Residual Sidebands Research Articles

Optimization and control of cold atom interference phase shift based on laser double-sideband suppression

Using the electro-optical modulation method to generate Raman beams for cold atom interference is one of the better methods for constructing a more compact and robust laser system. But this way will generate some residual sidebands resulting in the additional interference phase shift, which can affect the measurement accuracy of cold atom interferometer. In order to weaken the effect of laser modulation sidebands on the phase shift of cold atom interference, a double-sideband suppressed-carrier modulation laser system for cold atom interference is constructed. Based on the designed laser system, the principle of double-sideband generation and suppression is analyzed in detail, and some residual sidebands are adjusted and controlled. Moreover, some important optical parameters that affect the phase shift of cold atomic interference, such as the initial distance between the Raman retro-reflection mirror and the atomic cloud, the interrogation time between two adjacent Raman pulses, the laser modulation depth and the initial velocity of the atomic cloud, are discussed and optimized. By optimizing these relevant parameters, the influence of residual modulation sidebands on the phase shift of cold atomic interference is weakened drastically. The research results indicate, making use of the method of double-sideband suppression, the phase shift of cold atomic interference can be optimized to 0.7 mrad when the initial distance between the Raman retro-reflection mirror and the atomic cloud is 105 mm, and the interrogation time between two adjacent Raman pulses is 82 ms. More importantly, this work can provide a method for weakening the influence of Raman sideband effect on the phase shift of cold atom interferometer, and the corresponding laser system can be applied to other inertial sensors such as atomic gravimeter or atomic gravity gradiometer.

Robust single-sideband-modulated Raman light generation for atom interferometry by FBG-based optical rectangular filtration.

Low-phase-noise and pure-spectrum Raman light is vital for high-precision atom interferometry by two-photon Raman transition. A preferred and prevalent solution for Raman light generation is electro-optic phase modulation. However, phase modulation inherently brings in double sidebands, resulting in residual sideband effects of multiple laser pairs beside Raman light in atom interferometry. Based on a well-designed rectangular fiber Bragg grating and a plain electro-optic modulator, optical single-sideband modulation has been realized at 1560 nm with a stable suppression ratio better than -25 dB despite of intense temperature variations. After optical filtration and frequency doubling, a robust phase-coherent Raman light at 780 nm is generated with a stable SNR of better than -19 dB and facilitates measuring the local gravity successfully. This FBG-based all-fiber single-sideband-modulated Raman light source, proposed for the first time and characterized as robust, compact and low-priced, is practical and potential for field applications of portable atom interferometry.

Integrated Optical SSB Modulation / Frequency Shifting Using Cascaded Silicon MZM

A frequency conversion mixer or single side band modulator using two cascaded MZM is proven experimentally. The operation of the circuit is modelled by a transfer matrix approach and verified by simulation in support of the experiment. A 10 GHz shift of the optical carrier in both left and right direction is demonstrated. The residual sideband suppression relative to the enhanced sideband is 22 dB for the best cases. Numerical analysis shows that the circuit has 3-dB optical and 3-dB electrical intrinsic advantage over the functionally equivalent DP-MZM.

A Low-Complexity I/Q Imbalance Calibration Method for Quadrature Modulator

This brief presents a low-complexity I/Q (in-phase and quadrature components) imbalance calibration method for the transmitter using quadrature modulation. Impairments in analog quadrature modulator have a deleterious effect on the signal fidelity. Among the critical impairments, I/Q imbalance (gain and phase mismatches) deteriorates the residual sideband performance of the analog quadrature modulator degrading the error vector magnitude. Based on the theoretical mismatch analysis of the quadrature modulator, we propose a low-complexity I/Q imbalance extraction algorithm. After the parameter extraction, the transmitter is calibrated by imposing the counter imbalanced mismatch of the transmitter through the digital baseband. In comparison with existing I/Q imbalance calibration methods, the novelty of the proposed method lies in that: 1) only three spectrum measurements of the device-under-test are needed for extraction and calibration of gain and phase mismatches; 2) due to the blind nature of the calibration algorithm, the proposed approach can be readily applicable to an existing I/Q transmitter; 3) no extra hardware that degrades the calibration accuracy is required; and 4) due to the noniterative nature, the proposed method is faster and computationally more efficient than previously published methods.

