Second-order Sideband Generation Research Articles

Second-Order Sidebands and Group Delays in Coupled Optomechanical Cavity System with a Cubic Nonlinear Harmonic Oscillator

The generation of second-order sidebands and its associated group delay is an important subject in optical storage and switch. In this work, the efficiency of second-order sideband generation in a coupled optomechanical cavity system with a cubic nonlinear harmonic oscillator is theoretically investigated. It is found that the efficiency of second-order sideband generation can be effectively enhanced with the decrease in decay rate of optomechanical cavity, the increase in coupling strength between two cavities and the power of probe field. The slow light effect (i.e., positive group delay) is also observed in the proposed optomechanical cavity system, and can be controlled with the power of control field.

Generation of Second-Order Sideband through Nonlinear Magnetostrictive Interaction

Nonlinear interaction between the magnon mode and the mechanical mode in a magnomechanical system is treated analytically where the magnon mode is coherently driven by a bichromatic microwave drive field consisting of a strong pumping field and a weak probe field and that works within a perturbative regime. Using experimentally achievable parameters, we show that the magnonic second-order sideband is generated and can be considerably enhanced by increasing the power of the pumping field. The suppression of the magnonic second-order sideband generation at the resonance point is discussed. Furthermore, the efficiency of magnonic second-order sideband generation can be well controlled by adjusting the applied bias magnetic field strength, which is a particular feature compared to the optical second-order sideband. In addition to offering insights into the magnomechanical nonlinearity, the present results have the potential to pave the way for exploring practical applications for achieving high-precision measurement in magnonics.

Modulation of the second-order sideband efficiency of a double-cavity optomechanical system by mechanical pumps

We study the effect of external mechanical pumps on the second-order sideband generation (SSG) efficiency in a double-cavity optomechanical system. The SSG efficiency can be tuned by changing the amplitude and phase of the mechanical pumps. When external mechanical pumps are applied to both mechanical resonators, the influence on the SSG efficiency is a superposition of the two mechanical pumps driven separately. The SSG efficiency can be increased up to three times with the application of mechanical pumps compared to the case without external mechanical pumps. The present investigation proposes a method that can be applied to more cavity cascades to achieve more desirable SSG efficiency and optimize nonlinear optical properties.

Photothermal effects on optical bistability and second-order sidebands in a cavity

We theoretically study the optical bistability and second-order sideband generation (SSG) in an optical cavity having photothermal effect in our paper. Using the perturbation method, we give an explicit analytical expression for SSG, showing a conversion efficiency of over 30. With change in the system parameters, our numerical method shows that the transparency window of the photothermal induced transparency and the SSG can be significantly enhanced by the photothermal effects. Our obtained results in this study can provide a reference to develop a new way in all-optical switching and precision measurement.

Generation of second-order sideband and slow-fast light effects in a PT-symmetric optomechanical system

We theoretically study the second-order sideband generation and slow-fast light effects in a parity-time (PT) symmetric optomechanical system, which consists of an active cavity and a passive cavity containing optical parametric amplifier (OPA). Compared to the double-passive nonlinear system, we find that the second-order sideband efficiency can be significantly enhanced by the tunneling strength in the PT-symmetric system with OPA. The flexible manipulation of the second-order generation also can be realized by modulating OPA gain and phase. Moreover, the fast and slow light effects in the optomechanical system are discussed. When the tunneling strength J=3κ1, the time of the second-order sideband group delay can be effectively prolonged in a PT-symmetric cavity in the presence of OPA. The results may have some guidance for the enhancement of second-order sideband efficiency, which has potential applications in optical communication and storage.

