Phase-matching Condition Research Articles

Compact, High Extinction Ratio, and Low-Loss Polarization Beam Splitter on Lithium-Niobate-On-Insulator Using a Silicon Nitride Nanowire Assisted Waveguide and a Grooved Waveguide

We propose a compact, high extinction ratio, and low-loss polarization beam splitter (PBS) on a lithium-niobate-on-insulator (LNOI) platform, based on an asymmetrical directional coupler and using a silicon nitride nanowire assisted waveguide (WG) and a grooved WG. By properly designing Si3N4 nanowires and grooved LN WGs, TE polarization meets the phase matching condition, while significant mismatching exists for TM polarization. Numerical simulations show that the PBS has an ultra-high extinction ratio (ER) of TE0 and TM0 (larger than 40 dB and 50 dB, respectively). The device extinction ratios are larger than 10 dB over 100 nm wavelength ranges. Moreover, the device has an ultra-low insertion loss (IL less than 0.05 dB) at the wavelength of 1550 nm and maintains ILs less than 0.4 dB over 100 nm wavelength ranges.

Intermodal dispersive waves and soliton collision during multimode supercontinuum generation in chalcogenide glass fiber

Comparing with fused silica fiber, chalcogenide glass fibers are considered as an ideal platform for mid-infrared supercontinuum generation (SCG) because of its higher nonlinear coefficient and wider transparency window. Multimode fiber provides a new way to achieve special spectral characteristics in SCG by introducing intermodal interaction. We investigate the intermodal nonlinear phenomena associated with SCG in multimode chalcogenide fiber by numerically solving multimode generalized nonlinear Schrödinger equation. The results indicate that when the phase matching condition is satisfied, the intermodal interaction leads to the generation of dispersive waves at mid-infrared wavelength. Furthermore, intermodal and intramodal soliton collision are observed, and the bandwidth of the supercontinuum is increased by the intermodal interaction. These results may provide a new way for the generation of mid-infrared supercontinuum light source.

Computational Study of Dynamic Susceptibility and Phase-Matching Angle by Two-Photon Entangled Generation.

Two-photon entangled generation is used to produce an entangled photon source which is a key and core element concerning the technology applications of quantum computing, quantum communication, and quantum precision measurement. In this work, we have deduced the formulas of dynamic susceptibility and phase-matching angle of two-photon entangled generation in nonlinear optical crystals. The formulas are employed to compute the susceptibilities and phase-matching angles of these optical processes for uniaxial and biaxial crystals. The susceptibility magnitude and phase-matching condition of two-photon entangled generation affect the performance of the source. The calculated results by these formulas are employed to study properties and estimate the performance of an entangled photon source. In this way, we discuss the phase matching among waves and working wavelength in an entangled source that affects the efficiency of satellite communication with the ground during the day and night.

High-order orbital angular momentum mode conversion based on a chiral long period fiber grating inscribed in a ring core fiber.

A chiral long period fiber grating (CLPFG) was designed according to the phase-matching condition and conservation law of angular momentum, and was inscribed in a ring core fiber (RCF). This CLPFG was used to directly excite the ±2nd- and ±3rd-order orbital angular momentum (OAM) modes. The coupling efficiency of the OAM mode is up to 98.7% and the insertion loss is within 0.5 dB. The uniformity of the annular mode intensity distribution, polarization characteristics, and the mode purity of coupled OAM modes were investigated in detail. Results show that the coupled high-order OAM modes possess a relative uniform annular intensity distribution, its mode purity is up to 93.2%, and the helical phase modulation is independent on the polarization state of incident light. These results indicate that the RCF-based CLPFG is an ideal OAM mode converter for future high-capacity optical fiber communication systems.

