Computing the transmission loss in a misaligned open resonator with spherical mirrors

1967 ◽  
Vol 7 (3) ◽  
pp. 291-292
Author(s):  
E. I. Vitkin
Keyword(s):  
Transmission Loss ◽  
Open Resonator ◽  
Spherical Mirrors

A variational approach to the theory of the open resonator

1972 ◽  
Vol 329 (1577) ◽  
pp. 153-169 ◽  
Keyword(s):  
Resonant Frequency ◽  
Variational Approach ◽  
Open Resonator ◽  
Wave Theory ◽  
Variational Calculation ◽  
Beam Waist ◽  
Beam Wave ◽  
Inherent Error ◽  
Spherical Mirrors

A variational calculation of tho resonant frequency of an open resonator with spherical mirrors is used to establish the accuracy of the beam-wave theory of such resonators. It is concluded that the inherent error of the beam-wave formula for resonant frequency is of the order of (kw 0 ) -4 , where w 0 is the scale radius of the beam waist. This result is confirmed by experiment.

Measurement of permittivity by means of an open resonator. I. Theoretical

1982 ◽  
Vol 380 (1778) ◽  
pp. 49-71 ◽  
Keyword(s):  
Dielectric Material ◽  
Open Resonator ◽  
Variational Formula ◽  
Dielectric Materials ◽  
Companion Paper ◽  
Radius Of Curvature ◽  
Complex Source ◽  
Spherical Mirrors ◽  
Diffraction Effects ◽  
Plane Slab

The objective of this paper is to provide a reliable theoretical foundation for the open-resonator method of measuring permittivity and loss-tangent of dielectric materials. From an exact solution of Maxwell’s equations obtained by means of the complex-source-point method, simplified formulae for the six Cartesian components of the electromagnetic field are obtained. These are then used in a variational formula to obtain an accurate formula for the resonant frequency of an open resonator with spherical mirrors (of equal radius of curvature) having a parallel-plane slab of dielectric material located centrally between the two mirrors. It is assumed that the mirrors are sufficiently large for diffraction effects to be negligible. In the following companion paper II, experimental results are presented which verify the accuracy, within the usual limits of practical measurement, of the simple correction formulae deduced here.

Compound-Mirror Open Resonator

1973 ◽  
Vol 51 (13) ◽  
pp. 1409-1415
Author(s):  
John W. Y. Lit ◽  
Pierre Lavigne ◽  
Réal Tremblay
Keyword(s):  
Matrix Method ◽  
Open Resonator ◽  
Theoretical Method ◽  
Diffraction Loss ◽  
Field Distributions ◽  
Fabry Perot ◽  
The Matrix ◽  
Spherical Mirrors ◽  
Open Resonators

Open resonators with compound end mirrors (spherical mirrors with the central portions replaced by plane mirrors) have been theoretically analyzed by the matrix method. The diffraction loss of such a compound-mirror resonator depends very much on the relative sizes of the plane and curved mirrors. It can be made very much lower or higher than the equivalent Fabry–Perot resonator. Field distributions are examined and a summary of the theoretical method is also given.

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