Showing papers on "Phase noise published in 2009"

Hardware-Efficient Coherent Digital Receiver Concept With Feedforward Carrier Recovery for $M$ -QAM Constellations

Abstract: This paper presents a novel digital feedforward carrier recovery algorithm for arbitrary M-ary quadrature amplitude modulation (M-QAM) constellations in an intradyne coherent optical receiver. The approach does not contain any feedback loop and is therefore highly tolerant against laser phase noise. This is crucial, especially for higher order QAM constellations, which inherently have a smaller phase noise tolerance due to the lower spacing between adjacent constellation points. In addition to the mathematical description of the proposed carrier recovery algorithm also a possible hardware-efficient implementation in a parallelized system is presented and the performance of the algorithm is evaluated by Monte Carlo simulations for square 4-QAM (QPSK), 16-QAM, 64-QAM, and 256-QAM. For the simulations ASE noise and laser phase noise are considered as well as analog-to-digital converter (ADC) and internal resolution effects. For a 1 dB penalty at BER = 10-3, linewidth times symbol duration products of 4.1 x 10-4 (4-QAM), 1.4 x 10-4 (16-QAM), 4.0 x 10-5 (64-QAM) and 8.0 x 10-6 (256-QAM) are tolerable.

On the likelihood-based approach to modulation classification

Abstract: In this paper, likelihood-based algorithms are explored for linear digital modulation classification. Hybrid likelihood ratio test (HLRT)- and quasi HLRT (QHLRT)- based algorithms are examined, with signal amplitude, phase, and noise power as unknown parameters. The algorithm complexity is first investigated, and findings show that the HLRT suffers from very high complexity, whereas the QHLRT provides a reasonable solution. An upper bound on the performance of QHLRT-based algorithms, which employ unbiased and normally distributed non-data aided estimates of the unknown parameters, is proposed. This is referred to as the QHLRT-Upper Bound (QHLRT-UB). Classification of binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) signals is presented as a case study. The Cramer-Rao Lower Bounds (CRBs) of non-data aided joint estimates of signal amplitude and phase, and noise power are derived for BPSK and QPSK signals, and further employed to obtain the QHLRT-UB. An upper bound on classification performance of any likelihood-based algorithms is also introduced. Method-of-moments (MoM) estimates of the unknown parameters are investigated and used to develop the QHLRT-based algorithm. Classification performance of this algorithm is compared with the upper bounds, as well as with the quasi Log-Likelihood Ratio (qLLR) and fourth-order cumulant based algorithms.

A Low Noise Sub-Sampling PLL in Which Divider Noise is Eliminated and PD/CP Noise is Not Multiplied by $N ^{2}$

Abstract: This paper presents a 2.2-GHz low jitter sub-sampling based PLL. It uses a phase-detector/charge-pump (PD/CP) that sub-samples the VCO output with the reference clock. In contrast to what happens in a classical PLL, the PD/CP noise is not multiplied by N 2 in this sub-sampling PLL, resulting in a low noise contribution from the PD/CP. Moreover, no frequency divider is needed in the locked state and hence divider noise and power can be eliminated. An added frequency locked loop guarantees correct frequency locking without degenerating jitter performance when in lock. The PLL is implemented in a standard 0.18- ?m CMOS process. It consumes 4.2 mA from a 1.8 V supply and occupies an active area of 0.4 × 0.45 mm2. With a frequency division ratio of 40, the in-band phase noise at 200 kHz offset is measured to be -126 dBc/Hz. The rms PLL output jitter integrated from 10 kHz to 40 MHz is 0.15 ps.

