Modulation depth and bandwidth analysis of planar thermo-optic diamond actuators.

Thermo-optic actuators based on bulk materials are considered too slow in applications such as laser frequency control. The availability of high-quality optical materials that have extremely fast thermal response times, such as diamond, present an opportunity for increasing performance. Here, diamond thermal actuators are investigated for configurations that use a planar thermal resistive layer applied to a heat-sinked rectangular prism. A general analytical formulation is obtained which simplifies substantially for high thermal conductivity such as diamond. Expressions for modulation depth, bandwidth and power requirements are obtained as functions of modulator dimensions and heat-transfer coefficients. For a 1 mm × 1 mm cross-section diamond at wavelength of 1 µm, around 450 W of applied heat power is needed to achieve a π phase shift at a modulation frequency of 2 kHz.

Quantum-randomized polarization of laser pulses derived from zero-point diamond motion.

Intrinsic randomness in quantum systems is a vital resource for cryptography and other quantum information protocols. To date, randomizing macroscopic polarization states requires randomness from an external source, which is then used to modulate the polarization e.g. for quantum key-distribution protocols. Here, we present a Raman-based device for directly generating laser pulses with quantum-randomized polarizations. We show that crystals of diamond lattice symmetry provide a unique operating point for which the Raman gain is isotropic, so that the spontaneous symmetry breaking initiated by the quantum-random zero-point motion determines the output polarization. Experimentally measured polarizations are demonstrated to be consistent with an independent and identical uniform distribution with an estimated quantum entropy rate of 3.8 bits/pulse.

Photoreflectance/scattering measurements of spider silks informed by standard optics.

The silks of certain orb weaving spiders are emerging as high-quality optical materials. This motivates study of the optical properties of such silk and particularly the comparative optical properties of the silks of different species. Any differences in optical properties may impart biological advantage for a spider species and make the silks interesting for biomimetic prospecting as optical materials. A prior study of the reflectance of spider silks from 18 species reported results for three species of modern orb weaving spiders (Nephila clavipes, Argiope argentata and Micrathena Schreibersi) as having reduced reflectance in the UV range. (Modern in the context used here means more recently derived.) The reduced UV reflectance was interpreted as an adaptive advantage in making the silks less visible to insects. Herein, a standard, experimental technique for measuring the reflectance spectrum of diffuse surfaces, using commercially available equipment, has been applied to samples of the silks of four modern species of orb weaving spiders: Phonognatha graeffei, Eriophora transmarina, Nephila plumipes and Argiope keyserlingi. This is a different technique than used in the previous study. Three of the four silks measured have a reduced signal in the UV. By taking the form of the silks as optical elements into account, it is shown that this is attributable to a combination of wavelength-dependent absorption and scattering by the silks rather than differences in reflectance for the different silks. Phonognatha graeffei dragline silk emerges as a very interesting spider silk with a flat 'reflectance'/scattering spectrum which may indicate it is a low UV absorbing dielectric micro-fibre. Overall the measurement emerges as having the potential to compare the large numbers of silks from different species to prospect for those which have desirable optical properties.

Numerical study of optical feedback coherence in semiconductor laser dynamics.

The nonlinear dynamics of a semiconductor laser with coherent, as compared to incoherent, delayed optical feedback systems have been discussed and contrasted in prior research literature. Here, we report simulations of how the dynamics change as the coherence of the optical feedback is systematically varied from being coherent, through several levels of partial coherence, to incoherent. An increasing rate of phase disturbance is used to vary the coherence. An edge-emitting, 830 nm, Fabry-Perot semiconductor laser with a long external cavity is simulated. Following this study, consideration of prior and future experimental studies should include evaluation of where on the continuum of partial coherence the delayed optical feedback sits. The level of partial coherence is an important factor affecting the dynamics.

Mapping the dynamical regimes of a SESAM mode-locked VECSEL with a long cavity using time series analysis.

