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Optical phase modulation based on directly modulated reflection-mode optically injection-locked VCSEL is investigated based on standard OIL rate equations and reflection-mode OIL model. The phase information of both static and dynamic state is simulated. The difference of static state phase information between transmission- and reflection-mode OIL is numerically analyzed. With specific OIL parameters, the output power of directly modulated OIL-VCSEL remains constant and phase deviation of 0.934π rad is obtained. Results show that a directly modulated OIL-VCSEL can function as a key component in QPSK or 8PSK transmitters. Preliminary 2.5 Gb/s PSK modulation characteristic is demonstrated experimentally.
© 2013 Optical Society of America
1. Introduction
Vertical cavity surface emitting lasers (VCSELs) have established themselves as transmitter candidates for short distance optical links due to their low cost, low power consumption and high speed [1]. Still, more spectrally efficient, directly modulated (DM) high-speed transmitters are needed for next generation telecom and datacom systems [2]. One of the more promising ways to increase spectral efficiency is to directly modulate the phase of the laser, which is comparatively difficult to control. Optical injection locking (OIL) is a very effective technique to improve the modulation performance of DM lasers [3–5]. Optical phase modulation in an optically injection-locked semiconductor laser (OIL-SL) was first investigated by Kobayashi and Kimura in [6], followed by several other research groups [7, 8]. However, the prior work was all based on transmission-mode OIL-lasers: the injection and output were from different facets of the slave laser. Under such a condition, the slave laser was usually an edge-emitting laser.
Recently, we establish a model including the interference effect of the master laser reflection, which is a distinct feature for OIL-VCSELs [9]. This reflection-mode OIL model is used to explain the data pattern inversion, a phenomenon observed only on OIL-VCSELs. The inversion of data pattern leads to a sign change in the transient chirp of VCSEL modulation, which further results in an increase of single-mode fiber transmission distance [10–12]. As shown in [9], an increased wavelength detuning in the DM-OIL-VCSEL results in three specific output data patterns: (1) normal state, (2) transitional state, and (3) inverted state. With the inclusion of the interference effect of the master laser reflection, these phenomena are explained.
In [13], optical phase modulation of DM-OIL-VCSEL is for the first time investigated based on reflection-mode OIL model. We show that an OIL-VCSEL can function as a high-speed phase modulator due to the same, unique interference effect. In this paper, the work of phase modulation of OIL-VCSEL is significantly expanded on the basis of our previous work [13]: First of all, the phase information for both static and dynamic state is investigated theoretically based on reflection-mode OIL model, which manages to stand out compared with other previous theoretical works [6–8], since only reflection-mode OIL can thoroughly suppress modulation of output power at the transitional state [13]. With specific OIL parameters, a phase deviation of 0.934π rad is obtained while the output power of DM-OIL-VCSEL remains constant. In addition, with the simulation results, we propose configurations with which DM-OIL-VCSELs can be used as a key component in high-speed multiple-phase shift keying (MPSK) transmitters. These configurations can be compact, very high-speed (the same as the highest modulation speed demonstrated for OIL-VCSEL: > 100-GHz [4]), low power consuming and potentially cost-effective. Moreover, preliminary 2.5 Gb/s PSK modulation characteristic is demonstrated experimentally. Coherent detection is used to check the phase modulation. The degree of amplitude modulation is also measured on the locking map to test the range of locking condition, in which there exists phase modulation but no amplitude modulation for the achievement of a practical phase modulator.
2. Theoretical modeling and simulation
2.1 Phase information of static state
Figure 1 presents an intuitive vector picture to illustrate reflection-mode OIL model [9]. The master laser field Ainj impinges onto the front facet of the slave VCSEL and is divided into reflection and transmission parts. For the light’s field Ar of reflection part, the field magnitude Ar and phase shift ϕr can be calculated based on DBR structure on the front facet of the slave VCSEL, which is approximately Ainj and π respectively. The output optical field As from cavity is calculated with standard OIL rate equations and the phase shift (ϕs) ranges from −0.5π to cot−1α [5], with α being the linewidth enhancement factor of SL. As is observed to be phase coherent with Ar, so the total output light’s field is At in Fig. 1. Under transmission-mode OIL condition, the total output light’s field is only As.
