Phase matching in birefringent fibers

(C8H7N2O2)2[Bi2Br8]·2H2O and (C8H7N2O2)6[Bi2Cl10]Cl2·2H2O: Exploring Birefringent Crystals in Hybrid Halide Systems

In this study, new hybrid birefringent crystals of (C8H7N2O2)2[Bi2Br8]·2H2O and (C8H7N2O2)6[Bi2Cl10]Cl2·2H2O were successfully synthesized by introducing a new birefringent group [C8H7N2O2]+ by a simple aqueous solution evaporation method. They crystallize in the P21/n space group, and their structure consists mainly of the π-conjugated group [C8H7N2O2]+ and the octahedron centered on Bi3+. By first-principles calculations, the birefringence response comes from the [C8H7N2O2]+ group with a planar π-conjugated structure. Meanwhile, the synthesis, structure, first-principles calculations, and optical properties are reported in this paper.

Multiple intermodal-vectorial four-wave mixing bands generated by selective excitation of orthogonally polarized LP01 and LP11 modes in a birefringent fiber

This study investigates the nonlinear frequency conversions between the six polarization modes of a two-mode birefringent fiber. The aim is to demonstrate that the selective excitation of different combinations of linearly polarized spatial modes at the pump wavelength initiates distinct intermodal-vectorial four-wave mixing processes. In particular, this study shows that exciting two orthogonally polarized LP₀₁ and LP₁₁ modes can lead to the simultaneous generation of up to three pairs of different spatial modes of orthogonal polarizations at different wavelengths. The role of the phase birefringence of the spatial modes in the phase matching of such a four-wave mixing process is explained. Moreover, the theoretical predictions are verified through numerical simulations based on coupled nonlinear Schrödinger equations, and are also confirmed experimentally in a commercially available birefringent fiber.

Cross-phase modulational instability of circularly polarized helical Bloch modes carrying optical vortices in a chiral three-core photonic crystal fiber

We report the first, to the best of our knowledge, observation of cross-phase modulational instability (XPMI) of circularly polarized helical Bloch modes carrying optical vortices in a twisted photonic crystal fiber with a three-fold symmetric core, formed by spinning the fiber preform during the draw. When the fiber is pumped by a superposition of left-circular polarization (LCP) and right-circular polarization (RCP) modes, a pair of orthogonal circularly polarized sidebands of opposite topological charge is generated. When, on the other hand, a pure LCP (or RCP) mode is launched, the XPMI gain is zero, and no sidebands are seen. This observation has not been seen before in any system and is unique to chiral structures with N-fold rotational symmetry. The polarization state and topological charge of the generated sidebands are measured. By decomposing the helical Bloch modes into their azimuthal harmonics, we are able to deduce the selection rules for the appearance of modulational instability sidebands. We showed that the four waves in the nonlinear mixing process must exhibit the same set of azimuthal harmonic orders.

Widely tunable optical parametric oscillation in a Kerr microresonator

We report on the first experimental demonstration of widely tunable parametric sideband generation in a Kerr microresonator. Specifically, by pumping a silica microsphere in the normal dispersion regime, we achieve the generation of phase-matched four-wave mixing sidebands at large frequency detunings from the pump. Thanks to the role of higher-order dispersion in enabling phase matching, small variations of the pump wavelength translate into very large and controllable changes in the wavelengths of the generated sidebands: we experimentally demonstrate over 720 nm of tunability using a low-power continuous-wave pump laser in the C-band. We also derive simple theoretical predictions for the phase-matched sideband frequencies and discuss the predictions in light of the discrete cavity resonance frequencies. Our experimentally measured sideband wavelengths are in very good agreement with theoretical predictions obtained from our simple phase-matching analysis.