Broadband “Infinite-Speed” Magic-Angle Spinning NMR Spectroscopy

High-resolution magic-angle spinning NMR of high-Z spin-1/2 nuclei such as (125)Te, (207)Pb, (119)Sn, (113)Cd, and (195)Pt is often hampered by large (>1000 ppm) chemical-shift anisotropies, which result in strong spinning sidebands that can obscure the centerbands of interest. In various tellurides with applications as thermoelectrics and as phase-change materials for data storage, even 22-kHz magic-angle spinning cannot resolve the center- and sidebands broadened by chemical-shift dispersion, which precludes peak identification or quantification. For sideband suppression over the necessary wide spectral range (up to 200 kHz), radio frequency pulse sequences with few, short pulses are required. We have identified Gan's two-dimensional magic-angle-turning (MAT) experiment with five 90 degrees pulses as a promising broadband technique for obtaining spectra without sidebands. We have adapted it to broad spectra and fast magic-angle spinning by accounting for long pulses (comparable to the dwell time in t(1)) and short rotation periods. Spectral distortions are small and residual sidebands negligible even for spectra with signals covering a range of 1.5 gammaB(1), due to a favorable disposition of the narrow ranges containing the signals of interest in the spectral plane. The method is demonstrated on various technologically interesting tellurides with spectra spanning up to 170 kHz, at 22 kHz MAS.

Understanding a time reversal process in Lamb wave propagation

This study investigates the time reversal process (TRP) of Lamb wave signals which are transmitted and received by piezoelectric transducers bonded on plate-like structures. A number of previous studies have paid attention to spatial and temporal refocusing capability of an original excitation through the TRP in highly dispersive and complex media. However, when the TRP is applied to Lamb waves in a homogeneous regular waveguide, the refocusing capability is limited due to permanent residual side bands even if the duration of the time reversed signal increases. Based on the reciprocity of elastodynamics and linear piezoelectricity, theoretical interpretation is conducted for the main and residual side bands of the reconstructed signal in the time domain. In particular, the interpretation includes the temporal effect of velocity and amplitude dispersions, the existence of multimodes, and the reflections from boundaries during the TRP. Then, numerical and experimental tests are conducted to validate the theoretical findings of this paper. Practical issues for the successful implementation of the TRP of Lamb waves are briefly addressed as well.

Optical vector network analysis based on single-sideband modulation

We investigate an optical vector network analysis technique based on optical single-sideband modulation that can provide spectral characterization of optical components in terms of amplitude and phase shift with femtometer wavelength resolution. The fundamentals of the system are analyzed and a mathematical model for the measurement process is derived. Using this model and experimental results, the potential of the technique in terms of frequency resolution is demonstrated. However, it is also found that the measurement accuracy relies on a high suppression of the residual sideband in the optical single-sideband modulation deployed.

A two-dimensional experiment that separates decoupling sidebands from the main peaks.

Broadband decoupling techniques generate undesirable cycling sidebands. The new two-dimensional technique described here allows separation of these sidebands from the main peaks by spreading the sideband responses in the indirectly detected dimension (F(1)) according to their frequency separations from the parent peaks, leaving the main resonances at zero frequency in F(1). This trace at zero frequency shows a thousandfold suppression of the residual sidebands, making possible the detection of very weak signals from dilute constituents of the sample. The experimental results can be displayed as one-dimensional "quiet decoupling" spectra without any significant loss of sensitivity. The new technique (DESIRE-decoupling sideband resolved spectroscopy) is simple, robust, and straightforward to implement.

Manipulation of phase and amplitude modulation of spin magnetization in magic angle spinning nuclear magnetic resonance in the presence of molecular diffusion

Nuclear magnetic resonance (NMR) experiments with a spinning sample [magic angle sample spinning (MASS)] are used to remove the line broadening in composite systems, where the susceptibility contrast of its constituents gives rise to an inhomogeneous field that causes a line broadening and obscures chemical information. The NMR signal in these experiments has a phase and an amplitude part. In the absence of diffusion, i.e., in the MASS spectra of solids, the amplitude of the signal from an isochromat is a constant independent of position and time and the phase is a periodic function of the rotor frequency νr. In fluids, the amplitude of a spin packet is a function of its position and time. The amplitude modulation and relaxation in diffusive MASS encodes the dynamics of motion and the landscape (geometry of pores and field gradients) probed by the motion. Here we use spin manipulation—total suppression of sidebands (TOSS)—to suppress the effects of phase with the goal of isolating the amplitude term. By the TOSS sequence the phase factor at time t for a spin packet at an azimuthal angle φ is made to depend on φ only as a function of ωrt−φ, which suppresses the sidebands in solids upon an integration over φ. Due to molecular diffusion, the amplitude part depends on φ, and, thus, diffusive TOSS cannot suppress the sidebands. The residual sidebands carry the information of dynamics and pore and magnetic field geometry, in addition, by reducing the size of the sidebands, TOSS is of course, also useful in identifying various fluid components in situ. The diffusive MASS gives a measure of the spread in local fields and diffusive TOSS gives a measure of the spread in local gradients.

