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A novel and simple method for high frequency millimeter-wave signal generation with integrated twin DFB lasers is proposed and demonstrated. Both theoretical simulation and experimental results confirm that chaos induced by large-signal direct modulation of a solitary laser diode can be suppressed by introducing adequate optical coupling from another dc biased laser diode. Frequency multiplication has been demonstrated employing such chaos suppression scheme using monolithically integrated twin DFB lasers, and low phase noise millimeter wave carrier ten times the modulation frequency is generated.
©2013 Optical Society of America
1. Introduction
Optical generation of high frequency millimeter-wave (mm-wave) signals has a wide range of applications, such as 60-GHz wireless access network, satellite communication and phased array antenna [1]. Compared with electrical solutions, it has many advantages, such as low cost, high reliability [2], and free from the frequency bandwidth limitation of electronic components. Many techniques for mm-wave generation by optical means have been proposed, for instance, sideband injection [3–6], mode locked laser [7] and external modulation [8–10], most of which make use of external intensity modulators [8,9] or/and phase modulators [10]. By taking advantages of the inherent nonlinearity of the external modulators, a series of modulation sidebands are generated in the optical spectrum with frequency spacing equal to the modulation frequency. Beat signal at multiples of the modulation frequency can be obtained by heterodyning the modulation sidebands in a high-speed photodetector (PD). Such optical microwave sources are generally made up of one or more external modulators as well as discrete laser sources, resulting in a relatively complex system and high cost.
One possible way to simplify optical microwave generation systems is to adopt direct modulation in place of external modulators. However, there have been relatively few reports on high frequency microwave signal generation by direct modulation of semiconductor lasers. The reason may lie in two aspects: Firstly, compared with an external modulator, the modulation bandwidth of a semiconductor laser is limited by its relaxation oscillation frequency [11]. Secondly, due to the interaction between carriers and photons within the laser cavity, large modulation ratio of the injection current is required to realize high order frequency multiplication. However, large modulation index may bring about dynamic behaviors such as period doubling, period tripling and chaos [12, 13], which could severely deteriorate the spectral quality of the generated microwave signal. It is numerically shown that delayed or mutual optoelectronic coupling between two semiconductor lasers could suppress the modulation induced chaos [14, 15]. However, both cases necessitate discrete PDs to be part of the feedback link.
In this paper, we propose to use integrated twin DFB lasers to suppress chaos and improve the spectral purity of the generated mm-wave carrier. Although nonlinear dynamics [16] and mutual locking with linewidth reduction [17] have been demonstrated in coupled semiconductor lasers, to the best of our knowledge, this is the first report on chaos suppression for mm-wave signal generation by mutual optical injection between integrated lasers. In part 2, the model for two coupled semiconductor lasers is provided, and simulation results predict that chaos induced by large signal direct modulation on a solitary laser can be suppressed with favorable mutual injection. Based on the simulation results, monolithically integrated twin DFB lasers are fabricated. And part 3 provides the experimental results, which are in agreement with the simulation predictions.
2. Model and numerical simulations
We consider two laser diodes (LDs) with mutual optical injection, whose dynamic behavior can be described by a set of delay differential equations as follows [13,18].
Except for a difference in their free running optical frequencies, the two lasers (LD#1 and LD#2) are assumed to have identical structural parameters. In the above equations, Ei is the envelopes of the complex optical field Eieiωit, and ∆ω = ω1–ω2 is the frequency detuning between the two lasers in free running condition. Ii and Ni are the injection current and carrier density in each laser. We assume a symmetrical coupling, with the coupling strength given by κ. In other words, there is no optical isolator between the two lasers. The delay time τ corresponds to the time taken for light to travel from one laser to the other. Device parameters used in the coupled rate equation analysis are listed in Table 1 , where the values for each parameter are taken from Refs [12, 13].
Table 1. Typical device parameters adopted in our simulations
Firstly, we study the modulation characteristics of a solitary laser. The modulation behavior of LD#1 can be obtained from the first two equations of (1) by setting κ = 0. Setting the bias current Idc1 = 1.3Ith and the modulation frequency at 4 GHz, which is slightly larger than the relaxation oscillation frequency, we examine the change in photon density with different modulation indices m = Imod /(Idc − Ith).