Phase Estimation Methods for Optical Coherent Detection Using Digital Signal Processing

Abstract: The advent of digital signal processing (DSP) to optical coherent detection means that more phase estimation options are available, compared to the earlier generation where phase-locked loops (PLLs) were invariably deployed in synchronous coherent receivers. Several phase estimation methods are numerically modeled: the maximum a posteriori (MAP) phase estimate, decision directed estimate, power law-Wiener filter estimate and power law-PLL estimate. An asynchronous coherent detection case is also modeled. The phase estimates are evaluated with respect to their tolerance of finite laser linewidth and their suitability for implementation in a parallel digital processor. Laser phase noise causes transmission system performance to be degraded by excess bit errors and cycle slips. The optimal phase estimate is the MAP estimate, and it is also included as a baseline. The power law-Wiener filter phase estimate is found to perform only marginally worse than the MAP estimate. It must be recast using a look-ahead computation to be implemented in a parallel digital processor, and the impact is investigated of the increase in the number of computations required. Differential logical detection is often used to reduce the impact of cycle slip events, and the implications of this operation on the bit error rate are studied. It is found that by choosing the correct FEC scheme differential logical detection does not increase the Q-factor penalty.

Precise control of broadband frequency chirps using optoelectronic feedback

Abstract: We demonstrate the generation of wideband frequency sweeps using a semiconductor laser in an optoelectronic feedback loop. The rate and shape of the optical frequency sweep is locked to and determined by the frequency of a reference electronic signal, leading to an agile, high coherence swept-frequency source for laser ranging and 3-D imaging applications. Using a reference signal of constant frequency, a transform-limited linear sweep of 100 GHz in 1 ms is achieved, and real-time ranging with a spatial resolution of 1.5 mm is demonstrated. Further, arbitrary frequency sweeps can be achieved by tuning the frequency of the input electronic signal. Broadband quadratic and exponential optical frequency sweeps are demonstrated using this technique.

Jitter Analysis and a Benchmarking Figure-of-Merit for Phase-Locked Loops

Abstract: This brief analyzes the jitter as well as the power dissipation of phase-locked loops (PLLs). It aims at defining a benchmark figure-of-merit (FOM) that is compatible with the well-known FOM for oscillators but now extended to an entire PLL. The phase noise that is generated by the thermal noise in the oscillator and loop components is calculated. The power dissipation is estimated, focusing on the required dynamic power. The absolute PLL output jitter is calculated, and the optimum PLL bandwidth that gives minimum jitter is derived. It is shown that, with a steep enough input reference clock, this minimum jitter is independent of the reference frequency and output frequency for a given PLL power budget. Based on these insights, a benchmark FOM for PLL designs is proposed.

Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier

Abstract: A chain of four Tm-doped fibers amplified a single-frequency, 2040 nm diode laser to 608 W with M2=1.05±0.03, limited by available pump power. Stimulated Brillouin scattering limits were investigated by splicing different lengths of passive fiber to the output of the final amplifier stage. Integrated rms phase noise above 1 kHz was less than λ/30, suggesting the possibility of further scaling via coherent beam combining. To our knowledge, this is the highest power obtained from any single-frequency, single-mode fiber laser.

Multi-Level, Multi-Dimensional Coding for High-Speed and High-Spectral-Efficiency Optical Transmission

Abstract: We review and study several single carrier based multi-level and multi-dimensional coding (ML-MDC) technologies recently demonstrated for spectrally-efficient 100-Gb/s transmission. These include 16-ary PDM-QPSK, 64-ary PDM-8PSK, 64-ary PDM-8QAM as well as 256-ary PDM-16 QAM. We show that high-speed QPSK, 8PSK, 8QAM, and 16QAM can all be generated using commercially available optical modulators using only binary electrical drive signals through novel synthesis methods, and that all of these modulation formats can be detected using a universal receiver front-end and digital coherent detection. We show that the constant modulus algorithm (CMA), which is highly effective for blind polarization recovery of PDM-QPSK and PDM-8PSK signals, is much less effective for PDM-8QAM and PDM-16 QAM. We then present a recently proposed, cascaded multi-modulus algorithm for these cases. In addition to the DSP algorithms used for constellation recovery, we also describe a DSP algorithm to improve the performance of a coherent receiver using single-ended photo-detection. The system impact of ASE noise, laser phase noise, narrowband optical filtering and fiber nonlinear effects has been investigated. For high-level modulation formats using full receiver-side digital compensation, it is shown that the requirement on LO phase noise is more stringent than the signal laser. We also show that RZ pulse shaping significantly improves filter- and fiber-nonlinear tolerance. Finally we present three high-spectral-efficiency and high-speed DWDM transmission experiments implementing these ML-MDC technologies.

