Second-order Sideband Research Articles

Enhanced sideband responses in a PT -symmetric-like cavity magnomechanical system

Based on the cavity magnomechanical system, which consists of a microwave cavity and a small ferromagnetic sphere, we propose a scheme to construct a parity-time- $\left(\mathcal{PT}\ensuremath{-}\right)$ symmetric-like system formed by the active magnon mode and passive cavity mode. The effective gain of the magnon mode is achieved by resonantly driving the yttrium iron garnet (YIG) sphere and can be modulated by the power of the driving field. We show the $\mathcal{PT}$-symmetric phase transition following the variation of magnon-photon coupling strength in microwave regime. We find that the transmission amplitudes and time delays on the first- and second-order sidebands in the $\mathcal{PT}$-symmetric-like system can be enhanced for three to four orders, compared to the magnomechanical system, once the magnon-photon coupling strength is tuned to the critical point in the broken-$\mathcal{PT}$-symmetry regime. Particularly, we also show the switching between different transmission spectra (amplification or magnomechanically induced absorption) and time delay (positive or negative) on the first-order Stokes sideband can be achieved by modulating the power of the control field, cavity-waveguide coupling parameter, and magnon-photon coupling strength. Our study shows that the cavity magnomechanical system is a promising platform for exploring $\mathcal{PT}$-symmetric-like paradigms in microwave field, and a good candidate for the microwave control on both the first- and high-order sidebands simultaneously. Our study may inspire further applications in frequency combs and low-power magnomechanical amplifier.

Realization of a highly sensitive mass sensor in a quadratically coupled optomechanical system

We propose and analyze an efficient scheme for realizing high-sensitive mass sensor in a quadratically coupled optomechanical system via nonlinear second-order sideband process. This is achieved by exploiting a well-established optomechanical circumstance, where a degenerate parametric amplifier (DPA) is embedded into a membrane-in-the-middle cavity driven by a strong control field and a weak probe pulse. Beyond the conventional linearized approximation, we derive analytical expressions for the efficiency of a second-order sideband and the sensitivity of a mass sensor by using a perturbation method. In this scheme, an added mass deposited on the dielectric membrane can be measured by monitoring the efficiency variation of second-order sideband generation. Using experimentally achievable parameters, we identify the conditions under which nonlinear gain of DPA allows us to enhance the efficiency of a second-order sideband and improve the sensitivity of a mass sensor beyond what is achievable in the linearly coupled optomechanical system based on the detection of mechanical frequency shift. More importantly, we also find that the maximum efficiency of a second-order sideband and the optimum sensitivity of a mass sensor simultaneously serve as an efficient detection for the added mass of a membrane when a control field and nonlinear gain of DPA become strong. The present proposal offers a practical opportunity to design an all-optical nonlinear mass sensor at the picogram level.

Photonics-Assisted Super-Octave Microwave Phase Shifter

A photonics-assisted super-octave microwave phase shifter is proposed. The super-octave frequency range is achieved by eliminating the second-order distortions (SDs) with the techniques of polarization interleaving and second-order optical sidebands (2-OSBs) phase processing. Polarization interleaving is based on a polarization-multiplexing dual-drive Mach-Zehnder modulator (PM-DMZM) and single sideband with carrier (SSB+C) modulation. 2-OSBs phase processing is implemented by introducing opposite phase shifts to the ±2-OSBs in a Fourier-domain optical processor (FD-OP). The proposed phase shifter is experimentally verified by proof-of-concept experiments. Experimental results show that flat phase shifts cover a full 360° range with less than 3-dB power variation over 11.5-25 GHz. Besides, excellent long-term stability is presented with a maximum phase/power fluctuation of only 1.49°/0.57 dB. Compared with the conventional FD-OP-based photonic microwave phase shifter, the proposed one improves the second-order spurious free dynamic range (SFDR 2 ) by 13.57 dB.

