First-order Sidebands Research Articles

Compact silicon-based Ka-band tunable-phase photonic microwave frequency downconverter.

In this paper, a compact silicon-based photonic microwave frequency downconverter with broadband operation capability and continuous phase shift tunability is proposed and experimentally demonstrated. The photonic converter mainly comprises two micro-ring modulators (MRMs) connected in parallel and a cascaded resonator-based optical bandpass filter (OBPF) whose size is merely 200 × 700 µm2. In the proposed device, a radio frequency (RF) signal and a local oscillator (LO) signal drive the two MRMs for realizing the electro-optic conversion. The OBPF is utilized for selecting the first-order sidebands of both RF and LO signals. By manipulating the phase difference between the RF and LO optical sidebands through thermal-optic effect, the phase of the obtained intermediate frequency (IF) signal from a photodiode can be tuned continuously. Experimental results demonstrate a 137° phase shift while the RF signals of 20 and 40 GHz are downconverted to an IF signal of 0.4 GHz, which indicates the photonic microwave downconverter can be used in the Ka-band phased-array receiver.

Secure FSO communication based on optical frequency-hopping technology using delay interferometers

—A novel optical frequency-hopping (OFH) scheme using optical delay interferometers (DI) is proposed and demonstrated for secure transmission in free space. By performing carrier suppression modulation on the light wave emitted by the laser and connecting the phase modulator (PM) and DI in series, the conversion of the light wave modulated by the Mach-Zehnder modulator (MZM) from phase modulation to intensity modulation can be realized, and finally output the desired optical frequency-shift-keying (OFSK) carrier signal. Meanwhile, by controlling the positions of the frequencies of the positive and negative first-order sideband light waves on the DI frequency response curve, the OFSK signals output by the two ports of the DI can be complemented in the time domain. For the proposed OFH scheme, we carried out simulation experiments of 5 km free-space link transmission and back-to-back transmission with a communication rate of 10 Gbps, and the simulation results proved the feasibility of the scheme. Additionally, we also analyze the security performance of the proposed scheme and give the security space based on the eavesdropping probability.

Multiband Pattern Synthesis of Time-Modulated Conformal Array with Quadratic Convex Optimization Algorithm

Aiming at the multiband pattern synthesis problem of time-modulated conformal array antenna, a quadratic convex optimization algorithm is proposed for sum and difference beamforming with low sidelobe levels. This articles method synthesizes a difference beam with a low sidelobe level by generating nulls at the center frequency band and optimizing the switch-on duration time of array elements. And the sum beamforming and sidelobe suppression of the first-order sideband are realized by optimizing the switch-on instant time of the array elements. The proposed algorithm has excellent properties of sidelobe suppression and angular sweep. The simulation results of circular and satellite array antenna verify the effectiveness of the algorithm.

Characterization of sidebands in fiber lasers based on nonlinear Fourier transformation.

Phase evolution of soliton and that of first-order sidebands in a fiber laser are investigated by using nonlinear Fourier transform (NFT). Development from dip-type sidebands to peak-type (Kelly) sidebands is presented. The phase relationship between the soliton and the sidebands calculated by the NFT are in good agreement with the average soliton theory. Our results suggest that NFT can be an effective tool for the analysis of laser pulses.

Photonic approach for Doppler-frequency-shift and angle-of-arrival measurement with direction unambiguity and high precision.

A novel, to the best of our knowledge, scheme based on a dual-drive Mach-Zehnder modulator (DDMZM) is proposed for Doppler-frequency-shift (DFS) and angle-of-arrival (AOA) measurement without direction ambiguity. The echo signal from one antenna is coupled with a local oscillator and then fed into the upper RF port of the DDMZM, and the echo signal from the other one is directly fed to its lower RF port. The generated two first-order optical sidebands are separated by an interleaver to form two channels and then detected by two identical low-speed photodiodes, and so both magnitude and orientation of the AOA and DFS can be deduced from the power and frequency of the beating signals. The AOA measurement without direction ambiguity can be achieved by comparing the power of beating signals from two channels. In addition, through operating the DDMZM at different transmission points for different AOA measurement ranges, the range of high-precision AOA measurement can be extended. The system has the low complexity and high stability because only a DDMZM is used. The simulation results demonstrate the measurement of the DFS in the range of 500kHz with errors <0.05H z and the AOA from -90∘ to +90∘ with error <0.8∘.

