Nondegenerate Four-wave Mixing Research Articles

Color-switching in an optical parametric oscillator using a phase-conjugate mirror.

We construct a phase-conjugate resonator which passively produces stable pulses that alternate between the probe and the conjugate colors. The requisite phase-conjugate mirror inside the resonator is constructed using non-degenerate four-wave mixing (4WM) in rubidium vapor. The glancing-angle phase-conjugate mirror is a 100% output coupler, and therefore this resonator is unusual in that no light circulates the cavity more than once. Without the gain of the phase-conjugate mirror, the cavity boundary conditions, and thus resonant modes, are not defined and therefore can be tuned by the pump. The output of the optical parametric oscillator that is formed above threshold can passively mode-lock. The phase-conjugate mirror removes thermal or acoustic instabilities that are on a MHz or slower timescale. This work provides a new method for stable pulsing using phase-conjugate optics, and suggests a platform for producing mode-locked pulses with squeezed light, as the 4WM process has already demonstrated quantum correlations.

Microwave assisted efficient non-degenerate four-wave mixing in pulsed regime

We theoretically investigate a N-type 87Rb atomic system for efficient generation and control of a non-degenerate four wave mixing (FWM) signal in pulsed regime. The susceptibility of the atomic medium is customized as a gain profile by a weak probe pulse and two strong continuous wave control fields which allow us to generate the pulsed FWM signal. We study the propagation dynamics of the generated FWM signal inside the nonlinear medium. The FWM signal obtains the exact shape of the probe pulse and travels without changing the shape whereas, the probe pulse is absorbed inside the nonlinear medium. The conversion efficiency of this scheme without a MW field is 5.36%. However, a MW field that couples two metastable ground states enhances the conversion efficiency to 20.6%. The generation and control of such FWM signal in pulsed regime has important applications in signal processing, optical communication and information science.

Intrinsic polarization conversion and avoided-mode crossing in X-cut lithium niobate microrings

Compared with well-developed free space polarization converters, polarization conversion between TE and TM modes in the waveguide is generally considered to be caused by shape birefringence, like curvature, morphology of waveguide cross section and scattering. Here, we study the polarization conversion mechanism in 1-THz-FSR X-cut lithium niobate microrings with multiple-resonance condition, that is the conversion can be implemented by birefringence of waveguides, which will also introduce an avoided-mode crossing. In the experiment, we find that this mode crossing results in severe suppression of one sideband in local nondegenerate four-wave mixing and disrupts the cascaded four-wave mixing on this side. Simultaneously, we propose one two-dimensional method to simulate the eigenmodes (TE and TM) in X-cut microrings, and the mode crossing point. This work will provide one approach to the design of polarization converters and simulation for monolithic photonics integrated circuits, and may be helpful to the studies of missed temporal dissipative soliton formation in X-cut lithium niobate rings.

Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching

Normal Order Non-Classical Criteria In Non-Degenerate Four-Wave Mixing Process: Quantum Entanglement, Squeezing And Anti-Bunching

Nonlinear frequency conversion of nondiffracting modes via nondegenerate four-wave mixing in atomic vapor

Nonlinear frequency conversion of nondiffracting modes via nondegenerate four-wave mixing in atomic vapor

Polychromatic and collimated lights generated by nondegenerate four-wave mixing in cesium vapor.

We demonstrate the generation of polychromatic and collimated lights at 456 nm, 459 nm, and 761 nm based on cesium (133Cs) 6S1/2 - 6P3/2 - 8S1/2 - 7P3/2, 7P1/2, 6P1/2 - 6S1/2 multi-diamond-type atomic system via two-photon excitation with two IR pump lasers at 852 nm and 795 nm. The 456 nm, 459 nm (7P3/2, 7P1/2 → 6S1/2) collimated blue lights result from the self-seeded four-wave mixing process (FWM), and the 761 nm coherent light (8S1/2 → 6P1/2) is from a seeded FWM process with the injection of a third laser at 895 nm. We measure the dependency of generated polychromatic fields on the temperature of 133Cs vapor cell and the powers of input lasers, clearly demonstrating the competition between the self-seeded FWM and seeded FWM, as they share the same excitation path. This work is helpful to further produce entangled multi-color photons for quantum communication.

Narrow linewidth semiconductor multi-wavelength DFB laser array simultaneously self-injection locked to a single microring resonator.

