Algebraic expressions for the polarisation response of spin-VCSELs

Closed-form expressions are derived for the relationship between the polarisation of the output and that of the pump for spin-polarised vertical-cavity surface-emitting lasers. These expressions are based on the spin-flip model (SFM) combined with the condition that the carrier recombination time is much greater than both the spin relaxation time and the photon lifetime. Allowance is also included for misalignment between the principal axes of birefringence and dichroism. These expressions yield results that are in excellent agreement both with previously published numerical calculations and with further tests for a wide range of parameters. Trends with key parameters of the SFM are easily deduced from these expressions.