Quantitative Analysis of Magnon Induced Second-Order Sideband Generation

An analogous Kerr nonlinearity of a magnon would be a subject of interest and plays an important role in researching the interactions between the magnons and photons. Using the experimentally achievable parameters, we present a perturbed approach to deal with the nonlinear dynamics of magnon polaritons and obtain analytical formulas to understand the physical picture of magnon induced second-order sideband generation. We prove that this effect is modified by either adjusting the microwave drive power and the Kerr coefficient or the coupling strength. The numerical calculations of the system dynamic equations show an excellent agreement with our analytical results. In particular, an optimal parameter area is proposed, in which the signal of magnon-induced second-order sideband generation is robust. In addition to providing insight into the nonlinear interactions between the magnons and photons, our results may also offer attractive new prospects for the development of the magnon frequency comb.

Enhanced generation of charge-dependent second-order sideband and high-sensitivity charge sensors in a gain-cavity-assisted optomechanical system

We theoretically investigate the enhanced charge-dependent generation of the optical second-order sidebands (OSS) in a gain-cavity-assisted optomechanical (GCAOM) system coupled to a charged object. The hybrid optomechanical system is coherently driven by an external two-tone laser field which consists of a continuous-wave pump field and a pulsed probe field. Beyond the conventional linearized description of optomechanical interactions, the nonlinear optomechanical interactions are included in the Heisenberg-Langevin equations and are treated analytically by means of the perturbation method. It is shown that an assisted gain cavity can significantly enhance the OSS generation and can also lead to higher charge dependence of the output OSS spectrum than that achieved from a lossy cavity optomechanical system. Subsequently we discuss the application of such a GCAOM system as a family of high-sensitivity sensor for measuring the charges. Using experimentally achievable parameters, we identify the conditions under which the assisted gain cavity allows us to enhance the OSS generation and improve sensitivity of the sensor beyond what is achievable in a lossy cavity optomechanical system. The present investigation may provide a route toward modulating the nonlinear optical properties of the electro-optic hybrid system, as well as to guide the design of sensitive devices.

Photonic generation of background-free binary phase-coded microwave pulses.

We report a photonic scheme to generate background-free frequency-doubled binary phase-coded microwave pulses. The key component is a dual-polarization dual-parallel Mach-Zehnder modulator that is used to realize phase modulation and carrier-suppressed double second-order sideband modulation at two orthogonal polarization states, respectively. The π phase jump of the frequency-doubled phase-coded microwave pulse is dependent on the polarity of the coding signal rather than its amplitude. Besides, the generated microwave pulses are free from the baseband-modulated signals, because the optical power launched to a photodetector (PD) keeps constant all the time. Since no electrical or optical filters are involved, the photonic generator can ensure a broad operation bandwidth and wide tunability. Our scheme is theoretically analyzed and experimentally verified. The 4Gb/s at 16GHz and 7Gb/s at 28GHz background-free frequency-doubled phase-coded microwave pulses have been successfully generated.

Highly Sensitive Mass Sensing by Means of the Optomechanical Nonlinearity

Nanomechanical oscillator has attracted considerable attention in mass sensing applications because of its ability to connect mass variation and frequency change on mechanical oscillator. Here, using the exact same parameters with previous work based on the linearized dynamics of the optomechanical interactions, we show that the frequency shift of optomechanically induced second-order sideband is more sensitive to the mass change of mechanical oscillator. The proposed method may offer an approach to open up a broad application prospect for on-chip optomechanical devices in sensors by virtue of the achievable intrinsic optomechanical nonlinearity in the weak coupling regime under the currently existing experimental technique.

Precision Measurement of Magnetic Field Based on Second-Order Sideband Generation in a Hybrid Electromagnetic-Optomechanical System

Realizing the precise measurement of the magnetic field is of great significance in many fields, including optics, metrology, bioscience, and engineering technology. With the development of nanophotonics, optomechanical systems have provided an on-chip platform to explore new availability for high-sensitivity measurement due to its extreme sensitivity on weak force [ Ref. Nat. Nanotechnol. 7, 509 (2012) ]. In this paper, a theoretical scheme for precision measurement of magnetic field based on a nonlinear optomechanical effect: second-order sideband generation in a hybrid electromagnetic-optomechanical system is proposed. We find that the system exhibits a kenspeckle magnetic-field-dependent generation of the frequency component at the second-order sideband, which is more sensitive than the previous paper based on optomechanically induced transparency. Numerical calculations show that the measurement accuracy of the magnetic field in our scheme may reach the order of nT or even smaller, so our findings will provide a more accurate solution for the precise measurement of magnetic fields.

