Quantenmechanische Berechung der Photonenzahl und Amplitudenfluktuation einer Laserstrahlung



From the quantum mechanical equations describing the laser we derive a system of two coupled equations which contains only b+b, b+bb+b and the fluctuation operators. If we introduce a distribution function for the eigenvalues of b+b which depends on the parameters n0 = 〈b+b〉 (average photon number) and equation image (amplitude fluctuation) and neglecting noise terms of higher order, then it is easily possible to calculate the quantum mechanical expection values given above and derive two equations which determine n0 and α for the stationary case. Below the threshold of laser action these equations then describes thermal light with an amplitude fluctuation equation image and a photon number n0. These results agree with that of other authors. The same holds also above threshold for the photon number, if we neglect correction terms of the order nmath image. For the amplitude fluctuation we obtain equation image and it is shown, that far above the laser threshold the relative amplitude fluctuation decreases with increasing pumping intensity and therefore increasing photon number. However, the relative amplitude fluctuation remains approximately constant also in the case of increasing photon number if the latter is achieved by varying such experimental parameters which also increase the number of spontaneous quanta.