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We theoretically analyzed and experimentally demonstrated an injection-locking based all-optical flip-flop memory using a simple and compact tunable V-cavity laser (VCL). A bistable region in the tuning characteristics of the VCL is employed for the flip-flop operation. The state of the VCL can be set and reset by injecting signal pulses at two different wavelengths. The pulse power for both set and reset signal is only about 1 pJ. Short response times of about 150 ps are measured for storing and erasing.
© 2016 Optical Society of America
1. Introduction
With the development of optical communication networks, all-optical signal processing is very desirable to replace the bandwidth limited and power hungry optical-electrical-optical (OEO) processing. One of the key components for all-optical signal processing is optical buffer. An ideal optical buffer requires the following characteristics: low power consumption, small footprint, high response speed, controllable buffer time, and can be integrated with planar semiconductor technology. Several different methods for all-optical buffer have been proposed, including optical buffering using slow-light waveguides [1] or recirculating loops [2]. Instead of increasing the light travel path length or travel time, all-optical flip-flop (AOFF) is another method. Using bistable devices in combination with appropriate circuit design, we can achieve fully functional flip-flop operation [3].
Semiconductor optical bistable devices have been extensively investigated in the 1980~1990s, including optical memory and all-optical signal regenerators in passive devices [4, 5]. Active-passive integrated devices such as Mach-Zehnder interferometer integrated with semiconductor optical amplifiers (SOAs) are often used for AOFF in planar waveguide geometry [6, 7]. However, they require high current and difficult active-passive integration techniques. Bistable laser diodes are also often adopted, but the existing devices have some drawbacks. A multimode interference bistable laser diode has a high power consumption and a rather slow switching time [8]. Two coupled ring lasers can only operate in the pulsed regime [9]. A vertical cavity surface-emitting laser (VCSEL) [10] is not appropriate for planar integration. The distributed Bragg reflector (DBR) laser [11] needs very careful current control to work in the dual-mode state and quite sensitive to the power of set and reset signals. The distributed feedback laser diode [12] needs accurate antireflective coating and extra holding beam to obtain bistability.
In this paper, we theoretically analyze the bistability phenomenon of tunable V-cavity laser (VCL), whose structure is described in details in [13–15]. The VCL is designed to have a 0.8nm channel spacing and the bistable wavelength pair can be easily tuned to fit the ITU grid. The size of the chip is only about 500 μm × 300 μm, and the fabrication process is similar to a simple Fabry-Perot laser. The simulation result shows how the optical output is dependent on the prior current injection and light signal injection. Dynamic optical output characteristics are analyzed based on rate equations for the carrier density and photon density with consideration of nonlinear gain effect. Then, we experimentally demonstrated AOFF buffer using set and reset signals at two different wavelengths. Since this proposed optical buffer can be controlled by operating wavelength, it is very suitable as an element in a photonic integrated circuit for wavelength routing systems.
2. Concept
The VCL is optimized to reach a stable bistability. The lengths of fixed cavity L and channel selector cavity L’ are about 450 μm (corresponding to an FSR of 100 GHz) and 495 μm (corresponding to an FSR of 90.9 GHz), respectively, to obtain a 10% FSR difference, as shown in Fig. 1(a). The self-coupling coefficient of the half-wave coupler is 0.75. Figure 1(b) illustrates the lasing threshold gain of the cavity modes on such condition. The threshold difference between the main mode and the next threshold mode is about 4.5 cm−1. The photon life time τp of each longitudinal mode is related with lasing threshold gain by the following equation: <g>th = Γgth = 1/(vgτp). While the other two electrodes are applied with constant and relatively small current, the current injected on the long cavity is quite large in order to tune the wavelength as well as to provide the gain. When the current applied on the channel selector cavity increases, because of Vernier effect and asymmetric gain profile [15,16], the first side-mode (mode 2) at longer wavelength will start to lase.
The reasons for the mode bistability of a laser diode are classified into following categories: nonlinear refraction index, nonlinear absorption, and nonlinear gain, which are dependent on optical intensity. In our case, all the sections are active with the same multiple quantum wells. The dominant effect is the gain saturation. We therefore focus on the mode suppression between the two adjacent longitudinal modes due to nonlinear gain effect [17, 18].
