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Nonlinear Optics || The Electrooptic and Photorefractive Effects
摘要： The electrooptic effect is the change in refractive index of a material induced by the presence of a static (or low-frequency) electric field. In some materials, the change in refractive index depends linearly on the strength of the applied electric field. This change is known as the linear electrooptic effect or Pockels effect. The linear electrooptic effect can be described in terms of a nonlinear polarization given by Pi(ω) = 2ε0 Σj k χ(2)ij k (ω = ω + 0)Ej (ω)Ek(0). Since the linear electrooptic effect can be described by a second-order nonlinear susceptibility, it follows from the general discussion of Section 1.5 that a linear electrooptic effect can occur only for materials that are noncentrosymmetric. Although the linear electrooptic effect can be described in terms of a second-order nonlinear susceptibility, a very different mathematical formalism has historically been used to describe the electrooptic effect; this formalism is described in Section 11.2 of this chapter. In centrosymmetric materials (such as liquids and glasses), the lowest-order change in the refractive index depends quadratically on the strength of the applied static (or low-frequency) field. This effect is known as the Kerr electrooptic effect or as the quadratic electrooptic effect. It can be described in terms of a nonlinear polarization given by Pi(ω) = 3ε0 Σj kl χ(3)ij kl(ω = ω + 0 + 0)Ej (ω)Ek(0)El(0).
关键词： refractive index,electrooptic effect,Kerr electrooptic effect,Pockels effect,nonlinear polarization
更新于2025-09-23 15:21:01
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Recent advances with electro-optic polymers
摘要： In recent years the electro-optic polymers emerged as an important branch of material science. This growth and interest is fundamentally motivated by practical application of these materials in second-order nonlinear optics and in waveguiding configuration. Indeed, these materials marry excellent optical quality of amorphous r bonded polymers with enhanced first hyperpolarizability of imbedded organic nonlinear optical molecules. Although a big progress was achieved with them, concerning particularly the science, understanding and applications, some problems remain still incompletely solved, particularly the stability of induced polar order by the application of external electric field and the molecule aggregation. In this review paper we recall techniques of thin film fabrication, poling, characterization of NLO properties and discuss more precisely problems of molecule aggregation as well as the temporal decay of polar order. A novel 3D second-order NLO chromophores, namely the [2] paracyclophanes, which may help to limit the aggregation, are proposed. We show, in particular, that this molecule can be poled in doped PMMA thin films. Practical applications of electro-optic polymers are also reviewed and discussed.
关键词： pockels effect,electro-optic polymers,electric field poling,first hyperpolarizability,second harmonic generation,[2] paracyclophane,functionalized polymers
更新于2025-09-23 15:21:01
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Determination of the electric field and its Hilbert transform in femtosecond electro-optic sampling
摘要： We demonstrate time-domain sampling of mid-infrared electric ?eld transients and their conjugate counterparts exploiting the dynamical Pockels effect. To this end, the complete polarization change of few-femtosecond probe pulses is studied. An intuitive picture based on a phasor representation is established before gaining quantitative understanding in experiment and theory. In the standard version of electro-optic sampling, the electric ?eld is determined by analyzing the change of ellipticity of the probe polarization. Beyond this, we ?nd that a temporal gradient of the input electric ?eld manifests itself in a rotation of the polarization ellipsoid of the probe. The relative contribution of sum- and difference-frequency mixing processes and their spectral distribution over the near-infrared probe bandwidth are identi?ed as key aspects. If one of these processes dominates, detecting ellipticity changes and polarization rotation as a function of time delay results in two wave forms which are Hilbert transforms of each other. Such conditions may be achieved by angle phase matching in birefringent materials or spectral ?ltering of the probe after the nonlinear interaction. In this case, a static phase introduced by birefringence or re?ection at metallic mirrors results in a speci?c phase shift of both time traces with respect to the input electric ?eld. Contributions from sum- and difference-frequency generation are found to be equivalent when using electro-optic sensors with isotropic refractive index. Polarization rotations in the low- and high-frequency parts of the probe then tend to cancel out. In this limit, spurious additional phase shifts do not change the phase of the detected transients. This fact leads to a robust recovery of the carrier-envelope phase of the input wave form. Clarifying the role of imperfections of superachromatic phase retarders completes our survey on proper determination of the electric ?eld and its conjugate variable.
