Lloyd's Interferometer Research Articles

Green’s function analysis of the neutron Lloyd interferometer

Abstract The neutron optical Lloyd interferometer can serve as a potent experiment for probing fundamental physics beyond the standard models of particles and cosmology. In this article, we provide a full Green’s function analysis of a Lloyd interferometer in the limit that the reflecting mirror extends to the screen. We consider two distinct situations: first, we will review the theoretical case of no external fields being present. Subsequently, we will analyze the case in which a gravitational field is acting on the neutrons. The latter case provides the theory necessary for using a Lloyd interferometer as a probe of gravitational fields.

Generation of sub-micrometer surface relief gratings in an azobenzene-containing material using a 355 nm laser

Controlled effective fabrication of surface relief gratings (SRG) of different periods and dimensionality in an azobenzene-containing polyelectrolyte material using an UV-laser operating at 355 nm was demonstrated for the first time. The application of an UV-laser in combination with Lloyd's interferometer allows the accurate control of grating period and the generation of gratings with small period down to 180 nm. The SRG formation is related to the kinetics of the steady state of the trans-cis photoisomerization of a PAZO film at UV exposure. The replication of the manufactured gratings using soft lithography is demonstrated as well.

Employing refractive beam shaping in a Lloyd's interference lithography system for uniform periodic nanostructure formation

Uniform periodic structure formation over a large sample area has been challenging in laser interference lithography (LIL) mainly due to the Gaussian intensity distribution inherent to a laser beam. In this work, refractive beam shaping devices are applied in a Lloyd's interferometer to create a flat-top light field (2.8% intensity variation over an area of 20 × 20 cm2) for wafer-scale nanopatterning. Around 10−2 variation in fill factors are obtained for all the reported one dimensional and two dimensional periodic structures across a 2-in. wafer, which is 1 order of magnitude lower than the values obtained for the samples exposed to a Gaussian light field. The proposed LIL system also allows gradual light field transitions from the Gaussian, super-Gaussian, and flat-top to the inverse-Gaussian by simply adjusting the spot size of the laser incident to the beam shaper. The authors believe that the proposed LIL system can be applied for a variety of applications that benefit from the nature of periodic nanostructures.

Continuously tunable laser based on polarization gratings in azobenzene-containing material

Two simple procedures to manufacture continuously tunable miniature lasers in azobenzene-containing material were developed. Both types of lasers rely on the distributed feedback provided by polarization gratings. In a first approach tuning is achieved by changing the thickness of the active wave guiding layer by means of a wedge layer and in a second approach by gradually changing the spatial frequency of the refractive index grating obtained by modification of the Lloyd interferometer set-up used for holographic inscription of the gratings. A continuous tuning range of up to 35 nm has been demonstrated.

Suppression of side lobes in the fiber Bragg grating reflection spectrum

A revision of works on the methods of writing and apodization of fiber Bragg gratings (FBG) is presented. The possibilities of apodizing FBGs recorded by holographic methods with phase masks and Lloyd interferometer using laser radiation with a Gaussian intensity profile are considered. FBG reflection spectra are numerically simulated for different parameters of the writing beam and configurations of the experimental setup. Side-lobe suppression and FBG spectrum smoothing are experimentally demonstrated. It is shown that this effect is due to equalization of the average value of the induced refractive index in the FBGs. FBG applications, in particular, as frequency selectors in fiber lasers (tunable, narrow-band, and multiwavelength) are described.

