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note
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-3, d = 100 nm) of the structure facilitates lateral current spreading.
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34
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note
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2O = 1:1:10 for several minutes at room temperature.
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35
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note
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The rim of the top contact pad has the same distance from the edge of the laser disk (with a small variation of ≈5%) for each laser, in all directions Φ and at all deformations ε. The cylinder lasers have been fabricated with their long diameter oriented in 0°, 45°, and 90° relative to the major orientation of the semiconductor crystal. Finally, the processing leaves the surface clean without evident sources of surface roughness scattering. These precautions ensure that no additional directionality is introduced into the system other than through the flattened quadrupolar shape.
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The maximum peak power is a widely accepted valid measure of the power performance of semiconductor lasers because it refers to the actual useful power. In the QC laser the peak optical power is reached when the material gain decreases mainly as a result of two effects: the loss of optimum alignment of the ground state of the injector with the upper level of the laser transition with increasing voltage (39); and thermal population of the lower laser level with increasing current density. Therefore the peak power is primarily insensitive to size effects (when normalized to the unit area or volume).
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37
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note
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There is no strong theoretical basis for an "exponential" power increase, in particular because it is based on several different effects and is far-field dependent. Nevertheless, we chose the term "exponential" increase, because it represents the data qualitatively well.
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38
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2642695346
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note
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The continuity conditions at the boundary cannot be satisfied for real values of the wavevector if there is no incident wave, so one looks for solutions with complex wavevectors. It can be shown that the real part of these solutions gives the wavevector at which scattering resonances would occur for a wave incident from infinity, whereas the imaginary part gives the width (Q value) of the resonance. In a scattering experiment, the measured intensity in the far-field has contributions both from the resonant scattering and the incident beam, whereas in lasing emission only the resonant emission is present. Hence, it is the intrinsic emission pattern of the quasi-bound state that is measured in the experiments reported, above and it is this quantity that we plot in Fig. 3, B and D. See (13), chap. 1, for a detailed discussion.
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The Husimi function is the squared overlap of the interior electric field with a minimum-uncertainty wavepacket centered on a given point in the surface of section. It may be roughly interpreted as a phase-space probability density for the photons in the mode. A precise definition is given in P. LeBoeuf and M. Saraceno, J. Phys. A Math. Gen. 23, 1745 (1990).
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2642696421
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note
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In a generic period-doubling bifurcation, the shorter orbit becomes unstable as a new stable orbit with twice the period is born. Here, as a result of the symmetry, the shorter (diametral) orbit just reaches marginal stability, the three orbits described in the text are born, and the diametral orbit immediately restabilizes. This is consistent with the Poincaré index theorem because an even number of stable and unstable fixed points are created in this process.
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50
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We may regard the bow-tie resonances as associated with a four-mirror resonator defined by the tangents to the points of contact of the bow-tie orbit. Some general properties of these modes can be derived from this point of view, which will be presented elsewhere.
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note
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We are grateful to A. Tredicucci for useful discussions. E.E.N., J.U.N., and A.D.S. gratefully acknowledge support from the Aspen Center for Physics for part of this work. The work performed at Bell Laboratories was supported in part by DARPA (Defense Advance Research Project Agency)-U.S. Army Research Office under contract DAAH04-96-C-0026. The work performed at Yale was supported in part by NSF grant PHY9612200.
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