frequencies

The metal‐dielectric stacks‐based asymmetric Fabry–Perot (F–P) cavity systems have recently attracted much interest from the scientific community for realizing perfect absorption over the spectral bands from visible to infrared since they possess a lithography‐free design that is cost‐effective and scalable. This study experimentally demonstrates an asymmetric F–P cavity system for achieving tunable wide angle perfect absorption and phase singularity. The proposed system shows tunable multiband perfect absorption in the visible spectral region by incorporating an ultrathin layer of phase change material such as Ge₂Sb₂Te₅ (GST) in the stack. The system shows multi‐narrowband perfect absorption with a maximum of 99.8% at a specific incident angle and polarization state when the GST is in amorphous phase; however, the absorption bands blueshift and broaden after switching to the crystalline phase. More importantly, the proposed scheme shows tunable phase singularity at the reflection‐less point. The obtained tunable perfect absorption and abrupt phase change are solely due to the presence of a highly absorbing ultrathin layer of GST in the stack. Experimental results are validated using an analytical simulation model based on a transfer matrix method. The proposed scheme could find potential applications in active photonic devices such as phase‐sensitive biosensors and absorption filters.     

Phase-demodulation error of a fiber-optic Fabry-Perot sensor with complex reflection coefficients

The influence of reflector losses attracts little discussion in standard treatments of the Fabry-Perot interferometer yet may be an important factor contributing to errors in phase-stepped demodulation of fiber optic Fabry-Perot (FFP) sensors. We describe a general transfer function for FFP sensors with complex reflection coefficients and estimate systematic phase errors that arise when the asymmetry of the reflected fringe system is neglected, as is common in the literature. The measured asymmetric response of higher-finesse metal-dielectric FFP constructions corroborates a model that predicts systematic phase errors of 0.06 rad in three-step demodulation of a low-finesse FFP sensor (R = 0.05) with internal reflector losses of 25%.     

Control of resonant wavelength from organic light-emitting materials by use of a Fabry-Perot microcavity structure

We report the fabrication of Fabry-Perot microcavity structures with the organic light-emitting material tris-(8-hydroxyquinoline) aluminum (Alq3) and derive their optical properties by measuring their photoluminescence (PL) and absorption. Silver and a TiO2-SiO2 multilayer were used as metal and dielectric reflectors, respectively, in a Fabry-Perot microcavity structure. Three types of microcavity were prepared: type A consisted of [air[Ag[Alq3]Ag]glass]; type B, of [air[dielectric[Alq3]dielectric]glass]; and type C, of [air[Ag[Alq2]dielectric]glass]. A bare Alq3 film of [air[Alq3]glass] had its PL peak near 514 nm, and its full width at half-maximum (FWHM) was 80 nm. The broad FWHM of a bare Alq3 film was reduced to 15-27.5, 7-10.5, and 16-16.6 nm for microcavity types A, B, and C, respectively. Also, we could control the PL peak of the microcavity structure by changing the spacer thickness, the amount of phase change on reflection, and the angle of incidence.