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A hybrid modulation scheme that simultaneously applies the direct current modulation and intra-cavity loss modulation to a semiconductor laser is proposed. Both numerical calculations using rate equations and experiments using a fabricated laser show that the hybrid modulation scheme can control the frequency response of the laser by changing a modulation ratio and time delay between the two modulations. The modulation ratio and time delay provide the degree of signal mixing of the two modulations and an optimum condition is found when a non-flat frequency response for the intra-cavity loss modulation is compensated by that for the direct current modulation. We experimentally confirm a 8.64-dB improvement of the modulation sensitivity at 20 GHz compared with the pure direct current modulation with a 0.7-dB relaxation oscillation peak.
© 2016 Optical Society of America
1. Introduction
A direct current modulation (DM) scheme is the simplest modulation method for semiconductor lasers. Direct current modulation lasers (DMLs) provide a high-speed modulation over 10 Gbit/s by simply modulating their bias current. Thus, they have been used in Ethernet families that require low cost and high performance. The demand for high-speed DMLs has been increasing due to the recent explosive increase in data traffic worldwide. A trend in 3-dB bandwidth enhancement of DMLs is shortening of laser cavity length. The 3-dB bandwidth of 30 GHz was achieved with a 100-μm-long-cavity DML [1]. However, it is difficult to shorten the cavity length further due to the thermal problem and gain saturation effect in the active region.
There is another 3-dB bandwidth enhancement scheme that uses the photon-photon resonance (PPR) effect [2–6]. The PPR effect is caused by the interaction between the lasing light and feedback light from an external cavity. Thus, the PPR effect can be observed in external cavity lasers [2,3], distributed Bragg reflector (DBR) lasers [4,5], and distributed reflector laser [6]. Under appropriate conditions for phase and intensity of the feedback light, the PPR effect forms a second resonance peak on the frequency response that contributes to the enhancement of the 3-dB bandwidth of the laser (Fig. 1 (a)). DMLs based on the PPR effect have a potential to achieve much wider 3-dB bandwidth than that of an electroabsorption modulator. However, in the previous study, the PPR effect could not effectively contribute to enhancing the 3-dB bandwidth for DMLs due to the rapid degradation of modulation sensitivity at a high-frequency region above a relaxation oscillation frequency of a laser and the maximum 3-dB bandwidth was limited to 34 GHz [3]. Recently, the 3-dB bandwidth of 55 GHz was achieved by using the detuned loading effect and the PPR effect [6]. In order to achieve a higher 3-dB bandwidth, the PPR effect should be combined with a modulation scheme which has low modulation sensitivity degradation at a high-frequency region (Fig. 1 (b)). We previously demonstrated that the cross-gain modulation (XGM) scheme can suppress the modulation sensitivity degradation at a high-frequency region compared with that of the DM scheme [7], and we achieved a wider 3-dB bandwidth of 59 GHz by using the PPR effect with XGM scheme [8]. However, the XGM scheme requires an injection of modulated signal light to modulate the output power of the semiconductor laser, which limits possible applications of the laser. We suggested in a previous paper that the intra-cavity loss modulation (ICLM) scheme enables a direct intensity modulation of laser diodes by an electrical RF signal and provides low modulation sensitivity degradation [9]. However, the ICLM forms a strong relaxation oscillation peak at a resonant frequency that becomes a cause of substantial signal distortion when the laser is operated by a digital signal.
In this paper, we propose a hybrid modulation (HM) scheme based on the DM and ICLM to reduce the degradation of modulation sensitivity without inducing noticeable increase in relaxation oscillation peak strength. Frequency responses for this scheme are calculated using rate equations. We then confirmed that measured frequency responses of a fabricated HM laser reasonably agree with the calculation results.
2. Numerical simulations
The device structure of the HM laser is illustrated in Fig. 2. The ICLM section consisting of an electroabsorption waveguide is integrated with a distributed feedback (DFB) active section to modulate the intra-cavity loss. A semiconductor optical amplifier (SOA) is also integrated to compensate for the insertion loss of the ICLM section. Electrical pads of the DFB active and ICLM sections are compatible with RF signals and those parasitic capacitances are assumed to be 0.30 and 0.15 pF, respectively. The facet of the SOA-section side is coated with high-reflectivity (~80%) films. The HM, i.e., a combination of the DM and ICLM is done by modulating a bias current to the DFB active section and a bias voltage to the ICLM section simultaneously.
