Measurement of the Index of Refraction of a Flat Zinc Germanium Phosphide Wafer in the Infrared

We have developed and tested a novel application of interferometry to determine the absolute refractive index of individual infrared materials having flat and parallel surfaces without alteration of the sample in any way, and measured no for ZnGeP2

Application of Hertz Vector Diffraction Theory to the Diffraction of Focused Gaussian Beams and Calculations of Focal Parameters

Hertz vector diffraction theory is applied to a focused TEM00 Gaussian light field passing through a circular aperture. The resulting theoretical vector field model reproduces plane-wave diffractive behavior for severely clipped beams, expected Gaussian beam behavior for unperturbed focused Gaussian beams as well as unique diffracted-Gaussian behavior between the two regimes. The maximum intensity obtainable and the width of the beam in the focal plane are investigated as a function of the clipping ratio between the aperture radius and the beam width in the aperture plane

Large nonlinear absorption and refraction coefficients of carbon nanotubes estimated from femtosecond Z-scan measurements

Nonlinear transmission of 80 and 140 femtosecond pulsed light with $0.79 \mu m$ wavelength through single walled carbon nanotubes suspended in water containing sodium dodecyl sulphate is studied. Pulse-width independent saturation absorption and negative cubic nonlinearity are observed, respectively, in open and closed aperture Z-scan experiments. The theoretical expressions derived to analyze the z-dependent transmission in the saturable limit require two photon absorption coefficient $\beta_0\sim$ $1.4 cm/MW$ and a nonlinear index $\gamma \sim -5.5 \times10^{-11} cm^2/W$ to fit the data.Comment: 10 pages, 2 figures. Accepted and to appear in Applied Physics Letter

Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers

We present a method to independently measure the refractive index and the thickness of materials having flat and parallel sides by using a combination of Michelson and Fabry-Perot interferometry techniques. The method has been used to determine refractive-index values in the infrared with uncertainties in the third decimal place and thicknesses accurate to within Ϯ5 m for materials at room and cryogenic temperatures. © 2005 Optical Society of America OCIS codes: 120.2230, 120.3180, 120.4290, 160.4760. The refractive index, n, and the thermo-optic coefficient, dn͞dT, of materials are often determined by one's interferometrically measuring the phase change that light undergoes in passing through a plane-parallel slab of the material. Because the phase change depends on the value of n as well as the slab thickness, d, to obtain accurate values of n and dn͞dT, it is important to know d accurately. FabryPerot etalon interferometry has been used to optically measure d, 5 but the precision of thickness measurements with this method is limited by the precision of the known refractive-index value. Recent research by Coppala et al. 6 demonstrated that independent values for n and d can be obtained with interferometry and a continuously tunable laser source. In this paper we demonstrate that the Michelson and the Fabry-Perot interferometric methods can be used sequentially to determine independent and absolute values of both the material's thickness and the material's refractive index over a wide range of temperatures of practical interest. The method does not require that either quantity be initially well known. With this method, both n and d can be determined by use of a fixed-wavelength laser source. First, by use of data from both experiments, the material's physical thickness is determined. Then the thickness value is used to determine the material's refractive index (and thermo-optic coefficient) with either of the interferometric methods. We present experimental verification of this method by measuring n and d for a range of common infrared materials at both room temperature and cryogenic temperatures. The intensity of a coherent collimated beam of light transmitted by a plane-parallel transparent plate is given by the Airy formula 7 : where I o is the incident intensity, r is the reflection coefficient for the electric field, and f is the phase difference accumulated by the light beam in a double traversal through the plate. As the sample is rotated in the path of the laser light, the net transmitted intensity will modulate owing to the changing phase, f . The angle-dependent phase difference between subsequent transmitted light paths through the sample is given by 7 f () ϭ 4nd cos t ϭ 4d ͙n 2 Ϫ sin 2 , where d is the sample thickness, is the laser wavelength, t is the angle of refraction, and is the angle of incidence of the laser path with respect to the normal of the sample surface

Variation in brachial plexus formation, branching pattern and relation with major vessels

Background: Anatomical variations in the formation, branching pattern and relations of the brachial plexus have been described in humans by many authors; however these have not been extensively catalogued. The aim of the study was to describe variations in brachial plexus formation, branching pattern and relation with major vessels.Methods: This study included thorough dissection of 60 brachial plexuses which belonged to 30 cadavers (male: female ratio = 28:02 ) with age range of 20-60 years, obtained from the Department of Anatomy, College of Medical Sciences (CMS-TH), following standard guidelines. Results: Out of 60 limbs dissected in present study, the variation in formation was found in 20 limbs (33.3%), out of which 12 limbs (20%) had variations in the trunk and 8 limbs (13.3%) had variations in the cord, remaining 40 limbs (66.6%) were normal in the formation of brachial plexus. Normal branching pattern of the posterior cord was encountered in 52 (86.67%) limbs, the remaining 8 (13.33%) being variants in one form or the other. The upper subscapular nerve, the thoracodorsal nerve, the lower subscapular nerve and the axillary nerve were found to arise normally in 91.66%, 96.66%, 96.66% and 98.33% of the limbs respectively.Conclusion: The present study carried out on adult human cadavers revealed some rare variations in the formation, branching pattern and relations of the brachial plexus. These variations are of clinical significance for the surgeons, radiologists and the anesthesiologists.

Spectral and temperature dependence of two-photon and free-carrier absorption in InSb

The nonlinear absorption spectrum of InSb was measured using a combination of tunable similar to 160 fs, similar to 10 ps, and similar to 150 ns IR sources along with a cryostat for controlling the sample temperature to vary the band gap energy from 0.17 to 0.23 eV. The measured nonlinear optical properties in InSb are consistent with those predicted by the models which include two-and three-photon absorption (2PA and 3PA), multiphoton generated free-carrier absorption (FCA) and various recombination mechanisms. Temperature-dependent Z-scan and nonlinear transmission measurements yield information on the temperature and spectral dependence of 2PA, FCA, and carrier recombination processes of Shockley-Read-Hall, and Auger mechanisms. We find good agreement between the measured and the modeled nonlinear properties is possible only when the recently predicted temperature dependence of the FCA is considered. The wavelength-and temperature-dependent 2PA and 3PA coefficients in InSb were experimentally obtained. The inferred values of the 2PA and 3PA are consistent with the scaling rules of a simple two-parabolic band model. We further determine recombination rates from nonlinear transmittance of nanosecond pulses of CO2 laser