Distortion cancellation of frequency converted pulses with simple linear signal processing and application to frequency modulation to amplitude modulation conversion in high power lasers

It is known that a linear filter may be easily compensated with its inverse transfer function. However, it was shown that this approach could also be valid even for such a complex nonlinear system as frequency conversion. As a matter of fact, it is possible to at least partly precompensate for distortions occurring within, or even downstream from, frequency conversion crystals with a simple linear optical filter set upstream. In this paper, we give the theoretical background and derive the optimum precompensation filter from simple analytical formulas even in the case of saturation. We first show the relevance of our approach for Gaussian pulses: the pulse may be short or not and chirped or not, and the same linear precompensation filter may be used as long as saturation is not reached. We then study the case of phase-modulated pulses, as can be found on high power lasers such as lasers for fusion. We show that previous experimental results are in perfect agreement with these calculations. Finally, justified by our simple analytical formulas, we present a rigorous parametrical study giving the distortion reduction for any second and third harmonic generation system in the case of phase-modulated pulses.     

The Optical Signal Generator and Phase-locked Loop Based on a Triangularly Phase-modulated Fibre-optic Gyroscope

Abstract

A novel optical signal generator with purely sinusoidal waveform output has been demonstrated by applying a triangular phase modulation waveform to a fibre-optic gyroscope (FOG). A frequency-multiplied output in the format of an optical signal could be generated. An optical-type electrical phase-locked-loop system based on the intensity-modulated light source and this triangularly phase-modulated FOG has also been demonstrated.     

Optical diodes and omnidirectional reflectors based on one-dimensional quasiperiodic photonic crystals

The optical properties of one-dimensional quasiperiodic photonic crystals with linear profiles of modulation parameters are considered. It is shown that such systems possess a wider photonic band gap as compared to the ideal periodic system and can be used as omnidirectional reflectors. The asymmetric profiles of parameters in these systems results in the appearance of nonreciprocity of a new type that makes possible their use as the ideal, purely optical diodes.     

Photonic crystal fibre based all-optical modulation format conversions between NRZ and RZ with hybrid clock recovery from a PRZ signal

Several all-optical modulation format-converting schemes are described for non-return-to-zero (NRZ) and return-to-zero (RZ) modulation formats that make use of spectral filtering of either self-phase modulation (SPM) or cross-phase modulation (XPM) broadened signal spectrum in a highly-nonlinear dispersion-flattened photonic-crystal fibre. Format conversions have been performed between the most widely used modulation formats - NRZ and RZ. In addition, a hybrid clock recovery scheme is proposed to obtain the data rate of the NRZ signal for NRZ-to-RZ format conversion. All format-converting schemes are based on the extraction of the spectral components in a nonlinear phase modulation broadened signal spectrum. In NRZ-to-RZ format conversion, a periodic pulse train, at a repetition rate similar to the NRZ data rate, is used as a control that induces a nonlinear phase shift to the NRZ probe signal and broadens its spectrum. The spectral components, contributed by different time instances of the control pulse, can be extracted as the converted RZ signal output. In RZ-to-NRZ format conversion, the RZ signal serves as a control that induces a nonlinear phase shift to a continuous wave probe light, where a logic-inverted NRZ signal can be extracted by filtering out the chirped components. Format conversions between NRZ and RZ signals at 9.95328 GB/s (OC-192) are demonstrated. As the proposed optical signal-processing schemes make use of the fibre nonlinearity (SPM/XPM), it is possible to extend it to a high-speed operation <160 Gb/s. Therefore the proposed format-converting schemes can serve as a format converter between the optical time-division multiplexed networks and the wavelength division multiplexed networks     

Analytic phase-factor equations for Talbot array illuminations

Under specific circumstances the fractional Talbot effect can be described by simplified equations. We have obtained simplified analytic phase-factor equations to describe the relation between the pure-phase factors and their fractional Talbot distances behind a binary amplitude grating with an opening ratio of (1/M). We explain how these simple equations are obtained from the regularly rearranged neighboring phase differences. We point out that any intensity distribution with an irreducible opening ratio (M(N)/M) (M(N) < M, where M(N) and M are positive integers) generated by such an amplitude grating can be described by similar phase-factor equations. It is interesting to note that an amplitude grating with additional arbitrary phase modulation can also generate pure-phase distributions at the fractional Talbot distance. We have applied these analytic phase-factor equations to neighboring (0, pi) phase-modulated amplitude gratings and have analytically derived a new set of simple phase-factor equations for Talbot array illumination in this case. Experimental verification of our theoretical results is given.     