Enhanced 4×4 MIMO RoF architecture for 5G mmWave indoor applications at 60 GHz unlicensed band

4×4 Multiple Input Multiple Output (MIMO) optical architecture based on Radio over Fiber (RoF) is proposed for 5G millimeter Wave (mmWave) indoor applications in the unlicensed 60 GHz band. First-order and second-order sidebands, generated by Dual-Drive Mach-Zehnder Modulator (DD-MZM), are exploited as optical subcarriers in order to reduce the number of Local Oscillators (LOs) implemented. Four MIMO-OFDM signals are multiplexed using Dual-Parallel Mach-Zehnder Modulator (DP-MZM) configured to perform Optical Carrier Suppression (OCS) modulation. 60 GHz spacing is ensured between each data signal and its corresponding subcarrier which allows simple heterodyne detection at Radio Access Point (RAP) level. In addition, we have proposed a 4×4 MIMO extension of Triple-S-and-Valenzuela (TSV) radio channel model based on geometrical approach. We demonstrate that the proposed RoF system with adequate configuration can meet the 5G New Radio (NR) requirement in terms of Error Vector Magnitude (EVM). Moreover, Bit Error Rate (BER) performance is evaluated with and without 5G NR channel coding, for transmission over 25 km of optical fiber followed by 3 m of radio channel, by exploiting the overall allocated band at 60 GHz which allows to achieve a very high data rate up to 122.5 Gb/s.

Photonic Generation of Background-Free Phase-Coded Microwave Pulses with Elimination of Power Fading

We report a novel photonic scheme to generate background-free phase-coded microwave pulses with elimination of power fading by cascading a dual-polarization dual-parallel Mach–Zehnder modulator (DP-DPMZM) and a polarization modulator (PolM). The DP-DPMZM is driven by a radio frequency (RF) signal to generate two first-order optical sidebands with an orthogonal polarization state, while the PolM is driven by a three-level electrical coding signal. By properly adjusting the polarization state, a series of background-free frequency-doubled phase-coded microwave pulses can be generated after optical-to-electrical conversion. Benefiting from the carrier-suppressed single-sideband (CS-SSB) modulation, the proposed signal generator can suppress the chromatic-dispersion-induced power-fading effect, which has excellent potential for long-distance fiber transmission. In addition, the system can directly generate phase-coded microwave signals in pulse mode by truncating continuous wave (CW) microwave signals. Moreover, the microwave signal generator has wideband tunability since no optical filter is involved in our scheme. The proposed method was theoretically analyzed and experimentally verified. Phase-coded microwave pulses centered at 14 GHz and 19.2 GHz with a bit rate of 0.5 Gb/s were successfully generated.

Control of the VCSEL spectrum by dual microwave frequency modulation.

We propose and investigate a method for controlling the spectrum of the vertical-cavity surface-emitting laser by simultaneous modulation of the injection current at single and doubled frequencies. We experimentally demonstrate the ability to control the power asymmetry of the first-order sidebands and to suppress the carrier by the proposed method. These possibilities are beneficial to improve frequency stability of atomic clocks based on the effect of coherent population trapping.

Flexible demodulation for rotation-induced phase difference based on a phase-controlled microwave photonic filter.

High-performance demodulation of Sagnac effect is of great importance for rotation rate measurement in inertial navigation system. In this paper, we propose a flexible measurement of rotation rate based on a phase-controlled microwave photonic filter (MPF), which incorporates an orthogonal double-sideband (ODSB) modulator, a Sagnac loop, a linearly chirped fiber Bragg grating (LCFBG), a polarizer, and a photodetector. The ODSB modulator is used to generate optical carrier (OC) and first-order sidebands with mutually orthogonal polarizations. For the MPF, its central frequency can be tuned through changing the phase difference between the OC and first-order sidebands thanks to the dispersion of the LCFBG. Therefore, if the OC and first-order sidebands are separated by a polarization beam splitter and then travel along the Sagnac loop in opposite directions, the rotation-induced phase difference between them will lead to a shift on the frequency response of the MPF. Thus, two ways can be adopted to detect the rotation rate of the Sagnac loop for different applications: monitoring the frequency response shift of the MPF and measuring the power variation at a certain frequency. Besides, the measurement sensitivity can be easily adjusted to satisfy specific requirements by tuning a polarization controller or choosing a different operating frequency. An experiment is performed to validate the proposed scheme. The results show that the maximum frequency shift of the MPF can reach 1.7 GHz at a rotation rate of 1 rad/s, and a scale factor of 0.016 mW/(rad/s) is obtained at 4 GHz.

