Additional Phase Modulation Research Articles

Single-pulse ultrafast laser imprinting of axial dot arrays in bulk glasses

Ultrafast laser processing of bulk transparent materials can significantly gain flexibility when the number of machining spots is increased. We present a photoinscription regime in which an array of regular dots is generated before the region of main laser focus under single-pulse exposure in fused silica and borosilicate crown glass without any external spatial phase modulation. The specific position of the dots does not rely on nonlinear propagation effects but is mainly determined by beam truncation and is explained by a Fresnel propagation formalism taking into account beam apodization and linear wavefront distortions at the air/glass interface. The photoinscription regime is employed to generate a two-dimensional array of dots in fused silica. We show that an additional phase modulation renders flexible the pattern geometry.

Nonlinear dynamics of a nonlinear amplifier-based delayed PLL incorporating additional phase modulator

The present article examines the chaotic behaviour of a nonlinear amplifier (NLA)-based delayed phase-locked-loop (PLL) incorporating a first order phase modulator for a certain range of system parameters. The occurrence of the chaotic dynamics is confirmed by finding the Lyapunov exponents and dimension of the said system numerically. For a given set of initial conditions, the range of phase modulator gain and loop time delay for several fixed values of nonlinear parameter of the NLA between which chaos can be observed is indicated. The usefulness of NLA to avoid the unwanted chaos in case of conventional delayed PLL system is also examined.

Virtual Gires-Tournois etalons realized with phase-modulated wideband chirped fiber gratings

We propose and demonstrate novel virtual Gires-Tournois (GT) etalons based on fiber gratings. By introducing an additional phase modulation in wideband linearly chirped fiber Bragg gratings, we have successfully generated GT resonance with only one grating. This technique can simplify the fabrication procedure while retaining the normal advantages of distributed etalons, including their full compatibility with optical fiber, low insertion loss, and low cost. Such etalons can be used as dispersion compensation devices in optical transmission systems.

Optical modulation techniques for length sensing and control of optical cavities

We present a discussion of the use of amplitude modulation techniques with regard to the length sensing and control of optical cavities for laser interferometric gravitational-wave detectors. Traditional radio-frequency amplitude modulation techniques automatically include phase modulation as a product of the modulation process, which can contaminate the signal after demodulation. In particular, with many length-sensing and control schemes the detected signals are demodulated in quadrature, which, in the case of a traditional amplitude modulation scheme, will result in offsets due to the additional phase modulation. We demonstrate this effect using a simple optical cavity configuration and show that minor adjustments to the modulator system can be used to compensate for the extra modulation components and provide additional flexibility.

Interference method of measuring the extinction coefficient of birefringent optical fibers

The extinction coefficient of a birefringent optical fiber (the ratio between the radiation power output of the polarization mode and the radiation power transferred from this mode to another one) characterizes the capability of a birefringent fiber to retain the polarization state of the radiation. In relatively short birefringent fibers (1–100 m), the extinction coefficient may reach 104–106. Such high values of the extinction coefficient are difficult to measure by standard techniques (excitation of one polarization mode by an incoherent source with subsequent recording of the light intensity at the output of the analyzer). An interference method of measuring the extinction coefficient of birefringent fibers is suggested. It is based on using a coherent source and measuring interference oscillations caused by an additional phase modulation at the input of the fiber. This method does not require precise polarization matching between the laser source and fiber and considerably loosens requirements for the polarizer-analyzer extinction and resolution of the photodetector. As a result, using simple standard components (semiconductor laser, film polarizer, and photodetector), one can measure extinction coefficient as high as 106. The suggested interference method of measuring the extinction coefficient of birefringent fibers receives a theoretical analysis, and experimental data obtained for 2- to 1000-m-long fibers are presented.

Beam Shaping by Using the Liquid Crystal Panel of a CommercialDisplay Device

The liquid crystal (LC) panel of a commercially-available LCD projectoris successfully used for beam shaping, and a Gaussian beam is convertedto a square super-Gaussian beam using the configuration of amplitudemodulation. The additional phase modulations imposed by the LCmodulator on the shaped beams are measured precisely using aninterferometric technique. The experimental results have demonstratedthat such a commercially-available programmable spatial light modulatoris applicable to beam shaping with negligible additional phasemodulation.

