Two-mode Vertical-cavity Surface-emitting Laser Research Articles

Modeling and simulation of VCSELs noise and its influence on noise performance of RF fiber links

Abstract In this paper, we present numerical simulations of the dynamics and noise of directly modulated vertical-cavity surface-emitting lasers (VCSELs) as primary light sources in RF links. Contribution of the VCSEL noise to the noise performance of the RF link is evaluated in terms of the noise figure. The VCSEL characteristics are investigated under a variety of conditions, including CW operation and sinusoidal modulation. Both single and two transverse-mode oscillations of VCSELs are studied. The obtained results show that the frequency spectra of the relative intensity noise exhibit peaks at the mode-competition frequency, the modulation frequency and the higher harmonics. The low-frequency level of relative intensity noise is minimum when the modulated VCSEL signal is continuous and uniform, but is pronounced when the signal is pulsing and non-uniform. The noise level of the two-mode VCSELs is almost 20 dB/Hz higher than that of the single-mode VCSEL. The noise factor of the fiber link decreases with the increase of both the modulation frequency and the depth. The contribution of the VCSEL noise to the noise factor of the fiber link is much greater than that of the photodiode.

External cavity mode structure of a two-mode VCSEL subject to optical feedback

We consider a multi-transverse-mode vertical-cavity surface-emitting laser (VCSEL) subject to optical feedback. The system is modeled by a partial differential equation for the spatial carrier population, which is coupled to delay differential equations for the electric fields of the participating transverse modes that are subject to external optical feedback. We consider here the case that the VCSEL supports the two basic, rotationally symmetric, linearly polarized optical modes LP 01 and LP 02. In our model each LP mode receives feedback not only from itself but also from the other LP mode; the amount of cross-feedback can be controlled by a parameter. Specifically, we use numerical continuation techniques to present a detailed analysis of the steady state, external cavity mode (ECM) structure in dependence on the feedback strength, the feedback phase and the amount of cross-feedback. This shows that the case of zero cross-feedback is degenerate and changes quite dramatically even in the presence of small feedback from the other transverse mode. On the other hand, in an intermediate range of cross-feedback the ECM structure does not change qualitatively in a physically relevant range of feedback strength. We consider the entire transition from zero cross-feedback to zero self-feedback, in which we identify the key changes in the ECM structure.

Static and dynamic characteristics of VCSELs with polarisation-selective optical feedback

Static and dynamic characteristics of birefringent vertical-cavity surface-emitting lasers (VCSELs) subject to both isotropic and polarisation-selective optical feedback are investigated theoretically. The model considers two orthogonally polarised transverse modes; moreover, the spatial dependences of photon density, carrier density and injection current are taken into account. For a short external cavity, the two-mode VCSELs can be forced to operate with one mode by introducing the polarisation-selective optical feedback. It is further shown that the phase of feedback light determined by the external cavity length affects the laser operation characteristics greatly, that is, when the external cavity length is chosen, the reflected light strengthens (weakens) the optical field in the laser cavity, the mode that has the same polarisation direction can be enhanced (suppressed), while the other mode is suppressed (enhanced) correspondingly. For a relatively long external cavity, the continuous wave operation of VCSELs is destabilised and rich non-linear dynamics are excited. By increasing the external cavity length, the VCSELs follow a period-halving route to chaos. It is also found that the evolution of dynamics shows periodic repetition with respect to the external cavity length, and the period is half of the lasing wavelength. Further investigation shows that, for isotropic feedback, both modes exhibit the same dynamics and similar mode intensity; for polarisation-selective feedback, though similar non-linear behaviours are observed, the modal strengths are quite different, that is, the feedback light enhances one mode while greatly suppressing the orthogonally polarised mode.

Demonstration of single-mode operation of a vertical-cavity surface-emitting laser with optical feedback: the intensity-noise-measurement approach

We study the effect of polarization and frequency-selective feedback on a two-mode vertical-cavity surface-emitting laser. By investigating the polarization and spatial properties of the intensity noise, we demonstrate single polarization and single-transverse-mode operation.

Theoretical calculation of relative intensity noise of multimode vertical-cavity surface-emitting lasers

An analytical calculation of relative intensity noise spectra of weakly index-guided vertical-cavity surface-emitting lasers (VCSELs) in a multimode regime is performed. We obtain analytical expressions that incorporate the spatial dependence of electrical field and carrier density profiles. Expressions are derived for single-mode and two-transverse-mode operation. Our analysis shows 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. Simple analytical expressions are also derived for noise spectra at zero frequency.

Optical injection dynamics of two-mode vertical cavity surface-emitting semiconductor lasers

Two-mode vertical cavity surface-emitting lasers (VCSELs) subject to external optical injection are investigated experimentally. The spectrum of a VCSEL with two parallel-polarized modes demonstrates significantly different behavior compared to that of a VCSEL with two orthogonally-polarized transverse modes. In the latter, external optical injection can be used to achieve single-mode operation. However, in the case of two parallel-polarized transverse modes, VCSEL single-mode operation cannot be obtained via optical injection. In this case, when the injection frequency is close to one of the modes, the coexistence of the injected beam and that mode gives rise to very rich dynamical behavior; however, the other mode is unperturbed by the optical injection.

Effects of transverse-mode competition on the injection dynamics of vertical-cavity surface-emitting lasers

We investigate theoretically the static and dynamic characteristics of an optically injected vertical-cavity surface-emitting laser (VCSEL), under both single- and two-mode operation. Our model includes the spatial dependence of both the carrier density and the optical field. We find that within the locking range, a two-mode VCSEL can be forced to operate in a single transverse mode under appropriate conditions. Outside the locking range, the VCSEL shows a rich variety of nonlinear dynamics. Results show that the static and dynamic behaviours depend strongly on the frequency detuning, the injection power and the strength of the intermodal coupling induced by spatial hole burning. In particular, strong intermodal coupling can reduce the sensitivity of the VCSEL toward external injection, in terms of both static (locking) and dynamic (nonlocking) behaviours.