Lloyd's Mirror Research Articles

Measurement of autoproduct fields in a Lloyd's mirror environment.

Conventional frequency-domain acoustic-field analysis techniques are typically limited to the bandwidth of the field under study. However, this limitation may be too restrictive, as prior work suggests that field analyses may be shifted to lower or higher frequencies that are outside the field's original bandwidth [Worthmann and Dowling (2017). J. Acoust. Soc. Am. 141(6), 4579-4590]. This possibility exists because below- and above-band acoustic fields can be mimicked by the frequency-difference and frequency-sum autoproducts, which are quadratic products of frequency-domain complex field amplitudes at a pair of in-band frequencies. For a point source in a homogeneous acoustic half-space with a flat, pressure-release surface (a Lloyd's mirror environment), the prior work predicted high correlations between the autoproducts and genuine out-of-band fields at locations away from the source and the surface. Here, measurements collected in a laboratory water tank validate predictions from the prior theory using 40- to 110-kHz acoustic pulses measured at ranges between 175 and 475 mm, and depths to 400 mm. Autoproduct fields are computed, and cross-correlations between measured autoproduct fields and genuine out-of-band acoustic fields are above 90% for difference frequencies between 0 and 60 kHz, and for sum frequencies between 110 and 190 kHz.

Inscription and analysis of non-uniform diffraction gratings in azobenzene molecular glass thin films.

Non-uniform surface relief diffraction gratings were laser-inscribed on azobenzene molecular glass thin films using a modified Lloyd's mirror interferometer. The azobenzene films were exposed to an adjustable interference pattern produced by the recombination of collimated and spherically divergent laser wave fronts. The localized pitch, grating vector orientation and depth of the resulting non-uniform gratings were measured using an atomic force microscope and a theoretical model was analytically developed to explain the experimental results. The fabricated gratings exhibited a chirping or pitch variation along the imposed X-axis as well as an angular change in the grating vector orientation along the imposed Y-axis. Studies were conducted on various non-uniform grating configurations having central pitches of 500 nm, 1000 nm, 1500 nm and 2000 nm.

Generalized method for probing ideal initial polarization states in multibeam Lloyd's mirror interference lithography of 2D scale gratings

Delicate control of the initial polarization states of sub-beams incident to the interferometer unit in multibeam Lloyd's mirror interference lithography is of great significance for the fabrication of high-precision two-dimensional (2D) scale gratings. In this work, the optimization of the initial polarization states of incident sub-beams is formulated as a constrained multiobjective optimization problem. A generalized method that allows the incident sub-beams to initially have the general elliptical polarization states in the optimization is proposed based on the multiobjective genetic algorithm. It is demonstrated that the method is capable of delivering ideal initial polarization states with which the cross-interference between the two once-reflected sub-beams on the grating substrate of the interferometer unit can be completely eliminated from the resultant 2D interference fringes. The feasibility of the proposed method is verified through the comparison between the simulated 2D interference fringes and the fabricated 2D scale gratings under the achieved ideal initial polarization states.

Tunable colloidal quantum dot distributed feedback lasers integrated on a continuously chirped surface grating.

We report a colloidal quantum dot (CQD) distributed feedback (DFB) laser structure containing a chirped grating. The device exhibits single-mode DFB lasing, of which the wavelength is spatially dispersed in a single chip. A period-chirped surface grating is fabricated using a modified Lloyd-type laser interference lithography setup, where a flat Lloyd's mirror is replaced with a concave one. A dense red-emitting CdSe/CdS/ZnS CQD film is prepared on a temporary substrate by spin-coating, which is subsequently released and wet-transferred onto a period-chirped quartz surface grating. Upon optical excitation, the fabricated DFB laser device lases in a single mode at a laser threshold of ∼400 μJ cm-2, with its lasing wavelength shifted linearly (in proportion to the grating pitch) along the chirp direction from 613.4 nm to 623.2 nm over a distance of ∼5.6 mm.