Simultaneous Measurement of Microwave Doppler Frequency Shift and Angle of Arrival Based on a Silicon Integrated Chip

A system for simultaneous measurement of micro-wave Doppler frequency shift (DFS) and angle of arrival (AOA) is proposed based on a silicon integrated chip. In the chip, two dual-drive Mach–Zehnder modulators (DDMZMs) with a microring resonator (MRR) inserted between them are integrated. When an external laser is coupled into the chip, it is first modulated by two echo signals via the first DDMZM and then goes through the MRR to introduce an optical phase shift to one of the first-order sidebands that falls into the resonance of the MRR. After being remodulated by the transmitted signal at the other DDMZM, the lightwave is coupled out from the chip and separated into two channels by an optical coupler. In each channel, a bandpass filter (BPF) is employed to select the upper and lower sidebands. By measuring and comparing the powers, frequencies, and phases of the beat signals in the two channels, the DFS (without direction ambiguity) and AOA can be acquired. Based on the proposed method, DFS within ±100 kHz at 10, 15, and 20 GHz is successfully estimated with a maximum error of ±0.028 Hz, and AOA measurement from 0° to 75° with errors less than ±1.53° is also realized.

Single Sideband Suppressed Carrier Modulation With Spatiotemporal Metasurfaces at Near-Infrared Spectral Regime

Single sideband suppressed carrier (SSB-SC) modulation enables high efficiency and dispersion-tolerant shifting of light that is of great interest for many optical systems and applications. Herein, the design procedure of a spatiotemporal reflective metasurface is proposed to realize SSB-SC modulation in near-infrared spectral regime. The metasurface consists of a periodic array of plasmonic nanostrips integrated with indium-tin-oxide (ITO) in metal-insulator-metal configuration, wherein two sets of time-varying biasing signals are independently applied to the metasurface for modulating the permittivity of ITO in space and time. The spatiotemporal metasurface features a sawtooth phase profile with linear span over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\pi$</tex-math></inline-formula> and a constant amplitude in time domain, that can be obtained by judicious adjustment of the biasing waveforms. It is established that such spatiotemporal metasurface allows for spurious-free frequency conversion by transforming the incident signal into the first-order up-modulated sideband and suppressing all the undesired mixing products. The normalized conversion efficiency of more than 99% is achieved for the metasurface, while the peak levels of the largest undesired mixing product and the fundamental frequency are reduced down to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-39$</tex-math></inline-formula> dB and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-44$</tex-math></inline-formula> dB, respectively. The proposed spatiotemporal metasurface is exploited for multi-channel and multi-beam scanning via pixelated control over the modulation phase delays assigned to the constituent elements of the spatially-interleaved sub-arrays, rendering a shared-aperture metasurface in space-time. In this case, the crosstalk between the channels with identical operating frequencies is substantially reduced. In addition, spatiotemporal redirection of light based on frequency gradient metasurface is demonstrated, which enables ultrafast, all-angle, and continuous beam-scanning as progressing in time.

Simplified Doppler Frequency Shift Measurement Enabled by Serrodyne Optical Frequency Translation

A simplified Doppler frequency shift (DFS) measurement approach based on Serrodyne optical frequency translation is reported. A sawtooth wave with high amplitude is sent to one phase modulation arm of a Mach–Zehnder modulator in conjunction with the transmitted signal to implement the Serrodyne optical frequency translation, as well as the optical phase modulation of the transmitted signal on the frequency-shifted optical carrier. The echo signal is applied to the other arm of the modulator. The lower first-order optical sidebands from the modulator are selected by an optical bandpass filter and detected in a photodetector. By measuring the frequency of the output low-frequency signal, the value and direction of the DFS can be determined. DFS from −100 to 100 kHz is measured for 6- to 17-GHz microwave signals with a measurement error of ±0.03 Hz and a measurement stability of ±0.015 Hz in 30 min when a 500-kHz sawtooth wave is used.

A Novel Optical Frequency-Hopping Scheme Using Dual Drive Mach–Zehnder Modulator

A novel optical frequency-hopping (OFH) scheme using dual-drive Mach-Zehnder modulator (DD-MZM) is proposed and demonstrated for secure transmission in fiber-optic networks. In the proposed scheme, by adjusting the phase difference between the radio frequency (RF) signals loaded on the two arms of the DD-MZM, and filtering the center carrier by fiber Bragg grating (FBG), thus the upper and lower output spectra can be realized randomly hop between the positive and negative first-order sidebands and serve as carriers for data modulation. And the data of different users are divided into many data slices in the time domain and then modulated to these carriers. To verify the feasibility of the proposed OFH scheme, we demonstrate an error-free transmission through 40 km fiber with 10 Gbps hopping rate and 10 Gbps data rate by simulation tools. In addition, we also establish a theoretical model to evaluate the security performance quantitatively, and the results show that the computing power required by illegal third parties to crack through brute force reaches 1.0710e27 calculations per second under certain conditions, which is almost impossible. Our OFH scheme has provided a deeper insight into physical layer security.