Optomechanically induced transparency in optomechanics with both linear and quadratic coupling

We explore the optomechanically induced transparency (OMIT) of a compound optomechanical system, which contains two cavities and a membrane. Due to the linear and quadratic coupling between the membrane and the cavity, i.e., ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}$ and ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}^{\ifmmode\dagger\else\textdagger\fi{}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{a}}_{1}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q}}^{2}$, OMIT can be observed near $\ensuremath{\delta}={\ensuremath{\omega}}_{m}$ and $\ensuremath{\delta}=2{\ensuremath{\omega}}_{m}$ simultaneously. The transmission rate of the probe field near $\ensuremath{\delta}=2{\ensuremath{\omega}}_{m}$ has the same order of magnitude with the transmission rate near $\ensuremath{\delta}={\ensuremath{\omega}}_{m}$. This is in contrast to the second-order sideband OMIT effect which is caused by the intrinsic nonlinear optomechanical coupling. We also find that the positions of the two transmission windows depend on the power of the control field. By modulating the equilibrium position of the membrane, the transmission rate near $\ensuremath{\delta}={\ensuremath{\omega}}_{m}$ can be controlled. The group delay of the transmitted light near $\ensuremath{\delta}={\ensuremath{\omega}}_{m}$ is more sensitive to the equilibrium position of the membrane than the transmitted light near $\ensuremath{\delta}=2{\ensuremath{\omega}}_{m}$. So we can separate the two transmitted lights by modulating the equilibrium position of the membrane. Our investigation provides a method to steer the performance of OMIT devices.

A Microwave Photonic Mixer Using a Frequency-Doubled Local Oscillator

A microwave photonic mixer based on a frequency-doubled local oscillator (LO) is proposed. The carrier-suppressed single-sideband (CS-SSB) modulation of the –first-order radio frequency (RF) and +second-order LO sidebands can be generated by using a dual-polarization dual-parallel Mach–Zehnder modulator (DP-DPMZM), an electrical 90° hybrid coupler, and an optical bandpass filter. The upconverted intermediate frequency (IF) signal with the frequency of ${\omega _{\boldsymbol{RF}}} + 2{\omega _{\boldsymbol{LO}}}$ is output by frequency beat at a photodetector. Meanwhile, the –first-order RF sideband can be easily changed to +first-order RF sideband by adjusting one dc bias voltage of the DP-DPMZM. The downconverted IF signal with the frequency of ${\omega _{\boldsymbol{RF}}} - 2{\omega _{\boldsymbol{LO}}}$ is obtained correspondingly. The experimental results show that the spur suppression ratios of upconverted and downconverted IF signal are 19.0 dB and 25.5 dB, respectively. The spurious-free dynamic range of the proposed mixer is 96.5 dB·Hz2/3. The output electrical spectrums are pure owing to the optimal design of the CS-SSB modulation. The proposed mixer reduces the frequency requirement of LO signal since the second-order LO single sideband is used, and the upconversion and downconversion can be switched to each other by a simple electrical operation.

Ultrahigh‐resolution coherent optical spectrum analysis based on electrical frequency sweeping with a doubled measurement range

Based on electrical frequency sweeping, an ultrahigh-resolution coherent optical spectrum analyser with a doubled measurement range is proposed and experimentally demonstrated. In the scheme, a frequency-swept electrical signal is converted to the optical domain. By selecting one of the second-order sidebands of the generated optical signal, a wavelength-swept signal with a frequency range that is twice the bandwidths of the electro-optic and RF components is generated. With the wavelength-swept signal, high-resolution optical spectrum analysis with a doubled measurement range is implemented. In a proof-of-concept experiment, the spectrum of a multi-tone optical signal with a bandwidth of 20 GHz is measured with a resolution of 1.5 MHz by employing 10 GHz components.

