Sinusoidal Phase Modulation Research Articles

A low-finesse all-fiber sinusoidal phase modulation interferometer for displacement measurement

We present an all-fiber sinusoidal phase modulation (SPM) interferometer for displacement measurement based on an in-built electro-optical modulator (EOM). The interferometer consists of a fiber-optical Mach–Zehnder interferometer (MZI) and a low-finesse fiber-optic Fabry–Pérot interferometer (FPI) through a circulator. The EOM is combined in one arm of MZI for generating modulating reference beam. Reflected beams from an object and the end of the fiber interfere with the reference beam. The phase differences between the reflected beam from the object and the modulated reference beam are demodulated using an improved phase generated carrier demodulation algorithm which is realized on a field-programmable gate array. Compared with the conventional fiber-optic Fabry–Pérot interferometer, this SPM interferometer effectively expands the working distance. Furthermore, we also demonstrate the effect of the phase difference between the fiber end and the reference arm on the measurement. The displacement can only be extracted correctly when the phase difference deviation between the fiber end and the reference arm is smaller than +/−0.29 rad. The experiment results show that the measurement range of the presented interferometer is up to 20 mm with a nonlinear error of ±53.4 nm. The interferometer has a displacement resolution of 45 pm∕Hz over 20 Hz.

High-energy, narrow-linewidth, flat-top temporal profile nanosecond-pulses from ytterbium-doped tapered fiber amplifier with chirped-diode seeding

We present a narrow-bandwidth (167 pm) few-nanosecond fiber laser based on tapered fiber amplification and phase modulation to mitigate stimulated Brillouin scattering (SBS). We compare the use of chirped diode seeding and standard sinusoidal phase modulation. Below SBS appearance threshold, output temporal profiles can be accurately tailored. Typical results for flat-top profiles include 170 kW peak-power (for 3 ns duration) and 1.25 mJ pulse energy (for 10 ns duration).

Optimized dynamic interference smoothing via asynchronous phasemodulation of SSD

In dynamic interference smoothing (DIS) scheme, the speckles of focal spots are swept in multi-directions within several picoseconds, leading to the improvement of irradiation uniformity. In this work, the theoretical limitation of the smoothing performance of DIS scheme is revealed and then an optimized dynamic interference smoothing (ODIS) scheme is proposed. The ODIS scheme is implemented by applying asynchronous sinusoidal phase modulations induced by electro-optic modulators with time-delayed voltage signals to the beamlets in a laser quad. Results indicate that the irradiation uniformity of the ODIS scheme is further improved than that of DIS scheme owing to the asynchronous spatiotemporal phases. In addition, the polarization of the ODIS scheme also rotates on picosecond timescale, which may be potential to mitigate the parametric backscattering. Moreover, though the ODIS scheme has a relatively high requirement for temporal synchronization of beamlets, it shows a wide tolerance for the spatial wavefront distortion.

Wigner matrix formalism for phase-modulated signals.

Laser beams can carry multi-scale properties in space and time that ultimately impact their quality. The study of their evolution along complex optical sequences is of crucial interest, especially in high-intensity laser chains. For such analysis, results obtained with standard numerical methods strongly depend on the sampling. In this paper, we develop an analytic model for a sinusoidal phase modulation inside a sequence of first-order optics elements based on the Wigner matrix formalism. A Bessel decomposition of the Wigner function gives pseudo-Wigner functions that obey the general ABCD matrix law transformation without approximations and sampling considerations. Applied to a Gaussian beam, explicit expressions are obtained for the projections of the Wigner function in the sub-spaces and give a powerful tool for analyzing the laser beam properties. The formalism is established in the spatial and temporal domains and can be used to evaluate the impact of the phase noise on the beam properties and is not limited to small modulation depths. For the sake of illustration, the model is applied to the Talbot effect with the analysis of the propagation in the spatial and phase-space domains. A comparison with full numerical calculations evidences the high accuracy of the analytic model that retrieves all the features of the diffracted beam.