For microwave generation, we are mainly concerned with the electrical signal after the PD. Since the PD responds to the fluctuation of optical power, the Fourier transform of |E1|2 gives the radio frequency (RF) spectrum of the beat signal coming out of the PD. Figure 1 depicts the RF spectra under different modulation depths. The route to chaos via period doubling and period quadrupling is clearly shown with the increase of modulation depth. In Fig. 1(d), which corresponds to a large modulation ratio of m = 0.9, microwave carriers corresponding to high order frequency multiplication of the modulation signal is buried by the chaos. Such modulation induced chaos not only limits the intensity of the high order harmonics, but also severely degrades their spectral purity. As a result, a directly modulated solitary laser diode is not suitable for photonic microwave generation, despite its obvious advantages of low cost and system simplicity.
Fig. 1 Simulated RF spectra of a solitary diode laser under different modulation depth: (a) m = 0.25, small signal modulation with harmonic distortion, and the hump corresponds to the enhanced RIN noise around relaxation oscillation frequency; (b) m = 0.5, period doubling; (c) m = 0.8, period quadrupling; (d) m = 0.9, chaos.
If there is optical injection between the two laser diodes, i.e with a nonzero coupling coefficient κ, it is found that the direct modulation induced chaos can be suppressed and high frequency microwave signal is recovered. According to our simulations, coupling strength κ, time delay τ and frequency detuning ∆ω between the two lasers are the key parameters for chaos suppression.
Figure 2(a) depicts the RF spectrum under the same modulation condition as in Fig. 1(d), but with optical coupling between the two lasers characterized by κ = 0.02, τ = 4.2 ps, ∆f = ∆ω/2π = −17 GHz, and Idc1 = Idc2 = 1.3Ith. Compared with Fig. 1(d), it is seen that the broadband chaos is greatly reduced, and high order frequency multiplication signals begin to stand out. However, the phase portrait of the normalized optical intensities of LD#1 and LD#2 shown in Fig. 2(b) reveals some residual chaos in this case. To realize complete chaos suppression, the coupling strength between the two lasers is further increased to κ = 0.03, with the corresponding RF spectrum and phase plot shown in Figs. 2(c) and 2(d). Apart from the disappearance of the chaos, high order frequency multiplication signals become significant. Furthermore, our simulations confirm that, as long as there is a sufficient coupling strength κ between the two lasers, full suppression of chaos can be maintained for a certain range of τ and ∆ω. In other words, frequency multiplication with high spectral purity can be realized with careful control of the key parameters κ, τ and ∆ω.
Fig. 2 Simulated RF spectra of coupled laser diodes and the corresponding phase portraits. (a) and (b): κ = 0.02; (c) and (d): κ = 0.03.
The optical spectra of LD#1 and LD#2 under chaos suppression are plotted in Fig. 3 , with the free running wavelength of LD#1 as the reference. It is found that due to the optical coupling between the two lasers, LD#2 also undergoes a certain level of modulation. Moreover, the modulation sidebands in the spectrum of LD#2 coincide with those of LD#1. As a result of the mutual locking between the two lasers, LD#1 is stabilized. It is noticed that although the frequency detuning Δω between the free running LD#1 and LD#2 may not be an integral multiple of the modulation frequency, the refractive index changes induced by the variation of carrier density under mutual coupling would cause the modulation sidebands of the two lasers to be locked to each other upon chaos suppression.
The above analyses lead us to propose to adopt directly modulated coupled lasers for high frequency mm-wave generation. Since a symmetrical coupling is assumed in our simulations, the scheme is readily feasible with a monolithically integrated device, in which optical isolation is difficult to implement.
3. Device fabrication and experiments results
To demonstrate the feasibility of the proposed mm-wave generation scheme, coupled twin DFB lasers are monolithically integrated on 1.55 μm InGaAlAs multiple quantum well (MQW) material, as shown in Fig. 4 . Both DFB lasers have the same grating pitches and a cavity length of 400 μm. A 400-μm-long grating-less phase tuning section is inserted in between to regulate the coupling strength and time delay between the two lasers. Adjustment of the coupling strength and fine tuning of the time delay can be implemented by positive or reverse bias of the phase tuning section. Electrical isolation between the each section is realized by removing the ohmic contact layer and the electrode metal in between, resulting in an isolation resistance of more than 5 kΩ. Both DFB lasers exhibit excellent single-mode behavior above the threshold about 30 mA.
Fig. 4 Experimental setup for mm-wave generation with monolithically integrated twin DFB lasers. (ESA: electrical spectrum analyzer; OSA: optical spectrum analyzer; PD: photodetector.)