The different dynamical regions of an optically-pumped SESAM mode-locked, long-cavity VECSEL system with a fundamental pulse repetition frequency of ~200 MHz are investigated. The output power, captured as 250 µs long time series using a sampling rate of 200 GSa/s, for each operating condition of the system, is analyzed to determine the dynamical state. A wavelength range of 985-995 nm and optical pump powers of 10 W-16.3 W is studied. The system produces high quality fundamental passive mode-locking (FML) over an extensive part of the parameter space, but the different dynamical regions outside of FML are the primary focus of this study. We report five types of output: CW emission, FML, mode-locking of a few modes, double pulsing, and, semi-stable 4th harmonic mode-locking. The high sampling rate of the oscilloscope, combined with the long duration of the time series analyzed, enables insight into how the structure and substructure of pulses vary systematically over thousands of round trips of the laser cavity. Higher average output power is obtained in regions characterized by semi-stable 4th harmonic mode-locking than observed for FML, raising whether such average powers might be achieved for FML. The observed dynamic transitions from fundamental mode-locking provide insights into instability challenges in developing a stable, widely tunable, low repetition rate, turn-key system; and to inform future modelling of the system.

Variance of permutation entropy and the influence of ordinal pattern selection.

Permutation entropy (PE) is a widely used measure for complexity, often used to distinguish between complex systems (or complex systems in different states). Here, the PE variance for a stationary time series is derived, and the influence of ordinal pattern selection, specifically whether the ordinal patterns are permitted to overlap or not, is examined. It was found that permitting ordinal patterns to overlap reduces the PE variance, improving the ability of this statistic to distinguish between complex system states for both numeric (fractional Gaussian noise) and experimental (semiconductor laser with optical feedback) systems. However, with overlapping ordinal patterns, the precision to which the PE variance can be estimated becomes diminished, which can manifest as increased incidences of false positive and false negative errors when applying PE to statistical inference problems.

Permutation entropy with vector embedding delays.

Permutation entropy (PE) is a statistic used widely for the detection of structure within a time series. Embedding delay times at which the PE is reduced are characteristic timescales for which such structure exists. Here, a generalized scheme is investigated where embedding delays are represented by vectors rather than scalars, permitting PE to be calculated over a (D-1)-dimensional space, where D is the embedding dimension. This scheme is applied to numerically generated noise, sine wave and logistic map series, and experimental data sets taken from a vertical-cavity surface emitting laser exhibiting temporally localized pulse structures within the round-trip time of the laser cavity. Results are visualized as PE maps as a function of embedding delay, with low PE values indicating combinations of embedding delays where correlation structure is present. It is demonstrated that vector embedding delays enable identification of structure that is ambiguous or masked, when the embedding delay is constrained to scalar form.

Permutation entropy of finite-length white-noise time series.

Permutation entropy (PE) is commonly used to discriminate complex structure from white noise in a time series. While the PE of white noise is well understood in the long time-series limit, analysis in the general case is currently lacking. Here the expectation value and variance of white-noise PE are derived as functions of the number of ordinal pattern trials, N, and the embedding dimension, D. It is demonstrated that the probability distribution of the white-noise PE converges to a χ^{2} distribution with D!-1 degrees of freedom as N becomes large. It is further demonstrated that the PE variance for an arbitrary time series can be estimated as the variance of a related metric, the Kullback-Leibler entropy (KLE), allowing the qualitative N≫D! condition to be recast as a quantitative estimate of the N required to achieve a desired PE calculation precision. Application of this theory to statistical inference is demonstrated in the case of an experimentally obtained noise series, where the probability of obtaining the observed PE value was calculated assuming a white-noise time series. Standard statistical inference can be used to draw conclusions whether the white-noise null hypothesis can be accepted or rejected. This methodology can be applied to other null hypotheses, such as discriminating whether two time series are generated from different complex system states.

An exact surface-integral approach for accurate interferometric microscopy of single nanoparticles.

We present a half-plane surface-integral equation (SIE) approach for modeling the optical phase response of a single nanowire under phase-stepping interferometric (PSI) microscopy. This approach calculates scattered fields exactly from the Helmholtz equation in this 2D problem, obviating the need for ray-optic approximations. It is demonstrated that refractive index metrology is enabled by this method, with precision as low as 7 × 10(-5) possible for current state-of-the-art PSI microscopes. For nanowires of known refractive index, radii as small as 0.001λ are shown to yield a measurable phase signal and are therefore potentially measurable by this approach. Measurements are also demonstrated to be relatively insensitive to the spectral and coherence characteristics of the light source, the illumination conditions, and variations in nanowire cross-section shape. Prospects for measuring both the radius and refractive index simultaneously, and scope for generalizing this approach to arbitrary nanoparticle shapes are discussed.