Single-Element Dual-Interferometer for Precision Inertial Sensing

Tracking moving masses in several degrees of freedom with high precision and large dynamic range is a central aspect in many current and future gravitational physics experiments. Laser interferometers have been established as one of the tools of choice for such measurement schemes. Using sinusoidal phase modulation homodyne interferometry allows a drastic reduction of the complexity of the optical setup, a key limitation of multi-channel interferometry. By shifting the complexity of the setup to the signal processing stage, these methods enable devices with a size and weight not feasible using conventional techniques. In this paper we present the design of a novel sensor topology based on deep frequency modulation interferometry: the self-referenced single-element dual-interferometer (SEDI) inertial sensor, which takes simplification one step further by accommodating two interferometers in one optic. Using a combination of computer models and analytical methods we show that an inertial sensor with sub-picometer precision for frequencies above 10 mHz, in a package of a few cubic inches, seems feasible with our approach. Moreover we show that by combining two of these devices it is possible to reach sub-picometer precision down to 2 mHz. In combination with the given compactness, this makes the SEDI sensor a promising approach for applications in high precision inertial sensing for both next-generation space-based gravity missions employing drag-free control, and ground-based experiments employing inertial isolation systems with optical readout.

Resonant frequency doubling of phase-modulation-generated few-frequency fiber laser.

Resonant frequency doubling of periodically phase-modulated single-frequency fiber laser is investigated as a method for power scaling of visible fiber lasers. Sinusoidal phase modulation is applied to generate few-frequency lasers at 1064 nm in the proof of principle experiments. By adjusting the modulation frequency to match the free spectral range of a doubling cavity, a resonant enhancement condition can be achieved and a near 30 W 532 nm laser is generated with a maximum conversion efficiency above 80%. The indistinguishable conversion efficiencies between the single-frequency and few-frequency cases prove the feasibility of the approach. Interesting spectral evolvement of the phase-modulated laser in second-harmonic generation is analyzed theoretically and observed in the experiment.

Multiple self-mixing interferometry based on lock-in amplifier analysis for vibration measurement

In this paper, a novel phase demodulation method for multiple self-mixing interferometry (MSMI) is proposed, which can improve the resolution and accuracy of vibration measurement in laser self-mixing interferometry (SMI). The sinusoidal phase modulation of the beam is obtained by an electro-optic modulator (EOM), and phase demodulation is performed by a lock-in amplifier analysis method. The phase equation of MSMI was derived and the theory of the lock-in amplification technique was analyzed in detail. The validity of the proposed method is confirmed by means of simulated signals and then demonstrated by several experimental measurements. The experimental results indicated a good correspondence between theory and experiment.

Frequency‐swept high‐repetition rate optical source

AbstractWe propose and numerically validate an all‐optical scheme to generate optical pulse trains with varying temporal pulse‐to‐pulse delay and pulse duration. Our simulations confirm that applying a temporal sinusoidal phase modulation followed by a shaping of the spectral phase is efficient to maintain high‐quality Gaussian temporal profiles.

Akhmediev breather signatures from dispersive propagation of a periodically phase-modulated continuous wave

We investigate in detail the qualitative similarities between the pulse localization characteristics observed using sinusoidal phase modulation during linear propagation and those seen during the evolution of Akhmediev breathers during propagation in a system governed by the nonlinear Schrödinger equation. The profiles obtained at the point of maximum focusing indeed present very close temporal and spectral features. If the respective linear and nonlinear longitudinal evolutions of those profiles are similar in the vicinity of the point of maximum focusing, they may diverge significantly for longer propagation distance. Our analysis and numerical simulations are confirmed by experiments emulating an optical fibre.

Scale factor calibration method for integrating-bucket sinusoidal phase shifting interferometry

In order to recover the phase map φ(x, y) from sinusoidally phase-shifted interferograms obtained with the integrating-bucket method, two images Ψs and Ψc should be calculated first which are proportional to sin(φ) and cos(φ) respectively, and one of them needs to be scaled by a scale factor before they are used to solve the phase with the arctangent function. Because parameters deciding the scale factor such as the sinusoidal phase modulation amplitude and initial phase are difficult to be set accurately, miscalibration of it can always happen and result in significant error in the phase demodulation. Therefore, in this paper we propose a simple scale factor calibration method which performs the calibration directly with the phase-shifted interferograms and avoids the need for accurate parameter setting. First, we introduce high-density fringes to the interferograms; then, we construct a new image variable Γ with the squares of Ψs and Ψc; last, we find the value of the scale factor by minimizing the second harmonic amplitude in Γ’s spatial spectrum. Simulation results show that the proposed method is robust against noise and fringe distortion, and it was tested in a fiber-optic fringe projection profilometer.