Involvement of confinement voltage perturbations in the axial-motion spectrum of an ion confined in a quadrupole ion trap

The Fourier transform (FT) operating mode of a quadrupole ion trap leads to an axial secular frequency spectrum of the simultaneously confined ions. During confinement, an ion trajectory as pure as possible is sought. The addition of a pure frequency in a quadrupolar configuration to the confinement voltage is examined in detail. Simulation and experimental results concerning an axial-trajectory spectrum are presented. With an additional quadrupolar perturbation, the ion motion is frequency modulated and, as a result, a peak splitting of the axial ion motion is observed. The frequency modulation induces sideband frequency peaks with amplitudes that are higher for low frequencies of the perturbation. Since ion detection is destructive, a repetition of elementary experiments realized for increasing confinement times is needed. Therefore, for each confinement time, the initial phase of the perturbation can be different. As a result, an additional ion-motion phase modulation, which depends on the repetition mode and the duration of the elementary experiments, is induced. With a constant duration of the elementary experiments, phase modulation is made at discrete frequencies. This induces a new high frequency peak splitting. When the duration is equal to the period of the perturbation, solely the frequency modulation effect is visible. When the elementary experiments follow one another (with no lag time), the ion motion is phase modulated at a quasi-infinite range of frequencies. The result is a decreasing of the modulation index due to the frequency modulation and a background noise in the whole spectrum. For βz ≈ 0.798, a duration of the elementary experiment of 80 ms and a perturbation with an amplitude and a frequency of 10 mV and 50 Hz, respectively, the limit of the mass resolution is about 3800 for m/Z = 127 u. When the elementary experiments follow one another, the mass resolution limit is higher than 5600 but the signal-to-noise ratio is halved.

Measurements of Time-Varying Characteristics of Optical Signals and Inhomogeneities of Tested Substances with Additional Phase Modulation

The problem of investigation of the amplitude and phase structure of a time-varying probing optical signal and the structure of time-varying inhomogeneities of a substance tested by this signal is considered. The analysis is concerned, in particular, with determination of the structure of signals and processes with resolution in the pico- and femtosecond range. The scheme used for the analysis is based on registration of four spatially separated spectra of the studied radiation. The spectra are formed in a four-channel scheme with a twin-wave Michelson interferometer and a spectral device. Modulators based on electrooptical crystals (perovskites) are placed in the channels. The sum spectra are formed: without modulators, with the effect of either of the modulators, and with both of them affecting the radiation. The effect of the studied substance implies either modulating the radiation (in this case it is described by multiplication) or redistributing the radiation (then it is described by convolution).

Measurements of Optical Signals and Their Spectra in the Femtosecond Range with Additional Phase Modulation

A solution to the phase problem in optics is considered within the context of the analysis of signals changing in time and of the effect of an object under investigation on the probing radiation. The solution is based on the use of a twin-wave interferometer with phase modulation in one of the channels and a spectrometer. The analysis is concerned, in particular, with signals and processes of ultrashort duration. To shift the frequency in the interferometer channel, an electrooptical crystal of ferroelectric perovskite is used as the modulator. Errors of amplitude and phase structures determined are analyzed.

Polarization-Mode Dispersion Mitigation by a Fiber-Based 2R Regenerator Combined With Synchronous Modulation

Mitigation of polarization-mode dispersion (PMD) by an optical signal regenerator based on spectrum broadening and slicing using normal-dispersion fiber is analyzed. It is shown that pulse distortion caused by PMD can be restored by the 2R (amplitude regeneration and reshaping) regenerator when differential group delay between the orthogonal polarization components is roughly within the range of pulsewidth. Additional synchronous amplitude and phase modulation in front of the 2R regenerator significantly improves the performance.

Volume and contact photo-emf in GaAs adaptive photodetectors

The generation of non-steady-state photo-emf in an adaptive photodetector made of semi-insulating GaAs is studied. Single-and double-frequency excitation modes are considered. It is found that a contact component of the photocurrent arises in the detector when the spatial frequencies of the interference pattern and phase modulation frequencies are low. The contact signal, being sensitive to a slow drift of the interference pattern, adversely affects the adaptive properties of the device. It is shown theoretically and confirmed experimentally that the contact emf signal at the frequency of basic phase modulation can effectively be suppressed by specially selecting the amplitude of additional phase modulation and the spatial frequency of the interference pattern. The spectral components of the non-steady-state emf signal are calculated for the double-frequency excitation mode.