Hot and dense plasma probing by soft X-ray lasers

Soft X-ray lasers, due to their short wavelength, its brightness, and good spatial coherence, are excellent sources for the diagnostics of dense plasmas (up to 1025 cm−3) which are relevant to e.g. inertial fusion. Several techniques and experimental results, which are obtained at the quasi-steady state scheme being collisionally pumped 21.2 nm neon-like zinc laser installed at PALS Research Center, are presented here; among them the plasma density measurement by a double Lloyd mirror interferometer, deflectometer based on Talbot effect measuring plasma density gradients itself, with a following ray tracing postprocessing. Moreover, the high spatial resolution (nm scale) plasma images can be obtained when soft X-ray lasers are used.

Design and testing of a compact non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings

A compact and stable two-axis Lloyd’s mirror interferometer based on a new non-orthogonal type of mirror-substrate assembly is designed for fabrication of 100 mm × 100 mm large-area two-dimensional (2D) diffraction scale gratings in a research laboratory or a small-scale manufacturing facility. At first, the required mirror sizes used in the new non-orthogonal type and the conventional orthogonal type are compared based on geometrical analysis. It is identified that the width of the mirror can be reduced to half in the non-orthogonal type while the required mirror height and the expanded laser beam diameter are comparable to those in the orthogonal type. The shorter mirror width makes it possible to design a compact mirror-substrate assembly so that the overall interferometer can be realized in an overall size of 1480 mm × 730 mm for mounting on a commercially available general-purpose 1500 mm × 1000 mm vibration isolation table for use in research laboratories. It is then verified by simulation that the selected laser source and the designed beam expansion assembly, which are the other main parts of the interferometer, are effective for fabricating the designed grating structures. Experiments are also carried out to demonstrate the feasibility of the constructed interferometer for fabricating 100 mm × 100 mm 2D scale gratings with a short period of 1 μm.

Integrated Lloyd's mirror on planar waveguide facet as a spectrometer.

A low-cost and simple Fourier transform spectrometer based on the Lloyd's mirror configuration is proposed in order to have a very stable interferogram. A planar waveguide coupled to a fiber injection is used to spatially disperse the optical beam. A second beam superposed to the previous one is obtained by a total reflection of the incident beam on a vertical glass face integrated in the chip by dicing with a specific circular precision saw. The interferogram at the waveguide output is imaged on a near-infrared camera with an objective lens. The contrast and the fringe period are thus dependent on the type and the fiber position and can be optimized to the pixel size and the length of the camera. Spectral resolution close to λ/Δλ=80 is reached with a camera with 320 pixels of 25μm width in a wavelength range from O to L bands.

Optimal polarization modulation for orthogonal two-axis Lloyd's mirror interference lithography.

Polarization control is of vital importance in two-axis Lloyd's mirror interference lithography to achieve the preferred interference fringes. In this work, we first establish a three-dimensional polarization ray-tracing model to trace the evolution of polarization states of incident beams through the corner-cube-like interferometer unit of an orthogonal two-axis Lloyd's mirror interferometer. With the established model, we then derive the optimal combination of initial polarization directions of the incident beams according to the orthogonality of polarization states and the contrast of interference fringes. The comparison between the simulated and experimental interference fringes obtained under different combinations of initial polarization states of incident beams verify the feasibility of the established model and the achieved optimal polarization modulation.

Acoustic-intensity striations below the critical depth: Interpretation and modeling.

This paper presents a technique for calculating tracks of striations observed in the plot of acoustic intensity versus range and frequency. The striations result from the interference in acoustic propagation below the critical depth. The key of this technique is modeling Lloyd's-mirror interference fringes based on the ray-based description of the normal modes. Then, as the striations are interpreted as sampling fringes at different frequencies and ranges, a method to calculate their tracks is proposed based on the fringe model. Finally, experimental observations of striations are compared with results from the presented technique.

Deep-water measurements of container ship radiated noise signatures and directionality.