Frequency responses of the DM are represented by a Lorentzian function that has a low-pass filter response [7]. On the other hand, the frequency response of the ICLM has higher modulation sensitivity than DM's one at a high-frequency region since the bias voltage to the loss modulation section changes the effective photon lifetime [9,10]. The frequency response of the HM laser can be represented by superposition of these frequency responses. We use the following rate equations to investigate the behavior of the carrier density N and lasing mode photon density S in the laser cavity.
where I, vg, e, V, Ag, ε, N0, Γ, τp, and τs are respectively the bias current to the DFB section, group velocity of propagated light, elementary charge, active section volume, linear gain coefficient, gain saturation coefficient, transparent carrier density, optical confinement factor, photon lifetime, and carrier lifetime. Typical values for InGaAsP multiple quantum well DFB lasers [11] are used for the calculation which results in a threshold current Ith of 24.6 mA. The effect of the ICLM can be assumed to be the change in τp and can be written aswhere τp0 and Δτp are respectively the intrinsic photon lifetime determined by the laser structure and τp change by the ICLM. In small signal analysis, the I and 1/Δτp can be written as where Ι0 and Ι1 are the DC and AC components of the I and set to 98 mA (4Ith) and 1.2 mA. Δτp0 and Δτp1 are the DC and AC components of Δτp, ω is an angular modulation frequency, and Δt is the relative time delay between two modulation sinusoidal RF signals. A relative modulation ratio η (≤ 0 dB) is defined as a modulation sensitivity ratio between the two modulation schemes at 100 MHz, and it represents a dominance of the ICLM.Figure 3 shows the calculated frequency responses for the pure DM and pure ICLM. The modulation sensitivity of the pure DM rapidly degrades over the relaxation oscillation frequency resulting in the modulation sensitivity of −15.2 dB at 30 GHz and relaxation oscillation peak of 1.3 dB. On the other hand, the pure ICLM shows slow degradation of the modulation sensitivity over the relaxation oscillation frequency, however it has a strong relaxation oscillation peak.
Figure 4(a) shows the calculated unit step responses of the HM without time delay. The DM and ICLM components are also shown. A rising time of the ICLM components is faster than that of the DM because the ICLM has a high modulation sensitivity at a high frequency region compared with the DM. However, a strong relaxation oscillation occurs for the ICLM. The time evolution of the HM is given by the sum of the two components. Therefore, the HM without time delay shows a strong relaxation oscillation caused by the ICLM component. In Fig. 4(b), a 26-ps time delay which corresponds to the rising time of the ICLM component was introduced into the modulation signal for the DM. A fast rising edge derives from the ICLM component is inherited and the relaxation oscillation of the ICLM and DM components cancel out each other. These results indicate that an optimum delay time is determined by rising or falling time of the ICLM and roughly estimated by (4fr)−1 where fr is the relaxation ocsillation frequency.
Fig. 4 Calculated unit step responses of the HM scheme (a) without a time delay and (b) with a 26-ps time delay.
Figure 5(a) shows the calculated frequency responses of the HM laser with various η conditions for Δt of 26 ps. Under HM condition with η of −10.3 dB, the deep valley is observed at 10.4 GHz where the DM and ICLM are almost canceled out. The two modulations are in antiphase when Δt = 26 ps at 10.4 GHz. Δt is an important parameter to determine a frequency where the cancelation of modulation signal occurs. The flattest response is observed when η = −6.61 dB. We defined a maximum response deviation χ to evaluate the flatness of the frequency response. χ is given by a difference between the maximum and minimum values of the frequency response curve lower than 30 GHz. Also, we defined a sensitivity improvement δ to evaluate the improvement of the modulation sensitivity at a high frequency region. δ is given by a difference of the modulation sensitivity at 30 GHz between the HM and DM. Figure 5(b) shows the modulation ratio dependence of χ and δ for Δt of 26 ps. χ reaches a minimum value of 5.45 dB when η is −6.61 dB. The flattest frequency response with a 9.63-dB increase in δ is confirmed. Although larger η improves δ, it increases χ because of the enlargement of the relaxation oscillation peak. Conversely, for smaller η, both δ and χ degrade because of the rapid degradation of the DM's frequency response. Figures 6(a) and 6(b) show the calculated eye diagrams of 25-Gbps NRZ signal for the DM and HM for Δt = 26 ps and η = −6.61 dB. The DM's eye diagram is distorted due to the narrow 3-dB bandwidth. On the other hand, the HM's eye diagram shows a clear eye opening thanks to the improvement of the modulation sensitivity at a high frequency region. Figure 6(c) shows the frequency response dependence on Δt. A relatively flat frequency response is observed when Δt is in the range from 10 to 30 ps. When Δt is 50 ps, the DM and ICLM components are canceled out at undesired frequency of ~5 GHz resulting in a non-flat frequency response. On the other hand, when Δt is 0 ps, the frequency response is not severely distorted and the sensitivity is enhanced at the relaxation oscillation frequency around 8 GHz. Therefore, a larger torrerance of Δt can be obtained when Δt is smaller than an optimum value.
Fig. 5 (a) Calculated frequency responses of HM laser with various η conditions for Δt = 26 ps. (b) Modulation ratio dependences of maximum response deviation χ and sensitivity improvement δ for Δt = 26 ps.