Digital holography experiments with degraded temporal coherence

To simulate the effects of multiple-longitudinal modes and rapid fluctuations in center frequency, we use sinusoidal phase modulation and linewidth broadening, respectively. These effects allow us to degrade the temporal coherence of our master-oscillator laser, which we then use to conduct digital holography experiments. In turn, our results show that the coherence efficiency decreases quadratically with fringe visibility and that our measurements agree with our models to within 1.8% for sinusoidal phase modulation and 6.9% for linewidth broadening.

Hermite–Gaussian beams with sinusoidal vortex phase modulation

In this Letter, vortex phase and sinusoidal phase modulations of Hermite–Gaussian beams are studied theoretically and experimentally. The coding method of the experiment is introduced in detail, and the evolution law of focus under different beam order (m, n) and topological charge (l) is given. In order to verify the accuracy of the generation experiment, the optical field distribution under sinusoidal vortex modulation is analyzed deeply. The relevant analysis and methods provided in this Letter have certain practical significance for the development of laser mode analysis, optical communication, and other fields.

Multiwavelength high-repetition rate source

We propose and experimentally validate an all-optical approach to generate simultaneously several pulse trains with identical temporal and spectral properties. Applying a temporal sinusoidal phase modulation followed by a shaping of the spectral phase enables us to handle several channels. The principle of operation is experimentally demonstrated at repetition rates of 14 and 40 GHz with up to four channels.

Security-enhanced chaotic communications with optical temporal encryption based on phase modulation and phase-to-intensity conversion

We propose and numerically demonstrate a security-enhanced chaotic communication system by introducing optical temporal encryption (OTE) into the modulated chaotic carrier (chaos + message). In the proposed scheme, the message is firstly embedded into the original chaotic carrier generated by a conventional external-cavity semiconductor laser (ECSL), and before being transmitted to the receiver end, the modulated chaotic carrier propagates through an OTE module that consists of one phase modulator driven by a secret sinusoidal signal and one dispersive component. Our numerical results indicate that, as a direct result of the spectral expansion effect of the sinusoidal phase modulation and the phase-to-intensity conversion effect of the dispersive component, the original chaotic carrier can be encrypted as an uncorrelated chaotic signal with a flat spectrum and an efficiently-suppressed time delay signature, this greatly enhances the privacy of the modulated chaotic carrier. Moreover, comparing with the conventional ECSL-based chaotic communication systems without OTE, the proposed scheme not only shows significantly higher security against attacks including direct linear filtering and synchronization utilization, but also provides additional physical key space to further enhance the system security. In addition, by making use of the transmission dispersion for decryption, the proposed encryption scheme supports dispersion-compensation-free secure fiber communication, and it also supports centralized encryption/decryption in wavelength division multiplexing secure chaotic communication systems. The proposed scheme explores a novel encryption method for implementation in high-security chaotic communication systems.

Triangular spectral phase tailoring for the generation of high-quality picosecond pulse trains.

We theoretically and experimentally demonstrate a new electro-optic linear approach to generate high-repetition-rate picosecond pulse trains. This simple cavity-free method is based on a temporal sinusoidal phase modulation combined with a triangular spectral phase processing. Experimental results validate the concept at repetition rates ranging from 10GHz up to 40GHz with the generation of background-free pulse trains made of nearly Gaussian Fourier-transform-limited pulses.

Stimulated Brillouin scattering in optical fibers with end reflections excited by broadband pump waves

The transient theory of stimulated Brillouin scattering (SBS) in optical fibers is used to investigate the effects of weak feedback of incident broadband laser fields exhibiting different spectral shapes. The proper boundary conditions are given for the forward- and backward-propagating electric fields inside the fiber with a finite amount of reflectivity at the fiber ends. When the linewidth of the laser approaches the Brillouin frequency shift, a weak reflection of the laser field overlaps with the SBS gain and can be amplified in the fiber, resulting in an apparent reduction in SBS threshold. It is shown that the spectral shape of the incident field and its overlap with the SBS gain spectrum affects the SBS signal. Numerical examples are presented for incident laser fields that (1) simulate a pulsed, multilongitudinal-mode laser and (2) are a constant amplitude with a sinusoidal phase modulation. For the pulsed field with mode spacing much less than the Brillouin linewidth, calculations show that an end reflection of 0.01% (−40 dB) of the laser field with a linewidth equal to 0.75 of the Brillouin frequency shift can reduce the effective SBS threshold by a factor of 1.5. When the incident laser field is constant amplitude and phase modulated with a sinusoid, calculations predict sharp and distinct enhancement of the reflected power when the ratio of the Brillouin frequency shift to the modulation frequency is an integer for end reflections as low as 0.001% (−50 dB). Experiments performed with a sinusoidal phase modulated signal confirm the theoretical predictions. These results have implications on the design of high-power fiber laser systems that utilize spectral broadening to suppress SBS.