We experimentally demonstrate a narrow linewidth semiconductor multi-wavelength distributed feedback (DFB) laser array by simultaneously injection locking each laser to the corresponding resonance of a single on-chip microring resonator. The white frequency noises of all the DFB lasers is reduced by more than 40 dB once they are simultaneously injection locked to a single microring resonator with a quality factor (Q-factor) of 2.38 million. Correspondingly, the instantaneous linewidths of all the DFB lasers are narrowed by a factor of 104. In addition, frequency combs originating from non-degenerate four-wave mixing (FWM) between the locked DFB lasers are also observed. Simultaneously injection locking multi-wavelength lasers to a single on-chip resonator may enable the possibilities of integrating a narrow-linewidth semiconductor laser array on a single chip and having multiple microcombs in a single resonator, which are in high demand in wavelength division multiplexing coherent optical communication systems and metrological applications.

High-efficiency optical frequency mixing in an all-dielectric metasurface enabled by multiple bound states in the continuum

We present nonlinear optical four-wave mixing in a silicon nanodisk dimer metasurface. Under the oblique incident plane waves, the designed metasurface exhibits a multiresonant feature with simultaneous excitations of three quasi-bound states in the continuum (BIC). Through employing these quasi-BICs with maximizing electric field energy at the input bump wavelengths, significant enhancement of third-order nonlinear processes including third-harmonic generation, degenerate and nondegenerate four-wave mixing are demonstrated, giving rise to ten frequencies in the visible wavelengths. This work may lead to a new frontier of ultracompact optical mixer for applications in optical circuitry, ultrasensitive sensing, and quantum nanophotonics.

Wavefront shaping with nonlinear four-wave mixing

Wavefront manipulations have enabled wide applications across many interdisciplinary fields ranging from optics and microwaves to acoustics. However, the realizations of such functional surfaces heavily rely on micro/nanofabrication to define the structured surfaces, which are fixed and only work within a limited spectrum. To address these issues, previous attempts combining tunable materials like liquid crystal or phase-change ones onto the metasurfaces have permitted extra tunability and working spectra, however, these additional layers bring in inevitable loss and complicate the fabrication. Here we demonstrate a fabrication-free tunable flat slab using a nonlinear four-wave mixing process. By wavefront-shaping the pump onto the flat slab, we can successfully tune the effective nonlinear refraction angle of the emitting FWM beams according to the phase-matching condition. In this manner, a focusing and a defocusing nonlinear of FWM beam through the flat slab have been demonstrated with a converging and a diverging pump wavefronts, respectively. Furthermore, a beam steering scheme over a 20° angle has been realized through a non-degenerate four-wave mixing process by introducing a second pump. These features open up a door to manipulating light propagation in an all-optical manner, paving the way to more functional and tunable flat slab devices in the applications of imaging and all-optical information.

Spatial mapping of the polarization-resolved spectrum based on vector-beam-assisted nondegenerate four-wave mixing.

The introduction of vector beams (VBs), with space-variant polarization, into the polarization-resolved spectrum, provides a convenient and rapid pathway for revealing micro-structure. Here, we realize the spatial mapping of the polarization-resolved spectrum based on VB-assisted nondegenerate four-wave mixing (FWM) in a diamond atomic system of 85Rb. The 780 nm radial VB and 776 nm linearly polarized Gaussian beam serve as the probe and pump beams in the FWM process, respectively. The generated 420 nm coherent blue light (CBL) possesses a space-variant intensity profile due to the spatially polarized atomic medium. Accordingly, the polarization-resolved spectrum can be directly mapped from a single CBL profile and the polarization information of the input 776 nm beam can be accurately extracted. In particular, such nondegenerate FWM based on VB provides a proof of principle for rapid and visual polarization-related detection by converting to a frequency domain where efficient detectors are readily available.