“BEST” Homonuclear Adiabatic Decoupling for 13C- and 15N-Double-Labeled Proteins

The cyclic irradiation sidebands appearing in homonuclear adiabatic decoupling are calculated in detail, which reveals the origin of the antisymmetric sidebands. The sidebands can be inverted by inserting an initial decoupling with a different period, but the same f1rms as the main decoupling that is required for Bloch–Siegert shift compensation. The sidebands can be eliminated in a broad decoupling range by adding spectra of opposite sidebands. Based on this scheme, an offset-independent double-adiabatic decoupling, named Bloch–Siegert Shift Eliminated and Cyclic Sideband Trimmed Double-Adiabatic Decoupling, or “BEST” decoupling for short, is constructed, which not only compensates the Bloch–Siegert shift as shown earlier by Zhang and Gorenstein (1998) but also eliminates residual sidebands effectively.

High-resolution N14 NMR in polycrystalline solids

The N14 NMR spectra of solids are usually very broad due to the presence of large quadrupole coupling constants. However, even partial excitation of the whole spectrum can give valuable information. With magic angle spinning (MAS), the spectrum consists of a number of peaks, but normally the centerband cannot be readily distinguished from the spinning sidebands. Multiple-pulse methods of sideband elimination, such as TOSS and PASS, cannot be used for N14 because of its short spin–spin relaxation time. On the other hand, the sidebands can be eliminated by systematic data treatment. First, the signal-to-noise ratio (S/N) is enhanced by co-adding all the peaks in a MAS spectrum in a periodic way. Then, several spectra obtained at different spinning rates are added or multiplied together to identify the centerband. In the centerband region of the spectrum obtained from the addition method, the residual sidebands can be distinguished from the weak signals by the use of logical or digital filtering. Results obtained by using these methods to treat the spectra of two mixtures of KNO3, Pb(NO3)2, and NH4Cl are shown. The experimental requirements are not very stringent, the S/N ratio is good, and peaks covering a large range of chemical shifts can be readily observed with high-resolution.

Theorie und Realisierung von codierten 3APK-Einseitenbandsystemen

In this paper first redundant (m-2)-coding is characterized. Using this code n bit symbols are converted to 1 bit symbols containing only one logical-one state. Next these symbols are parallel-series-AMI converted to a zero-mean pseudo ternary signal. Modulating a sinussoidal carrier with this signal a (m-2)-3APK-coded signal with low average signal power is generated, which can be transmitted by single-sideband transmission systems. Bit-error-probability of (m-2)-3APK-coded signals is calculated. These signals can be demodulated coherently by using carrier recovery circuits or non-coherently by using squaring circuits. For demonstration a (16-2)-3APK-coded SSB system is realized and error probability tests are performed. While using well-known WEAVER method of SSB modulation, a new type of signal processing is used for signal acquisition and coherent demodulation, which does not need auxiliary signals like suppressed carrier or residual sideband.

The effect of experimental imperfections on TOSS spectra

The effect of imperfections on the TOSS experiment, used to suppress rotational sidebands in magic-angle-spinning NMR, is examined. We consider the effects of errors in pulse lengths, phases, and timing as well as resonance offset effects. Errors in the phases of the π pulses have no effect on the efficiency of sideband suppression, and only introduce a phase shift into the spectrum. In contrast, errors in the length of the π pulses or in their timing lead to an attenuated center-band as well as the reintroduction of residual sidebands. Our results show that phase alternation of the π pulses does not necessarily compensate for pulse length errors and can, in fact, exacerbate their effects. The use of composite π pulses in TOSS is briefly examined and is shown to yield superior performance for spectral lines far from resonance.

Design aspects of FM stereo tuners and adaptors

The stereophonic composite signal may be decoded in adaptor circuitry by time multiplex or sum-and-difference approaches. To obtain suppression of SCA (background music) signals while maintaining adequate separation of the two stereophonic audio signals double, single, or residual sideband demodulation of the stereo subcarrier can be employed. Satisfactory reception of FM stereo signals requires tuner circuitry of higher performance than for equal monophonic performance. Calculated and measured stereophonic separation, distortion, and signal-to-noise ratio are shown with major causes of these performance aspects.