Fig. 6 Calculated eye diagrams of 25-Gbps NRZ signal for (a) DM and (b) HM for Δt = 26 ps and η = −6.61 dB. (c) Frequency response dependence on Δt.
We confirmed that the HM scheme improves the flatness of the frequency response of the laser by properly setting the values of η and Δt.
3. Experiments
We fabricated an HM laser and measured its frequency response. The device dimensions are shown in Fig. 2. It has a 300-μm DFB section, a 150-μm loss modulation section, and a 50-μm SOA section. The spatial hole burning effect can be neglected because the DFB active section has an uniformed Bragg grating with a small coupling factor of 30-cm−1. There are passive waveguides between these sections for electrical isolation. The active section has six periods of 6-nm-thick InGaAlAs quantum wells separated by 10-nm-thick InGaAlAs barriers [12]. The electrical pads of the DFB and loss modulation sections are compatible with RF signals and have matching resisters of 45 ohms in series and 50 ohms in parallel, respectively.
Figure 7(a) shows a schematic of the experimental setup. Δt is set to 26 ps by controlling a circuit length difference between the DM and ICLM. The optical signal from the HM laser is converted into an electrical signal by using a photo detector with 3-dB bandwidth of 40-GHz, then the amplitude of the converted signal is measured using a 30-GHz RF spectrum analyzer. The bias current for the SOA section (ISOA) is set to 5 mA. The applied voltages to the DFB section (VLD) and loss modulation section (VLM) can be written as
where VLD0, VLD1, VLM0, and VLM1 are the DC and AC components of the bias voltage for the DFB section and those of the loss modulation section. The VLD0 VLD1, and VLM1 are set to 6.8 V, 158 mV, and 158 mV. VLM0 is changed within a range of −0.3 to −1.2 V. Figures 7(b) and 7(c) show the schematics of voltage dependences of the output power for the DFB section and loss modulation section. Because of the nonlinearity of the extinction ratio in Fig. 7(c), a modulation depth of the ICLM (SLM1) can be changed by VLM0. Therefore, η is controlled by changing VLM0. In this experiment, the DC bias current for the DFB section is kept to 80 mA (4Ith) and a single-mode spectrum with a wavelength of 1557 nm is observed.Fig. 7 (a) Experimental setup for measurement of frequency responses. Schematics of voltage dependences of output power for (b) DFB active section and (c) ICLM section.
Figure 8(a) shows the measured frequency responses of the laser for the pure DM condition and HM ones with various η. The frequency response of the laser under pure DM condition shows a rapid modulation sensitivity degradation at high-frequency region and a low modulation sensitivity of −16.3 dB at 20 GHz. When η is −16.0 dB, the modulation sensitivity is rapidly degraded at the frequency region below 10 GHz according to the DM's frequency response, however it is relaxed at a high-frequency region above 10 GHz because of a contribution of the ICLM. When η is −14.2 dB, the frequency response has a deep valley at 8 GHz, where the DM and ICLM are almost canceled out. This clear characteristic is confirmed in the calculation and supports our concept. When η is −8.7 dB, the flattest frequency response with the relaxation oscillation peak of 0.7 dB is obtained. When η is −5.65 dB, the modulation sensitivity at a high frequency region is enhanced, but the relaxation oscillation peak is enlarged to 5.74 dB because a contribution of the ICLM becomes strong. Modulation ratio dependences of χ and δ are shown in Fig. 8(b). Here, the experimental values of χ and δ were respectively calculated from a difference between the maximum and minimum values of the frequency response curve lower than 20 GHz and the modulation sensitivity at a 20 GHz. The minimum value for χ (8.65 dB) and δ of 8.64 dB are confirmed when η is −8.7 dB. The measured frequency responses of a fabricated HM laser qualitatively agree with the calculation results shown in Fig. 5, which demonstrates the frequency response control of a semiconductor laser by the HM scheme. These results indicate that the HM scheme is expected to widen the 3-dB bandwidth of a semiconductor laser integrated with an external cavity for introducing the PPR effect.
Fig. 8 (a) Measured frequency responses with various η conditions for Δt = 26 ps. (b) Modulation ratio dependences of maximum response deviation χ and sensitivity improvement δ for Δt = 26 ps.
4. Conclusion
We numerically and experimentally analyzed the frequency response of a semiconductor laser introducing an HM scheme. The frequency response of the HM laser could be controlled by changing the modulation ratio and time delay between the DM and ICLM. By properly setting the modulation ratio and time delay, we experimentally confirmed that the modulation sensitivity at 20 GHz was increased by 8.64 dB compared with the pure DM with keeping the flatness of the frequency response. The HM scheme will provide a much wider bandwidth when it collaborates with the PPR effect.
Funding
JSPS KAKENHI (15K13961).
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