Eﬀect of the spectral width on mode partition noise in multimode VCSELs Moncef B. Tayahi Author1a , Sivakumar Lanka Author2a , Jan Carstens Author3b , Lutz Hoﬀmann Author4b , a Aﬃliation1, Advanced Photonics Research Lab, EE dept., University of Nevada, Reno, Nevada, USA; b Aﬃliation2, EE dept., Chemnitz University of Technology, Chemnitz, Germany ABSTRACT The dependence of the mode partition noise (MPN) and the power penalty associated with it can be measured from the source spectral width. Our ﬁndings show that there is strong dependence of the carrier lifetime on the bit error rate degradation caused by MPN on the spectral width of the vertical cavity surface emitting laser (VCSEL). VCSELs with smaller spectral width (shorter carrier lifetime) exhibited smaller MPN induced power penalty. We found that the theoretical calculation of the power penalties caused by MPN from the carrier lifetime and the spectral width is in good agreement with the measured system penalties. Keywords: VCSELs, mode partition noise, source spectral width, power penalty. 1. INTRODUCTION High-speed vertical cavity surface emitting lasers (VCSELs) continue to be important in many applications such as gigabit Ethernet and optical backplanes. The interest in these low cost devices stem from some unique properties that VCSELs have compared with edge-emitting lasers. The main advantages of VCSELs are its low beam divergence, high-speed direct modulation, the ease of integration, and array design. In general, VCSEL based transmission links are loss limited at low speed, however as the bit rate increases the link becomes dispersion limited. The spectral width of the source is one of the most important parameters that determine the allowable bit rate length product. The combination of multimode VCSELs with wide spectral width and dispersive ﬁber induces a large power penalty due to mode partition noise. In this study, we investigate the dependence of the carrier lifetime on the spectral width and therefore the power penalty associated with MPN. We found that VCSELs with shorter spectral width have less power penalty induced by MPN. 2. MODE PARTITION ANALYSIS Previous studies for Fabry-Perot (FP) relied on the carrier lifetime as an important factor for characterizing the performance of high-speed lightwave transmission systems.1 Theoretically the carrier lifetime can be calculated if one knows the doping concentration of the undoped active layer; however, measurement of the doping concentration is diﬃcult and cumbersome especially in packaged devices. In our approach we used the well known electrical modulation technique.2 At the threshold, the carrier lifetime can be determined by measuring the damping factor as function of power using a parasitic free electrical modulation scheme. By plotting the measured damping factor at various electrical biases currents, the carrier lifetime was obtained. Figure 1 shows the measured carrier lifetime using the method described above. This is an all-electrical technique which yields much more accurate results than the commonly used optical technique. This accurate carrier lifetime measurements allow for proper estimation of the threshold carrier density. The total carrier density in the ′ I active region is then found by integrating the current times the carrier lifetime, n(I) = 0 τe (I )dI which yield Figure 1. Measured and ﬁtted carrier lifetime Vs current bias Figure 2. Carrier lifetime Vs spectral width of diﬀerent VCSEL’s a carrier concentration of 3 ∗ 1018 cm−3 . Using traditional optical technique for the carrier density measurement, we would have overestimated the threshold carrier density by 36%. In order to study the relationship of the carrier lifetime to the spectral width of the VCSELs, we measured the carrier lifetime as previously described and plot the carrier lifetime for each VCSEL as a function of its respective spectral width. Six VCSELs were investigated: two were designed for 1 Gb/s transceivers, two other were Honeywell VCSELs with a bit rate capability of 2.5 Gb/s, and the last two VCSELs were designed for high speed operation up to10 Gb/s. Similar to edge emitting lasers, the cause for spectral width broadening in VCSELs is the increase in the carrier noise enhancement factor 