Underwater radiated noise from merchant ships was measured opportunistically from multiple spatial aspects to estimate signature source levels and directionality. Transiting ships were tracked via the Automatic Identification System in a shipping lane while acoustic pressure was measured at the ships' keel and beam aspects. Port and starboard beam aspects were 15°, 30°, and 45° in compliance with ship noise measurements standards [ANSI/ASA S12.64 (2009) and ISO 17208-1 (2016)]. Additional recordings were made at a 10° starboard aspect. Source levels were derived with a spherical propagation (surface-affected) or a modified Lloyd's mirror model to account for interference from surface reflections (surface-corrected). Ship source depths were estimated from spectral differences between measurements at different beam aspects. Results were exemplified with a 4870 and a 10 036 twenty-foot equivalent unit container ship at 40%-56% and 87% of service speeds, respectively. For the larger ship, opportunistic ANSI/ISO broadband levels were 195 (surface-affected) and 209 (surface-corrected) dB re 1 μPa2 1 m. Directionality at a propeller blade rate of 8 Hz exhibited asymmetries in stern-bow (<6 dB) and port-starboard (<9 dB) direction. Previously reported broadband levels at 10° aspect from McKenna, Ross, Wiggins, and Hildebrand [(2012b). J. Acoust. Soc. Am. 131, 92-103] may be ∼12 dB lower than respective surface-affected ANSI/ISO standard derived levels.

Effects of depth-dependent sound speed on Lloyd mirror patterns

The classical Lloyd mirror describes the interference pattern in pressure magnitude between direct and reflected propagation paths arising from a point source at depth d in the water column at a receiver located at range R, R &amp;gt;&amp;gt; d. In a homogeneous medium, the magnitude of acoustic pressure has a simple expression in terms of (approximate) propagation angle: |p|=(2/R0)|sin kd cos Θ0. For fast calculation of reverberation strength, we can apply this pattern to capture the effects of reflections from an idealized flat sea surface. However since we are interested in long range calculations, it is expected that the existence of sound speed gradients will affect the shape of this pattern, but how significant are these effects? To study this question, we derive a generalized Lloyd mirror for a linear-in-depth sound speed profile. We present results and discuss the implications. [Work supported by ONR through a STTR partnership with OASIS.]

Surface plasmon bandwidth increase using chirped-pitch linear diffraction gratings.

Large-scale linear diffraction gratings with gradually varying pitch were photo-inscribed onto the surface of azobenzene thin films using a 532 nm laser and a modified Lloyd mirror set-up. By placing a cylindrical lens in front of the direct half of the inscribing beam, gratings with a chirping rate as high as 12.9 nm/mm were produced. Subsequently, when these chirped-pitch gratings were coated with silver, over three-fold bandwidth increase was observed in the surface plasmon transmission peaks at FWHM, when compared to constant-pitch gratings. This was made possible due to the simultaneous excitation of surface plasmon resonance in a band of light wavelengths.

Polarization ray-tracing model for orthogonal two-axis Lloyd's mirror interference lithography

Polarization ray-tracing model for orthogonal two-axis Lloyd's mirror interference lithography

Fabrication of a two-dimensional diffraction grating by a two-axis Lloyd's mirror interferometer

Fabrication of a two-dimensional diffraction grating by a two-axis Lloyd's mirror interferometer

Influences of misalignment errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer.

This paper presents a detailed analysis on the influence of misalignment errors of optical components in an orthogonal two-axis Lloyd's mirror interferometer, which can fabricate two-dimensional grating structures in a single exposure. In an ideal condition, defect-free two-dimensional grating structures can be fabricated by the interferometer. However, in a real case, visible stripes caused by misalignment errors of the optical components in the interferometer always appear on the fabricated grating structures. In this paper, theoretical analysis and experiments are carried out to analyze the influences of the misalignment errors of the optical components in the orthogonal two-axis Lloyd's mirror interferometer.