The experimental setup for mm-wave generation with the integrated twin DFB laser is shown in Fig. 4. Modulation signal is applied to one of the DFB lasers (LD#1) via a bias Tee, while the other laser (LD#2) is dc biased. The output light from the facet of the modulated laser is fed into a high-speed PD by way of a tapered fiber. An electrical spectrum analyzer (ESA) is adopted to record the RF spectrum of the beat signal from the PD. And the optical spectrum of the light coming out of LD#1 is simultaneously monitored with an optical spectrum analyzer (OSA).
First, we examine the modulation characteristics of LD#1 with the dc bias of LD#1 set to 40 mA and the injection current into LD#2 turned off. The modulation frequency is chosen to be 4 GHz, which is near the relaxation resonance frequency of LD#1, thus enhancing the nonlinearity of modulation response [11]. The measured optical spectra and the corresponding RF spectra under different modulation depths are shown in Fig. 5 . According to Fig. 5(a), as the modulation index increases, the number of modulation sidebands multiplies, and the high order harmonics in Fig. 5(b) becomes stronger. However, when the power of the RF modulation signal increases to 15 dBm, the spectrum floor in Fig. 5(b) increases abruptly and the modulation sidebands in Fig. 5(a) can no longer be discerned from each other. Furthermore, the peaks at 2, 6, and 10 GHz correspond to the remnant period doubling in the transition to chaos. Such phenomena are in agreement with the above simulation prediction, indicating that chaos sets in.
Next, optical injection is introduced into LD#1 by biasing LD#2 above the threshold. The wavelength detuning between the two lasers is tuned by adjusting the current of LD#2. It is found that chaos suppression could be achieved with a LD#2 injection current in the range of 40-52 mA. Figure 6 provides a comparison of the optical and RF spectra with LD#2 turned on and off. A heating induced red shift of the optical spectrum is observed when LD#2 is turned on, and in Fig. 6(a), the optical spectrum with LD#2 turned off is intentionally red shifted by 1.2 nm so as to make a better comparison. As is evident from Fig. 6(a), modulation sidebands become distinct with LD#2 turned on. About 20 sidebands with comparable intensity and 4-GHz frequency spacing are generated. Meanwhile, as shown in Fig. 6(b), the chaos is greatly reduced and high order harmonics of the modulation frequency stand out. Harmonics at 10 times the modulation frequency is generated.
Fig. 6 Measured (a) optical and (b) RF spectra of light coming out of LD#1with LD#2 turned ON and OFF
To confirm the simulation results given in Fig. 3, the optical spectra of light coming out of LD#1 and LD#2 are compared in Fig. 7 . It is seen that LD#2 is also under modulation due to optical coupling, and the modulation sidebands of the two LDs are mutually locked, thus pulling the LD#2 from chaos to a stable state.
Generation of higher order harmonics is believed possible, yet is not observed with our experimental setup due to the bandwidth limit of the PD and the ESA. Moreover, frequency of the generated mm-wave could be further increased by improving the relaxation resonance frequency of the laser diode.
Furthermore, the modulation frequency can be tuned up to a range of GHz without adjustment of bias currents under chaos suppression condition, resulting in a frequency tunable mm-wave carrier. Different from the case of sideband injection locking [3–6], where precise adjustment of bias currents are required to keep the slave laser in locked state when modulation frequency is tuned, there is no need for precise adjustments of the bias currents of the two lasers in our experiment. Thus the tuning process is greatly simplified. Figure 8 shows the frequency spectra obtained with modulation frequency at 4 and 5.5 GHz. The phase noise of the 33-GHz mm-wave carrier, corresponding to 6-fold multiplication of the 5.5 GHz modulation signal, is measured to be −95.2 dBc/Hz at 10 kHz offset and −100 dBc/Hz at 100 kHz offset, as shown in Fig. 9 . The roughly 15 dB degradation in phase noise compared with the modulation signal is in good accord with 6-fold frequency multiplication.
4. Conclusions
A novel and simple approach for optical generation of mm-wave signal is proposed and realized by adopting integrated twin DFB lasers. It is experimentally demonstrated that with two lasers coupled together, chaos induced by large signal direct modulation of a solitary laser is suppressed and frequency multiplication up to 10 times of the modulation frequency has been realized with high spectral purity. Moreover, the robustness of chaos suppression effect is demonstrated. As a result, the integrated twin DFB lasers are believed to be a promising candidate for high-frequency and low-phase-noise microwave generation applications.
Acknowledgments
This work was supported in part by the National Basic Research Program of China (Grant Nos. 2012CB315605, and 2011CB301900), the National Natural Science Foundation of China (Grant Nos. 61176015, 60723002, 61176059, 60977022, and 51002085).
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