Imaging in diffuse media with pulsed-ultrasound-modulated light and the photorefractive effect

Acousto-optic imaging in diffuse media is a dual wave-sensing technique in which an acoustic field interacts with multiply scattered laser light. The acoustic field causes a phase modulation in the optical field emanating from the interaction region, and this phase-modulated optical field carries with it information about the local optomechanical properties of the media. We report on the use of a pulsed ultrasound transducer to modulate the optical field and the use of a photorefractive-crystal-based interferometry system to detect ultrasound-modulated light. The use of short pulses of focused ultrasound allows for a one-dimensional acousto-optic image to be obtained along the transducer axis from a single, time-averaged acousto-optic signal. The axial and lateral resolutions of the system are controlled by the spatial pulse length and width of the ultrasound beam, respectively. In addition, scanning the ultrasound transducer in one dimension yields two-dimensional images of optical inhomogeneities buried in turbid media.     

General problem of signal modulation on the basis of time-pulse modulation

The proposed general approach to the synthesis of precise amplitude- and phase-modulated signals is based on equivalent modulation of the time parameters and the position of the initial carrier pulse train with an arbitrary waveform. Typical cases of such modulation are investigated and expressions are derived for the transition from time-pulse modulation to amplitude and phase modulation of a signal with a harmonic carrier. Translated from Izmeritel'naya Tekhnika, No. 4, pp. 47–51, April, 1998.     

Simplified optical scatterometry for periodic nanoarrays in the near-quasi-static limit

Scatterometry is now proven to be a very powerful technique for measurement of subwavelength periodic structures. However it requires heavy numerical calculations of the scattered optical waves from the structure. For periodic nanoarrays with feature size less than 100 nm, it is possible to simplify this using the Rytov near-quasi-static approximation valid for feature periods only few time less than the wavelength. The validity is investigated by way of comparison with exact numerical results obtained with the eigenfunctions approach. It is shown to be adequate for the determination of the structure parameters from the specularly reflected or transmitted waves and their polarization or ellipsometric properties. The validity of this approach is applied to lamellar nanoscale grating photoresist lines on Si substrate. The high sensitivity of the signals to the structure parameters is demonstrated using wavelengths of only few times the period.     

Saturated semiconductor optical amplifier phase modulation for long range laser radar applications

We investigate the use of a semiconductor optical amplifier operated in the saturation regime as a phase modulator for long range laser radar applications. The nature of the phase and amplitude modulation resulting from a high peak power Gaussian pulse, and the impact this has on the ideal pulse response of a laser radar system, is explored. We also present results of a proof-of-concept laboratory demonstration using phase-modulated pulses to interrogate a stationary target.     

Measuring the best linear approximation of systems suffering nonlinear distortions: an alternative method

When measuring the best linear approximation of systems suffering nonlinear distortions, a specific class of periodic multiharmonic signals is normally used. These are signals with uniformly distributed random phases, termed random phase multisines. In this paper, it is shown that measurements of the best linear approximation of nonlinear systems can also be obtained by using a special type of low crest factor multisines. These signals are compared to random phase multisines and their properties are analyzed in detail.     

Frequency domain photothermoacoustic signal amplitude dependence on the optical properties of water: turbid polyvinyl chloride-plastisol system

Photoacoustic (more precisely, photothermoacoustic) signals generated by the absorption of photons can be related to the incident laser fluence rate. The dependence of frequency domain photoacoustic (FD-PA) signals on the optical absorption coefficient (micro(a)) and the effective attenuation coefficient (micro(eff)) of a turbid medium [polyvinyl chloride-plastisol (PVCP)] with tissuelike optical properties was measured, and empirical relationships between these optical properties and the photoacoustic (PA) signal amplitude and the laser fluence rate were derived for the water (PVCP system with and without optical scatterers). The measured relationships between these sample optical properties and the PA signal amplitude were found to be linear, consistent with FD-PA theory: micro(a)=a(A/Phi)-b and micro(eff)=c(A/Phi)+d, where Phi is the laser fluence, A is the FD-PA amplitude, and a, ...,d are empirical coefficients determined from the experiment using linear frequency-swept modulation and a lock-in heterodyne detection technique. This quantitative technique can easily be used to measure the optical properties of general turbid media using FD-PAs.     

