Intensity dependent residual amplitude modulation in electro-optic phase modulators

Residual amplitude modulation (RAM) mechanisms in electro-optic phase modulators are detrimental in applications that require high purity phase modulation of the incident laser beam. While the origins of RAMare not fully understood, measurements have revealed that it depends on the beam properties of the laser as well as the properties of the medium. Here we present experimental and theoretical results that demonstrate, for the first time, the dependence of RAM production in electro-optic phase modulators on beam intensity. The results show an order of magnitude increase in the level of RAM, around 10 dB, with a fifteenfold enhancement in the input intensity from 12 to 190 mW/mm 2. We show that this intensity dependent RAM is photorefractive in origin. © 2012 Optical Society of America.

Polarization dependent photorefractive amplitude modulation production in MgO:LiNbO 3 phase modulators

We present experimental and theoretical results of the intensity dependence of residual amplitude modulation (RAM) production in electro-optic phase modulators. By utilizing the anisotropy of the medium, we show that RAM has a photorefractive origin.

Reducing residual amplitude modulation in electro-optic phase modulators by erasing photorefractive scatter

Residual amplitude modulation (RAM) is an unwanted noise source in electro-optic phase modulators. The analysis presented shows that while the magnitude of the RAM produced by a MgO:LiNbO3 modulator increases with intensity, its associated phase becomes less well defined. This combination results in temporal fluctuations in RAM that increase with intensity. This behaviour is explained by the presented phenomenological model based on gradually evolving photorefractive scattering centres randomly distributed throughout the optically thick medium. This understanding is exploited to show that RAM can be reduced to below the 10-5 level by introducing an intense optical beam to erase the photorefractive scatter.

Investigation of the intensity dependence of amplitude noise in electro-optic phase modulators

This thesis studied the source of instability in optical phase modulators used in high accuracy laser measurement systems. The nonlinear origin of the amplitude noise helped further reducing this instability in applications that rely on phase modulators to function. This outcome will have positive impacts on the development of new methods in the amplitude noise suppression.

Dependence of residual amplitude noise in electro-optic phase modulators on the intensity distribution of the incident field

Our results demonstrate that photorefractive residual amplitude modulation (RAM) noise in electro-optic modulators (EOMs) can be reduced by modifying the incident beam intensity distribution. Here we report an order of magnitude reduction in RAM when beams with uniform intensity (flat-top) profiles, generated with an LCOS-SLM, are used instead of the usual fundamental Gaussian mode (TEM00). RAM arises from the photorefractive amplified scatter noise off the defects and impurities within the crystal. A reduction in RAM is observed with increasing intensity uniformity (flatness), which is attributed to a reduction in space charge field on the beam axis. The level of RAM reduction that can be achieved is physically limited by clipping at EOM apertures, with the observed results agreeing well with a simple model. These results are particularly important in applications where the reduction of residual amplitude modulation to 10^-6 is essential.

Amplitude equations and asymptotic expansions for multi-scale problems

In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases. © 2010 - IOS Press and the authors. All rights reserved.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.

A survey in mathematics for industry: Two-timing and matched asymptotic expansions for singular perturbation problems

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383-410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations. © 2011 Cambridge University Press.

Cone Ratios in Myopia and Emmetropia: A Pilot Study

Purpose There is a suggestion that the long wavelength-sensitive (LWS)-to-middle wavelength-sensitive (MWS) cone ratio in the retina is associated with myopia. The aim was to measure the LWS/MWS amplitude modulation ratio, an estimate of the LWS/MWS cone ratio, in young adult emmetropes and myopes. Methods Multifocal visual evoked potentials were measured when the LWS and MWS cone systems were excited separately using the method of silent substitution. The 30 young adult participants (22 to 33 years) included 10 emmetropes (mean [±SD] refraction, +0.3 [±0.4] diopters [D]) and 20 myopes (mean [±SD] refraction, -3.4 [±1.7] D). Results The LWS/MWS amplitude modulation ratios ranged from 0.56 to 1.80 in the central 3- to 13-degree diameter ring and from 0.94 to 1.91 in the peripheral 13- to 30-degree diameter ring. Within the central ring, the mean (±SD) ratios were 1.20 (±0.26) and 1.20 (±0.33) for the emmetropic and the myopic groups, respectively. For the peripheral ring, the mean (±SD) ratios were 1.48 (±0.27) and 1.30 (±0.27), respectively. There were no significant differences in the ratios between the emmetropic and myopic groups for either the central (p = 0.99) or peripheral (p = 0.08) rings. For the latter, more myopic refractive error was associated with lower LWS/MWS amplitude modulation ratio; the refraction explained 16% (p = 0.02) of variation in ratio. Conclusions The relationship between the LWS/MWS amplitude modulation ratios and refraction at 13 to 30 degrees indicates that a large longitudinal study of changes in refraction in persons with known cone ratio is required to determine if a low LWS/MWS cone ratio is associated with myopia development.