Fig. 1 OIL-VCSEL model with the interference effect: an intuitive vector figure to explain destructive interference.
The relative phase ϕs under transmission-mode OIL condition is different from the relative phase ϕt under reflection-mode OIL condition. Recently, the phase response of OIL-SL is analyzed for linear interferometric intensity modulation application [14, 15]. Judging from the different experimental setups in [14] and [15], the setups correspond with transmission- and reflection-mode OIL respectively. It’s important to distinguish the difference between the two setups, so Fig. 2 is plotted with α = 0. Figure 2(a) and 2(b) show the relative phase of static state under the low injection ratio condition. Under transmission-mode OIL condition in Fig. 2(a), the simulation result is coherent with [14], and ϕs is strictly limited between −0.5π and 0.5π. The simulation result shows that the curves in Fig. 2(b) demonstrate high similarities with those of Fig. 2(a), and ϕt in Fig. 2(b) could slightly break through the limitation of −0.5π and 0.5π. However, under the high injection ratio condition, the range of ϕt could almost approach -π and π as is shown in Fig. 2(d), which is significantly different from ϕs in Fig. 2(c). Figure 2(e) shows a detailed version of the extreme phases in one direction of detuning.
Fig. 2 Relative phase versus wavelength detuning for different injection ratios with α = 0: (a, c) transmission-mode OIL, (b, d) reflection-mode OIL, and (e) detailed version of the extreme phases in one direction of detuning. Under low injection ratio condition (a) and (b), relative phase curves are similar after we compare transmission- and reflection-mode OIL. Under high injection ratio condition (c) and (d), relative phase curves are significantly different after we compare transmission- and reflection-mode OIL.
To further understand the vector figure above in Fig. 1, the static state of As and At are calculated on the locking map with α = 7 which is a reasonable parameter of VCSEL. The locking maps shown in Fig. 3 are asymmetric due to the non-zero α of VCSEL. Under the transmission-mode OIL condition, Fig. 3(a) shows that the amplitude of As grows with increased injection ratio or wavelength detuning. Also, the phase of As smoothly changes from −0.5π to cot−1α with increased wavelength detuning in Fig. 3(c) [5]. Under the reflection-mode OIL condition, Fig. 3(b) shows that the amplitude of At decreases with increased wavelength detuning. Compare Fig. 3(a) and 3(b), and we will find that power trends with increased wavelength detuning are different in these two conditions because of destructive interference effect [16]. Similar to Fig. 1, the endpoint traces of output optical field vector As and At with increased wavelength detuning (Δλ) for different injection ratios (Rinj = 0.0 dB, 3.0 dB, 6.0 dB, 9.0 dB, 12.0 dB and 15.0 dB respectively) are plotted in polar coordinate system, which is depicted in Fig. 4. Taking into account of the destructive interference with Ar, all the traces in Fig. 4(a) shift Ar leftward to Fig. 4(b).
Fig. 3 Simulation results of locking maps of OIL-VCSEL for various injection locking states with α = 7, showing steady state: (a, b) amplitude of output optical field under transmission- and reflection-mode OIL condition respectively, (c, d) phase of output optical field under transmission- and reflection-mode OIL condition respectively.
Fig. 4 The endpoint traces of output optical field for different injection ratios are plotted in polar coordinate system: (a) transmission-mode OIL, and (b) reflection-mode OIL.
2.2 Phase information of dynamic state
In this part of our simulation, OIL-VCSEL is directly modulated by multi-level driving signals under different wavelength detuning conditions when injection ratio is fixed at 9.0 dB. The total output optical field At is amplitude and phase modulated simultaneously [17]. With 10-level 1 GS/s driving signals sweeping up and down, the output waveforms are simulated shown in Fig. 5(a). The upper part of Fig. 5(a) shows the VCSEL’s output waveform under the free running condition. When VCSEL is injection locked, the waveform changes from red to black cure with increased wavelength detuning in the lower part of Fig. 5(a). By adjusting the wavelength detuning (Δλ = 0.73 nm) with fixed injection ratio (Rinj = 9.0 dB), the destructive interference can effectively suppress the amplitude modulation leaving only phase modulation. The constellation diagram which reveals the phase modulation of this condition is shown in Fig. 5(b) with black points. Maximum phase swing of 0.852π is achieved based on this calculation.