Predicting the Phase Noise and Jitter of PLL-Based Frequency Synthesizers

Abstract: Version 4i, 23 October 2015 Two methodologies are presented for predicting the phase noise and jitter of a PLLbased frequency synthesizer using simulation that are both accurate and efficient. The methodologies begin by characterizing the noise behavior of the blocks that make up the PLL using transistor-level RF simulation. For each block, the phase noise or jitter is extracted and applied to a model for the entire PLL.

Study of Subharmonically Injection-Locked PLLs

Abstract: A complete analysis on subharmonically injection-locked PLLs develops fundamental theory for subharmonic locking phenomenon. It explains the noise shaping phenomenon, locking range and behavior, PVT tolerance, and pseudo locking issue. All of the analyses are verified by real chip measurements. Two 20-GHz PLLs based on the proposed theory are designed and fabricated in 90-nm CMOS technology to demonstrate the superiority and robustness of this technique. The first chip aims at low-noise/low-power/high-divide-ratio design, achieving 149-fs rms jitter (integrated from 100 Hz to 1 GHz) while consuming 38 mW from a 1.3-V supply. The second prototype shoots for the lowest noise performance, presenting 85-fs rms jitter (the same integration interval) with a power dissipation of 105 mW. The jitter generation (from 50 kHz to 80 MHz) measures 48 fs, which is at least twice as small as that of any other known circuits.

A single-chip dual-band 22-to-29GHz/77-to-81GHz BiCMOS transceiver for automotive radars

Abstract: Integration of multi-mode multi-band transceivers on a single chip will enable low-cost millimeter-wave systems for next-generation automotive radar sensors. The first dual-band millimeter-wave transceiver operating in the 22-29-GHz and 77-81-GHz short-range automotive radar bands is designed and implemented in 0.18-? m SiGe BiCMOS technology with fT/fmax of 200/180 GHz. The transceiver chip includes a dual-band low noise amplifier, a shared downconversion chain, dual-band pulse formers, power amplifiers, a dual-band frequency synthesizer and a high-speed highly-programmable baseband pulse generator. The transceiver achieves 35/31-dB receive gain, 4.5/8-dB double side-band noise figure, >60/30-dB cross-band isolation, -114/-100.4-dBc/Hz phase noise at 1-MHz offset, and 14.5/10.5-dBm transmit power in the 24/79-GHz bands. Radar functionality is also demonstrated using a loopback measurement. The 3.9 × 1.9-mm2 24/79-GHz transceiver chip consumes 0.51/0.615 W.

Optical frequency transfer via 146 km fiber link with 10 -19 relative accuracy.

Abstract: We demonstrate the long-distance transmission of an ultrastable optical frequency derived directly from a state-of-the-art optical frequency standard. Using an active stabilization system we deliver the frequency via a 146-km-long underground fiber link with a fractional instability of 3×10−15 at 1 s, which is close to the theoretical limit for our transfer experiment. After 30,000 s, the relative uncertainty for the transfer is at the level of 1×10−19. Tests with a very short fiber show that noise in our stabilization system contributes fluctuations that are 2 orders of magnitude lower, namely, 3×10−17 at 1 s, reaching 10−20 after 4000 s.