Tunable microwave generation based on frequency quadrupling

To generate linearly chirped microwave signals with large frequency tunable range, a photonic approach is proposed. A dual-output dual-parallel Mach–Zehnder modulator followed by a polarisation beam combiner and an optical filter are utilised to generate orthogonally polarised ± second-order optical sidebands. A polarisation modulator is employed to achieve phase modulation of the two wavelengths. The balanced detection is applied to suppress the distortion and background noise. The central frequency of the generated signal is four times that of the local oscillator frequency. Simulation results show that a linear pulse is produced with time-bandwidth as well as a compression ratio for the pulse of 11 and 9.3 respectively. Moreover, a peak-to-sidelobe ratio of 7.4 dB is generated. The system has both good reconfigurability and tunability, and its frequency can be continuously adjusted from about 10 GHz to as much as 50 GHz in principle.

Full duplex radio over fiber system with frequency quadrupled millimeter-wave signal generation based on polarization multiplexing

A full duplex radio over fiber system with frequency quadrupled millimeter-wave signal generation based on polarization multiplexing using a single-drive intensity modulator is proposed and experimentally demonstrated. At the central station, downstream signal modulated on the single-drive intensity modulator is polarization multiplexed with pure optical carrier by a polarization beam combiner (PBC) before transmitted over the single mode fiber to the base station. The single-drive intensity modulator is biased at the maximum transmission point to generate optical carrier and two second-order sidebands. At the base station, by simply adjusting the difference angle between the principle axis of polarizer and one principle axis of PBC to 135°, a frequency quadrupled millimeter-wave signal is generated. In addition, when the difference angle between the principle axis of polarizer and one principle axis of PBC is adjusted to 90°, the original pure optical carrier is recovered, which is wavelength reused to provide light source for the uplink to deliver upstream signal. A proof-of-concept experiment is performed. Pure optical carrier and 40 GHz millimeter-wave signal with 20 dB optical harmonic suppression ratio are obtained. The power penalties of the bidirectional links are less than 0.3 dB after transmitted over 10.5 km single mode fiber. The measured power fluctuation of the generated millimeter-wave signal is less than 1 dB in one hour, showing the proposed scheme is relatively stable for long-distance transmission system.

Highly Sensitive Optical Detector for Precision Measurement of Coulomb Coupling Strength Based on a Double-Oscillator Optomechanical System

An optomechanical system combining a Coulomb interaction degree of freedom provides a unique platform for precision measurement of electrical charges via the optomechanically induced transparency. A new property of a second-order sideband in a double-oscillator optomechanical system is investigated beyond the conventional linearized description of optomechanical interaction. The results show that the single-second-order sideband will split into the double-second-order sideband under a weak driving field, and the separation of the split second-order sideband shows a strong dependence on the Coulomb coupling strength. Based on the current experimental conditions, such a Coulomb-interaction-induced split of the second-order sideband may enable an all-optical sensor for precision measurement of the Coulomb coupling strength with lower power.

Optomechanical second-order sidebands and group delays in a Kerr resonator

We theoretically study high-order optomechanically-induced transparency (OMIT) process in a nonlinear Kerr resonator. A frequency shift induced by the Kerr effect, is identified for the optical cavity mode, which results in asymmetric OMIT windows of the signal and its higher-order sidebands. We also find that both the sideband amplitude and its associated group delay sensitively depend on the strength of the Kerr nonlinearity. This indicates the possibility to enhance or steer the performance of OMIT devices with various nonlinear optical cavities.