Magnonic frequency combs based on the resonantly enhanced magnetostrictive effect

A magnonic counterpart to optical frequency combs is vital for high-precision magnonic frequency metrology and spectroscopy. Here, we present an efficient mechanism for the generation of robust magnonic frequency combs in a yttrium iron garnet (YIG) sphere via magnetostrictive effects. We show that magnonic and vibrational dynamics in the ferrimagnetic sphere can be substantively modified in the presence of magnetostrictive effects, which results in degenerate and non-degenerate magnonic four-wave mixing and frequency conversion. Particularly, resonantly enhanced magnetostrictive effects can induce phonon laser action above a threshold, which leads to significant magnonic nonlinearity and enables a potentially practical scheme for the generation of robust magnonic frequency combs. Numerical calculations of both magnonic and phononic dynamics show excellent agreement with this theory. These results deepen our understanding of magnetostrictive interaction, open a novel and efficient pathway to realize magnonic frequency conversion and mixing in a magnonic device, and provide a sensitive tool for precision measurement.

Experimental realization of efficient nondegenerate four-wave mixing in cesium atoms.

Nondegenerate four-wave mixing (FWM) in diamond-type atomic systems has important applications in a wide range of fields, including quantum entanglement generation, frequency conversion, and optical information processing. Although the efficient self-seeded nondegenerate FWM with amplified spontaneous emission (ASE) has been realized extensively, the seeded nondegenerate FWM without ASE is inefficient in reported experiments so far. Here we present the experimental realization of the seeded nondegenerate FWM in cesium atoms with a significantly improved efficiency. Specifically, with two pump lasers at 852 and 921 nm and a seed laser at 895 nm, a continuous-wave laser at 876 nm is efficiently generated via FWM in a cesium vapor cell with a power up to 1.2 mW, three orders of magnitude larger than what has been achieved in previous experiments. The improvement of the efficiency benefits from the exact satisfaction of the phase-matching condition realized by an elaborately designed setup. Our results may find applications in the generation of squeezing and entanglement of light via nondegenerate FWM.

Two-pump parametric amplification in the presence of fiber dispersion fluctuations: a comparative study.

Fiber optical parametric amplifiers (FOPAs) operating based on four-wave mixing (FWM) are versatile devices with increasing applications in optical communication systems. In this paper, the effects of dispersion fluctuations on the performance of bandwidth, ripple, parametric gain, and saturation power of a two-pump FOPA based on four-wave and six-wave models are studied and compared. Coupled-amplitude equations representing the non-degenerate FWM process in optical fiber are solved numerically to compute the parametric gain over the communication wavelengths. The behaviors of the performance parameters are critically analyzed and compared with different types of fluctuation strengths (or amplitudes) specified by the combinations of correlation length (Lc) and fluctuation amplitude (σ). Based on the results, it was found that the flat gain bandwidth for the four-wave model remains unchanged and is insensitive to the strengths of fluctuations. The gain ripples, however, get higher as the fluctuation strengths increase. On the other hand, the flat gain bandwidths of the six-wave model are hardly identified due to the tremendous and continuous ripples within the pump wavelengths. In addition, the minimum parametric gain values for both four-wave and six-wave models reduce as the fluctuation strengths increase. Also, the lowest value of parametric gain leads to the highest saturation power and vice versa. The dispersion fluctuations affect the FWM process's efficiency and deteriorate the overall amplifier performance, particularly for the six-wave model. The numerical analysis obtained via the six-wave model is especially useful since this model closely matches with practical circumstances.

High-extinction CROW filters for scalable quantum photonics.

We report an integrated tunable-bandwidth optical filter with a passband to stop-band ratio of over 96 dB using a single silicon chip with an ultra-compact footprint. The integrated filter is used in filtering out the pump photons in non-degenerate spontaneous four-wave mixing (SFWM), which is used for producing correlated photon pairs at different wavelengths. SFWM occurs in a long silicon waveguide, and two cascaded second-order coupled-resonator optical waveguide (CROW) filters were used to spectrally remove the pump photons. The tunable bandwidth of the filter is useful to adjust the coherence time of the quantum correlated photons and may find applications in large-scale integrated quantum photonic circuits.

Multidimensional four-wave-mixing spectroscopy with squeezed light

A set of nonlinear spectroscopic measurements with quantum light is presented. It involves a strong pump with frequency ωpu and a weak probe at ωpr interacting with a solid state target to generate a conjugated beam ωc=2ωpu−ωpr via nondegenerate four-wave mixing. The χ(3) susceptibility can be measured by the noise spectra of the intensity difference of the squeezed beams. We discuss three spectroscopic setups based on squeezed light: first, single four-wave mixing in a single crystal; second, cascading scheme involving two crystals; third, an SU(1, 1) interferometer based on two separate four-wave mixing processes. We further investigate the microscopic noise and optical losses in all three setups. Simulations are presented for silicon-vacancy color centers in diamond.