Spatial effect on the interference of light propagated in a film structure

The interference of light has been analyzed for a film structure by considering that a spatial separation exists for the two neighboring light beams to be interfered in the space. There is a significant difference between the situations of the interference with or without consideration of the spatial effect, especially around the region where the phase delay delta=pi and 2pi by taking the example of the one-layered SiO2/Si structure. It is reasonable to extract the optical parameters by neglecting the spatial effect only for the thinner film with a thickness much smaller than a wavelength, which satisfies the condition that delta相似文献   

Passive directional discrimination in laser-Doppler anemometry by the two-wavelength quadrature homodyne technique

We report a method for passive optical directional discrimination in laser-Doppler anemometers. For this purpose frequency-shift elements such as acousto-optic modulators, which are bulky and difficult to align during assembly, have traditionally been employed. We propose to use a quadrature homodyne technique to achieve directional discrimination of the fluid flow without any frequency-shift elements. It is based on the employment of two laser wavelengths, which generate two interference fringe systems with a phase shift of a quarter of the common fringe spacing. Measurement signal pairs with a direction-dependent phase shift of +/- pi/2 are generated. As a robust signal-processing technique, the cross-correlation technique is used. The principles of quadrature homodyne laser-Doppler anemometry are investigated. A setup that provides a constant phase shift of pi/2 throughout the entire measurement volume was achieved with both single-mode and multimode radiation. The directional discrimination was successfully verified with wind tunnel measurements. The complete passive technique offers the potential of building miniaturized measurement heads that can be integrated, e.g., into wind tunnel models.     

An algorithm for accurately estimating the harmonic magnitudes and phase shifts of periodic signals with asynchronous sampling

A digital sampling algorithm that uses two high-resolution integrating voltmeters in a master-slave configuration for accurately measuring the harmonic magnitudes and phase angles of two low-noise, low-frequency, arbitrary voltage signals is presented. It is shown that it is possible to measure up to 64 harmonic magnitudes of 60-Hz signals with an uncertainty of less than 13 /spl mu/V/V relative to the fundamental using commercial stable signal generators and high-resolution digital voltmeters. It is also possible to measure the phase shift between the fundamental components of two equally-synthesized 60-Hz signals with about 3.8% total harmonic distortion with an uncertainty of less than 2.5 /spl mu/rad. Even lower uncertainties can be obtained for low-distortion signals. The algorithm was applied to the measurement of the harmonics of periodic arbitrary signals generated by a commercial source. The differences between computed and measured values of harmonic magnitude suggest that stable digitally-synthesized signal generators can be used as calculable standards of harmonic distortion with an accuracy of less than 6 parts in 10/sup 5/ relative to the fundamental.     

Periodic soliton trains in nonlinear magneto-optical media

The combination of the vector nature (i.e. polarization) of light in materials with nonlinearity can give rise to outstanding phenomena in the transmission of nonlinear optical fields. When the optical medium has been initially altered by a magnetic field, magneto-optical effects introduce additional interesting phenomena such as the possible control of optical signals by a magnetic field. The present work addresses the problem of optical-soliton generation from pulsed radiations interacting with a quasi-resonant magneto-optical medium, under normal Zeeman effect. It is shown that multi-soliton structures can be generated in the magneto-optical medium under specific conditions, these include periodic trains of bright and dark optical solitons having finite temporal periods.     

