Comments on the equivalence of different integral equations formulated to describe the Fabry-Perot interferometer

Lotsch, H. K. V.

doi:10.1016/0031-9163(65)90397-5

Cited by 7 publications

(5 citation statements)

References 6 publications

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“…When x1 moves in the interval (-1,l) the contributions are the same over entire range and the FRESNEL Integral may be evaluated to a constant. Hence, the diffraction effects vanish in this limit and we are left with the simple H n Y a E N S Principle, [9]. This pict m , however, changes if F is large but finite.…”

Section: Asymptotic Expansionmentioning

confidence: 94%

“…The first-order approximation corresponds t o the geometrical-optics formulation and thus does not account for diffraction. The integral equations in the more familiar papers are identical t o this first-order approximation of (9) and hence, they discount diffraction effects. Those results and conclusions are therefore qnestionable since too small a value for the FRESNEL Number has seemingly been used.…”

Section: Asymptotic Expansionmentioning

confidence: 99%

“…The FRESNEL Integral of the kernel (8) represents the significant difference as compared to the more familiar formulations of the problem under investigation, [9] . The FRESNEL Integral accounts for the diffraction phenomenon due to the finite size of the mirrors.…”

Section: Asymptotic Expansionmentioning

confidence: 99%

“…The analysis presented ignores all the losses except the ones due t o diffraction. Note that we also neglect the diffraction losses if we ignore the second term with D in (9). This reduced integral equation…”

Section: Resonant Wavesmentioning

confidence: 99%

“…Thus, as xo m x2 become about f . l,i.e., close to the rim of the system, the second term with D gets significant in (9) and finally predominates. The reflectors coincide with a surface of constant phase close to the axis and here HELMHOLTZ'S Equation is solved by a standing-wave type ,,Ansatz".…”

Section: Diffraction Phenomenonmentioning

confidence: 99%

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The Fabry‐Perot Interferometer with a Large Fresnel Number

Lotsch

1965

Annalen der Physik

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The FABRP-PEROT Interferometer is investigated on the basis of the HUYGENS-FRESNELPrinciple. An integral equation is derived which describes its features when used as a laser resonator. An asymptotic expansion is given for a large FRESNEL Number. The first-order approximation describes the waves resonating between the mirrors. A formal solution is obtained which is consistent from the viewpoint of the diffraction theory. This solution reveals the most significant result that in the region close t o the axis the observable single mode patterns are in the form of parabolic cylinder functions. Thus, apart from an immaterial phase variation, the lowest-order eigenfunction associated with the resonating waves is a Gaussian and not a cosine function as is widely believed.The theoretical results presented are obviously in favorable agreement with the familiar experimental observations. They predict, for instance, the filamentary nature of the laser action in an imperfect ruby crystal. Inhaltsiibersich tDas FABRY-PEROT-Interferometer wird auf der Grundlage des HUYGEKS-FRESNELschen Prinzipes untersucht. Eine Integralgleichung wird abgeleitet, die seine Eigenschaften in der Anwendung als Laser-Resonator beschreibt. Eine asymptotische Entwicklung fur eine groBe FRESNEL-Zahl wird angegeben. Die Niiherung erster Ordnung beschreibt die zwischen den Spiegeln resonierenden Wellen. Eine formale Losung wird ermittelt. die im Einklang mit der Beugungstheorie steht. Diese Losung enthiillt das LuSerst wichtige Ergebnis, daS die Schwingungsformen in Achsennilhe durch die parabolischen Zylinder-Funktionen ausdriickbar sind. Demnach ist, abgesehen von einer unwesentlichen Phasenvariation, die niedrigste Eigenfunktion, welche die resonierenden Wellen beschreibt, eine GauBsche Funktion und nicht eine Kosinus-Funktion, wie es allgemein angenommen wird.Die theoretischen Ergebnisse sind augenscheinlich in guter Obereinstimmung mit den bekannten experimentellen Resultaten. Sie lassen zum Beispiel den f adenformigen Laser-Mechanismus in einem mit Fehlern behafteten Rubin-Kristall erwarten.

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Section: Asymptotic Expansionmentioning

confidence: 94%

Section: Asymptotic Expansionmentioning

confidence: 99%

Section: Asymptotic Expansionmentioning

confidence: 99%

Section: Resonant Wavesmentioning

confidence: 99%

Section: Diffraction Phenomenonmentioning

confidence: 99%

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The Fabry‐Perot Interferometer with a Large Fresnel Number

Lotsch

1965

Annalen der Physik

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On the integral equations for Fabry-Perot interferometer modes

Streifer¹

1965

Physics Letters

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Laser Interferometer for Repetitively Pulsed Plasmas

Hooper

Bekefi

1966

Journal of Applied Physics

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A three-mirror laser interferometer for measuring electron densities in repetitively pulsed plasmas is described and analyzed. The instrument has a sensitivity equivalent to a density of 1013/d cm−3, where d is the length of the plasma in centimeters. It has a time resolution of a few microseconds. The response of the laser intensity to a changing dielectric (e.g., plasma) is calculated in the quasistatic approximation, and the factors contributing to the finite time response are considered. The analysis applies to laser interferometers in general, as well as to the present instrument.

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Comments on the equivalence of different integral equations formulated to describe the Fabry-Perot interferometer

Cited by 7 publications

References 6 publications

The Fabry‐Perot Interferometer with a Large Fresnel Number

The Fabry‐Perot Interferometer with a Large Fresnel Number

On the integral equations for Fabry-Perot interferometer modes

Laser Interferometer for Repetitively Pulsed Plasmas

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