Cavity linewidth

Consider a cubic cavity of length L and quality factor Q. Owing to the finite Q, the cavity exhibits some losses which yield a cavity linewidth Au) = w/Q. For a Lorentzian lineshape, the density of modes around a cavity mode of frequency and mode volume is given by... 

Chapter 1. Cavity Linewidth Controls with an Intracavity Three-level Atomic Medium... 

The Chapter is organized as follows. First the theoretical calculations with A -type three-level atoms in the optical ring cavity are described. The EIT-enhanced linear and nonlinear dispersions are calculated, and their effects to the cavity linewidth are discussed in different parametric regions. Second, various experimental observations are presented to demonstrate those interesting effects on cavity linewidth narrowing and broadening, as well as WLC. The last part serves as the summary with some discussions. 

Without the medium inside the cavity the phase shift is given by O = AA / c, where A = o)p-0 is the frequency detuning from the cavity resonant frequency 6)q and c is the speed of light in vacuum. The empty cavity linewidth [full width at half maximum (FWHM)] is... 

Drop the higher order terms, the cavity transmission intensity and the cavity linewidth can be written as... 

Checking Eq. (11), not only the eavity transmission linewidth ean be larger than the empty cavity linewidth (when< ) but it can also become infinite when 1 + //L n — 1) = 0 (actually it cannot be infinite due to the eontributions of the higher-order dispersions which have neglected here). This condition is if the medium fills the cavity (1=L). Otherwise, it is given in general by [17]... 

Fig. 9. Ratio of ElT-narrowed linewidth Av to the empty cavity linewidth (Av) measmed as a function of the couphng power for T = 87 °C. The solid curve is the fitting curve with the parameters y = 27Ty.4.0 MHz, y =27Tx3.2 MHz. Adopted from Ref [7],...

Fig. 11. Experimentally measured cavity linewidth as a function of the couphng laser power. The curve (a) is for = 7.4 mW (in the superluminal region) and curve (b) for = 2.7 mW (in the...

Fig. 12. Experimentally measured cavity linewidth versus the cavity input power. Dotted horizontal line corresponds to the empty cavity linewidth Squares are the linewidths measured. Inset "empty"...

Figure 12 shows the measured eavity trausmission liuewidth as a function of the cavity input power (which is proportional to / ). At the low cavity input powers (P < 5.6 mW), the cavity linewidth is less than the empty cavity linewith and is approximately IMHz as in the case of the linear case [7], As the cavity input power increases to about. 6 mW (corresponding... 

As increases further, (Av) goes back to the empty cavity linewidth and keeps there. 

Fig. 14. (a)Measured cavity linewidth as a function of coupling laser power at the "critical" intensity (the cavity input intensity satisfying WLC condition), (b) The appropriate coupling laser power for the cavity input power when the white-light condition is satisfied. Inset the corresponding linewidths measured for each point on Fig. 14 (b). Solid line is the best fit with a quadratic function. Adopted from Ref [17]. 

Wang H, Goorskey D, Burkett WH and et al. Cavity-linewidth narrowing by means of electromagnetieally indueed transparency. Optics Letters 2000 Dec 1 25(23) 1732-1734. 

Wu H and Xiao M. Cavity linewidth narrowing and broadening due to competing linear and nonlinear dispersions. Optics Letters 2007 Nov 1 32(21) 3122-3124. 

As one can see that this e-book has covered a broad speetrum of research topics from experimental demonstrations of EIT-related effects (such as cavity linewidth modification, phase-dependent interferenee, and optical storage) to several interesting theoretieal predictions (e.g. localization of atoms, quantum correlation, and tunable photonie bandgaps). Also, in the experimental demonstrations of atomic coherence effects, different multi-level media, such as hot atomic cell in an optieal cavity (Chapter 1), cold atoms in the magneto-optical trap (Chapter 2), and solid crystal at low temperature (Chapter 6), are used, which show the broad applicabihty of atomic coherence effects and their potential applications. 

From equation (13.6) it would appear that the intensity of radiation bouncing to and fro inside the laser cavity would increase indefinitely. This is an unphysical situation and occurs because we have so far neglected the effect of stimulated emission on the populations of the laser levels. As soon as oscillation commences, stimulated transitions start to reduce the inversion density below the value that it had in the absence of oscillation. In a time of the order of the inverse of the cavity linewidth, Au, a steady state is established in which the gain at the oscillation frequency is reduced to a value equal to that required to replace the cavity losses. This process is known as gain saturation. 

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