Two-photon sideband interaction in a driven quantum Rabi model: Quantitative discussions with derived longitudinal drives and beyond the rotating wave approximation

In this paper, we analytically and numerically study the sideband interaction dynamics of the driven quantum Rabi model (QRM). We focus in particular on the conditions when the external transverse drive fields induce first-order sideband interactions. Inducing sideband interactions between two different systems is an essential technique for various physical models, including the QRM. However, despite its importance, a precise analytical study has not been reported yet that successfully explains the sideband interaction rates in a driven QRM applicable for all system parameter configurations. In our paper, we analytically derive the sideband interaction rates based on second-order perturbation theory, not relying on the rotating wave approximation (RWA). Our formula are valid for all ranges of drive frequencies and system's parameters. Our analytical derived formula agrees well with the numerical results in a regime of moderate drive amplitudes. Interestingly, we have found a nontrivial longitudinal drive effect derived from the transverse drive Hamiltonian. This accounts for significant corrections to the sideband interaction rates that are expected without considering the derived longitudinal effect. Using this approach, one can precisely estimate the sideband interaction rates in the QRM not confining themselves within specific parameter regimes for moderate drive amplitudes. This provides important contributions for quantitatively understanding experiments described by the driven QRM.

Anti-Error Robust Pattern Synthesis Algorithm in Time-Modulated Array Antenna

Compared with the traditional antenna array, the time-modulated array can increase the flexibility of the array by adding time switches. However, due to the introduction of time switches, the time-modulated array antenna is more sensitive to random errors than the traditional array. Besides random errors caused by unavoidable factors such as array deformation and defects of processing and assembly in the traditional array, time-modulation parameter errors will be introduced by time switches. As errors in the traditional array can degrade the performance of the array, time-modulation parameter errors can lower the performance of the array pattern as well, which will lift the side-lobe and increase the dynamic range of the side-lobe. Aiming at the time-modulation parameter errors in the time-modulated array, an anti-error robust pattern synthesis algorithm (AERPS) based on the convex optimization (CVX) is proposed in this paper. In the algorithm, the optimization model for the pattern synthesis of the time-modulated array is established and analyzed. Then the model is divided into two sub-models of the center frequency and the first sideband, and the convex optimization solution is first performed on the center frequency model. After the center frequency model is solved, the convex optimization solution is used to solve the first-order sideband model to obtain the final results. The simulation results of the time-modulated array in this paper show that the algorithm can reduce the average value and the dynamic range of the normalized side-lobe level, thus verifying the effectiveness and the robustness of the algorithm.

High Modulation Efficiency and Dynamic Range Optical Single Sideband Modulation Without Gain Penalty in Nonlinear Distortion Suppression

The optical single sideband (OSSB) modulation with tunable optical carrier to sideband ratio (OCSR) is a promising and popular technique in wideband analog signal transmission and microwave signal processing, which can improve modulation efficiency and combat the fiber chromatic dispersion. However, in all reported schemes for achieving OSSB modulation with tunable OCSR, the spurious free dynamic ranges (SFDR) of the systems are all limited by the third-order intermodulation distortion (IMD3). In this paper, our object is to improve the SFDR and suppress the IMD3 in a novel OSSB modulation with tunable OCSR. The proposed system consists of a primary channel and a secondary channel. In primary channel, an OSSB modulation with tunable OCSR is implemented. In secondary channel, the optical carrier and first-order sidebands are perfectly cancelled out, which can suppress the IMD3 without gain penalty at the same received optical power. In this way, a large-SFDR OSSB modulation with tunable OCSR is realized. Experimental results exhibit that the IMD3 gets effective cancellations without gain penalty under unchanged total received power, and the output microwave signal power obtains about 11-dB improvement by optimizing the OCSR. A greatly increased SFDR of over 128 dBHz4/5 is achieved in the proposed system.

All-optical enhancement of minimum detectable perturbation in intensity-based fiber sensors.