Two-color second-order sideband generation in an optomechanical system with a two-level system

Second-order sideband generation in an optomechanical system with the coupling between a mechanical resonator and a two-level system is discussed beyond the conventional linearized description of optomechanical interactions. The features of two-color second-order sideband generation are demonstrated in this hybrid system. We discovery that the switch between one- and two-color second-order sideband generation is easily realized by shifting the detuning between the control field and the cavity field or the transition frequency of the two-level system. The efficiency of two-color second-order sideband generation increases monotonously with the control field strength. The coupling strength between the mechanical resonator and the two-level system plays a decisive role in the appearance of the two-color second-order sidebands. The two-color second-order sideband generation may provide measurement with higher precision in new degrees of freedom.

Tunable two-phonon higher-order sideband amplification in a quadratically coupled optomechanical system

We propose an efficient scheme for the controllable amplification of two-phonon higher-order sidebands in a quadratically coupled optomechanical system. In this scheme, a strong control field and a weak probe pulse are injected into the cavity, and the membrane located at the middle position of the cavity is driven resonantly by a weak coherent mechanical pump. Beyond the conventional linearized approximation, we derive analytical expressions for the output transmission of probe pulse and the amplitude of second-order sideband by adding the nonlinear coefficients into the Heisenberg-Langevin formalism. Using experimentally achievable parameters, we identify the conditions under which the mechanical pump and the frequency detuning of control field allow us to modify the transmission of probe pulse and improve the amplitude of two-phonon higher-order sideband generation beyond what is achievable in absence of the mechanical pump. Furthermore, we also find that the higher-order sideband generation depends sensitively on the phase of mechanical pump when the control field becomes strong. The present proposal offers a practical opportunity to design chip-scale optical communications and optical frequency combs.

Simultaneous transmission of wired and wireless signals based on double sideband carrier suppression

Abstract In this paper, we proposed and experimentally demonstrated simultaneous transmission of wired and wireless signals based on double sideband optical carrier suppression. By properly adjusting the bias point of the dual-output mach-zehnder modulator (MZM), a central carrier in one output port and a pair of first-order sidebands in another output port are generated. The pair of first-order sidebands are fed into a second MZM to generate second-order order sidebands. A wired signal is embedded on the central carrier while a wireless signal is embedded on the second-order sidebands. Unlike other schemes, we did not use optical filter to separate the carrier from the optical sidebands. The measured bit error rate (BER) and eye-diagrams after a 25 km single-mode-fiber (SMF) transmission proved that the proposed scheme is successful for both wired and wireless signals transmission. Moreover, the power penalty at the BER of 10−9 is 0.3 and 0.7 dB for wired and wireless signals, respectively.

Microwave Frequency Quadrupling Based on Distributed Feedback Laser and a Single Intensity Modulator

ABSTRACTIn this article, we have proposed and experimentally demonstrated a directly modulated distributed feedback laser (DFB-LD) to generate microwave and millimeter-wave signals. The proposed scheme uses DFB-LD and intensity modulator (IM) biased at null point. A radio frequency (RF) signal from a signal generator is split into two branches and one branch directly modulates the DFB-LD, while the other branch drives the IM. Two second-order sidebands separated by four times the frequency of the input RF signal are generated. Experimental results indicated that we can generate a four-fold microwave signal with a good optical signal to noise ratio.

Efficient Raman sideband cooling of trapped ions to their motional ground state

Efficient cooling of trapped ions is a prerequisite for various applications of the ions in precision spectroscopy, quantum information, and coherence control. Raman sideband cooling is an effective method to cool the ions to their motional ground state. We investigate both numerically and experimentally the optimization of Raman sideband cooling strategies and propose an efficient one, which can simplify the experimental setup as well as reduce the number of cooling pulses. Several cooling schemes are tested and compared through numerical simulations. The simulation result shows that the fixed-width pulses and varied-width pulses have almost the same efficiency for both the first-order and the second-order Raman sideband cooling. The optimized strategy is verified experimentally. A single ${^{25}\mathrm{Mg}}^{+}$ ion is trapped in a linear Paul trap and Raman sideband cooled, and the achieved average vibrational quantum numbers under different cooling strategies are evaluated. A good agreement between the experimental result and the simulation result is obtained.