Cascaded χ(2) nonlinearity in QND measurement

 QND measurement schemes often use Kerr nonlinearity to couple the intensity fluctuations of the signal beam to the phase fluctuations of the probe beam by means of the cross-phase modulation effect. Such schemes use materials with intrinsic χ⁽³⁾nonlinearity. However, it has already been shown that Kerr-effect-like correlation between two light waves may be achieved through cascaded χ⁽²⁾: χ⁽²⁾ processes. The value of the nonlinearity induced by cascading χ⁽²⁾ can, in many cases, be much higher than fibre χ⁽³⁾. The authors point out the possibility of using the cascaded χ⁽²⁾ nonlinearity instead of intrinsic χ⁽³⁾ nonlinearity in the scheme which resembles the well-known photon number QND measurement scheme. The non-degenerate second-harmonic generation (SHG) with a large phase mismatch is considered. The harmonic wave influence on the measurements is shown. High QND measurement characteristics can be achieved with the use of an appropriate set of parameters. Received: 6 April 1996     

Eine Charakterisierung der Schwartzschen Distributionen

Ohne ZusammenfassungHerrn ProfessorGottfried Köthe zum 60. Geburtstag gewidmet     

The status of the Super-FRS at FAIR

The Super-FRS will be a large-acceptance two-stage superconducting fragment separator with three exit branches serving different experimental areas. Due to the high primary-beam intensity of up to 10¹² ions/s a challenging design of the target area and the components used in the first dipole Super-FRS is necessary. These efforts include high-power production targets, beam-dumps to catch the remaining primary beam, and radiation resistant magnets. In this contribution we summarize the recent developments on these issues.     

Optimal symplectic approximation of Hamiltonian flows

Long term simulations of Hamiltonian dynamical systems benefit from enforcing the symplectic symmetry. One of the several available methods to perform this symplectification is provided by the recently developed theory of extended generating functions. The theory offers an infinite supply of generator types that can be used for symplectification. Using Hofer's metric, a condition for optimal symplectification is given. In the weakly nonlinear case, the condition provides a generator type that, based on the limited information available on the system, in general gives optimal results.     

Kegelschnitte in desarguesschen Ebenen

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Lösung der linearen Differentialgleichung durch Transformation in einen Schiefkörper

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