We analyze the static and dynamic behavior of the bistability using the rate equation below
where m and n represents the mode number which are most likely to lase, namely mode 1 and mode 2 in Fig. 1(b); N is carrier density; ηi is initial quantum efficiency; I is injected current; q is electric charge of single electron; τm and τn refer to photon life time of longitudinal mode m and n; η is the coupling coefficient; Iim and Iin are the intensity of injected optical signals which have the same wavelength as mode m and mode n. The injected light is coupled to the lasing mode of the same wavelength with a coupling coefficient η, thus the number of photons of the specific mode can be expressed as in the last term of each equation above. In the dynamics study, the Iim and Iin vary with time. Because the wavelength difference between the two modes is quite small, material gain g(N) is approximated to be wavelength independent as g(N) = aN-b. εmm and εnn is self-saturation coefficient, εmn is cross-saturation coefficient. These coefficients are obtained from the literature [11, 19, 20] with some fittings to experiment results, and are dependent on the current and temperature. The parameters used for simulations are summarized in Table 1.
Table 1. Parameters used in the simulations.
Figure 2 shows the tuning hysteresis loop between mode 1 (1550 nm) and mode 2 (1550.8 nm) versus the applied current. The laser is deemed to switch from one mode to the other when the power in the latter mode exceeds that in the former one. The threshold current is higher for mode 1 switching to mode 2 with increasing current, compared to the threshold current of mode 2 switching to mode 1 when the current decreases, resulting in a hysteresis loop. When the parameters of the half-wave coupler changes, the threshold gain difference between mode 1 and mode 2 will change. The variation of threshold gain difference results in the change of the hysteresis loop size. Figures 2(a)-2(d) show the tuning characteristics when the threshold difference is 5.7 cm−1, 4.75 cm−1, 4.5 cm−1 and 4.25 cm−1, respectively. If the threshold gain difference is large enough, the hysteresis loop is very small, as shown in Fig. 2(a), or can no longer exist. In the case of Fig. 2(b), the threshold difference between the main mode and side mode is assumed to be 4.75cm−1. When the current increases, the output is switched from mode 1 to mode 2 at 121mA. When the current decreases, the output is switched from mode 2 to mode 1 at 118mA. The bistable current range is about 3mA. With threshold gain difference decreasing, the hysteresis loop covers a larger tuning current range, making it easier for the bistablity to occur. The bistable current range increases to 6.5 mA and 8.6mA, respectively, when the threshold difference is decreased to 4.5 cm−1 and 4.25 cm−1, as shown in Fig. 2(c) and 2(d). However, if the threshold gain difference is too small, the laser will be less stable and easily switch between the two modes when facing current or temperature fluctuations.
Fig. 2 Simulated tuning hysteresis loop assuming the threshold gain difference between mode 1 and mode 2 is (a) 5.7 cm−1; (b) 4.75 cm−1; (c) 4.5 cm−1; and (d) 4.25 cm−1.
For optical-controlled flip-flop operation, the laser is biased in the middle of the hysteresis loop and is expected to be locked at one state even after the injected optical signal is turned off. The state of the laser is therefore determined by its former state and the injected optical signal. In the following dynamic simulations, we use the value of 4.5 cm−1 for the threshold gain difference between mode 1 and mode 2, and the tuning current is set at 117 mA. As shown in Fig. 3(a), the dash lines indicate the time window of an input optical signal with a time duration of 1.6 ns. The laser is originally working at mode 1. The injected set-signal is of the same wavelength as mode 2. When the input signal has an appropriate power, such as the case of −33 dBm and −25 dBm, the output is switched from mode 1 to mode 2 smoothly. The transition time is shorter for larger signal. If the input power is too weak, such as the case of −35 dBm, the flip-flop cannot happen. The lasing wavelength will return to mode 1 again after a few nanoseconds. However, if the incident power is too high, such as the case of −7 dBm, although the rising edge is very sharp, there is a significant overshoot during the existence of the injected signal. After that, because of the deep depletion of the carriers, the output power experiences a period of time to recover before reaching the steady state in mode 2. It is similar for switching from mode 2 to mode 1. As shown in Fig. 3(b), the laser is originally stable at mode 2. During the dash-lined time window, the reset-signal is injected at the same wavelength as mode 1. The output power of mode 2 is switched off during a few nanoseconds. The switching time decreases with increasing signal power. When the reset-signal power is too low such as the case of −33 dBm, the flip-flop cannot happen and the laser is switched back to mode 2 after a competition period of a few nanoseconds.
Fig. 3 Calculated VCL output at mode 2: (a) with a 1.6 ns set-signal at wavelength 2; (b) with a 1.6 ns reset-signal at wavelength 1.