Observation of the interplay between seeded and self-seeded nondegenerate four-wave mixing in cesium vapor.

Nondegenerate four-wave mixing (NFWM) is a practical and effective technique for generating or amplifying light fields at different wavelengths, and could be used to create color correlation and entanglement. Here we experimentally investigate the NFWM process in diamond atomic system via two-photon excitation with two pumps at 852 nm and 921 nm, demonstrating that a seeded NFWM with a third laser at 895 nm and two self-seeded NFWMs due to amplified spontaneous emission (ASE) occur simultaneously. We compare the two kinds of processes and show that the single- and two-photon detunings hold the key role in distinguishing them. As a result, the enhancement of seeded NFWM is obtained by selecting large one- and two-photon detunings, in which case the ASE induced self-seeded NFWM can be largely suppressed. In contrast, the ASE and its induced NFWM are effectively achieved with one- and two-photon resonant excitations allowing for population inversion for efficient ASE.

Designing silicon-core fiber tapers for efficient supercontinuum generation in the greenhouse gas absorption region

We propose a tapered silicon-core optical fiber design for extending the long-wavelength edge of supercontinuum generation to obtain a high spectral density source across the 3–4.5 µm regime. The taper works by generating sufficient spectral broadening of the driving laser pulse to produce a series of pumps for nondegenerate four-wave mixing, and then opening up new phase-matching conditions to transfer the power from these pumps to a target region of mid-infrared wavelengths. We show, by simulation, that this taper design works effectively when pumped with a conventional 2.1 µm femtosecond fiber laser, significantly improving the spectral coverage obtained with a fixed-diameter fiber. Thus, these tapered silicon-core fibers offer a potential platform for an efficient all-fiber spectroscopy solution to measure greenhouse gases.

Heralded single-photon and correlated-photon-pair generation via spontaneous four-wave mixing in tapered optical fibers

We study the generation of correlated photon pairs and heralded single photons via strongly non-degenerate spontaneous four-wave mixing (SFWM) in a series of identical micro-/nano fibers (MNF). Joint spectral intensity of the biphoton field generated at the wavelength of about 880 nm and 1310 nm has been measured under excitation by 100 ps laser pulses demonstrating good agreement with the theoretical prediction. The measured zero-time second-order autocorrelation function was about 0.2 when the emission rate of the heralded photons was of 4 Hz. The MNF-based source perfectly matches standard single-mode fibers, which makes it compatible with the existing fiber communication networks. In addition, SFWM observation in a series of identical MNFs allows increasing generation rate of single photons via spatial multiplexing.

Generation, control, storage and retrieval of complicated shaped four-wave mixing signal

We present an efficient scheme for the generation and control of a non-degenerate four-wave mixing (FWM) signal in an N-type inhomogeneously broadened 87Rb atomic system. We observe the propagation dynamics of the generated FWM signal along with the probe pulse under the condition of electromagnetically induced transparency. The FWM signal acquiring the scaled shape of the probe field travels through the medium without changing its shape and intensity. We have also shown that a time-dependent control field permits the storage and retrieval of these optical signals without losing their identity. This work allows us to generate, control, store and retrieve FWM signals of complicated shape.

Influence of co- and counter-propagating light on the phase-mismatch effect in semiconductor optical amplifiers

The phase-mismatch effect, caused by the difference in confinement factor between transverse electric (TE) and transverse magnetic (TM) modes, has not been observed in semiconductor optical amplifiers (SOAs) and is not typically accounted for. In this work, we investigate the characteristics of the phase-mismatch four wave mixing (FWM) effect, which occurs in SOA devices. Our results reveal a sinc-like response in the intensity of co- and counter-FWM conjugates as a function of the detuning shift between interacting beams. It is demonstrated that the coherence lengths between the phase match/mismatch cycles differ between co- and counter-propagating nondegenerate FWM experiments and depend on the amplified TE/TM polarizations of interacting waves aligned with respect to the birefringent axes of SOAs. The coherence lengths between each phase match/mismatch cycle in co-propagation experiments are found to be 1600 and infinite GHz, respectively, compared to 800 and 400 GHz found in counter-propagation experiments.