Dynamic ESPI with subtraction–addition method for obtaining the phase

Dynamic electronic speckle pattern interferometry (DESPI) was developed for in situ observations. The quantitative evaluation of the deformation field was performed through 2-D subtraction–addition method (SAM) for phase analysis. This method does not require additional phase modulation, which makes it applicable to studying dynamic events. The method utilizes the ratio of the subtraction and addition correlation fringe patterns. The bias intensity that has to be removed from the addition images was determined by temporal averaging of a sequence of speckle patterns. To reduce the error, Gaussian filter was applied to the correlation fringe patterns. The deformation field was evaluated with accuracy of λ/10.

Measurement for Scattering Media by Synthesis of Optical Coherence Function with Super-Structure Grating Distributed Bragg Reflector Laser Diode

The application of the technique of synthesis of optical coherence function for detection in scattering media is investigated. By modulating the optical frequency, the technique synthesizes the coherence function into a delta-function-like peak at an arbitrary location, and thus can select interferometrically the information at that location. The location is adjustable by the modulation parameter or additional phase modulation. A multi-section super-structure grating distributed Bragg reflector laser diode (SSG-DBR-LD) of THz-order tunable range is employed to enhance the spatial resolution for suppressing the multiple scattering from locations other than that detected. In a preliminary experimental demonstration, a reflectometry of 550 μm spatial resolution was achieved and was used to detect scattering media.

Stability conditions of a class of delayed PLL systems through linear and non-linear techniques

A study of the stability problems of a class of heterodyne second-order phaselocked loops incorporating an additional phase modulator has been reported in this paper. Conditions of stability of this system in terms of loop design parameters have been obtained through the Liapunov method, the Routh-Hurwitz method and the Nyquist method. Also reported are simulation results finding design parameters for stable operation of the system. Comparing the results obtained through different techniques, it can be noted that linear analytical methods provide design parameters which are consistent with simulation results for small loop phase errors, but for large loop errors design parameters predicted by the Liapunov method should be used for system design.

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.

Ultrashort-pulse-formation mechanism by slow-loss saturation and self-phase modulation in solid-state lasers

It is shown that, under the balance between slow-loss saturation and self-phase modulation, the solid-state laser is capable of generating a chirped frequency-shifted quasi soliton. The gain saturation, negative group-velocity dispersion, or additional phase modulation stabilizes the quasi soliton.

Modified electronic speckle pattern interferometer with reduced number of elements for vibration analysis

An improved electronic speckle pattern interferometry (ESPI) system for vibration analysis by the time-average method is presented. The optical path length imbalance introduced in the interferometer allows us to implement a new phase shift heterodyning technique for vibration analysis by wavelength modulation of the light source. All the functions required for obtaining good visibility time average vibration fringes are implemented using laser diode modulation only. No additional phase modulator is required, the number of elements is reduced resulting in a greater flexibility of measurement procedures, equipment simplification and cost reduction are obtained. Illustrative results of studies of vibration objects are given.

Optical PSK homodyne system using a switched residualcarrier for phase synchronisation

In this new concept for a digital optical homodyne transmission system, phase synchronisation of the receiver&apos;s local oscillator relies on an additional low-key phase modulation at the clock frequency. The front-end uses a 180° hybrid and is AC coupled.

New principle of formation of ultrashort pulses in solid-state lasers with self-phase-modulation and gain saturation

It is shown for the first time that the balance between self-phase-modulation (SPM) and gain saturation in an active medium of a solid-state laser with a limited gain bandwidth can generate a chirped frequency-shifted quasisoliton. Introduction of additional amplitude or phase modulation stabilises this quasisoliton.

Differentiating optical-fiber Mach–Zehnder interferometer

We introduce a new type of optical-fiber Mach-Zehnder interferometer whose output depends on phase differentials or the time rate of change of the unknown phase-modulating signal. Whereas the actual phase excursion introduced by the signal could cause interference over several fringes in a conventional Mach-Zehnder interferometer, the differential phase shifts may be restricted to the linear range of the phase detector. Being of simple construction, the interferometer can be operated without active biasing, additional phase modulation, or complex signal-processing techniques. We analyze a prototype architecture to explain the principle of operation of the system and to derive design formulas. This is followed by experimental evaluation of a more practical configuration.