Analytical calculation of the relative intensity noise of multitransverse mode vertical-cavity surface-emitting lasers

摘要

Relative intensity noise spectra of weakly index guided VCSELs in a multi-transverse mode regime are analytically obtained. Analytical expressions incorporate the spatial dependence of electrical field and carrier density profiles. Expressions are derived for single and two-mode operation. We show that single-mode noise spectrum depends on the spatial mode profile through a modal effective volume. Two-mode noise spectra also incorporate the dependence on the degree of spatial overlapping between the modes. Two resonance peaks appear in the noise spectra of the individual modes and total power of the two-mode VCSEL. We analytically show that those peaks appear at frequencies that correspond to the relaxation oscillation frequencies of the multimode laser.