Apodization of Silicon Integrated Bragg Gratings Through Periodic Phase Modulation

The sinusoidal phase modulation apodization technique, owing to its high precision and resolution and very low phase noise, shows great promise for spectral tailoring of silicon integrated Bragg grating (IBG) devices for optical telecommunications and signal processing. Here, we extend this promising sinusoidal phase modulation technique by showing that phase modulation apodization of a silicon IBG can actually be accomplished based on any periodic function. This paper also shows a dependence of the apodization characteristic, physical grating structure, and actual apodized grating performance on the periodic function used. Then, we propose a general implementation process of the periodic phase modulation apodization to achieve a desired response on a silicon IBG, and study the limiting factors of the apodization performance, design tradeoffs and optimization, and grating robustness against fabrication constraints for different periodic phase functions, using a computational lithography model together with a structure-aware grating emulator. Finally, the extended periodic phase modulation apodization technique is validated by demonstrating a series of differently designed phase-modulated silicon IBGs, including Gaussian-apodized gratings, single- and multi-channel flat-top filters, and flat-top dispersion-compensating filters, using different periodic phase functions. The work offers an additional degree of freedom for the design and optimization of phase-modulated gratings, and has significant implications for practical implementation of the phase modulation apodization for spectral engineering of silicon Bragg grating devices.

Quadrature demodulation based on lock-in amplifier technique for self-mixing interferometry displacement sensor.

A new self-mixing interferometry quadrature demodulation method based on a lock-in amplifier technique is proposed. Sinusoidal phase modulation of the beam is obtained by an electro-optic modulator (EOM) in the external cavity. Then the real phase of the external target can be calculated by lock-in amplifier analysis method. In this paper, the validity of the proposed method is confirmed by theoretical analysis and means of simulated signals, and then it is demonstrated by several experimental measurements for target harmonic and arbitrary motion. The results show that the proposed method can get a high-precision measurement, even using a diffusive target.

Applications of sinusoidal phase modulation in temporal optics to highlight some properties of the Fourier transform

Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools do not necessarily understand all the richness that can be derived from joint analysis in the temporal and spectral domains, particularly in the field of optics. As part of the second year of the master’s degree in Physics Lasers and Materials at the University of Burgundy, we have set up a series of experiments to highlight these concepts and to show, on a non-trivial example of periodic phase modulation, the precautions to be taken in the interpretation of the various experimentally accessible spectra. This hands-on session, made possible through the use of research infrastructure, is also an introduction to the use of standard optical telecommunications equipment.

Highly flat optical frequency comb generation based on pulse carving and sinusoidal phase modulation

We investigate the relationship between an optical pulse shape and a time lens implemented by means of sinusoidal phase modulation. Based on this investigation, two schemes are proposed to obtain an optical frequency comb (OFC) with exceptionally high flatness and a large number of spectral lines by carving an optical pulse shape to result in a quasilinear chirp via a simple sinusoidal phase modulation technique. The first scheme utilizes an intensity modulator with a single-drive port or with dual-drive ports to carve a narrow pulse. The experimental results show very good spectral profiles with 38 OFC lines at 1.2-dB flatness and 53 lines at 1.5-dB flatness when the intensity modulator is combined with two and three phase modulators for sinusoidal phase modulation, respectively. The second scheme is implemented by replacing the intensity modulator by a dual-parallel Mach–Zehnder modulator (DP-MZM). In this case, we obtain 35 OFC lines at nearly perfect flatness of less than 1 dB and 53 lines at 1.5-dB flatness after combining the DP-MZM with two and three phase modulators, respectively.