Two-color second-order sideband generation via magnon Kerr nonlinearity in a cavity magnonical system

We investigate the enhanced generation of the optical second-order sideband (OSS) via magnon Kerr nonlinearity from a cavity magnonical hybrid system consisting of a single small yttrium iron garnet (YIG) crystal sphere and a three-dimensional (3D) rectangular cavity driven with a weak probe and a strong control field. Beyond the linear approximation, we solve the nonlinear Heisenberg–Langevin equations for achieving the analytical solutions by employing the perturbation technique. Using the experimentally achievable parameter settings, we demonstrate that the OSS generation can be significantly enhanced via increasing the magnon Kerr nonlinearity even if the coupling between the cavity and magnon is weak. Interestingly, two-color OSS generation can be observed when the cavity-magnon coupling is in the strong-coupling regime, which results from the magnonical polaritons induced by the hybrid of cavity and magnon modes. The present results illustrate the potential to utilize magnon Kerr nonlinearity for enhancing optical higher-order sidebands and controlling optical frequency combs, as well as to guide the design of experimental implementation.

Robust Four-Wave Mixing and Double Second-Order Optomechanically Induced Transparency Sideband in a Hybrid Optomechanical System

We theoretically research the four-wave mixing (FWM) and second-order sideband generation (SSG) in a hybrid optomechanical system under the condition of pump on-resonance and pump off-resonance, where an optomechanical resonator is coupled to another nanomechanical resonator (NR) via Coulomb interaction. Using the standard quantum optics method and input–output theory, we obtain the analytical solution of the FWM and SSG with strict derivation. According to the numerical simulations, we find that the FWM can be controlled via regulating the coupling strength and the frequency difference of the two NRs under different detuning, which also gives a means to determine the coupling strength of the two NRs. Furthermore, the SSG is sensitive to the detuning, which shows double second-order optomechanically induced transparency (OMIT) sidebands via controlling the coupling strength and frequencies of the resonators. Our investigation may increase the comprehension of nonlinear phenomena in hybrid optomechanics systems.

Nonreciprocal enhancement of optomechanical second-order sidebands in a spinning resonator

We theoretically study optomechanically induced second-order sideband generation in a spinning resonator. Due to the splitting of resonance frequencies of the countercirculating modes via the Sagnac effect, we find that second-order sidebands can be enhanced in one direction but suppressed in the other. Furthermore, the enhancement or suppression of second-order sidebands is closely related to the rotation speed of a resonator, incident direction of input fields, and frequency of driving fields. Finally, we study the influence of power of control fields on second-order sidebands, and find that the operating bandwidth for observing an obvious nonreciprocal enhancement of second-order sidebands can be significantly widened as the power of control fields increases. Our paper offers a promising route towards achieving tunable optical nonlinearity and convenient nonreciprocal optomechanical control in integrated photonic chips.

Gain-nonlinearity-induced tunable phonon sideband spectrum and frequency comb

We propose a scheme for generation of the high-order phonon sideband spectra (HPS) and frequency comb arising from the strain-induced coupling of a nitrogen-vacancy (NV) impurity to a resonant vibrational mode of a diamond nanoresonator. The underlying nonlinear process of the nanomechanical system, due to the coupling between the NV center and an additional pump laser in a phonon nanoresonator, results in the formation of efficient HPS and the frequency comb. Using a perturbation method, we give an explicit analytical expression for second-order phonon sideband generation. Our numerical simulations show that the HPS and frequency comb exhibit ultralow power consumption and good tunability of phonon sideband-line spacing, number, and intensity in a wide parameter range. The sideband-line spacing is determined entirely by the beating frequency between the two input lasers and is as low as a few megahertz. Of particular interest is that the symmetry of the phonon frequency comb can be controlled by adjusting some parameters. Our approach based on a solid system with good integration and expansibility may be useful for the construction of phonon networks.

The Optomechanical Response of a Cubic Anharmonic Oscillator

The nonlinearity of a mechanical oscillator may lead to the generation of the macroscopic quantum states, which are useful for precision measurement. Measuring the nonlinearity of a mechanical oscillator becomes important in order to effectively assess its performance. In this paper, we study the electromagnetically induced transparency (EIT) in an optomechanical system with a cubic nonlinear movable mirror. In the presence of the nonlinearity of the movable mirror, we show that the intensity of the output probe field exhibits an asymmetric shape with the transparency peak shifted to a frequency lower than the cavity resonance frequency. This shift can be used to measure the nonlinearity strength of the movable mirror. We also show that the mechanical nonlinearity gives rise to the enhancement of the intensity of the second-order upper sideband generation.