Azobenzene Lasers Tuned Over a 200 nm Range

An application of red emitting rod‐like dyes similar to Pyridine 1 in an epoxy‐based oligomeric azobenzene system leads to optically pumped distributed feedback (DFB) lasers tunable over a spectral range of 200 nm. DFB structures in azobenzene films doped with laser dyes are created by a reliable and simple holographic technique using Lloyd's interferometer. In this way, surface relief gratings serving as DFBs can be routinely inscribed in 1 min time, which protect laser dyes from bleaching. The emitting wavelength of the laser device can be tuned by small adjustments of the interference pattern period in Lloyd's interferometer, by film thickness, and by changing the laser dye. The fabricated miniature lasers emit from 680 to 875 nm. In addition to laser devices emitting at the 2nd diffraction order, devices fabricated with a grating period of ca. 250 nm emitting at the 1st diffraction order are also demonstrated. The lasers support several tens of thousands of pulses without encapsulation and have an efficiency of up to 0.6% in the case of a laser working in the 1st diffraction order.

Large area periodic, systematically changing, multishape nanostructures by laser interference lithography and cell response to these topographies

The fabrication details to form large area systematically changing multishape nanoscale structures on a chip by laser interference lithography (LIL) are described. The feasibility of fabricating different geometries including dots, ellipses, holes, and elliptical holes in both x- and y- directions on a single substrate is shown by implementing a Lloyd's interferometer. The fabricated structures at different substrate positions with respect to exposure time, exposure angle and associated light intensity profile are analyzed. Experimental details related to the fabrication of symmetric and biaxial periodic nanostructures on photoresist, silicon surfaces, and ion milled glass substrates are presented. Primary rat calvarial osteoblasts were grown on ion-milled glass substrates with nanotopography with a periodicity of 1200 nm. Fluorescent microscopy revealed that cells formed adhesions sites coincident with the nanotopography after 24 h of growth on the substrates. The results suggest that laser LIL is an easy and inexpensive method to fabricate systematically changing nanostructures for cell adhesion studies. The effect of the different periodicities and transition structures can be studied on a single substrate to reduce the number of samples significantly.

Large Area Extreme-UV Lithography of Graphene Oxide via Spatially Resolved Photoreduction

The ability to pattern graphene over large areas with nanometer resolution is the current request for nanodevice fabrication at the industrial scale. Existing methods do not match high throughput with nanometer resolution. We propose a high-throughput resistless extreme-UV (EUV) photolithographic approach operating with sub-micrometer resolution on large area (~10 mm(2)) graphene oxide (GO) films via spatially resolved photoreduction. The efficiency of EUV photoreduction is tested with 46.9 nm coherent light produced by a table top capillary discharge plasma source. Irradiated samples are studied by X-ray photoemission spectroscopy (XPS) and micro-Raman Spectroscopy (μRS). XPS data show that 200 mJ/cm(2) EUV dose produces, onto pristine GO, a 6% increase of sp(2) carbon bonds and a 20% decrease of C-O bonds. μRS data demonstrate a photoreduction efficiency 2 orders of magnitude higher than the one reported in the literature for UV-assisted photoreduction. GO patterning is obtained modulating the EUV dose with a Lloyd's interferometer. The lithographic features consist of GO stripes with modulated reduction degree. Such modulation is investigated and demonstrated by μRS on patterns with 2 μm periodicity.

Smoothing of the spectrum of fibre Bragg gratings in the Lloyd-interferometer recording scheme

The possibility of apodization of fibre Bragg gratings (FBGs) recorded in the region of interference of the two parts of a Gaussian beam in a Lloyd interferometer is considered. The reflection spectra of FBGs are numerically simulated for different parameters of the recording beam and its displacement with respect to the dividing axis in the interferometer. Aconsiderable suppression of sidelobe resonances in the FBG spectrum during the displacement of the beam centre with respect to the dividing axis by half the beam radius is predicted and experimentally demonstrated. It is shown that this is caused by the equating of the mean value of the refractive index in the FBG region.