High-resolution microwave frequency dissemination on an 86-km urban optical link

Abstract: We report the first demonstration of a long-distance ultra stable frequency dissemination in the microwave range. A 9.15 GHz signal is transferred through a 86-km urban optical link with a fractional frequency stability of 1.3x10-15 at 1 s integration time and below 10-18 at one day. The optical link phase noise compensation is performed with a round-trip method. To achieve such a result we implement light polarisation scrambling and dispersion compensation. This link outperforms all the previous radiofrequency links and compares well with recently demonstrated full optical links.

Voltage controlled oscillator, mmic, and high frequency wireless device

Abstract: A voltage controlled oscillator having low phase noise and including: a variable resonator including a varactor and a control voltage terminal; and an open-end stub connected in parallel to the variable resonator, the open-end stub having a length shorter than or equal to an odd multiple of one quarter of a wavelength of a harmonic signal plus one sixteenth of the wavelength of the harmonic signal, and longer than or equal to an odd multiple of one quarter of the wavelength of the harmonic signal minus one sixteenth of the wavelength of the harmonic signal. In this structure, a high Q value is realized for a fundamental wave frequency. Fluctuation in a control voltage due to a harmonic signal is controlled.

Signal-to-Noise Ratio in Doppler Radar System for Heart and Respiratory Rate Measurements

Abstract: A CMOS Doppler radar sensor has been developed and used to measure motion due to heart and respiration. The quadrature direct-conversion radar transceiver has been fully integrated in 0.25-mum CMOS, the baseband analog signal conditioning has been developed on a printed circuit board, and digital signal processing has been performed in Matlab. The theoretical signal-to-noise ratio (SNR) is derived based on the radar equation, the direct-conversion receiver's properties, oscillator phase noise, range correlation, and receiver noise. Heart and respiration signatures and rates have been measured at ranges from 0.5 to 2.0 m on 22 human subjects wearing normal T-shirts. The theoretical SNR expression was validated with this study. The heart rates found with the radar sensor were compared with a three-lead electrocardiogram, and they were within 5 beats/min with 95% confidence for 16 of 22 subjects at a 0.5-m range and 11 of 22 subjects at a 1.0-m range. The respiration rates found with the radar sensor were compared with those found using a piezoelectric respiratory effort belt, and the respiration rates were within five respirations per minute for 18 of 22 subjects at a 0.5-m range, 17 of 22 subjects at a 1.0-m range, and 19 of 22 subjects at a 1.5-m range.

A Digital PLL With a Stochastic Time-to-Digital Converter

Abstract: A new dual-loop digital phase-locked loop (DPLL) architecture is presented. It employs a stochastic time-to-digital converter (STDC) and a high-frequency delta-sigma dithering to achieve wide PLL bandwidth and low jitter at the same time. The STDC exploits the stochastic properties of a set of latches to achieve high resolution. A prototype DPLL test chip has been fabricated in a 0.13-mum CMOS process, features a 0.7-1.7-GHz oscillator tuning range and a 6.9-ps rms jitter, and consumes 17 mW under 1.2-V supply while operating at 1.2 GHz.

A Low-Noise Wideband Digital Phase-Locked Loop Based on a Coarse–Fine Time-to-Digital Converter With Subpicosecond Resolution

Abstract: This paper presents the design of a digital PLL which uses a high-resolution time-to-digital converter (TDC) for wide loop bandwidth. The TDC uses a time amplification technique to reduce the quantization noise down to less than 1 ps root mean square (RMS). Additionally TDC input commutation reduces low-frequency spurs due to inaccurate TDC scaling factor in a counter-assisted digital PLL. The loop bandwidth is set to 400 kHz with a 25 MHz reference. The in-band phase noise contribution from the TDC is -116 dBc/Hz, the phase noise is -117 dBc/Hz at high band (1.8 GHz band) 400 kHz offset, and the RMS phase error is 0.3deg.

