Small-signal analysis of a slow-light VCSEL amplifier is introduced using a traveling-wave rate equations model. Theoretical calculations show that the small-signal optical modulation bandwidth of the slow-light mode has strong dependences on the slowdown factor and length of the amplifier; it can be boosted to more than 50 GHz.
We develop a simple model for the slow lights in Vertical Cavity Surface Emission Lasers (VCSELs), with the combination of cavity and population pulsation effects. The dependences of probe signal power, injection bias current and wavelength detuning for the group delays are demonstrated numerically and experimentally. Up to 65 ps group delays and up to 10 GHz modulation frequency can be achieved in the room temperature at the wavelength of 1.3 μm. The most significant feature of our VCSEL device is that the length of active region is only several μm long. Based on the experimental parameters of quantum dot VCSEL structures, we show that the resonance effect of laser cavity plays a significant role to enhance the group delays.
The slow light effect in SOAs has many applications in microwave photonics such as phase shifting and filtering. Models are needed to predict slow light in SOAs and its dependence on the bias current, optical power and modulation index. In this paper we predict the slow light characteristics of a tensile-strained SOA by using a detailed time-domain model. The model includes full band-structure based calculations of the material gain, bimolecular recombination and spontaneous emission, a carrier density rate equation and travelling wave equations for the input signal and amplified spontaneous emission. The slow light effect is caused by coherent population oscillations, whereby beating between the spectral components of an amplitude modulated lightwave causes carrier density oscillations at the beat frequency, leading to changes in the group velocity. The resulting beat signal at the SOA output after photodetection, is phase shifted relative to the SOA input beat signal. The phase shift can be adjusted by controlling the optical power and bias current. However the beat signal gain is low at low frequencies, leading to a poor beat signal output signal-to-noise ratio. If the optical input and SOA drive current are simultaneously modulated, this leads to forced population oscillations that greatly enhance the low frequency beat signal gain. The model is used to determine the improvement in gain and phase response and its dependency on the optical power, bias current and modulation index. Model predictions show good agreement with experimental trends reported in the literature.
An analytical expression for the delay-bandwidth product (DBP) of slow light in a vertical-cavity surface-emitting laser (VCSEL) is derived and experimentally confirmed. The expression and theoretical results show that the DBP has a maximum value, which is only dependent on the front facet reflectivity of the VCSEL. For a practical VCSEL with the front facet reflectivity exceeding 90%, the resulting maximum DBP is close to a fixed value of 0.64. The expression and the results are also verified by the measured DBP of a VCSEL with different bias currents.
The dependence of slowing light on the saturation effect in the vertical-cavity surface-emitting laser (VCSEL) is demonstrated. Combining the boundary conditions with the optical field distribution in VCSEL, the phase expression and the delay expression of the signal are derived. Based on these expressions and the rate equation, the relation between signal power and time delay is presented. Then the experimental demonstration shows the delays and the eye diagrams of a 2.5 Gbps pseudo-random binary sequence (PRBS) signal, when the VCSEL is working in the saturation condition. The theoretical and experimental results show that the high-power signal transmitted in the VCSEL could achieve better signal quality at the expense of the lower time delay. In order to obtain larger delay, on the one hand, the signal power should be controlled. On the other hand, the signal wavelength should be carefully adjusted to track the peak gain wavelength of the VCSEL caused by the saturation effect.
We present a theoretical study of the slow and fast light propagation in semiconductor optical amplifiers based on coherent population oscillations. By modulating the injection current to force the population oscillations we can modify the delay or advancement of light signals. Specifically, it is shown that the relative phase of the optical signal to the bias current modulations can be used as a knob for changing light propagation from delay to advancement. In addition, we analyze the effect of the modulation current for slow light in vertical cavity surface emission lasers (VCSELs) by taking into account the cavity effects. It is shown that the change of the depth of the modulation allows to tune the structural resonance, which in turn produces an enhancement of the delay.
We develop a model for the slow light in the vertical cavity surface emission lasers (VCSELs), with the combinations of cavity and the population pulsation effects. The dependences of pumping power, injection current and wavelength detuning for the group delays are demonstrated theoretically and experimentally. Up to 65 ps group delays and up to 10 GHz modulation frequency can be achieved in the room temperature at the wavelength of 1.3 mum. Based on the experimental parameters of quantum dot VCSEL structures, we show that the resonance effect of laser cavity plays a significant role to enhance the group delays.