We present a novel optical signal processing scheme for enhancing the minimum detectable environmental perturbation of intensity-based fiber sensors. The light intensity is first stabilized by inducing a sinusoidal intensity modulation and extracting the first-order sideband generated by self-phase modulation (SPM) in a nonlinear medium. The light with stabilized intensity is then sent through a sensor and the sensor induced power variation is magnified by first inducing a sinusoidal intensity modulation, then undergoing SPM, and finally extracting a higher-order sideband. The advantage of the proposed stabilization-magnification (SM) sensing scheme is experimentally demonstrated by applying a damped vibration on an intensity-based fiber sensor and comparing the minimum detectable strain value of the proposed scheme with that of a conventional sensing scheme. Experimental results demonstrate minimum detectable strain improvement by a factor of 3.93. This new SM sensing scheme allows for the detection of perturbations originally too weak to be detected by a given intensity-based fiber sensor, which will be beneficial for a variety of applications such as high frequency ultra-sound detection.

Constructing qudits from infinite-dimensional oscillators by coupling to qubits

An infinite dimensional system such as a quantum harmonic oscillator offers a potentially unbounded Hilbert space for computation, but accessing and manipulating the entire state space requires a physically unrealistic amount of energy. When such a quantum harmonic oscillator is coupled to a qubit, for example via a Jaynes-Cummings interaction, it is well known that the total Hilbert space can be separated into independently accessible subspaces of constant energy, but the number of subspaces is still infinite. Nevertheless, a closed four-dimensional Hilbert space can be analytically constructed from the lowest energy states of the qubit-oscillator system. We extend this idea and show how a $d$-dimensional Hilbert space can be analytically constructed, which is closed under a finite set of unitary operations resulting solely from manipulating standard Jaynes-Cummings Hamiltonian terms. Moreover, we prove that the first-order sideband pulses and carrier pulses comprise a universal set for quantum operations on the qubit-oscillator qudit. This work suggests that the combination of a qubit and a bosonic system may serve as hardware-efficient quantum resources for quantum information processing.

Based on electro-optic phase modulation broadband synthetic aperture imaging lidar

This paper proposes a broadband synthetic aperture imaging lidar based on electro-optic phase modulation, which uses an electro-optic phase modulator to generate a series of broadband chirp signals after the narrow linewidth seed source laser passes through the phase modulator. The de-chirp method is used to achieve pulse compression, and by adopting analogy filters to filter out the interference of multiple harmonics, the near ideal de-chirp signal is attained. The experimental results show that when selecting the first-order sideband signal as the desired signal, we obtain a linear frequency modulated signal with a frequency modulated bandwidth of 3 GHz and a tuning rate of 10 THz/s, and it is achieved the resolution of 0.06 m in the range and 0.02 m in the azimuth.

Broadband continuous beam-steering with time-modulated metasurfaces in the near-infrared spectral regime

A time-modulated metasurface integrated with indium-tin-oxide (ITO) can dynamically manipulate the scattered light by imparting dispersionless phase discontinuities with 2π span on wavefronts of the generated sidebands. However, maximal frequency conversion efficiency is restricted to a narrow bandwidth at the vicinity of the resonant wavelength due to the dispersive nature of light–matter interactions in such ITO-integrated metasurfaces. Herein, a multiwavelength time-modulated meta-molecule is numerically investigated, which consists of four metal–insulator–metal meta-atoms that are judiciously designed to support four resonant wavelengths at the near-infrared regime. The metasurface platform allows for application of four sets of independent radio-frequency signals to each meta-molecule, which are optimized to excite the output spectra with dominant first-order up-modulated sidebands. Individual modulation of each meta-atom leads to efficient sideband generation at resonant wavelength corresponding to the biased meta-atom. Nevertheless, the conversion efficiency decays rapidly at off-resonant wavelengths. Concurrent modulation of all four meta-atoms within the meta-molecule configuration offers a pathway to simultaneously generate dominant sidebands at all resonant wavelengths while enhancing the frequency conversion efficiency at inter-resonant wavelengths. As the potential application, beam-steering at the up-modulated sideband by both individually and simultaneously biased meta-atoms is demonstrated. It is revealed that simultaneous modulation enables continuous dynamic light deflection over a broad spectrum spanning on 1–1.8 μm, while the steering angle of the wavelengths changes in the range of 34°–85°. Broadband continuous beam-scanning is a non-trivial task that cannot be accomplished by a quasi-static metasurface relying on dispersive resonant phase shift, which hinders simultaneous implementation of linear phase gradients at all incident wavelengths.