Optical mosaic method for orthogonally crossed gratings by utilizing information about both main periodic directions simultaneously

We present a method to make optical mosaic orthogonally crossed gratings by utilizing information about both main periodic directions simultaneously. The whole mosaic system for orthogonally crossed gratings is set up based on the dual Lloyd's mirror interferometer that fabricates orthogonally crossed gratings through a single exposure. The interference fringes formed by the diffractions of the exposure beams from the exposed grating areas are used as the reference to fine tune the position and attitude of the exposure beams relative to the substrates during consecutive exposures. A procedure to make mosaic for two main periodic directions simultaneously is proposed based on the presupposition that the angle between two sets of main lattice lines is constant during the mosaic. Experimentally we made a 2×1 mosaic crossed grating with a period of 574nm in (30+30) mm ×35mm area. The peak-valley errors of the (−1, 0)th- and (0, −1)st-order diffraction wavefronts over the whole mosaic grating area are 0.104λ and 0.163λ, respectively.

Deep learning approach to passive monitoring of the underwater acoustic environment

A cost effective approach to remote monitoring of protected areas such as marine reserves, harbors and restricted naval waters, is to use passive sonar to detect, classify, localize, and track marine vessel activity (including small boats and autonomous underwater vehicles). This paper uses data from a single hydrophone mounted above the sea floor to compare a conventional cepstral analysis method with a deep learning approach for monitoring marine vessel activity. Cepstral analysis of the underwater acoustic data enables the time delay between the direct path arrival and the first multipath to be measured, which in turn enables estimation of the instantaneous range of the source (a small boat). However, this conventional method is limited to ranges where the Lloyd's mirror effect (interference pattern formed between the direct and first multipath arrivals) is discernible. It is shown that a Convolutional Neural Network (CNN) operating on cepstrum data with a regression output improves the single sensor ranging performance by considering additional multipath arrivals. To demonstrate the effectiveness of the approach, a surface vessel is ranged using the CNN and the results compared with the conventional method.

TPCO single-crystal optical devices equipped with one-dimensional diffraction gratings

ABSTRACTWe have formed one-dimensional (1D) diffraction gratings on a photoresist polymer (SU-8) by interference exposure using a Lloyd mirror. A single crystal of thiophene/phenylene co-oligomers (TPCOs) grown in a vapor phase was placed on the 1D diffraction grating. Excitation of the single crystal by an ultraviolet light of a mercury lamp produced spectrally-narrowed fluorescence. On the basis of the grating periods and emission peak locations, we evaluated effective refractive indices and diffraction orders. The relevant information enables us to design and fabricate the 1D diffraction gratings that cause the spectrally-narrowed emission lines to superimpose inherently occurring high-intensity fluorescence peaks.

Phase stepping optical profilometry using fiber optic Lloyd's mirrors.

A three-step phase stepping profilometry based on a fiber optic Lloyd's mirror assembly is employed in the optical profilometry for the first time to measure the shapes of 3D objects. Required π/2 phase shifts for interference fringe pattern are obtained by mechanically sliding the Lloyd assembly via an ordinary micrometer stage. The experimental setup is simple and low cost to construct, and is insensitive to the ambient temperature fluctuations and environmental vibrations that cause unwanted effects on the projected fringe pattern. Consecutive interferograms are captured by a CCD camera and are processed with an algorithm to accomplish 3D topographies.

Period-chirped gratings fabricated by laser interference lithography with a concave Lloyd's mirror.

We developed a laser interference lithography (LIL) system for fabrication of period-chirped gratings, which would be useful for sophisticated optical components. Despite its simplicity, the developed LIL system, based on a Lloyd's mirror interferometer with a cylindrically concave mirror, can generate chirped gratings, yet over a large area at high throughput owing to the nature of LIL. We have derived exact theoretical equations needed for system design, built the LIL system, and subsequently realized period-chirped gratings. A fabricated sample whose center period is Λ≈600 nm exhibits a continuous period variation of ΔΛ=92 nm across 17mm width.