Mid-infrared electronic wavelength tuning through intracavity difference-frequency mixing in Cr:ZnSe lasers

Mid-infrared tunable coherent light sources are used in various laser applications, such as trace gas detection, laser processing, and biomedical diagnostics. This study demonstrates mid-infrared generation in the 8.3–11 µm (i.e., 900–1200 cm−1) spectral range by configuring intracavity difference-frequency generation (DFG) using ZnGeP2 (ZGP) in an electronically tuned Cr:ZnSe laser. The broad tunability is achieved with the maximum pulse energies exceeding 100 μJ by combining the electronic wavelength tuning with sligh angle adjustments (Δθ < 0.5°) of ZGP under the spectral noncritical phase-matching condition of the nonlinear material. The proposed DFG method is generalized to give access to a significant fraction of the molecular fingerprint region by utilizing selenide compounds (e.g., AgGaSe2, CdSe) in addition to ZGP, revealing the remarkable potential of ultrabroadband electronic mid-infrared scanning for numerous spectroscopic applications.

Third-harmonic-assisted four-wave mixing in a chip-based microresonator frequency comb generation.

Microcombs generated in photonic integrated circuits can provide broadband and coherent optical frequency combs with a high repetition rate from microwave to terahertz. Coherent microcombs formed in normal group velocity dispersion microresonators usually have a flat-top temporal profile, called platicon. Here, we propose a novel scheme to generate platicon in Si3N4 microresonator with the assistance of third-harmonic generation. The nonlinear coupling between the fundamental and the third-harmonic waves that draws support from third-order sum/difference frequency generation provides a new mechanism to achieve the phase matching of four-wave mixing in normal dispersion microresonators. We show that single or multiple platicons can be obtained by changing the third-harmonic nonlinear coupling strength and phase matching condition for third-order sum/difference frequency generation. Our work provides a promising solution to facilitate coherent and visible microcomb generation in a pure χ(3) microresonator, which is potential for self-referencing combs and optical clock stabilization.

Hybrid plasmonic–dielectric metal-nanowire coupler for high-efficiency broadband nonlinear frequency conversion

Pursuing nanometer-scale nonlinear converters based on second harmonic generation (SHG) is a stimulating strategy for bio-sensing, on-chip optical circuits, and quantum information processing, but the light-conversion efficiency is still poor in such ultra-small dimensional nanostructures. Herein, we demonstrate a highly enhanced broadband frequency converter through a hybrid plasmonic–dielectric coupler, a ZnTe/ZnO single core–shell nanowire (NW) integrated with silver (Ag) nanoparticles (NPs). The NW dimension has been optimized to allow the engineering of dielectric resonances at both fundamental wave and second harmonic frequencies. Meanwhile, the localized surface plasmon resonances are excited in the regime between the Ag NPs and ZnTe/ZnO dielectric NW, as evidenced by plasmon-enhanced Raman scattering and resonant absorption. These two contributors remarkably enhance local fields and consequently support the strong broadband SHG outputs in this hybrid nanostructure by releasing stringent phase-matching conditions. The proposed nanoscale nonlinear optical converter enables the manipulation of nonlinear light–matter interactions toward the development of on-chip nanophotonic systems.

Dispersion-Suppressed Mode Depletion by Exceptional Points for On-Chip Nonlinear Optics

Dispersion-suppressed mode depletion in a resonant cavity is usually challenging due to the entanglement of amplitude and phase response dictated by the Kramers-Kronig relationship. In this study, we examine the dispersion-suppressed mode depletion induced by parity--time- (PT-) symmetric dual resonators by taking advantage of the exotic property at the exceptional point (EP). We show that this technique can modify the linear spectrum of an optical resonator for relaxed phase-matching conditions in nonlinear optics, thus profoundly altering the nonlinear behavior of integrated Kerr combs. Indeed, dissipation-induced modulation instability (MI) is predicted and numerically verified in normal group-velocity dispersion (GVD) microresonators, and the single-soliton-generation probability is greatly enhanced in the anomalous GVD regime. The merging of two vibrant disciplines, i.e., non-Hermitian optics and nonlinear optics, especially Kerr microcombs, can deepen our understanding of non-Hermitian optical frequency combs and opens broad applications ranging from fiber-optic communications, microwave photonics, and ultrafast optics to quantum state manipulations.

