Realizing that vertical cavity surface emitting lasers (VCSELs) are continuously breaking higher bandwidth limits, it is essential to understand their basic material constituting properties and extract their physical characteristics, in order to fine tune their high-speed performance. Throughout the past decade, the device performance was continuously optimized towards higher bandwidths, faster data rates, and efficient operation. Therefore, for a successful further optimization of their dynamic characteristics, the extraction of a reliable set of their physical parameters becomes indispensable. Consequently, the main objective of this work is to provide accurate physical parameter values of cutting-edge high-speed VCSELs. The extraction process of these set of parameters is based on the novel intrinsic and extrinsic dynamic models that were recently developed by our research group. For the intrinsic dynamics, the advanced split carrier reservoir multimode model is employed. Furthermore, the pure intrinsic modulation response is de-embedded from the total measured device response using our recently proposed novel parasitic-network model. Moreover, the extraction of these device physical parameters is based on the device’s performance indicators, such as the relaxation oscillation frequencies and damping coefficients obtained by fitting the intrinsic model to the measured modulation data. Furthermore, since these performance indicators can be expressed in terms of a combination of these physical parameters, a precise estimation of their values and their possible ranges, along with a carefully designed fitting process, is crucial. Consequently, for extracting a reliable set of data, the accurate prior estimation of these parameters was conducted based on the device physical structure and reported material properties, leading to the establishment of an accurate set of parameters along with their possible ranges. These final calculations are based on simple device geometrical considerations, reported physical and material properties and device static performance measurements. Finally, the estimated values and their ranges are further validated by comparing them to ones in standard literature.
An innovative model to describe the small-signal modulation response of high-speed multi-mode vertical-cavity surfaceemitting lasers (VCSELs) is presented. Using an advanced theoretical approach, multi-mode rate equations for these VCSELs are established. Moreover, in order to characterize the dynamic performance, a comprehensive analytical fitting function based on this novel approach is derived. This allows the extraction of consistently expanded figures of merit for these laser devices. The main concept of our novel approach is based on carrier reservoir splitting. This is a result of numerous effects such as mode competition and spatial hole burning (SHB). Furthermore, compared to other standard approaches, our novel model includes the effects of carrier diffusion, gain compression and inhomogeneous current injection. Beside the traditionally extracted figures of merit, this model gives insight into photon lifetime and the local distribution of the injection current.
To establish highly performing vertical cavity surface-emitting lasers (VCSELs), it is essential to have an adequate understanding of the intrinsic laser dynamics of these devices. However, this is done while bearing in mind that extrinsic parasitic elements in VCSELs play an important role in limiting the intrinsic modulation bandwidth. Compared to largesignal analyses, the small-signal modulation response of a VCSEL can be isolated from the entire system, thus providing accurate information on the intrinsic laser dynamics. An alternative approach to that of using the rate equations is to transform theses rate equations to an equivalent circuit model. In this work, we firstly present advanced electrical circuit modeling of the intrinsic dynamic performance of multi-mode VCSELs, for the case where lasing modes do not share a common carrier reservoir. The electrical circuit model is derived from innovative advanced multi-mode rate equations that take into account the effect of spatial hole burning, gain compression, and inhomogeneity in the injection current. Secondly, we analyse different electrical parasitic equivalent circuit models in the aim of comparing them and selecting the one that can best describe and represent the physical properties of our high-performance VCSELs. Through measuring the microwave reflection coefficient S11(f) and fitting it into the calculated counterpart from the equivalent-circuit impedance model, the parasitic components of the equivalent circuit model are extracted.