Figure 4 shows the rise time and fall time as a function of the input power of the optical signal. Within the appropriate power window, the rise time and fall time decrease with increasing input power. However, we need to compromise the switch time with over shoot and gain recovery time as discussed earlier.
3. Experimental results
We experimentally demonstrate the flip-flop operation based on an optimized VCL described in section 2. The VCL used in the experiment has a designed threshold gain difference of 4.5 cm−1 between the main mode and its adjacent mode, the same as the case of Fig. 2(c). The coupler electrode and the short cavity electrode are injected with 38 mA and 28 mA currents, respectively. The bistable hysteresis loop is observed in the tuning characteristics, as shown in Fig. 5. Figure 5(a) and 5(b) give the power of mode 1 and mode 2, respectively, versus current variation. When the current increases, the power of mode 1 drops and that of mode 2 increases sharply at 119.02mA. When the current decreases, the switching point occurs at 114.23mA. The wavelength of the dominant mode is plotted in Fig. 5(c). The bistability is obtained when the long cavity electrode is tuned between 114.23 mA and 119.02 mA. The variation of the measured wavelength of each mode is negligible due to the discrete tuning characteristics of the VCL. The hysteresis loop covers about 5 mA that matches well with the simulation.When 116.46 mA is applied on the long cavity electrode, we can switch the lasing state by injecting optical signals at the wavelength of the corresponding mode. As shown in Fig. 6, the V-cavity laser is in good single mode condition with SMSR more than 35 dB in both states.
Fig. 5 Measured hysteresis characteristics of mode 1 at 1549.56 nm (a) and mode 2 at 1550.30 nm (b), and the corresponding wavelength hysteresis loop (c).
The flip-flop experimental setup is shown in Fig. 7. Two tunable lasers emitting at λ1 = 1549.56 nm and λ2 = 1550.30 nm are combined and modulated together by a Mach-Zehnder modulator and then separated by a commercial AWG with 100 GHz channel spacing. A tunable mechanical optical delay based on lenses is placed in one link to adjust the time difference between set signal and reset signal. EDFA is used to balance the power of each path. The two signals are combined again and injected into the VCL through a circulator, after passing through a polarization controller. The signal power of λ1 and λ2 before the injection is −1.82 dBm and −1.93 dBm, respectively. Because the fiber based system is of less stability, the signal pulse duration time is set to 1.6ns to decrease the influence from delay time fluctuation. The net set and reset signal energies with coupling loss subtracted are 0.97 pJ and 1.1 pJ, respectively. The output signal at λ2 is then filtered out by passing an optical filter with a narrow bandwidth (0.04 nm).
Fig. 7 Schematic of the experiment setup (PC: polarization controller; MZ: Mach-Zehnder modulator; PPG: pulse pattern generator; AWG: arrayed waveguide grating).
The dynamic flip-flop characteristics are shown in Fig. 8. We can see that the set signal at 1550.30nm switchs the laser from mode 1 to mode 2, while the reset signal at 1549.56nm switch the laser back from mode 2 to mode 1. The rising and falling times indicates the storing time and erasing time of mode 2 are about 150 ps and 159 ps, respectively, while they are 137 ps and 144 ps for mode 1. With the consideration of 7 dB coupling loss, the net injected power is about −10 dBm. Therefore, the switching times agree well with our simulation results shown in Fig. 4. This flip-flop operation still has potential to support a higher bit rate with shorter pulse duration time and higher injected power.
Fig. 8 Dynamic all-optic flip-flop operation: (a) set signal at 1550.30nm; (b) reset signal at 1549.56nm; (c) output at 1550.30 nm; (d) output at 1549.56nm. The rising and falling edges of the output signals are shown, respectively, in (e) and (f) for 1550.30 nm, and in(g) and (h) for 1549.56 nm.
4. Conclusion
We have investigated the nonlinear bistability in V-cavity laser through both numerical simulations and experiments. All-optical flip-flop memory function has been successfully demonstrated based on two bistable modes in the V-cavity laser. The storing and erasing response times are only about 150 ps, with small net input pulse energies of about 1 pJ. Benefitting from its compact size, low-energy consumption, simple fabrication, as well as the advantage that the flip-flop is controlled by operating wavelengths, the device is promising to work as a part of an on-chip all-optical signal processing system.
Acknowledgment
This work was supported by the National High-Tech R&D Program of China (grant No. 2013AA014401), and the National Natural Science Foundation of China (grant No. 61377038).
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