Polarization component method for calculation of the multiple-frequency lasing regime

Abstract

We have shown that the polarization component method can be extended to the case of broadband emission (multiple-frequency approximation) if we make the approximation of slowly varying amplitudes and statistical independence of the polarization components. From the results of numerical modeling for the case of a liquid dye laser, it follows that the multiple-frequency approximation is meaningful to use for analysis of the spectral, polarization, and energy parameters in the region near and below the lasing threshold, and also for the statistical characteristics but taking into account saturation effects for the laser emission.Introduction. In a series of papers [1-5], a new generalized approach was proposed and developed to describing the formation of polarized radiation in laser systems. It was based on the idea of laser emission as the superposition of polarization components whose polarization vectors span the entire set of possible polarized states. Based on the polarization component method, it was possible to explain a number of characteristic features on the energy and polarization characteristics of a liquid dye laser near the lasing threshold [1,2,5], and also to derive analytical relationships to describe their statistical properties [4]. In particular, distribution functions of the degree of polarization of the output radiation were found [4], and their variation as a function of the laser system parameters was studied. Based on the polarization component method, it was possible to quite correctly describe the appearance of the complex phase polarization structure of liquid dye laser radiation observed in the experiment [6,7]. We should note that, although initially the polarization component method was developed with an aim toward liquid dye lasers, it has been demonstrated that it can be used to analyze dynamic states in the polarization instability region in VCSEL systems [8].However, the developed polarization component method involves two aspects which considerably limit its applicability as a general approach to describing formation of polarized radiation in laser systems. The first aspect is connected with the single-frequency approximation, the basis for all subsequent conclusions. Generally speaking, such an approximation is widely used in laser theory, including to describe polarization effects [9]. At the same time, within the polarization component method, the process of formation of laser emission is described as successive enhancement of spontaneous emission, so taking into account the spectral composition of the latter seems quite reasonable. Furthermore, it has been shown [10-12] that, for example, in semiconductor injection lasers, we need to take into account enhanced luminescence in principle for correct determination of threshold and dynamic characteristics.A second limitation of the developed approach was neglect of laser intensity saturation effects, which considerably simplified the calculations and made it possible in principle to construct analytical expressions for the distrib...

Dynamics of polarization switching in single-mode injection semiconductor lasers

“…In particular, detailed studies of the statistical characteristics of a dye laser based on the PCM have shown [24] that the dispersion in the distribution functions for the individual polarization components can be an order of magnitude greater than that for the total intensity. Something similar is also observed in multimode semiconductor lasers [25], where the dispersion in the distribution functions for the individual modes is considerably greater than that for the total intensity. The difference in the magnitudes of these effects compared to the results obtained using the SFM can now be understood since, in the latter case, there are only two independent polarization modes.…”

Polarization switching in single-mode injection semiconductor laser

“…This approach (the polarization component method) turned out to be especially effective in the region near the lasing threshold, where the standard polarization mode method is not generally workable [21,22]. Later it was shown [23] that the polarization component method can be used for describing the formation of polarized radiation in semiconductor lasers. Thus, it seems fully logical to use the polarization component method for describing polarization switching effects in semiconductor lasers, since, in the polarization switching region, owing to the equality of the difference in the gain and loss coefficients for waves with different polarizations, it is hardly possible to justify the concept of a "polarization mode" because of its instability.…”

“…The polarization component method is discussed in detail elsewhere [21][22][23], so here we shall only discuss some key points to be used in constructing the theoretical model. In the polarization component method the field E(z, t) of a plane wave propagating along the z axis is written in the form of a superposition of polarization components:…”