Three-beam interference lithography: upgrading a Lloyd's interferometer for single-exposure hexagonal patterning

Three-beam interference lithography is used to create hole/dot photoresist patterns with hexagonal symmetry. This is achieved by modifying a standard two-beam Lloyd's mirror interferometer into a three-beam interferometer, with the position of the mirrors chosen to guarantee 120 degrees symmetry of exposure. Compared to commonly used three-beam setups, this brings the advantage of simplified alignment, as the position of the mirrors with respect to the substrate is fixed. Pattern periodicities from several wavelengths lambda down to 2/3lambda are thus easily and continuously accessible by simply rotating the three-beam interferometer. Furthermore, in contrast to standard Lloyd's interferometers, only a single exposure is needed to create hole/dot photoresist patterns.

Spectral transfer function of the Fourier transform spectral imager

The spectral transfer function of the imaging spectrometer is defined on the basis of the linear system theorem. The spectral transfer functions including spectral modulation transfer functions and the spectral phase transfer functions of the temporally modulated Fourier transform spectral imager based on Michelson interferometer and those of the spatially modulated Fourier transform spectral imagers based on Sagnac interferometer,Fresnel interferometer, and Lloyd interferometer are deduced. These spectral transfer functions could be regarded as an objective criteria in the spectral domain of spectral imagers. Together with the well known optical transfer function, the performance of the imaging spectrometer could be described comprehensively.

Refractive-index saturation-mediated multiple line emission in polymer thin-film distributed-feedback lasers

We report experimental and theoretical investigations of multiple laser-line emission in a distributed-feedback dye laser pumped by two coherent optical beams. We have used a Lloyd interferometer configuration with second- and third-order Bragg reflections to study the interaction between the two incident pumps in an organic thin film. We demonstrated theoretically that the number of laser emission lines can be interpreted with reference to the saturation effect in the refractive index.

Measurement of the refractive-index profile of planar waveguides by the use of a double Lloyd's interferometer

We present a nondestructive experimental method to measure monotonically varying refractive-index profiles of planar waveguides. The technique is a modification of the Lloyd's mirage setup proposed by Allman et al. [Appl. Opt. 33, 1806 (1994)] in order to have a reference phase distribution for the interference pattern. The theoretical calculations have been implemented to account for multiple reflections inside the sample. An application of the method to ion-exchanged glass waveguides is reported.

Direct measurement of birefringence in ion-exchanged planar waveguides

A direct measurement of the birefringence of a planar waveguide obtained by Na(+) -K(+) ion exchange was performed with a double Lloyd interferometer. The results are compared with those obtained by a roundrobin test involving the same sample. Birefringence of as much as Deltan = (2.0 +/- 0.2) x 10(-3) was measured.

What was expected from the Michelson-Morley experiment - a simple classroom demonstration

As a follow-up to the recent celebrations of the Michelson-Morley centenary, an ultrasonic variant of the Lloyd interferometer is used in a classroom demonstration to clarify the motives of the 1887 experiment

Higher-Order Lloyd Interferometer

The Lloyd moiré interferometer was introduced in Appl. Opt. 6, 1707 (1967), as a means of testing interferometrically a path across very large surfaces in oblique to grazing incidence. The width of the path is determined by the optics in use. For any sensible angle of incidence, the Lloyd interference fringes will be very narrowly spaced, but they are transformed into conveniently visible fringes by a moiré grating. The precision of the Lloyd moiré interferometer is limited by the very large angle of incidence and by the relatively poor definition of the moiré fringes. The objective of the present paper is to show an improved Lloyd interferometer technique, which with equally simple instrumentation permits one to vary and increase the sensitivity in testing large surfaces in oblique incidence by decreasing the angle of incidence.

Lloyd Interferometer Applied to Flatness Testing

Lloyd's mirror experiment is applied to testing flatness of large surfaces. Because of the grazing incidence, even rough surfaces provide the characteristic interference pattern. In the case of a perfectly flat surface, that pattern consists of narrowly and equally spaced two beam interference fringes. Departures from flatness are reflected in changes of the fringe spacing. Moiré techniques are used for visualizing and measuring these changes in the deviation from straightness of the Moiré fringes. Qualitative examples are given.