Competition of collimated ultraviolet lights generated by four-wave mixing process in Cs vapor

Using the two-color two-photon scheme, caesium (Cs) atoms were excited to (or around) the 112D5/2 level, generating terahertz (THz) and infrared (IR) radiations. then, a series of collimated ultraviolet (UV) lights were obtained through the four-wave mixing process. There was a competition among the collimated UV lights. The pump intensity directly affects the refractive index of Cs vapor at the pump laser wavelength, affecting the phase matching. Under the good phase-matching condition, 334.7 nm (UV1) and 339.8 nm (UV2) collimated lights were used to study the competition between ∼1.1 THz (THz1) and ∼20.9μm (IR2) radiations. After tuning the wavelength combination of the pump lasers, the intensities of THz and IR radiations were affected by the competition among parametric four-wave mixing, stimulated Raman scattering, and amplified spontaneous emission.

Perspective on Terahertz Applications of Molecular Crystals

In this review, we present a survey on the use of molecular nonlinear crystals in the context of terahertz (THz) photonics. The fundamentals of nonlinear optics for converting optical and infrared radiation into THz radiation with the basic theory of femtosecond optical rectification and difference frequency generation are described. Various types of phase-matching conditions that can be achieved in molecular crystals are discussed. It is shown that one of the unique features of molecular crystals is the ability to generate tunable narrowband terahertz radiation using femtosecond lasers. We also provide a detailed description of the most commonly used and promising molecular crystals such as DAST, DSTMS, OH1, HMQ-TMS, DCMBI, and GUHP. This review also presents a description of recent publications which show the prospects of using molecular nonlinear optical crystals in THz photonics.

High-resolution mapping of phase-matching conditions in second-order nonlinear crystals

We demonstrate the spatial mapping of phase-matching conditions in nonlinear crystals using detuned second-harmonic generation. A beam-stabilization system cancels out the angular wobbling of the translation stages that scan the crystal under test in front of the static probe beam at the fundamental frequency. A submillimeter resolution over the full scanned aperture, 50 × 50 mm2, is demonstrated. The mapping of several partially deuterated potassium dihydrogen phosphate (DKDP) crystals reveals the spatially nonuniform phase-matching conditions due to internal variations in crystal properties and high-frequency surface variations.

Simultaneous Trapping of Two Optical Pulses in an Atomic Ensemble as Stationary Light Pulses.

The stationary light pulse (SLP) refers to a zero-group-velocity optical pulse in an atomic ensemble prepared by two counterpropagating driving fields. Despite the uniqueness of an optical pulse trapped within an atomic medium without a cavity, observations of SLP so far have been limited to trapping a single optical pulse due to the stringent SLP phase-matching condition, and this has severely hindered the development of SLP-based applications. In this Letter, we first show theoretically that the SLP process in fact supports two phase-matching conditions and we then utilize the result to experimentally demonstrate simultaneous SLP trapping of two optical pulses for the duration from 0.8 to 2.0 μs. The characteristic dissipation time, obtained by the release efficiency measurement from the SLP trapping state, is 1.22 μs, which corresponds to an effective Q factor of 2.9×10^{9}. Our Letter is expected to bring forth interesting SLP-based applications, such as, efficient photon-photon interaction, spatially multimode coherent quantum memory, creation of exotic photonic gas states, etc.

Spontaneous parametric down-conversion in bottom-up grown lithium niobate microcubes

Nonclassical light sources are highly sought-after as they are an integral part of quantum communication and quantum computation devices. Typical sources use bulk nonlinear crystals that rely on stringent phase-matching conditions, limiting the operating wavelength and bandwidth. In this work, we demonstrate the generation of photon pairs from a free-standing lithium niobate microcube at the telecommunication wavelength of 1.56 µm through the spontaneous parametric down-conversion process. The maximum photon pair generation rate obtained from a single microcube with the size of 3.6 µm is 490 Hz, resulting in an efficiency of 20.6 GHz/Wm, which is three orders of magnitude larger than the efficiency of biphoton generation in bulk nonlinear crystals. The microcubes are synthesized through a solvothermal method, offering the possibility for scalable devices via bottom-up assembly on any substrates. Our work constitutes an important step forward in the realization of compact nonclassical light sources with a wide bandwidth for various quantum applications.

