Microwave photonic signal generation in an optically injected 2 discrete mode semiconductor laser 3

In this paper, microwave photonic signal generation based on period-one dynamic of op8 tically injected discrete mode (DM) semiconductor lasers has been experimentally demonstrated 9 and numerically simulated. The results show that the frequency of the generated microwave in10 creases linearly with the frequency detuning or optical injection ratio. In addition, a single optical 11 feedback loop is sufficient to reduce the microwave linewidth without significantly deteriorating 12 side mode suppression. The simulation results using a model considering the nonlinear dependen13 cies of the carrier recombination agree well with the experimental results, which indicates that the 14 nonlinear carrier recombination effect is important in determining the nonlinear dynamics of opti15 cally injected DM lasers. 16


20
In the fast-developing information society, radio and microwave signals play signif-21 icant roles in the field of communication, radar, and sensing systems [1-3]. To implement 22 high speed transmission in wireless networks as well as high-resolution detection in radar 23 and sensing systems, high-frequency microwave signals with salient features such as ul-24 tra-low phase noise and broad tunable range is highly required. However, it is compli- 25 cated and costly to generate such desired high-frequency microwaves by multiple fre-26 quency doubling based on conventional electronic circuits [4]. Moreover, such high-fre-27 quency electrical microwave signals inevitably suffer enormous attenuation in coaxial ca-28 ble transmissions for most practical scenarios [5]. To address these technical challenges, 29 photonic approach, well-known as microwave photonics, has been applied to overcome 30 the bottleneck of microwave generation in electrical domain. Generally speaking, pho-31 tonic generation of microwave signals have superior advantages in terms of high fre-32 quency (up to millimeter-wave band), broad frequency tunability, low propagation loss 33 in optical fibers and high robustness to electromagnetic interference . Additionally, 34 recently reported InP and silicon based photonic integrated devices/circuits [6-8] further 35 expand the perspective of photonic high-frequency microwave and thus it becomes a very 36 hot research topic in the field of radio-over-fiber (RoF), optical signal processing, true-37 time delay beamforming, and subnoise detection etc. [9][10][11][12]. 38 Compared with the microwave synthesis using electronics, which has been exten-39 sively explored and developed over the past decades, high-frequency microwave pho-40 tonic (MWP) signal generation in the optical domain is more convenient and cost-effec- 41 tive. Various approaches of MWP signal generation can generally be classified into optical 42 heterodyning [13,14], direct and external modulation [15][16][17], self-pulsating and mode-43 locking [18,19], optoelectronic oscillators (OEOs) [20][21][22][23][24], and laser dynamics of period-44 one (P1) [25][26][27][28][29][30][31][32][33][34][35][36]. The optical heterodyne technique can easily achieve terahertz photonic 45 microwaves by beating between two optical beams with certain wavelength spacing, as 46 such the technique has very wide tunability [13]. However, the inevitable mismatch of 47 optical phases and fluctuated amplitudes between two non-coherent lasers result in ex-48 tremely poor microwave stability, which becomes an Achilles' heel for applications re-49 quiring high stability. Direct and external modulation schemes are also very important for 50 high-frequency MWP signal generation. The former possesses the simplest architecture 51 for MWP signal generation, but its modulation bandwidth is limited by the relaxation 52 oscillation frequency of the lasers, which is usually less than 15GHz, and the modulation 53 depth is also relatively low [15]. On the other hand, MWP signal generation utilizing ex-54 ternal modulation can attain very high frequency and low phase noise microwave signals, 55 but there is a drawback resulting from the insertion loss of the modulators [16]. An OEO 56 is another paradigmatic method to obtain narrow-linewidth microwave signals in both 57 the electrical and optical domains by introducing a feedback loop as a high-quality-factor 58 optoelectronic oscillating cavity to a pump laser [20][21][22][23][24]. Consequently, the phase noise of 59 generated microwaves can be comparable with those produced by mode-locked lasers 60 [19], but the frequency tunability is compromised. 