Measuring nanoparticle size using phase-stepping interferometry: quantifying measurement sensitivity to surface roughness.

A method for sizing nanoparticles using phase-stepping interferometry has been developed recently by Little et al. [Appl. Phys. Lett. 103, 161107 (2013)]. We present an analytical procedure to quantify how sensitive measurement precision is to surface roughness. This procedure computes the standard deviation in the measured phase as a function of the surface roughness power spectrum. It is applied to nanospheres and nanowires on a flat plane and also a flat plane in isolation. Calculated sensitivity levels demonstrate that surface roughness is unlikely to be the limiting factor on measurement precision when measuring nanoparticle size using this phase-shifting-interferometry-based technique. The need to use an underlying surface that is very smooth when measuring nanoparticles is highlighted by the analysis.

Subdiffraction-limited radius measurements of microcylinders using conventional bright-field optical microscopy.

A technique for measuring the radius of dielectric microcylinders with subdiffraction-limited precision is presented. Diffraction fringes arising from the dielectric cylinder are measured using conventional bright-field optical microscopy and compared with theory to deduce the radii. The technique has been demonstrated measuring the radii of the major-ampullate silks from Plebs eburnus spiders. Precision better than 50 nm is demonstrated, using a standard optical microscope with a numerical aperture of 0.6 for the objective. Accuracy was verified using scanning electron microscopy. This technique will facilitate rapid, precise measurement of dielectric microcylinder radii, enabling a new optical-microscopy-based measurement approach for these challenging micro-optics.

Measuring nanoparticle size using optical surface profilers.

Optical surface profilers are state-of-the-art instruments for measuring surface height profiles. They are not conventionally applied to nanoparticle measurements due to the presence of diffraction artifacts. Here we use a theoretical model based on wave-optics to account for diffraction-based artifacts in optical surface profilers. This then enables accurate measurement of nanoparticles size of a known geometry. The model is developed for both phase shifting interferometry and vertical scanning interferometry modes of operation. It is demonstrated that nanosphere radii as small as 12 nm, and nano-cylinder radii as small as 10-15 nm can be measured from a standard profile measurement using phase shifted interferometry interpreted using the wave-optics approach.

Image contrast immersion method for measuring refractive index applied to spider silks.

A technique for measuring the refractive index of micron sized fibers using a series of immersion index matching oils, and image contrast measurements is proposed and demonstrated. It has been applied to radial silks of the orb web weaving spider Plebs eburnus. These have widths of ~1-2 microns. Values about 1.5500 are obtained, with birefringence values between 0.0000 and 0.0133 for individual silks. An uncertainty in the range ± 5 × 10(-4) to ± 2 × 10(-3) is achieved for these challenging samples. This accuracy is about a twenty times improvement on previously reported measurements for spider silks using other techniques. The technique is used to obtain measurements of the refractive index of spider silks as a function of wavelength, for the first time. An Abbe number for the radial silks of Plebs eburnus of ~32 is found.

Hybrid immersion-polarization method for measuring birefringence applied to spider silks.

A technique for accurate measurement of the principle refractive indices and birefringence for silklike samples is presented. It is based on rotating the linear polarization of the illuminating light on a silk immersed in reference liquid to achieve index matching at the silk/liquid interface. The technique was used to measure the principal refractive indices of a P. eburnus radial silk at different strains. This in turn allows the calculation of strain-optic coefficients. The first measurement of the strain-optic coefficients of spider silk is presented. The technique is more generally applicable to strain-optic study of birefringent micro-optic samples.

Femtosecond laser modification of fused silica: the effect of writing polarization on Si-O ring structure.

A femtosecond laser with a 1 kHz repetition rate and two different polarization states was used to fabricate low-loss waveguides in fused silica. Investigations of chemically-mechanically polished waveguide regions using near-field scanning optical microscopy revealed the presence of modifications outside the glass regions directly exposed to a circularly polarized writing laser. These waveguides also exhibited refractive index contrast up to twice as large as that of waveguides written with linearly polarized radiation. The observed differences in refractive index were shown by Raman spectroscopy to correlate to an increased concentration of 3-member silicon-oxygen ring structures. We propose that the observed differences in material properties are due to the polarization dependence of photo-ionization rates in fused silica.