Theory of intermodal four-wave mixing with random linear mode coupling in few-mode fibers

We study intermodal four-wave mixing (FWM) in few-mode fibers in the presence of birefringence fluctuations and random linear mode coupling. Two different intermodal FWM processes are investigated by including all nonlinear contributions to the phase-matching condition and FWM bandwidth. We find that one of the FWM processes has a much larger bandwidth than the other. We include random linear mode coupling among fiber modes using three different models based on an analysis of the impact of random coupling on differences of propagation constants between modes. We find that random coupling always reduces the FWM efficiency relative to its vale in the absence of linear coupling. The reduction factor is relatively small (about 3 dB) when only a few modes are linearly coupled but can become very large (> 40 dB) when all modes couple strongly. In the limit of a coupling length much shorter than the nonlinear length, intermodal FWM efficiency becomes vanishingly small. These results should prove useful in the context of space-division multiplexing with few-mode and multimode fibers.

Optical parametric gain and bandwidth in highly nonlinear tellurite hybrid microstructured optical fiber with four zero-dispersion wavelengths

The parametric amplification gain and bandwidth in highly nonlinear tellurite hybrid microstructured optical fiber (HMOF) are simulated based on four wave mixing process. The fiber core and cladding materials are made of TeO(2)–Li(2)O–WO(3)–MoO(3)–Nb(2)O(5) and TeO(2)–ZnO–Na(2)O–P(2)O(5) glass, respectively. The fiber has four zero-dispersion wavelengths and the chromatic dispersion is flattened near the zerodispersion wavelengths. A broad gain bandwidth as wide as 1200 nm from 1290 to 2490 nm can be realized in the near infrared window by using a tellurite HMOF as short as 25 cm.

On-chip low loss heralded source of pure single photons

A key obstacle to the experimental realization of many photonic quantum-enhanced technologies is the lack of low-loss sources of single photons in pure quantum states. We demonstrate a promising solution: generation of heralded single photons in a silica photonic chip by spontaneous four-wave mixing. A heralding efficiency of 40%, corresponding to a preparation efficiency of 80% accounting for detector performance, is achieved due to efficient coupling of the low-loss source to optical fibers. A single photon purity of 0.86 is measured from the source number statistics without narrow spectral filtering, and confirmed by direct measurement of the joint spectral intensity. We calculate that similar high-heralded-purity output can be obtained from visible to telecom spectral regions using this approach. On-chip silica sources can have immediate application in a wide range of single-photon quantum optics applications which employ silica photonics.

High-power picosecond terahertz-wave generation in photonic crystal fiber via four-wave mixing

We demonstrate picosecond terahertz (THz)-wave generation via four-wave mixing in an octagonal photonic crystal fiber (O-PCF). Perfect phase-matching is obtained at the pump wavelength of 1.55 μm and a generation scheme is proposed. Using this method, THz waves can be generated in the frequency range of 7.07-7.74 THz. Moreover, peak power of 2.55 W, average power of 1.53 mW, and peak conversion efficiency of more than -66.65 dB at 7.42 THz in a 6.25 cm long fiber are realized with a pump peak power of 2 kW.

Surface plasmon polariton enhanced by optical parametric amplification in nonlinear hybrid waveguide

We theoretically studied nonlinear interactions between surface plasmon polariton (SPP) and conventional waveguide mode in nonlinear hybrid waveguide and proposed a possible method to enhance SPP wave via optical parametric amplification (OPA). The phase matching condition of this OPA process is fulfilled by carefully tailoring the dispersions of SPP and guided mode. The influences of incident intensity and phase of guided wave on the OPA process are comprehensively analyzed. It is found that not only a strong enhancement of SPP but also modulations on this enhancement can be achieved. This result indicates potential applications in nonlinear optical integration and modulations.

Photon pair generation in birefringent optical fibers

We study both experimentally and theoretically the generation of photon pairs by spontaneous four-wave mixing (SFWM) in standard birefringent optical fibers. The ability to produce a range of two-photon spectral states, from highly correlated (entangled) to completely factorable, by means of cross-polarized birefringent phase matching, is explored. A simple model is developed to predict the spectral state of the photon pair which shows how this can be adjusted by choosing the appropriate pump bandwidth, fiber length and birefringence. Spontaneous Raman scattering is modeled to determine the tradeoff between SFWM and background Raman noise, and the predicted results are shown to agree with experimental data.

