Analysis of the cylindrical confocal laser resonator having a single circular coupling aperture

McNice, G. T.; Derr, V. E.

doi:10.1109/jqe.1969.1075711

Cited by 26 publications

(6 citation statements)

References 14 publications

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“…As the hole becomes larger, the mode structure becomes more complicated. For a confocal resonator, which has been extensively studied in the literature, the change of the mode profile as a function of the hole size is continuous [8]. However, for the case of the near concentric resonator, we have observed a discontinuous change in the mode profile.…”

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confidence: 59%

“…Confocal resonator was analyzed by McCumber [6] and Shennagel [7] using a perturbation technique, and by McNice and Derr [8] and Moran [9] using Fox-Li method. FabryPerot resonator was treated by Li and Zucker [10] and Yoshida et al [11].…”

Section: Introductionmentioning

confidence: 99%

“…The mode degeneracy here is similar to that found in the unstable resonator [15] . In fact, we conjecture that a near concentric resonator with holes becomes effectively an unstable resonator due to the additional focusing by the holes.In Fig.3, the total fractional power loss per round trip, the hole coupling efficiency defined to be the ratio of the useful loss through the hole to the total loss [8] and the number of the iteration required for the convergence are shown as a function of the hole radius. The evidence of mode 4 degeneracy is clearly seen at hole radius = 4 mm; Although the total loss is continuous, the coupling efficiency changes in a discontinuous step across this point.…”

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confidence: 99%

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Hole coupling resonator for free electron lasers

Xie

Kim

1991

Nuclear Instruments and Methods in Physics Research Section A:

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The performance of two mirror resonators with holes for output coupling is studied for free electron laser application using a Fox-Li type code. The mode profiles inside and outside the cavity, the diffraction losses at the mirror edges and apertures, the amount of useful power coupled through the hole, e.t.c., are calculated for the dominant mode for different hole and mirror dimensions. It is found that resonators in near concenoic geometry can develop a mode degeneracy in certain cases, which should be avoided for the stability of the free electron laser gain and output.A resonator configuration for a free electron laser at Lawrence Berkeley Laboratory was found which can provide satisfactory performance over a wavelength range from 25 to 50 microns. The possibility of further increasing the tuning range by an adjustable intracavity aperture is discussed. IntroductionAn infrared free electron laser (FEL) operating between 3 and 50 microns is being designed for the Chemical Dynamics Research Laboratory (CDRL) at Lawrence Berkeley Laboratory [1). In search for efficient, broadly tunable optical output coupling schemes for the CDRL-FEL, we are investigating resonators with a circular hole in the center of one of the end mirrors. This paper is a summary of our study so far on this subject.Hole coupling has been proven to be effective in the far-infrared region where dielecoic mirrors are not available. and an arbitrary set of intracavity apertures. In our numerical study we pay close attention to the issues important for FEL operation in a user facility: The intracavity mode profile should have a good overlap with the electron beam for efficient energy extraction; A sufficient fraction of the energy should be coupled out through the hole; The out coupled mode should be close to the free space Gaussian mode for an efficient transport to the experimental station; A single cavity configuration should cover as wide a wavelength range as possible to avoid a frequent change of sensitive optical components.In studying the resonators for the CDRL-FEL, it is found that the behavior of a hole coupling resonator in the near concentric geometry is somewhat different from those in the other stable configurations. Thus the mode profile across the hole remains more or less uniform, ensuring a good output coupling. Also, the mode can develop a degeneracy at a certain hole size.Avoiding the mode degeneracy is an important consideration for the design of a hole coupling resonator.The analysis in this paper is approximate in the sense that the effect of the FEL interaction 2 on the cavity mode has not been taken into account. Such effect is expected to be small when the saturated gain (which is equal to the total round trip loss) is small, as are the cases studied here. apertures at each end of the undulator, the aperture radius chosen to be the same as that of the bore. Calculation of the HoleWe expect the approximation to be adequate provided the loss at the undulator bore is small.However, we have not studied in detail t...

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confidence: 59%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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Hole coupling resonator for free electron lasers

Xie

Kim

1991

Nuclear Instruments and Methods in Physics Research Section A:

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“…As the input hole diameter is increased, there is a increase in , which is comparable to the loss through aperture 1. This effect has been noted by a number of researchers and demonstrates why the maximum coupling efficiency from a centered hole is approximately 50% [9], [10]. The increase in diffraction loss can be approximated as , provided that the input hole diameter is not too large.…”

Section: A Diffraction Theory Model Of Resonator Couplingmentioning

confidence: 75%

Cold tests and modeling of low-Q quasi-optical resonators

Fischer

Fliflet

2001

IEEE Trans. Microwave Theory Techn.

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Measurements are reported on low-open resonators at 85 GHz with a large centered coupling hole in each mirror. This is the first study of open resonators with large diffraction losses and efficient input coupling at millimeter wavelengths. The input resonator for a quasi-optical gyroklystron is described with quality factor = 2000 and 13% round-trip losses where approximately 65% of the incident power in the waveguide is coupled to the fundamental TEM 00 mode. Two models have been developed to calculate the coupling from the rectangular waveguide through a circular aperture into the open resonator. Both models properly account for the increased diffraction loss of the resonator when coupling apertures are present. Measured results are in reasonably good agreement with values calculated using both scalar diffraction theory and an equivalent-circuit model.

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“…The situation is different in the case of confocal resonator where the transition is smooth [4]. This is related to the fact that the phase advances for different radial modes are the same for a confoeal resonator, and thus a linear combination of the modes may also give a stable profile [5].…”

Section: ) O_tmentioning

confidence: 99%