Ultra-low-noise microwave extraction from fiber-based optical frequency comb

Abstract: In this Letter we report on an all-optical-fiber approach to the generation of ultra-low-noise microwave signals. We make use of two erbium fiber mode-locked lasers phase locked to a common ultrastable laser source to generate an 11.55 GHz signal with an unprecedented relative phase noise of -111 dBc/Hz at 1 Hz from the carrier. The residual frequency instability of the microwave signals derived from the two optical frequency combs is below 2.3x10(-16) at 1 s and about 4x10(-19) at 6.5x10(4) s (in 5 Hz bandwidth, three days of continuous operation).

Wideband Multi-Mode CMOS VCO Design Using Coupled Inductors

Abstract: Coupled inductors can create multiple resonant frequencies in a compact high-order resonator. Together with proper nonlinear active circuitry, such a high-order resonator realizes a multi-mode oscillator covering a wide frequency range. Compared with conventional switched-resonator-based approaches that consume the same chip area, the proposed coupled-inductor-based resonator results in larger quality-factor, and hence, lower oscillator phase noise. In the proposed multi-mode oscillator that uses the multi-port coupled inductors, mode switching is achieved using independent active cores without using lossy switches in the resonator path. The behavior of the multi-mode resonator as a multi-port network in an oscillator, design trade-offs, and switching transient response of the multi-mode oscillator have been studied analytically. As a proof of concept, an integrated voltage-controlled oscillator (VCO) with a 1.28-6.06 GHz tuning range is designed and fabricated in a 0.13 mum CMOS technology. The triple-mode VCO uses a sixth-order resonator based on three coupled inductors with a compact common-centric layout. Depending on the oscillation frequency, the VCO current consumption is automatically adjusted from 2.9 to 6.1 mA to achieve a low phase noise throughout the frequency range. The measured phase noises at 1 MHz offset from carrier frequencies of 1.76, 2.26, 3.3, 4.5, and 5.6 GHz are -119.3 , -120.15 , -118.1 , -117 , and -113.5 dBc/Hz , respectively. The chip area, including the pads, is 1 mm times 1 mm and the supply voltage is 1.5 V.

Improved signal-to-noise ratio of 10 GHz microwave signals generated with a mode-filtered femtosecond laser frequency comb.

Abstract: We use a Fabry-Perot cavity to optically filter the output of a Ti:sapphire frequency comb to integer multiples of the original 1 GHz mode spacing. This effectively increases the pulse repetition rate, which is useful for several applications. In the case of low-noise microwave signal generation, such filtering leads to improved linearity of the high-speed photodiodes that detect the mode-locked laser pulse train. The result is significantly improved signal-to-noise ratio at the 10 GHz harmonic with the potential for a shot-noise limited single sideband phase noise floor near -168 dBc/Hz.

A Frequency-Doubling Optoelectronic Oscillator Using a Polarization Modulator

Abstract: A novel realization of a frequency-doubling optoelectronic oscillator (OEO) using a polarization modulator (PolM) is proposed and experimentally demonstrated. In the proposed system, the PolM in combination with two optical polarizers connected via two polarization controllers (PCs) is operating as a two-output intensity modulator. One output of the intensity modulator is connected to the radio-frequency port of the PolM, to form an optoelectronic loop for the generation of a microwave signal with the fundamental frequency determined by the center frequency of a narrowband electronic filter. The other output of the intensity modulator provides a fundamental or frequency-doubled optically modulated microwave signal depending on the static phase term introduced by the PC before the polarizer. The proposed OEO is experimentally demonstrated. A fundamental microwave signal at 10 GHz or a frequency-doubled microwave signal at 20 GHz is generated. The phase noise performance of the generated microwave signal is also investigated.

