Polarization statistical properties of the emission from the single mode Vertical-Cavity Surface-Emitting Lasers with the equally living laser levels

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The full quantum-statistical theory of the Vertical-Cavity Surface-Emitting Laser (VCSEL) in the form of the Langevin equations is constructed for arbitrary relations between the frequency parameters. The same theoretical treatment as in Ref.[1,2] are used. For detailed analysis the theory is applied for lasers with equally living laser levels and on this basis the analytical expressions for the spectral densities of the Stokes parameter fluctuations are obtained in the explicit dependence on the physical phenomena, including the spin-flip and the optical anisotropy. It is demonstrated the arbitrary distribution of electrons between the sub-levels under pumping does not restrict a possibility to achieve the noise reduction below the quantum limit. Under comparison with phenomenological treatment Ref.[3] it is shown this approach turns out to be not quite satisfied.