关键词： polarization rotation,sum-frequency generation,difference-frequency generation,electro-optic sampling,Pockels effect,mid-infrared,Hilbert transform
更新于2025-09-19 17:13:59
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[IEEE 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) - Paris, France (2019.9.1-2019.9.6)] 2019 44th International Conference on Infrared, Millimeter, and Terahertz Waves (IRMMW-THz) - Time-Domain Detection of the Electric Field and its Conjugate Variable in Ultrabroadband Electro-Optic Sampling
摘要： We demonstrate unambiguous detection of the conjugate variable to the electric field in a time-domain experiment. The polarization change induced by nonlinear mixing of probe and multi-THz fields via the Pockels effect is examined concerning changes in ellipticity and tilting of the polarization ellipsoid. Spectrally resolved measurements yield crucial insights into how sum and difference frequency generation processes shape the electro-optic signal for different detection crystals. This approach enables precise, even simultaneous, measurement of the electric field and its conjugate variable by combinations of different phase biases ((cid:2)/4 and (cid:2)/2) and spectral filtering.
关键词： sum and difference frequency generation,ultrabroadband electro-optic sampling,Pockels effect,electric field,conjugate variable
更新于2025-09-16 10:30:52
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Ultra-Low Power Tuning in Hybrid Barium Titanate-Silicon Nitride Electro-Optic Devices on Silicon
摘要： As the optical analogue to integrated electronics, integrated photonics has already found widespread use in data centers in the form of optical interconnects. As global network traffic continues its rapid expansion, the power consumption of such circuits becomes a critical consideration. Electrically-tunable devices in photonic integrated circuits contribute significantly to the total power budget as they traditionally rely on inherently power-consuming phenomena such as the plasma dispersion effect or the thermo-optic effect for operation. Here, we demonstrate ultra-low power refractive index tuning in a hybrid barium titanate (BTO)-silicon nitride (SiN) platform integrated on silicon. We achieve tuning by exploiting the large electric field-driven Pockels effect in ferroelectric BTO thin films of sub 100 nm thickness. The extrapolated power consumption for tuning a free spectral range (FSR) in racetrack resonator devices is only 106 nW/FSR, several orders of magnitude less than many previous reports. We demonstrate the technological potential of our hybrid BTO-SiN technology by compensating thermally-induced refractive index variations over a temperature range of 20 °C and by using our platform to fabricate tunable multi-resonator optical filters. Our hybrid BTO-SiN technology significantly advances the field of ultra-low power integrated photonic devices and allows for the realization of next-generation efficient photonic circuits for use in a variety of fields, including communications, sensing, and computing.
关键词： ferroelectric,Pockels effect,silicon nitride,electro-optic,barium titanate,integrated photonics,optical tuning
更新于2025-09-16 10:30:52
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Twin boundary dominated electric field distribution in CdZnTe detectors
摘要： The performance of CdZnTe X/γ-ray detectors is strongly affected by the electric ?eld distribution in terms of charge transport and charge collection. Factors which determine the electric ?eld distribution are not only electric contact, but also intrinsic defects, especially grown-in twin boundaries. Here, the electric ?eld distribution around twin boundaries is investigated in a CdZnTe bicrystal detector with a {111}–{111} twin plane using the Pockels electro-optic effect. The results of laser beam induced current pulses are also obtained by the transient current technique, and we discuss the in?uence of the twin boundary on the electric ?eld evolution. These studies reveal a signi?cant distortion of the electric ?eld, which is attributed to the buildup of space charges at twin boundaries. Also, the position of these space charge regions depends on the polarity of the detector bias. An energy band model based on the formation of an n–n+–n junction across the twin boundary has been established to explain the observed results.
关键词： electric ?eld distribution,Pockels effect,CdZnTe,twin boundary
更新于2025-09-11 14:15:04