Measurement of small birefringence and loss in a nonlinear single-mode waveguide

We design and fabricate a birefringent semiconductor waveguide for application to nonlinear photonics, demonstrating that it is possible to engineer a small birefringence into such a device using multiple core layers. We also demonstrate a simple technique to accurately determine small waveguide birefringence using a differential measurement, present useful methods for coupling light into and out of the device, and make estimates of coupling and linear device losses.

Tailored photon-pair generation in optical fibers

We experimentally control the spectral structure of photon pairs created via spontaneous four-wave mixing in microstructured fibers. By fabricating fibers with designed dispersion, one can manipulate the photons' wavelengths, joint spectrum, and, thus, entanglement. As an example, we produce photon pairs with no spectral correlations, allowing direct heralding of single photons in pure-state wave packets without filtering. We achieve an experimental purity of (85.9+/-1.6)%, while theoretical analysis and preliminary tests suggest that 94.5% purity is possible with a much longer fiber.

Polarization-independent amplification and frequency conversion in strongly-birefringent fibers

The inverse modulation interaction is a degenerate four-wave mixing process in which two strong pumps drive a weak signal, whose frequency is the average of the pump frequencies. Theoretical analyses and numerical simulations of this process are made for wave frequencies that are near the zero-dispersion frequency of a fiber, in which case dispersion is unimportant, and wave frequencies that are far from the zero-dispersion frequency, in which case dispersion is important. The results show that the inverse modulation interaction in a strongly-birefringent fiber amplifies a linearly-polarized signal by an amount that depends on its phase angle, but not its polarization angle. Phase conjugation and Bragg scattering are nondegenerate four-wave mixing processes in which two strong pumps drive a weak signal and a weak idler. Studies show that phase conjugation and Bragg scattering in strongly-birefringent fibers produce polarization-independent phase-insensitive amplification and frequency conversion, respectively.

Polarization modulation instability in photonic crystal fibers

Polarization modulation instability (PMI) in birefringent photonic crystal fibers has been observed in the normal dispersion regime with a frequency shift of 64 THz between the generated frequencies and the pump frequency. The generated sidebands are orthogonally polarized to the pump. From the observed PMI frequency shift and the measured dispersion, we determined the phase birefringence to be 5.3 x 10(-5) at a pump wavelength of 647.1 nm. This birefringence was used to estimate the PMI gain as a function of pump wavelength. Four-wave mixing experiments in both the normal and the anomalous dispersion regimes generated PMI frequency shifts that show good agreement with the predicted values over a 70 THz range. These results could lead to amplifiers and oscillators based on PMI.

Cross-phase modulation instability in photonic crystal fibers

We report on the observation of cross-phase modulation instability in a highly nonlinear photonic crystal fiber. In such fibers the presence of higher orders of dispersion results in a complex phase-matching curve. We are able to observe this behavior experimentally and obtain excellent agreement between the measured and predicted shifts.

Self-induced phase matching in stimulated four-wave mixing in a nonbirefringent single-mode optical fiber

Self-induced phase matching in stimulated four-wave mixing in a nonbirefringent single-mode optical fiber has been observed. It is shown that in a nonbirefringent single-mode fiber the phase matching that is necessary for stimulated four-wave mixing can be accomplished with a combination of self-phase modulation and cross-phase modulation induced by a pump-laser pulse.

Nondegenerate four-wave mixing in a birefringent optical fiber pumped by a dye laser

An efficient nondegenerate four-wave-mixing process in a highly birefringent optical fiber pumped by a dye laser is reported. The output beam from a dye laser (at ~610 nm) was found to mix with the accompanying superfluorescent light (from 575 to 600 nm) in a birefringent fiber to generate a distinct frequency-shifted beam, which could be Stokes or anti-Stokes radiation, depending on which mode of the fiber was excited. The frequency shift was comparable with that observed in the well-known pump-divided degenerate process, as confirmed by the theory.