Tunable fast to slow light and second-order sideband generation in an optomechanical system with phonon pump

We theoretically demonstrate optomechanically induced transparency (OMIT) and its related coherent optical propagation properties such as fast and slow light effects in a cavity optomechanical system driven by a weak coherent phonon pump for suitable parametric and detuning regimes. The probe transmission spectrum experiences different processes under different detuning regimes, and the numerical simulations indicating a tunable and controllable fast-to-slow light propagation can be achieved by controlling the driving amplitudes and phase of the phonon pump. Further, the second-order sideband (SOS) generation is also demonstrated in the system, and it is found that the efficiency of the SOS generation can be significantly enhanced with manipulating the phonon pump in the resonance regime with numerical simulations. More interestingly, the SOS generation is also sensitive to the detuning (the off-resonance regime), and a robust SOS can be induced and the efficiency of the SOS generation even presents mode splitting which is similar to the linear OMIT. These results lead to good tunability of SOS generation and may find applications in manipulation of light propagation.

Tunable optical second-order sideband effects in a parity-time symmetric optomechanical system

We theoretically investigate the optical second-order sideband generation (OSSG) in an optical parity-time (PT) symmetric system, which consists of a passive cavity trapping the atomic ensemble and an active cavity. It is found that near the exceptional point (EP), the efficiency of the OSSG increases sharply not only for the blue probe-pump detuning resonant case but also for the red one. Using experimentally achievable parameters, we study the effect of the atomic ensemble on the efficiency of the OSSG. The numerical results show that the efficiency of the OSSG is 30% higher than that of the first-order sideband, which is realized easily by simultaneously modulating the atom-cavity coupling strength and detuning. Moreover, the efficiency of the OSSG can also be tuned effectively by the pump power, and the efficiency is robust when the pump power is strong enough. This study may have some guidance for modulating the nonlinear optical properties and controlling light propagation, which may stimulate further applications in optical communications.

Exceptional points enhancing second-order sideband generation in a whispering-gallery-mode microresonator optomechanical system coupled with nanoparticles

We theoretically investigate the second-order sideband generation (SSG) in a whispering-gallery-mode (WGM) microresonator optomechanical system, in which the WGM microresonator couples with two nanoparticles. The nanoparticles can induce the optical coupling of the clockwise (CW) and the counterclockwise (CCW) WGM fields. And by continuously adjusting the relative phase angle between two nanoparticles, two eigenmodes of the optomechanical system coalesce and the so-called exceptional points (EPs) emerge periodically. It is shown that in the WGM microresonator optomechanical system coupled with nanoparticles in the second-order sideband can be generated due to the nonlinear optomechanical interactions, modulated periodically by the relative phase angle between two nanoparticles, and enhanced significantly at the EPs. Particularly, considering the frequency shift caused by the nanoparticles at the EPs, the generation and absorption of the second-order sideband can be flexibly realized. These results may have potential applications for high precision measurements and the manipulation of light propagation in optical cavities.

Fano resonance and amplification in a quadratically coupled optomechanical system with a Kerr medium

We discuss the Fano resonance and amplification in a quadratically coupled optomechanical system with a nonlinear Kerr medium. We find that effective cavity detuning and the strength of the Kerr nonlinearity lead to the appearance of the Fano resonance in the output probe field at room temperature, respectively. We show that the Kerr nonlinearity causes the asymmetric line shape to appear in the intensities of the output Stokes field and the second-order upper sideband generation. We also show that the Kerr nonlinearity can amplify the intensities of the output Stokes field and the second-order upper sideband generation, and the amplification factor is related to the strength of the Kerr nonlinearity. The findings of this study have potential applications in optical switching and frequency conversion.

Optomechanical second-order sideband effects in a Laguerre–Gaussian rotational-cavity system

We theoretically investigate the second-order sideband generation in an optomechanical system, comprised of two spiral phase elements, with a focus on the influence of pumping power and detunings on second-order upper sideband effects. By analyzing the solutions of the second-order sideband, based on a perturbation method, the efficiency of the second-order sideband generation in both resonance and near resonance conditions is discussed. It is found that the second-order sideband can be significantly modified, by tuning the pumping power and the pump-cavity detuning. Interestingly, the efficiency of the second-order sideband generation around the resonance frequency can be enhanced, under the near resonance regime.