Fig. 5 OIL-VCSEL is directly modulated by 10-level driving signals under different wavelength detuning conditions when injection ratio is fixed at 9.0 dB: (a) waveforms under different OIL condition, and (b) constellations under different OIL condition.
The transitional states are plotted on the locking map in Fig. 6(a) [9]. When OIL-VCSEL works at the transitional state, modulation of output power is constant leaving only phase modulation. Even though the injection ratio is changing from 0.0 dB to 15.0 dB, the wavelength detuning of transitional state is always ~0.73 nm, which is shown in Fig. 6(a). The transitional curve on the locking map is strongly dependent on three main parameters of the slave VCSEL: top mirror field reflectivity, cavity length and linewidth enhancement factor. The slop of the transitional curve approaches zero or remains negative, which is device-dependent [9]. For each injection ratio under transitional state, the transfer curves of phase shift (Δϕt) versus peak to peak modulation voltage (Vpp) are plotted in Fig. 6(b). The low level of modulation voltage is fixed during the whole calculation. The nonlinear transfer curves look like an arcsine function [15], and the maximum phase shift (Δϕmax) of output optical field is only limited by maximum Vpp under the stable locking condition.
Fig. 6 (a) The transitional states are plotted on the locking map. (b) The transfer curves of phase shift versus peak to peak modulation voltage are plotted under different injection ratio.
The Δϕmax is calculated with different injection ratios, as is shown in Fig. 7. If the modulation voltage is larger than maximum Vpp to obtain the larger Δϕ, the slave laser VCSEL will be unlocked. The maximum phase swing of 0.934π is achieved with Rinj = 15 dB based on our simulation, and Δϕmax can even be larger with an increased injection ratio.
Fig. 7 The maximum phase shift with different injection ratios is plotted. The maximum phase swing of 0.934π is achieved with Rinj = 15 dB.
2.3 MPSK modulation by OIL-VCSEL
Figure 8 shows simulation results for the MPSK application. When OIL-VCSEL is modulated by binary driving signals under a specific OIL condition (Rinj = 9.0 dB, Δλ = 0.73 nm), the output could be π/2 phase-shift-keying (PSK) optical signal shown in Fig. 8(b). Also, if the OIL-VCSEL is modulated by 4-level driving signals under the same OIL condition, the output intensity will still be constant in time domain. By finely adjusting the current of these four modulation levels, we could obtain π/4 PSK optical signal, as is shown in Fig. 8(d). The sensitivity of OIL condition for phase modulator application will be deliberately discussed in the following experiment.
Fig. 8 Simulated 2/4-level modulation output of an OIL-VCSEL for MPSK transmitter application: (a, b) for QPSK transmitter application, (c, d) for 8PSK transmitter application.
It’s difficult to achieve a π shift with an OIL-VCSEL based on reasonable parameters, so MPSK transmitter may require another π shift phase modulator. Figure 9 shows that directly modulated OIL-VCSEL can function as a key component in QPSK or 8PSK transmitters. This configuration lowers the complexity of high-speed electrical modulation signals. This configuration is also less complex than conventional setups. All the constellation diagrams inserted in Fig. 9 are simulation results.
Fig. 9 Schematics for MPSK transmitters: (a) QPSK transmitter, (b) 8PSK transmitter. (PC: polarization controller, OC: optical circulator, PM: phase modulator)
3. Experimental results
To demonstrate that the condition mentioned above can be achieved, i.e. an OIL-VCSEL can emit phase modulated signal with hardly any intensity modulation, we set up the following experiment, as is shown in Fig. 10. In this experiment, an interference arm is added to coherently detect the output optical signal. The VCSEL is biased at 7.0 mA with 2.0 dBm output power. A CW-operated DFB laser is used as the master laser. The injection ratio is fixed at 10.2 dB and wavelength detuning is changing from −0.16 nm to 0.38 nm. A variable optical attenuator (VOA) and polarization controller (PC) are used on the interference arm to control the reference light from master laser.