1 + α2 where α is the so-called linewidth enhancement factor. The VCSEL linewidth is given by the modiﬁed Schawlow-Towns linewidth enhancement formula.3 Designing a narrow spectralwidth VCSELs is currently being explored for longer wavelengths sources as well as coherent sources. Further author information: (Send correspondence to M.B.A.) M.B.A.: E-mail: email@example.com, Telephone: 1 775 784 6103 S.L.A.: E-mail: firstname.lastname@example.org, Telephone: 1 775 784 6092 J.C.A.: E-mail: email@example.com, Telephone: 1 775 784 6092 L.H.A.: E-mail: firstname.lastname@example.org, Telephone: 1 775 784 6092 A straightforward method in decreasing the α factor is to increase the carrier concentration doping levels in the active region which increases the diﬀerential gain of the VCSEL. Moreover, a p-type doping of the carrier concentration will decrease the chirping width.4 3. MPN POWER PENALTY CALCULATION In multimode VCSELs, the dispersion induced power penalty caused by MPN is given as in equation 1.5 ∂mpn = −5log10 [1 − (Q.σmpn )2 ] , (1) where σmpn is the relative noise level of the received power in the presence of MPN, and Q is the Q-factor ( Q = 6, BER = 10−9 ). In a digital lightwave system the σmpn can be expressed as in equation 2.6 k σmpn = √ [1 − exp(−(ΠBLδλ D)2 )] , 2 (2) where where B, L, δλ , and D are the bit rate, the ﬁber length, the root mean square spectralwidth of the laser source, and is the ﬁber dispersion, respectively. The k factor is known as the mode partition noise coeﬃcient with values between 0-1. An accurate value of k is diﬃcult to measure and it is likely to vary from one VCSEL to another. Measured k values for edge emitters are in the range of 0.6 - 0.8.6 In VCSELs, a single longitudinal mode is supported in a cavity that can support multiple transverse modes. Transverse mode can have signiﬁcant diﬀerences in their coupling eﬃciency into a ﬁber. Therefore, mode selective loss is easily introduced and MPN noise becomes a dominant factor in the optical link. We expect the value of the k coeﬃcient to be dependant on the cavity size of the VCSEL, however; the rms spectralwidth and the carrier lifetime are also representative of the cavity size. Lasers with large cavity lase in many modes and have wider spectral width. Therefore, we expect that large cavity VCSELs will exhibit higher value for k. Until we measure this value accurately we are going to assume that k to be 0.5 which is an underestimation for VCSELs with large aperture and there is a possibility of overestimation for high speed VCSELs that are either single moded or have two modes at most. In the limit (πBLσmpn ) << 1, MPN has a square law dependence on the source spectral width. We used the above equations to calculate the power penalty due to degradation caused by MPN with a k coeﬃcient of 0.5. 4. CONCLUSION The eﬀect of the spectralwidth on the mode partition noise power penalty in multimode VCSELs has been investigated. It was found that VCSELs with shorter life exhibited a wider spectralwidth, and therefore less MPN power penalty. VCSELs with narrow spectralwidth (small aperture) are better suited for higher bandwidth length product applications compared to low bit rate VCSELs (large aperture). We used an estimated value for the k coeﬃcient; we are in the process of measuring it. To the best of our knowledge, the MPN k coeﬃcient in VCSELs has not been measured. REFERENCES 1. W. Cheng, and A. Chu, “The Dependence of Carrier Lifetime on Spectral Width in Multimode Semiconductor Lasers,” in IEEE Photonics Letters,vol 8, No 5 pp. 611–613, 1996. 2. C. H. Henry, “Theory of the linewidth of semiconductor lasers,” in IEEE. J. Quantum Electronics,vol 18, No 5 pp. 259–265, 1982. 3. L. A. Coldren and S. W. Corzine, Chapter 5 in Diode Lasers and Photonics Integrated Circuits, Wiley & Sons, New York, 1995. 4. G. P. Agrawal, P. J. Anthony and T. M. Shen, “Dispersion penalty for 1.3 lightwave system wit multimode semiconductor lasers,” in J. Lightwave Technol.,vol 6, pp. 620–625, 1988. 5. K. Ogawa, “Analysis of mode partition noise in laser transmission systems,” IEEE. J. Quantum Electron,” IEEE. J. Quantum Electronics,vol 18, pp. 849–855, 1989. 6. G. P Agrawal, Chapter 5 in Fiber Communication Systems, Wiley & Sons, New York, 1995.