Polarization modulation instability in weakly birefringent fibers

Modulation instability generated by the coherent interaction of two polarization modes in a weakly birefringent optical fiber has been observed in the normal dispersion regime. In contrast to previous observations of crossphase-modulation instability in the visible, the two generated sidebands have the same polarization, which is orthogonal to that of the pump, and their frequency shift is readily controlled by variation of the birefringence of the fiber. The frequency of the modulation and its qualitative features agree with those theoretically predicted.

Energy conversion in degenerate four-photon mixing in birefringent fibers

We predict that the third-order parametric mixing of a pump with a pair of orthogonally polarized sidebands in a birefringent single-mode optical fiber may be spatially unstable. The interaction may exhibit both periodic and nonperiodic energy conversion and period doubling. This analysis allows us to propose a new scheme for all-optical switching as well as to predict the most efficient conditions for energy conversion when pump depletion is accounted for.

Stimulated four-photon mixing with crossed pump dividing in an optical fiber

An experimental study of stimulated four-photon mixing with crossed pump dividing in a birefringent optical fiber is described. The interactive four photons are all in the same mode but with different polarizations. The pump wave is distributed in two orthogonal linear polarizations, and the polarizations of Stokes and anti-Stokes waves are also orthogonal. It is shown that the Stokes shift of this stimulated four-photon mixing process is related not only to the material dispersion but also to the waveguide dispersion and is directly proportional to the birefringence.

Raman-assisted parametric frequency and polarization conversion in a birefringent fiber

Highly efficient energy conversion of the pump into the downshifted parametric Stokes radiation resulting from the phase-matched parametric four-photon mixing and subsequent perpendicular Raman amplification in a birefringent fiber is presented. We also observed significant polarization conversion from the fast y axis to the slow x axis of the birefringent fiber as a consequence of group-velocity-matched perpendicular Raman amplification of the x-polarized parametric Stokes radiation by the y-polarized pump.

Pump-intensity-dependent frequency shift in Stokes and anti-Stokes spectra generated by stimulated four-photon mixing in birefringent fiber

The output spectra of the Stokes and anti-Stokes fields generated by stimulated four-photon mixing in birefringent fiber are investigated both experimentally and theoretically and are found to be dependent on the pump intensity. The pump-intensity-dependent changes in their frequency shifts are measured in 15-m long birefringent fiber by time-resolved spectroscopy using a 500-H(z)Q-switched Nd:YAG laser (lambda = 1.0642microm) as the pump source. Also, the Stokes gain coefficient is calculated as a function of the frequency shift and the pump power for the present phase-matching process where the mutually perpendicular polarization components are involved. The theoretical results agree well with the experimental data obtained.

Four-photon mixing and dispersion in single-mode fibers

We show that phase matching for the four-photon mixing process in a single-mode fiber depends only on the propagation constant total dispersion beta(II)(omega). Frequencies omega(s) and omega(a), for the Stokes and anti-Stokes waves must satisfy omega(s) < omega(zd) < omega(a), where omega(zd) is the frequency for which dispersion is zero; beta(II)(omega(zd)) = 0. Variations in the frequency shift Omega(omega(p)) are described for pump frequency omega(p) around omega(zd), i.e., in the region where delicate balances of material and waveguide dispersion effects are used in fiber design. We show that no new waves are created when the pump and zero-dispersion frequencies coincide, i.e., Omega(omega(zd)) = 0. Since the creation of Stokes and anti-Stokes waves is intimately related to the beta(II)(omega) versus omega curve, some interesting results are predicted for advanced design fibers.

Evaluation of bending-induced birefringence based on stimulated four-photon mixing

In a single-mode fiber, the birefringence introduced by lateral internal stress caused by bending is evaluated from the measurement of the frequency shift of anti-Stokes light generated by stimulated four-photon mixing. The birefringence as a function of bending curvature is measured at a pump wavelength of 1.06 microm. Bending-induced birefringence of 7 x 10(-5), which corresponds to a frequency shift of 1060 cm(-), is found to be introduced by a bending curvature of 2.8 mm. Experimental results are in good agreement with theoretical predictions.