Experimental Uhrig Dynamical Decoupling using Trapped Ions

Abstract: We present a detailed experimental study of the Uhrig dynamical decoupling UDD sequence in a variety of noise environments. Our qubit system consists of a crystalline array of 9 Be + ions confined in a Penning trap. We use an electron-spin-flip transition as our qubit manifold and drive qubit rotations using a 124 GHz microwave system. We study the effect of the UDD sequence in mitigating phase errors and compare against the well known Carr-Purcell-Meiboom-Gill-style multipulse spin echo as a function of pulse number, rotation axis, noise spectrum, and noise strength. Our results agree well with theoretical predictions for qubit decoherence in the presence of classical phase noise, accounting for the effect of finite-duration pulses. Finally, we demonstrate that the Uhrig sequence is more robust against systematic over- or under-rotation and detuning errors than is multipulse spin echo, despite the precise prescription for pulse timing in UDD.

Nanoscale CMOS Transceiver Design in the 90–170-GHz Range

Abstract: This paper reviews recent research conducted at the University of Toronto on the development of CMOS transceivers aimed at operation in the 90-170-GHz range. Unique nanoscale CMOS issues related to millimeter-wave circuit design in the 65-nm node and beyond are addressed with an emphasis on transistor and top-level layout issues, low-voltage circuit topologies, and design flow. A Doppler transceiver and two receivers fabricated in a 65-nm GPLP CMOS technology are described, along with a single pole, double throw antenna switch with better than 5-dB insertion loss and 25-dB isolation in the entire 110-170-GHz band. The first receiver has an IQ architecture with a fundamental frequency voltage-controlled oscillator, and is intended for wideband passive imaging applications at 100 GHz. The measured noise figure and downconversion gain are 7-8 and 10.5 dB, respectively, while the 3-dB bandwidth extends from 85 to 100 GHz. The second receiver has double-sideband architecture, operates in the 135-145-GHz range (the highest for CMOS receivers), and features an 8-dB gain LNA, a double-balanced Gilbert cell mixer, and a dipole antenna. The 90-94-GHz Doppler transceiver, the highest frequency reported to date in CMOS, is intended for the remote monitoring of respiratory functions. A Doppler shift of 30 Hz, produced by a slow-moving (4.8 cm/s) target located at a distance of 1 m, was measured with a transmitter output power of approximately + 2 dBm and a phase noise of -90 dBc/Hz at 1 MHz offset. The range correlation effect is demonstrated for the first time in CMOS by measuring the phase noise of the received baseband signal at 10-Hz offset, clearly indicating that 1/f noise has been canceled and it does not pose a problem in short-range applications, where neither a phase-locked loop nor a frequency divider are needed.

High-performance, vibration-immune, fiber-laser frequency comb

Abstract: We demonstrate an environmentally robust optical frequency comb based on a polarization-maintaining, all-fiber, figure-eight laser. The comb is phase locked to a cavity-stabilized cw laser by use of an intracavity electro-optic phase modulator yielding 1.6 MHz feedback bandwidth. This high bandwidth provides close to shot-noise-limited residual phase noise between the comb and cw reference laser of -94 dBc/Hz from 20 Hz to 200 kHz and an integrated in-loop phase noise of 32 mrad from 1 Hz to 1 MHz. Moreover, the comb remains phase locked under significant mechanical vibrations of over 1 g. This level of environmental robustness is an important step toward a fieldable fiber frequency comb.

A 4.39–5.26 GHz LC-Tank CMOS Voltage-Controlled Oscillator With Small VCO-Gain Variation

Abstract: A wide band CMOS LC-tank voltage controlled oscillator (VCO) with small VCO gain (KVCO) variation was developed. For small KVCO variation, serial capacitor bank was added to the LC-tank with parallel capacitor array. Implemented in a 0.18 mum CMOS RF technology, the proposed VCO can be tuned from 4.39 GHz to 5.26 GHz with the VCO gain variation less than 9.56%. While consuming 3.5 mA from a 1.8 V supply, the VCO has -113.65 dBc/Hz phase noise at 1 MHz offset from the carrier.