61 Recently, a competitive approach of MWP signal generation based on P1 dynamic of 62 semiconductor lasers has been proposed and explored [25][26][27][28][29][30][31][32][33][34][35][36]. P1 dynamic of semicon-63 ductor lasers can be achieved by optical injection under certain injection parameters, 64 which causes the optical output intensity of semiconductor lasers to undergo self-sus-65 tained oscillation at a microwave frequency [25]. The MWP signal is generated when the 66 optical output of semiconductor lasers at P1 dynamic is detected by a photodetector. Due 67 to the injection pulling effect and the red shifting effect, the generated photonic micro-68 wave frequency can be tens of times higher than the relaxation resonance frequency of the 69 semiconductor laser while a relatively simple system setup still remains to support flexi-70 ble tunability [26]. Therefore, considering the characteristics such as cost, power effective-71 ness and all-optical broad frequency tunability, MWP signal generation based on P1 dy-72 namic of semiconductor lasers become a promising method, which has been widely stud-73 ied for different types of semiconductor lasers. For distributed feedback (DFB) semicon-74 ductor lasers, Chan  As a special type of Fabry-Perot semiconductor lasers, discrete mode (DM) lasers 90 have similar geometry structure with standard Fabry-Perot lasers but contain a small 91 number of etching features along the ridge waveguide. This unique feature guarantees 92 DM lasers achieving single longitudinal mode operation with high sidemode suppression 93 [39]. DM lasers also have many other impressive characteristics, such as, very narrow lin-94 ewidth, wide temperature operation range, low cost, and easy integration [40]. These sa-95 lient features undoubtedly imply that DM lasers are a good candidate for P1 dynamic 96 based low phase noise photonic microwave generation. However, the previous reports on 97 DM lasers [41][42] do not address the photonic microwave generation in optically injected 98 DM lasers. Therefore, in this paper, we focus on photonic microwave generation based on 99 period-one dynamic of optically injected DM semiconductor lasers. The main parameters 100 affecting the fundamental frequency, power, linewidth, and phase noise of the generated 101 photonic microwave have been experimentally studied. In addition, optical feedback is 102 also adopted to further optimize the linewidth of the generated microwave. Finally, a 103 modified rate equation model is proposed to numerically analyze the frequency of the 104 generated microwave in DM lasers. 105

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The schematic diagram of the experimental setup in a slave -master lasers configu-107 ration is illustrated in Figure 1. In this experiment, a commercially available TO-56 can-108 packaged fiber pigtailed DM laser (Eblana Photonics EP1550-DM-01-FA) with a lasing 109 wavelength of about 1550 nm is used as a slave laser (SL). The DM laser is driven by an 110 ultra-low noise current source (YOKOGAWA, GS200) and the temperature is stabilized at 111 24 °C by a temperature controller (Tektronix, TED 200) with an accuracy of 0.01 °C. A 112 tunable laser (Agilent 8164A) is used as a master laser (ML). The emission of the ML injects 113 into the SL after traveling through a polarization controller (PC1), a 50: 50 fiber coupler 114 (FC1) and an optical circulator (OC). The PC1 is used to match the polarization of the 115 injection beam to the SL's polarization. The output of the DM laser passes through the OC 116 and is divided into a feedback path and a detection path by a 90: 10 fiber coupler (FC2). 117 The feedback loop composes of PC2, a variable attenuator (VA) and FC1. The polarization 118 of the feedback light is controlled by PC2 to be parallel to the polarization of the DM laser. 119 The detection path is further split by FC3 and the light beams are detected by a photode-120 tector (PD, RXM40AF, 40 GHz bandwidth) and a high resolution optical spectrum ana-121 lyzer (OSA, APEX 2070, 4 pm resolution), respectively. The output of the PD is recorded 122 by an electrical spectrum analyzer (ESA, Anritsu MS2667C, 30 GHz bandwidth) or an os-123 cilloscope (OSC, Tektronix 71254C, 12.5 GHz bandwidth). 124 The DM laser is biased at 30 mA, which is 2.5 times of its threshold current. Under 125 this operation condition, the output power of the free-running DM laser is 0.6 mW, and 126 the relaxation oscillation frequency is about 6.2 GHz. In this paper, the optical injection 127 ratio (ξinj) is defined as the optical injection power divided by the output power of the free 128 running DM laser, and the injection power is measured just before the injection beam en-129 ters the SL. The feedback ratio is defined as the ratio between the feedback power and the 130 free running DM laser output power. The feedback power is measured just before the 131 feedback beam is fed into the DM laser. The frequency detuning (Δf) is defined as finj -fSL, 132 where finj and fSL are the frequencies of the ML and the free running SL, respectively. ξinj 133 and Δf can be tuned by adjusting the output power and the frequency of the ML, respec-134 tively, and the feedback ratio is controlled by tuning the VA.

