There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

/pdf/roadmap-on-structured-light-3r840pnxka.pdf

Roadmap on structured light

Micro-combs: A novel generation of optical sources

The current count of extrasolar planets (on planetquest.jpl.nasa.gov) stands at 277, none of them Earth-like. Most were detected as a Doppler shift in stellar spectral lines, a method that 'sees' planets down to about five times the mass of the Earth. If Earth-sized planets are to be revealed by this observational approach, better Doppler shift resolution via improved spectrograph wavelength calibration will be required. A newly developed instrument, the 'astro-comb', achieves just that by adapting the laser frequency comb, a device that has revolutionized laboratory spectroscopy, to the needs of astrophysics. This involves reducing the density of comb lines, without compromising spectral resolution. A performance test of the astro-comb is reported in this issue, and in May 2008, the new device joins the search for 'exoearths' in earnest. Searches for extrasolar planets using the periodic Doppler shift of stellar spectral lines have recently achieved a precision of 60 cm s−1, sufficient to find a 5-Earth-mass planet in a Mercury-like orbit around a Sun-like star. The fabrication of an 'astro-comb' that should allow a precision as high as 1 cm s−1 in astronomical radial velocity measurements is reported Searches for extrasolar planets using the periodic Doppler shift of stellar spectral lines have recently achieved a precision of 60 cm s-1 (ref. 1), which is sufficient to find a 5-Earth-mass planet in a Mercury-like orbit around a Sun-like star. To find a 1-Earth-mass planet in an Earth-like orbit, a precision of ∼5 cm s-1 is necessary. The combination of a laser frequency comb with a Fabry–Perot filtering cavity has been suggested as a promising approach to achieve such Doppler shift resolution via improved spectrograph wavelength calibration2,3,4, with recent encouraging results5. Here we report the fabrication of such a filtered laser comb with up to 40-GHz (∼1-A) line spacing, generated from a 1-GHz repetition-rate source, without compromising long-term stability, reproducibility or spectral resolution. This wide-line-spacing comb, or ‘astro-comb’, is well matched to the resolving power of high-resolution astrophysical spectrographs. The astro-comb should allow a precision as high as 1 cm s-1 in astronomical radial velocity measurements.

A laser frequency comb that enables radial velocity measurements with a precision of 1 cm s -1

Over the last decade, control of atomic-scale electronic motion by non-perturbative optical fields has broken tremendous new ground with the advent of phase-controlled high-energy few-cycle pulse sources1. The development of close to single-cycle, carrier-envelope phase controlled, high-energy optical pulses has already led to isolated attosecond EUV pulse generation2, expanding ultrafast spectroscopy to attosecond resolution1. However, further investigation and control of these physical processes requires sub-cycle waveform shaping, which has not been achievable to date. Here, we present a light source, using coherent wavelength multiplexing, that enables sub-cycle waveform shaping with a two-octave-spanning spectrum and a pulse energy of 15 µJ. It offers full phase control and allows generation of any optical waveform supported by the amplified spectrum. Both energy and bandwidth scale linearly with the number of sub-modules, so the peak power scales quadratically. The demonstrated system is the prototype of a class of novel optical tools for attosecond control of strong-field physics experiments. Researchers present a waveform synthesis scheme that coherently multiplexes the outputs from two broadband optical parametric chirped-pulse amplifiers. The technique provides control at the sub-cycle scale and generates high-energy ultrashort waveforms for use in strong-field physics experiments.

/pdf/high-energy-pulse-synthesis-with-sub-cycle-waveform-control-2lgl1w9idz.pdf

High-energy pulse synthesis with sub-cycle waveform control for strong-field physics

We present a new method for measuring the spectral phase of ultrashort pulses that utilizes spectral shearing interferometry with zero delay. Unlike conventional spectral phase interferometry for direct electric-field reconstruction, which encodes phase as a sensitively calibrated fringe in the spectral domain, two-dimensional spectral shearing interferometry robustly encodes phase along a second dimension. This greatly reduces demands on the spectrometer and allows for complex phase spectra to be measured over extremely large bandwidths, potentially exceeding 1.5 octaves.

Two-dimensional spectral shearing interferometry for few-cycle pulse characterization

Advances in technology for optical arbitrary waveform generation will be described. Combs spanning two octaves, from 500nm to 2µm, based on GHz modelocked Ti:sapphire and erbium-fiber lasers, have been carrier-envelope stabilized and frequency referenced.

Optical arbitrary waveform generation

Beamsplitters are used in projectors with retarder stack filters to orthogonally polarize primary colors, thus converting polarizing beamsplitters to color splitters and combiners. Beamsplitters at moderate f-numbers induce geometric polarization rotations in skew rays which may degrade performance of conventional retarder stacks, resulting in color cross-talk. Retarder stacks presented herein are sensitive to the symmetries between input and output polarizer configurations. These stacks provide the polarization transformations to compensate for skew rays, such that normal incidence performance is maintained for all incident light. Systems are disclosed utilizing color selective polarization filters 'CSP' and polarizing beamsplitters without the need for an output analyzer. The CSP may be included in the above system. One exemplary CSP architecture includes two CSPs (404, 318), a single polarizing beamsplitter/combiner (324) between two (326, 330) of the three panels, and an output polarizing beamsplitter (316) element used as an analyzer such that a single CSP (318) is in the projection path. A second architecture uses an output combining chromatic polarizing beamsplitter. A third architecture uses chromatic sheet polarizers to enhance CSP performance. In all of the architectures, an output CSP and clean-up polarizer directly in front of the projection optics need not be included, thereby increasing transmission, improving imaging crispness by increasing the optical phase flatness of the projecting light, and reducing cost.

Compensated color management systems and methods

Carrier-envelope phase stabilization of a 200MHz octave-spanning Ti:sapphire laser without external broadening is demonstrated. The individual comb lines spaced by 200MHz can conveniently be resolved using commercial wavemeters. The accumulated in-loop carrier-envelope phase error (integrated from 2.5 mHz to 10 MHz) using a broadband analog mixer as phase detector is 0.117 rad, equivalent to 50 attosecond carrier-envelope phase jitter at 800 nm.

Jonathan R. Birge

Papers

High-energy pulse synthesis with sub-cycle waveform control for strong-field physics

Two-dimensional spectral shearing interferometry for few-cycle pulse characterization

Optical arbitrary waveform generation

Compensated color management systems and methods

Self-Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser with 50 Attosecond Carrier-Envelope Phase Jitter