Vertical cavity surface emitting lasers (VCSELs) are the key laser sources in the high-performance computers (HPCs) and data centers (DCs). The explosive growth of data traffic in the HPCs and DCs requires increased bandwidths of VCSELs. In this paper, we deduce the Time-Delay (T-D) model considering the multiple round trips of light in VCSELs with an optical feedback cavity to enhance the modulation bandwidth. The T-D model is suitable for the VCSEL with an arbitrary optical feedback intensity. The influences of the round trip time m of light in the optical feedback cavity on the intensity-modulation responses with strong and weak optical feedback are studied. The feedback coefficients considering the multiple round trips of light in the optical feedback cavity and the dispersions of the distributed Bragg reflector are deduced, and are suitable for the arbitrary optical feedback intensity. The feedback coefficients are influenced by the value of m and the optical feedback intensity, and decrease as the value of m under arbitrary optical feedback intensity increases. The feedback coefficients under strong optical feedback are larger than that under weak optical feedback with the same value of m. The theories are useful for the high-speed VCSELs with optical feedback.
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