Disturbance-free distributed Bragg reflector laser-diode interferometer with a double sinusoidal phase-modulating technique for measurement of absolute distance

A new range-finding technique that uses both double sinusoidal phase modulation and quasi-two-wavelength interferometry is described. Two independent interference signals are generated with respect to two different wavelengths on a time-sharing basis. We clarify that external disturbances of these interference signals are eliminated by both feedback control and differential detection and that the feedback control does not affect the distance measurement. A single distributed Bragg reflector laser diode allows us to simplify the optical setup and to improve the measurement accuracy. After discussing a measurement range, we estimate a measurement error by making several measurements.     

Near-lossless continuous phase modulation using the analog switching mode (V-shaped switching) in ferroelectric liquid crystals

The analog switching mode in ferroelectric liquid crystals, sometimes referred to as 'V-shaped switching,' has, thanks to its submillisecond switching capability, attracted much interest for future fast electro-optic displays where it is to be used for amplitude modulation. We have studied this mode for analog phase-only modulation. As V-shaped switching is based on a conical motion of the index ellipsoid this presents a challenging problem since both the orientation of the slow and fast axes, as well as the amount of birefringence varies in the switching process. We show theoretically, partly by means of Poincaré sphere analysis, that it is in fact possible to obtain near-lossless analog phase modulation between zero and pi radians in an ideal V-shaped switching cell through careful tuning of the polarization state of the input light. Furthermore, we were able to demonstrate this experimentally in a fabricated cell. Although this cell deviated slightly from the ideal conditions, e.g., the tilt cone half-angle was 38 degrees instead of the desired 45 degrees , we still obtained a continuous phase modulation between zero and 0.78pi rad with less than 2% modulation of the amplitude; the measured values agree very well with our numerical simulations of the real device.     

Multiplexed optical operation of distributed nanoelectromechanical systems arrays

We report a versatile all optical technique to excite and read-out a distributed nanoelectromechanical systems (NEMS) array. The NEMS array is driven by a distributed, intensity modulated optical pump through the photothermal effect. The ensuing vibrational response of the array is multiplexed onto a single probe beam in the form of a high frequency phase modulation. The phase modulation is optically down converted to a low frequency intensity modulation using an adaptive full-field interferometer, and subsequently detected using a CCD array. Rapid and single step mechanical characterization of ～44 nominally identical high-frequency resonators is demonstrated. The technique may enable sensitivity improvements over single NEMS resonators by averaging signals coming from a multitude of devices in the array. In addition, the diffraction limited spatial resolution may allow for position-dependent read-out of NEMS sensor chips for sensing multiple analytes or spatially inhomogeneous forces.     

Expansion of linear range of Pound-Drever-Hall signal

We propose new solutions for expanding the linear signal range between the laser frequency deviation (or mirror position) and the voltage signal derived by the Pound-Drever-Hall (PDH) method for optical Fabry-Perot cavity resonance control. One solution is to perform not in-phase demodulation but near-Q-phase demodulation. Another solution is to take a suitable combination of signals demodulated by odd-harmonic modulation frequencies in the in phase. Although the PDH signal sensitivity will be diminished, the PDH signal linear range can be extended. From a practical standpoint, it is desirable that a sideband frequency for the PDH method is near the FP cavity resonance.     

Modulation light efficiency of diffractive lenses displayed in a restricted phase-mostly modulation display

We present an analysis of the diffraction efficiency of diffractive lenses displayed on spatial light modulators that depends on the modulation response of the display. An ideal display would produce continuous phase-only modulation, reaching a maximum phase-modulation depth of 2pi. We introduce the concept of modulation diffraction efficiency that accounts for the effect of nonlinearities only in the phase modulation of the display. We review a diffractive model with which to evaluate this modulation efficiency, including modulation defects such as nonlinear phase modulation, coupled amplitude modulation, phase quantization, and a limited modulation depth. We apply this diffractive model to Fresnel lenses and show that these modulation defects produce a lens multiplex effect. Finally we demonstrate that the application of a minimum Euclidean projection principle leads to high modulation diffraction efficiency even if the phase-modulation depth is much less than 2pi. We demonstrate that the modulation efficiency can exceed 90% for a modulation depth of 1.4pi and can exceed 40% (the equivalent for a binary phase element) for a modulation depth of only 0.7pi. Experimental results from use of a twisted nematic liquid-crystal display are presented to confirm these conclusions.