GPS-Based Time & Phase Synchronization Processing for Distributed SAR

Abstract: Distributed synthetic aperture radar (DiSAR), including bi- and multistatic SAR, operates with distinct transmitting and receiving antennas that are mounted on separate platforms. Spatial separation has several operational advantages, such as reduced vulnerability in military applications and increased radar cross section (RCS); which may increase the capability, reliability, and flexibility of future aerospace remote sensing missions. However, in this configuration, there is no cancellation of reference oscillator phase noise as in monostatic cases. There are additional technical problems associated with temporal synchronization of the transmit and receive systems. Therefore, highly accurate time and phase synchronization must be provided. Little work on these challenges has been reported. This paper presents a Global Positioning System (GPS)-based technique for achieving successful time and phase synchronization for DiSAR. This technique offers high-frequency stability. More importantly, residual time synchronization errors may be compensated for with a high-precision range alignment method, and residual phase synchronization errors may be compensated for with a subaperture autofocus algorithm.

A Low Jitter Programmable Clock Multiplier Based on a Pulse Injection-Locked Oscillator With a Highly-Digital Tuning Loop

Abstract: This paper introduces a pulse injection-locked oscillator (PILO) that provides low jitter clock multiplication of a clean input reference clock. A mostly-digital feedback circuit provides continuous tuning of the oscillator such that its natural frequency is locked to the injected frequency. The proposed system is demonstrated with a prototype consisting of a custom 0.13 mum integrated circuit with active area of 0.4 mm2 and core power of 28.6 mW, along with an FPGA, a discrete DAC and a simple RC filter. Using a low jitter 50 MHz reference input, the PILO prototype generates a 3.2 GHz output with integrated phase noise, reference spur, and estimated deterministic jitter of 130 fs (rms), -63.9 dBc, and 200 fs (peak-to-peak), respectively.

Noise Analysis and Minimization in Bang-Bang Digital PLLs

Abstract: In digital bang-bang phase-locked loops (BBPLLs), both the hard nonlinearity of the phase detector and the frequency granularity of the digitally controlled oscillator (DCO) can give rise to undesired tones or peaking in the output spectrum. This work derives the maximum ratio between DCO resolution and jitter, which avoids limit cycles, in the case of dominant DCO noise over reference noise. Moreover, the output jitter is expressed in closed form as a function of the loop parameters and latency, revealing the existence of a minimum and suggesting an optimum design criterion. Finally, an estimation of the BBPLL output spectrum taking into account the quantization noise is provided.

Phase-noise induced limitations on cooling and coherent evolution in optomechanical systems

Abstract: We present a detailed theoretical discussion of the effects of ubiquitous laser noise on cooling and the coherent dynamics in optomechanical systems. Phase fluctuations of the driving laser induce modulations of the linearized optomechanical coupling as well as a fluctuating force on the mirror due to variations of the mean cavity intensity. We first evaluate the influence of both effects on cavity cooling and find that for a small laser linewidth, the dominant heating mechanism arises from intensity fluctuations. The resulting limit on the final occupation number scales linearly with the cavity intensity both under weak- and strong-coupling conditions. For the strong-coupling regime, we also determine the effect of phase noise on the coherent transfer of single excitations between the cavity and the mechanical resonator and obtain a similar conclusion. Our results show that conditions for optical ground-state cooling and coherent operations are experimentally feasible and thus laser phase noise does pose a challenge but not a stringent limitation for optomechanical systems.

Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm

Abstract: We address a framework to reduce the unwrapping errors of the measurement system using a digital multiple-wavelength phase- shifting algorithm. In particular, the following framework is proposed: 1 smooth the raw phase by smoothing the sine and cosine images of the phase computation of the inverse tangent function; 2 locate and re- move the incorrectly unwrapped points by the monotonicity condition of the phase map; 3 obtain the unwrapped phase map for the shortest wavelength without smoothing; 4 detect holes and fill them to preserve as much useful information as possible. Experiments demonstrated that the proposed framework significantly alleviated the measurement errors caused by the phase noise. © 2009 Society of Photo-Optical Instrumentation