Dual-channel refractive index sensor based on coupling between LP01 and LP11 modes in the tapered hole-assisted dual-core fiber.

We propose a refractive index (RI) sensor based on a tapered hole-assisted dual-core fiber (HADCF). The sensor is fabricated by splicing a tapered HADCF between two single-mode fibers and operates on the coupling between the fundamental mode and the low-order mode in two cores. The HADCF is tapered to meet the phase matching condition between the fundamental mode (LP01) in the central core and the low-order mode (LP11) in the eccentric core. The tapered waist of the fiber becomes thinner; the coupling wavelength has a blue shift. Glycerin solutions of different RIs were injected into the air hole. The RI sensitivity of 936.69 nm/RIU is obtained in the RI range of 1.335-1.360. The multi-channel RI sensor cascaded by HADCFs with different taper lengths is obtained and can simultaneously measure the RI of different solutions. The proposed device has the advantages of high sensitivity, simple structure, and stable performance. The special microfluidic channel in the HADCF can protect the tested solution from external environmental pollution.

High-dimensional orbital angular momentum entanglement from an ultrathin nonlinear film

Entanglement, as a crucial feature of quantum systems, is essential for various applications of quantum technologies. High-dimensional entanglement has the potential to encode arbitrary large amount of information and enhance robustness against eavesdropping and quantum cloning. The orbital angular momentum (OAM) entanglement can achieve the high-dimensional entanglement nearly for free stems due to its discrete and theoretically infinite-dimensional Hilbert space. A stringent limitation, however, is that the phase-matching condition limits the entanglement dimension because the coincidence rate decreases significantly for high-order modes. Here we demonstrate relatively flat high-dimensional OAM entanglement based on a spontaneous parametric down conversion (SPDC) from an ultrathin nonlinear lithium niobite crystal. The difference of coincidences between the different-order OAM modes significantly decreases. To further enhance the nonlinear process, this microscale SPDC source will provide a promising and integrated method to generate optimal high-dimensional OAM entanglement.

Reconfigurable Guided‐Mode Conversion Using Cladding Medium Switching Strategy in Subwavelength Grating Waveguide

AbstractIn a waveguide‐based coupled‐mode system, various mode conversions are achieved by designing mode evolution procedures. However, the differences of refractive indices among modes exceed the capability of conventional tuning mechanism, so most reported mode manipulation devices can only realize fixed mode conversions. This paper introduces the cladding medium switching strategy to the subwavelength grating waveguide‐based coupled‐mode system, and proposes a reconfigurable mode converter on silicon nitride platform. This work systematically analyzes the phase matching conditions on a coupled‐mode system. Results show that for both whole and partial upper‐cladding switchable, it is possible to achieve reconfigurable mode conversions. For whole cladding switchable case, this work demonstrates a double‐state mode converter, which converts the input mode to TE2 and TE1 modes under cladding refractive indices of 1 and 1.7. This work expands it to triple‐state mode conversion with window‐style cladding, which converts the input to TE2, TE1, and TE0 modes under cladding of 1, 1.54, and 1.7. The optical bandwidths are relatively large, and the conversion efficiencies exceed 56% for all cases. The mechanism provides a non‐volatile and energy‐efficient way for tunable mode conversions, which is promising for applications in optical networks, communications, and sensors, etc.

Optimization of Magnetoplasmonic ε-Near-Zero Nanostructures Using a Genetic Algorithm.