Mechanical Exceptional-Point-Enhanced Second-Order Sideband Generation

Realizing the enhancement and control of the optomechanical induced second-order sideband generation is of great significance in making a low-power optomechaical amplifier and highly sensitive sensor. Here we analyze theoretically light transmission obtained from a hybrid optomechanical system composed of an optical cavity and a pair of directly coupled PT-symmetric mechanical resonators, and in which the cavity is coherently driven by a bichromatic input field consisting of a strong control field and a weak probe field and that works within the perturbative regime. Using experimentally achievable parameters, we show that the transmission of the probe field changes from single to double transparency window via the transition from a broken mechanical PT-symmetric phase to an unbroken mechanical PT-symmetric phase, correspondingly, the second-order sideband generation can be also split from one frequency center into two frequency centers. Especially, when the assisted mechanical PT-symmetric systems reach the vicinity of the exceptional point, the efficiency of second-order generation can be significantly enhanced, compared to the conventional optomechanical system, what can be improved about four orders of magnitude, which is a manifestation of the unique property of mechanical PT-symmetric systems. The proposed mechanism of reaching new levels of second-order sideband generation for optomechanical systems, offers a promising route towards achieving the multimode higher-order sidebands generation and controlling optical frequency combs with an integrable structure.

Saturable nonlinearity-induced high-order sideband generation in a parity–time symmetric double-cavity system

A coupled active–passive double-cavity system with balanced effective gain and loss provides a powerful platform for sideband generation. In different input limits, we explore the gain-saturation nonlinearity of the active cavity with regard to sideband generation. Using a perturbation method, we give an explicit analytical expression for second-order sideband generation (SSG), showing a conversion efficiency of over 80% and pump powers as low as ∼μW. A remarkable mode-splitting is also observed during the SSG process in the unbroken parity–time () symmetry phase. With change in the system parameters, our numerical method shows that high-order sideband generation (HSG) in the unbroken phase is controllable, including increasing its amplitude and changing its order number, especially when switching HSG between perturbative and non-perturbative regimes. In the broken phase, field localization effect leads to a stronger output spectral intensity than that in the unbroken phase.

Controllable optical response properties in a hybrid optomechanical system

In this paper, we study theoretically the optical response properties of the output field in a hybrid optomechanical system, in which a degenerate optical parametric amplifier (OPA) and a $$\varLambda $$ -type three-level atomic ensemble are placed in a driven optical cavity with a moving end mirror. We show that due to the presence of the OPA and the atomic medium, our proposal has the ability to exhibit the optical tristability and multiple optomechanically induced transparency (OMIT)-like effects. Moreover, the combined effects of optical amplification and OMIT-like as well as the tunable switch from slow-to-fast light can be realized by tuning the gain coefficient of the OPA and the phase of the field driving the OPA. In addition, the role of the OPA on the higher-order sideband generation has also been investigated. We find that the presence of the OPA contributes to the enhancement of the second-order sideband generation. These results provide a new way to engineer the hybrid optomechanical devices for applications in optical communications and signal processing.

Atom-assisted second-order sideband generation in an optomechanical system with atom-cavity-resonator coupling

Second-order sideband generation (SSG) is investigated in an optomechanical system with atom-cavity-resonator coupling. We focus mainly on the effect of the atomic ensemble trapped in the cavity on the SSG. The numerical results show that the second-order sideband is induced not only for the blue probe-pump detuning resonant case but also for the red one while coupling the atoms with the cavity. Moreover, it is found that the efficiency of the SSG can be significantly enhanced while increasing the atom-cavity coupling strength. More interestingly, the SSG is also sensitive to the atom-pump detuning. It is demonstrated that when optimizing this detuning and the atom-cavity coupling strength together, a robust second-order sideband can be induced and the efficiency of the SSG even surpasses the one of the first-order sideband generation. In addition, the efficiency of the SSG can also be tuned effectively by the decay rate of the atom.

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.