# Modulation Characteristics of High-Speed Transistor Lasers
## 3 Modulation Characteristics of TL
### Intracavity Photon-Assisted Tunneling
In microwave photonic links, the TL of the current modulation is similar to that of the traditional DML, and the modulation frequency cannot be higher than the relaxation frequency \(\rm f_{R}\) in practical applications. In contrast, although the bandwidth of the voltage modulation is small, the frequency response up to \(\rm f_{3}\) dB is flat. Therefore, voltage modulation may be more suitable for high-speed signal transmission than current modulation. Further, the input resistance of voltage modulation is higher than that of current modulation, which makes it easier to match with the external resistance. It must be noted that the conditions for the analysis are that the bias is different and the output power is the same. Current modulation is better than voltage modulation in resistance matching when current and voltage modulations are under the same bias conditions [66]. The bandwidth variation trend with respect to \(\rm I_{B}\) and \(V_{CB}\) under the two modulation schemes differs [67, 68]. In the current modulation process, as \(\rm I_{B}\) increases, the number of photons increases and the bandwidth increases. However, at large injections, the photon concentration is notably reduced owing to thermal effects, making it difficult to increase the bandwidth. In the process of voltage modulation, as \(V_{CB}\) increases, the modulation bandwidth decreases. Under high reverse-biased \(V_{CB}\), the photon density and modulation bandwidth are considerably reduced due to the significant FK absorption effect. In the analysis of the voltage modulation response curve, in addition to the inherent optical response, it is also necessary to consider the electronic transfer function of the optical response feedback; otherwise, it will lead to a large AC enhancement peak on the voltage modulation response curve [67]. The amplitude of the relaxation oscillation of the voltage modulation is greatly reduced after the introduction of the electron transfer function. According to [PERSON] et al. [69], under the same bias condition, the bandwidth in the voltage modulation case can reach more than 21.4 GHz, which can achieve a 30 Gb/s data transmission rate. In contrast, the bandwidth in the current modulation case is only 5.5 GHz, which can only achieve a 10 Gb/s data transmission rate. The voltage modulation of TL is more complicated than of the current modulation model due to FK absorption. Changes in the current \(\rm I_{B}\) and voltage \(V_{CB}\) cause chirp in the TL [70]. Although the chirp produced by current modulation is similar to the DML case, the chirp produced by voltage modulation is different. Changes in the FK absorption coefficient and the base refractive index cause chirping with the change in \(V_{CB}\). In the photon-assisted process, the holes generated in the valence band of the transition region diffuse into the active region and then change the carrier density distribution in the QW, which can also cause chirping [71]. Figure 11: (**a**) Dependence of light output on \(\rm V_{CE}\). Compared with ordinary TL, the output light intensity of \(\rm TJ\)–TL is more dependent on voltage [61]. (**b**) The sensitivity of the output light intensity change \(\rm\Delta L\) to \(\rm V_{CE}\) with various \(\rm I_{B}\) values [64]. Reproduced from Refs. [61, 64], with the permission of AIP Publishing. [PERSON] et al. proposed and modeled a dual-and-direct current-voltage modulation method to solve the chirp problem that occurs in TL voltage modulation [72]. The scheme is based on the opposite frequency shifts produced by current modulation and voltage modulation. The aim is to induce chirps during modulation through \(\mathrm{I_{B}}\) and \(V_{CB}\) such that they negate each other. Let \(\Delta\
u\) denote the total instantaneous frequency shift due to modulation; the frequency shift due to current modulation is \(\Delta\
u(\mathrm{I})\) and that due to voltage modulation is \(\Delta\
u(\mathrm{V})\) (i.e., \(\Delta\
u=\Delta\
u(\mathrm{I})+\Delta\
u(\mathrm{V})\)).