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Metropolitan counties: Large central metro counties in MSA of 1 million population that: 1) contain the entire population of the largest principal city of the MSA, or 2) are completely contained within the largest principal city of the MSA, or 3) contain at least 250,000 residents of any principal city in the MSA.Large fringe metro counties in MSA of 1 million or more population that do not qualify as large central Medium metro counties in MSA of 250,000-999,999 population.Small metro counties are counties in MSAs of less than 250,000 population.Nonmetropolitan counties: Micropolitan counties in micropolitan statistical area; Noncore counties not in micropolitan statistical areas data access website.
Metropolitan counties: Large central metro counties are counties in metropolitan statistical areas (MSA) of 1 million or more population that 1) contain the entire population of the largest principal city of the MSA, or 2) are completely contained in the largest principal city of the MSA, or 3) contain at least 250,000 residents of any principal city of the MSA. Large fringe metro counties are counties in MSAs of 1 million or more population that do not qualify as large central. Medium metro counties are counties in MSAs of 250,000 to 999,999 population. Small metro counties are counties in MSAs of less than 250,000 population.Nonmetropolitan counties: Micropolitan counties are counties in micropolitan statistical areas. Non-core counties are nonmetropolitan counties that are not in a micropolitan statistical area.
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Based on differences in mandibular formula and fore wing marginal fringe, Bouček (1965) divided the genus into two subgenera Dibrachys Förster s. str. and Dibrachys (Allodibrachys Bouček). Nineteen valid species of Dibrachys are recognized, of which 13 are known from the Palearctic region, 8 from the Nearctic region, 4 from the Oriental region, 1 from the Australasian region, 1 from the Afrotropical region and 2 from the Neotropical region (Noyes 2016). Most species are parasitoids of insect pests, and play an important role in biological control, with 372 different host species being reported for Dibrachys (Grissell 1974; Noyes 2016), including species of Lepidoptera, Hymenoptera, Diptera, Coleoptera, Dermaptera, Hemiptera, Neuroptera, Strepsiptera, and several species of Arachnida (Araneidae and Philodromidae). However, as Graham (1969) noted, almost all the host records are associated with Dibrachyscavus.
The determination of the second-order susceptibility (χ(2)) of thin film samples can be a delicate matter since well-established χ(2) measurement methodologies such as the Maker fringe technique are best suited for nonlinear materials with large thicknesses typically ranging from tens of microns to several millimeters. Here we compare two different second-harmonic generation setups and the corresponding measurement methodologies that are especially advantageous for thin film χ(2) characterization. This exercise allows for cross-checking the χ(2) obtained for identical samples and identifying the main sources of error for the respective techniques. The development of photonic integrated circuits makes nonlinear thin films of particular interest, since they can be processed into long waveguides to create efficient nonlinear devices. The investigated samples are ABC-type nanolaminates, which were reported recently by two different research groups. However, the subsequent analysis can be useful for all researchers active in the field of thin film χ(2) characterization.
Equation 1 is only strictly valid for monochromatic waves. When working with short laser pulses, there will be a temporal walk-off between the SH pulse generated at the front and back surface of the sample which Eq. 1 does not account for. The pulse at the fundamental wavelength will travel at a different group velocity through the substrate than the SH pulse generated at the front and thus there will be a small delay between both generated SH pulses. This reduces the depth of the interference fringes. If this effect is not taken into account, it will result in an overestimation of χ(2) of the thin film. The temporal walk-off effect is implemented in the model by introducing sech2 pulses46
The KIT model is based on the approach of Herman and Hayden23 which solves the nonlinear wave equation and satisfies the boundary conditions for the SH wave at all interfaces of the sample: at the air-film, the film-substrate, and the substrate-air interface. The approach has been generalized for arbitrary polarization of the fundamental pump beam39. The model takes into account the thickness of the nanolaminate and therefore also the phase mismatch between fundamental and SH wave which becomes of importance for thick or very dispersive nonlinear films. However, the effect of multiple reflections inside the nanolaminate as well as inside the glass substrate at both the fundamental and SH frequency are neglected due to the small index difference. In addition, the small birefringence of the nanolaminate is neglected. Also, the formalism does not take into account the SH wave that is generated by the second-order nonlinearity of the substrate-air interface. For the p/s-polarized peak SH power which is generated in the sample the following expression is derived
To determine the second-order nonlinearity of a sample the s- and p-polarized SH power is recorded as a function of the polarization of the fundamental beam φ for a fixed angle of incidence. The detected s- and p-polarized SH power are fitted simultaneously with the theoretical expressions presented in Eq. 4, where the three independent tensor elements of χ(2) are the corresponding fitting parameters. The parameter α is determined in an independent Maker fringe measurement of a Y-cut quartz crystal with known second-order nonlinearity of 47. This is done immediately after the χ(2) measurement on the nanolaminate in order to avoid the influence of possible laser fluctuations.
Lastly, the Maker fringe reference measurement on a Y-cut quartz plate that is necessary for the determination of the quantity α in Eq. 4 is briefly discussed. To validate the stability of the calibration measurement and the corresponding fit, a set of Maker fringe measurements is performed, see Supplementary Fig. S2. The fitting results vary by less than 1% for consecutive measurements. Therefore it can be assumed that the calibration technique does not introduce any significant error.
In summary, both χ(2) measurement techniques represent attractive alternatives to the traditional Maker fringe technique if thin film samples are investigated. For thin films generating high levels of SH power with negligible interference from the substrate, the KIT technique is very well suited. On the other hand, the UGent technique is the technique of choice when very thin and weakly nonlinear films are investigated, provided that a reliable measurement of the backside nonlinearity is available. Because of the interesting application perspectives of nonlinear thin films in photonic integrated circuits, the use of reliable χ(2) measurement techniques is of considerable importance to the research community.
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