Magnetoplasmonic permittivity-near-zero (-near-zero) nanostructures hold promise for novel highly integrated (bio)sensing devices. These platforms merge the high-resolution sensing from the magnetoplasmonic approach with the -near-zero-based light-to-plasmon coupling (instead of conventional gratings or bulky prism couplers), providing a way for sensing devices with higher miniaturization levels. However, the applications are mostly hindered by tedious and time-consuming numerical analyses, due to the lack of an analytical relation for the phase-matching condition. There is, therefore, a need to develop mechanisms that enable the exploitation of magnetoplasmonic -near-zero nanostructures’ capabilities. In this work, we developed a genetic algorithm (GA) for the rapid design (in a few minutes) of magnetoplasmonic nanostructures with optimized TMOKE (transverse magneto-optical Kerr effect) signals and magnetoplasmonic sensing. Importantly, to illustrate the power and simplicity of our approach, we designed a magnetoplasmonic -near-zero sensing platform with a sensitivity higher than and a figure of merit in the order of . These last results, higher than any previous magnetoplasmonic -near-zero sensing approach, were obtained by the GA intelligent program in times ranging from 2 to 5 min (using a simple inexpensive dual-core CPU computer).

Coherent control of extreme ultraviolet emission generated through frustrated tunneling ionization

Coherent extreme ultraviolet (EUV) line emissions can be generated from an atom excited through frustrated tunneling ionization (FTI). The phase variation of the EUV emission in a generation medium along the propagation direction is a critical parameter that determines the phase-matching condition of this new light source. Here we show that the EUV emission sensitively depends on the intensity and phase of a driving laser pulse and the target position. Angle-resolved EUV spectra measured at different target positions and the carrier-envelope phases of the laser pulse exhibit an intensity modulation, showing similar behavior to that of a long-trajectory high harmonic radiation. The four-step model developed for the FTI emission accurately describes the coherent control of the EUV emission. These findings are essential ingredients for developing coherent extreme ultraviolet sources with high photon flux and for utilizing the FTI emission in time-resolved spectroscopy.

Second-harmonic generation in a high-index doped silica micro-ring resonator.

We report the first, to the best of our knowledge, observation of second-harmonic generation (SHG) in a high-index doped silica micro-ring resonator, due to the symmetry-breaking-induced χ(2) at the core and cladding interface of the waveguide. The generated SH power is shown to have quadratic dependence on the in-cavity power of the fundamental pump at around 1550 nm. The pumping wavelength sweep method is adopted to fulfill the phase-matching condition for maximum conversion efficiency of SHG. This work offers a new approach to generate a visible source for the visible-light integrated optical platform from infrared-visible light conversion.

Dual-Polarization Bandwidth-Bridged Bandpass Sampling Fourier Transform Spectrometer from Visible to Near-Infrared on a Silicon Nitride Platform.

On-chip broadband optical spectrometers that cover the entire tissue transparency window (λ = 650–1050 nm) with high resolution are highly demanded for miniaturized biosensing and bioimaging applications. The standard spatial heterodyne Fourier transform spectrometer (SHFTS) requires a large number of Mach–Zehnder interferometer (MZI) arrays to obtain a broad spectral bandwidth while maintaining high resolution. Here, we propose a novel type of SHFTS integrated with a subwavelength grating coupler (SWGC) for the dual-polarization bandpass sampling on the Si3N4 platform to solve the intrinsic trade-off limitation between the bandwidth and resolution of the SHFTS without having an outrageous number of MZI arrays or adding additional active photonic components. By applying the bandpass sampling theorem, the continuous broadband input spectrum is divided into multiple narrow-band channels through tuning the phase-matching condition of the SWGC with different polarization and coupling angles. Thereby, it is able to reconstruct each band separately far beyond the Nyquist criterion without aliasing error or degrading the resolution. We experimentally demonstrated the broadband spectrum retrieval results with the overall bandwidth coverage of 400 nm, bridging the wavelengths from 650 to 1050 nm, with a resolution of 2–5 nm. The bandpass sampling SHFTS is designed to have 32 linearly unbalanced MZIs with the maximum optical path length difference of 93 μm within an overall footprint size of 4.7 mm × 0.65 mm, and the coupling angles of SWGC are varied from 0° to 32° to cover the entire tissue transparency window.