To establish highly performing vertical cavity surface-emitting lasers (VCSELs), it is essential to have an adequate understanding of the intrinsic laser dynamics of these devices. However, this is done while bearing in mind that extrinsic parasitic elements in VCSELs play an important role in limiting the intrinsic modulation bandwidth. In this work, we analyse different electrical parasitic equivalent circuit models in the aim of comparing them and selecting the one that can best describe and represent the physical properties of our high-performance VCSELs. Through measuring the microwave reflection coefficient S11(f), then fitting it with the calculated one from the equivalent circuit impedance model, the parasitic components of the equivalent circuit model can be extracted. The S11(f) data was collected over different ranges of operating bias currents and using a 7 μm oxide aperture diameter VCSEL. This allows us to observe the variations of these circuit elements with respect to the current and compute the transfer function and the resulting parasitic cut-off frequencies (bandwidth limitation) for each model. After plotting and comparing the transfer functions of the different models together, under the same driving current, it was found that the discrepancy between the two curves, in a specific frequency range, is rather small over the VCSEL bandwidth of interest, hence allowing us to use the first-order low pass filter to de-embed the parasitic contributions and separate them from the device intrinsic response. However, over higher frequency ranges, the deviation is found to be substantial and the extract parasitic transfer function should be taken into consideration.
Another issue to be addressed is the reliability of the simple circuit models to extract accurate circuit component values, especially when the deviation between the measured microwave reflection coefficient S11(f) and the fitted model is substantially large. This discrepancy is due to the oversimplification imposed on the equivalent circuit model, leading to a high level of uncertainty in the extracted circuit component values. Thus, sufficient modelling and accurate fitting strategies are needed for a reliable parasitic de-embedding approach.
Vertical-cavity surface-emitting lasers (VCSELs) have emerged as a pioneering solution for many high-speed data communication challenges. Compared to large-signal analyses, the small-signal modulation response of a VCSEL can be isolated from the entire system, thus providing accurate information on the intrinsic laser dynamics. An alternative approach to that of using the rate equations is to transform theses rate equations to an equivalent circuit model. The dynamic operation characteristics including the device-circuit interaction can then be modeled and optimized using a circuit simulation software. Until now, it was assumed that the dynamic behavior of oxide-confined multi-mode VCSELs can be modeled using the single-mode rate equations developed for edge-emitters, even though the deviation between the single-mode based model and the measured data is substantially large. Furthermore, equivalent electrical circuit modeling of the VCSELs’ intrinsic dynamics was only done by modeling derived from the single-mode rate equations. Therefore, a new electrical circuit model, that can accurately describe the dynamic behavior of these VCSELs, is needed. In this work, electrical circuit modeling of the dynamic performance of multi-mode VCSELs, for the case where lasing modes do not share a common carrier reservoir, is presented. The electrical circuit model is derived from innovative advanced multi-mode rate equations that take into account the effect of spatial hole burning, gain compression, and inhomogeneity in the carrier distribution. The validity of the model is affirmed through experimental data fittings and plots of their modulation response are presented.
Vertical-cavity surface-emitting lasers (VCSELs) have emerged as a pioneering solution for many high-speed data
communication challenges. Therefore, higher bandwidth optical interconnects with data rates in the range of 100 Gbit/s
require directly modulated VCSELs with ultimate speed ratings. The small-signal modulation response of a VCSEL can
be isolated from the entire system, thus providing accurate information on the intrinsic laser dynamics. Until now, it is
assumed that the dynamic behavior of oxide-confined multi-mode VCSELs can be fully modeled using the single-mode
rate equations developed for edge-emitters, even though the deviation between the single-mode based model and the
measured data is substantially large. Using an advanced theoretical approach, rate equations for multi-mode VCSELs
were developed and the small-signal modulation response of ultra-high speed devices with split carrier reservoirs
corresponding with the resonating modes were analyzed. Based on this theoretical work, and including gain compression
in the model, the analyzed VCSELs showed modulation bandwidth around and exceeding 30 GHz. The common set of
figures of merit is extended consistently to explain dynamic properties caused by the coupling of the different reservoirs.
Furthermore, beside damping and relaxation oscillation frequency, the advanced model, with gain compression included,
can reveal information on the photon lifetime and highlights high-speed effects such as reduced damping in VCSELs due
to a negative gain compression factor.
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