Dimensionless quantities for the light field, and introduction of a coupling constant |
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Dimensionless quantities for the light field, and introduction of a coupling constant
In the following we shall introduce dimensionless variables bλ and bλ* instead of the mode amplitudes Eλ(+) and Eλ(-) respectively. The quantities Eλ and bλ differ by a simple factor only, namely
(1.1)
(1.2)
As one may show, the energy of an electric field with mode amplitude Eλ is proportional to |Eλ|2. On the other hand, in a quantum theoretical treatment h⍵λ is just the energy of a photon. Since bλ is dimensionless we recognize that |bλ|2 must have the meaning of a photon number, may be except for a numerical factor. As it will turn out later, |bλ|2 is precisely the average photon number. We shall elucidate this relation in a later chapter when dealing with the laser equations quantum theoretically. We then recognize that there always the combination ϑ21 uλ (xμ)occur s (or the conjugate complex quantity). Furthermore the factor occurs. In order to save space it suggests itself to replace this combination by a quantity which we define by
(1.3)
It is a rather simple but boring task to rewrite the laser equations by means of the new quantities just introduced. Therefore we shall write down the laser equations in the next section without any intermediate steps
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دراسة يابانية لتقليل مخاطر أمراض المواليد منخفضي الوزن
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اكتشاف أكبر مرجان في العالم قبالة سواحل جزر سليمان
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اتحاد كليات الطب الملكية البريطانية يشيد بالمستوى العلمي لطلبة جامعة العميد وبيئتها التعليمية
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