Pharmacological consequence of the A118G μ opioid receptor polymorphism on morphine-and fentanyl-mediated modulation of Ca2+ channels in humanized mouse sensory neurons

Background: The most common functional single nucleotide polymorphism of the human OPRM1 gene, A118G, has been shown to be associated with interindividual differences in opioid analgesic requirements, particularly with morphine, in patients with acute postoperative pain. The purpose of this study was to examine whether this polymorphism would modulate the morphine and fentanyl pharmacological profile of sensory neurons isolated from a humanized mouse model homozygous for either the 118A or 118G allele. Methods: The coupling of wild-type and mutant μ opioid receptors to voltage-gated Ca channels after exposure to either ligand was examined by employing the whole cell variant of the patch-clamp technique in acutely dissociated trigeminal ganglion neurons. Morphine-mediated antinociception was measured in mice carrying either the 118AA or 118GG allele. RESULTS:: The biophysical parameters (cell size, current density, and peak current amplitude potential) measured from both groups of sensory neurons were not significantly different. In 118GG neurons, morphine was approximately fivefold less potent and 26% less efficacious than that observed in 118AA neurons. On the other hand, the potency and efficacy of fentanyl were similar for both groups of neurons. Morphine-mediated analgesia in 118GG mice was significantly reduced compared with the 118AA mice. Conclusions: This study provides evidence to suggest that the diminished clinical effect observed with morphine in 118G carriers results from an alteration of the receptor's pharmacology in sensory neurons. In addition, the impaired analgesic response with morphine may explain why carriers of this receptor variant have an increased susceptibility to become addicted to opioids. © 2011 the American Society of Anesthesiologists, Inc. Lippincott Williams & Wilkins. Anesthesiology.

Mesopic rod and S-cone interactions revealed by modulation thresholds

We analyzed mesopic rod and S-cone interactions in terms of their contributions to the blue-yellow opponent pathway. Stimuli were generated using a 4-primary colorimeter. Mixed rod and S-cone modulation thresholds (constant L-, M-cone excitation) were measured as a function of their phase difference. Modulation amplitude was equated using threshold units and contrast ratios. This study identified three interaction types: (1) A linear and antagonistic rod:S-cone interaction, (2) probability summation (3) and a previously unidentified mutual nonlinear reinforcement. Linear rod:S-cone interactions occur within the blue-yellow opponent pathway. Probability summation involves signaling by different post-receptoral pathways. The origin of the nonlinear reinforcement is possibly at the photoreceptors.

Higher harmonic large-amplitude fourier transformed alternating current voltammetry : analytical attributes derived from studies of the oxidation of ferrocenemethanol and uric acid at a glassy carbon electrode

An analytical evaluation of the higher ac harmonic components derived from large amplitude Fourier transformed voltammetry is provided for the reversible oxidation of ferrocenemethanol (FcMeOH) and oxidation of uric acid by an EEC mechanism in a pH 7.4 phosphate buffer at a glassy carbon (GC) electrode. The small background current in the analytically optimal fifth harmonic is predominantly attributed to faradaic current associated with the presence of electroactive functional groups on the GC electrode surface, rather than to capacitive current which dominates the background in the dc, and the initial three ac harmonics. The detection limits for the dc and the first to fifth harmonic ac components are 1.9, 5.89, 2.1, 2.5, 0.8, and 0.5 µM for FcMeOH, respectively, using a sine wave modulation of 100 mV at 21.46 Hz and a dc sweep rate of 111.76 mV s−1. Analytical performance then progressively deteriorates in the sixth and higher harmonics. For the determination of uric acid, the capacitive background current was enhanced and the reproducibility lowered by the presence of surface active uric acid, but the rapid overall 2e− rather than 1e– electron transfer process gives rise to a significantly enhanced fifth harmonic faradaic current which enabled a detection limit of 0.3 µM to be achieved which is similar to that reported using chemically modified electrodes. Resolution of overlapping voltammetric signals for a mixture of uric acid and dopamine is also achieved using higher fourth or fifth harmonic components, under very low background current conditions. The use of higher fourth and fifth harmonics exhibiting highly favorable faradaic to background (noise) current ratios should therefore be considered in analytical applications under circumstances where the electron transfer rate is fast.