Fig. 10 Experimental setup (PC: polarization controller, OC: optical circulator, VOA: variable optical attenuator)
To test the sensitivity of locking condition for phase modulation application of OIL-VCSEL, we define degree of amplitude modulation (ΔI/I) in Eq. (1).
where Imax and Imin are maximum and minimum output signal intensity respectively.Figure 11 shows the experimental results. Under large signal modulation, the top gray curve in the Fig. 11(a) is the free-running output waveform. After we injection lock the VCSEL, VOA is set to the blocking state in the experiment. Figure 11(b)-11(d) are the output waveforms for the normal state (Δλ = −0.16 nm), transitional state (Δλ = 0.15 nm), and inverted state (Δλ = 0.38 nm) respectively under OIL conditions. For traces (e) and (f), attenuation of VOA is changed to 1.5 dB for coherent detection on output port under transitional state (Δλ = 0.15 nm). By adjusting the phase difference between the two arms, we observe the two opposite waveforms in Fig. 11(e) and 11(f) respectively. These results confirm that OIL-VCSEL can function as a phase modulator. Though the speed demonstrated here is 2.5 Gb/s, limited by instrumentation, we have reason to believe that the speed can reach ~100 GHz, since resonance frequency is more than 100 GHz and 3-dB bandwidth up to 80 GHz has been demonstrated by using strong OIL [4].
Fig. 11 Experimentally measured bit sequence when the VCSEL is free running as well as injection-locked at special conditions: (a) free running, (b) normal state under OIL, (c) transitional state under OIL, (d) inverted state under OIL, (e) and (f) coherent detection at transitional state (CD: coherent detection).
To test the sensitivity of locking condition for phase modulation application of OIL-VCSEL, the degree of amplitude modulation (ΔI/I) is measured and plotted on the locking map in Fig. 12. The black points are experimentally measured, and we accordingly use linear interpolation method to depict Fig. 12 below. The red zone in Fig. 12 means that the degree of amplitude modulation is less than 1%, so there is almost no unwanted intensity modulation under these locking conditions. When injection ratio is fixed at 12 dB in Fig. 12, the accuracy requirement of wavelength detuning is ± 0.1 nm in the red zone (ΔI/I < 1%). The accuracy of wavelength detuning is usually dependent on the temperature controller. The wavelength of VCSEL will increase ~0.1 nm with each increased 1 °C, so accuracy requirement of temperature controller is ± 1 °C. It is easy to satisfy such requirements for phase modulation application of OIL-VCSEL. The shape of the narrow red zone in Fig. 12 is quite consistent with simulation result in Fig. 6(a). Yet the definition of Δλ in the experiment leads to the disagreement of Δλ between theory (0.73 nm) and experiment (0.15 nm). For single transverse mode of VCSEL, it has two polarization modes. The space between these two modes is ~0.5 nm. The master laser can lock both polarization modes of VCSEL [18]. However, only the wavelength of strong polarization mode is usually defined as the wavelength of VCSEL in the experiment, which results in the disagreement of Δλ between theory and experiment.
4. Discussion and conclusion
We have theoretically investigated the phase modulation of a directly modulated reflection-mode OIL-VCSEL. The phase information of output optical field is calculated based on the reflection-mode OIL model. The maximum of phase shifting of output optical field can reach 0.934π with hardly any intensity modulation output by OIL technique in the simulation. Results show a directly modulated OIL-VCSEL can function as a key component in MPSK transmitters. These configurations can be compact, very high-speed, low power consuming and potentially cost-effective. Preliminary 2.5 Gb/s PSK modulation characteristic is demonstrated experimentally which enables OIL-VCSELs to function as a key component in QPSK or 8PSK transmitters for spectrally efficient fiber transmission. An interesting thing is that there exists another report about detection of phase-modulated optical signals using OIL-VCSEL [19]. A comparison between the phase-detection in [19] and the phase-modulation in this paper shows that they are totally opposite processes. The relationship of internal mechanism between them needs to be further studied. Also, a real-time experimental measurement of optical phase amplitude modulation is proposed in [17], which enables us to further experimentally study in detail phase information in the future.
Acknowledgments
The authors wish to acknowledge the support of the National Basic Research Program of China (973 Program 2012CB315606 and 2010CB328201), the State Key Laboratory of Advanced Optical Communication Systems and Networks, China. CCH acknowledges support by the US Department of Defense National Security Science and Engineering Faculty Fellowship N00244-09-1-0013, and Chang Jiang Scholar Endowed Chair Professorship. The authors thank Ms. Rongrong Gu for correcting the English manuscript.
References and links
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