Experimental Results
Firstly the dynamical evolution of the DM laser subject to optical injection is exam-141 ined. The DM laser subject to optical injection without applying optical feedback is 142 achieved by disconnecting PC2 from the rest experimental setup. Figure 2 displays the (a) 143 time series, (b) power spectra, (c) optical spectra and (d) phase portraits of dynamical be-144 haviours of the DM laser with different ξinj when Δf is fixed at 10 GHz. The phase portrait 145 is defined as the local N-th intensity as a function of (N-1)-th intensity. When ξinj = 0.06 146 (row 1), obviously, the DM laser experiences Hopf bifurcation and oscillates at P1 state 147 with a fundamental frequency (f0) of 10.1 GHz. The tunability and quality of microwave 148 generated in the optically injected DM laser based on P1 dynamic will be discussed in the 149 next section. When ξinj is increased to 0.36 (row 2), the DM laser shows period two (P2) 150 oscillation. Further increase ξinj to 0.56 (row 3), the laser is in chaos dynamic. The above 151 results indicate that the optically injected DM laser enters chaos through period doubling. 152 In order to find P1 operation regions, the dynamics of the optically injected DM laser 157 in a parameter space of frequency detuning Δf and injection ratio ξinj are measured and 158 plotted in Figure 3. In the map, the stable (S), P1, P2, quasi period (QP) and chaos (C) 159 dynamics are denoted by dark blue, light blue, green, orange, and red, respectively. Two 160 non-P1 regions over the injection parameter space of 4GHz< Δf <14GHz and 0.2<ξinj<1, and 161 -16GHz< Δf <-8GHz and 0.1<ξinj<1 are larger than those in DFB lasers [28], but P1 dynamic 162 still dominates on the region above the Hopf bifurcation line. Now, we focus on MWP signal generation based on P1 dynamic in the optically in-167 jected DM laser. The effect of Δf and ξinj on the fundamental frequency (f0) and the power 168 of the generated microwave is presented in Figure 4. The power of the generated micro-169 wave is defined as the peak power at the fundamental frequency. Figure 4(a) shows the 170 frequency of the generated microwave as a function of injection ratio. Three frequency 171 detuning of 15GHz, 17GHz and 20GHz are studied here because the optically injected DM 172 laser operates at P1 dynamic over a very wider injection ratio range with Δf15GHz. The 173 results reveal that the microwave frequency increases linearly with the increase of injec-174 tion ratio, and the change rate of the microwave frequency drops when the frequency 175 detuning increases, which is similar to that in the DFB laser and VCSEL [28,34]. The rela-176 tionship between the generated microwave power and the injection ratio is shown in Fig-177 ure 4(b), which shows that the power of the generated microwave first increases as the 178 injection ratio increases, when ξinj = 0.92, the microwave powers reach their maximum 179 values. Further increasing the injection ratio, the microwave powers decrease again. The 180 reason for the maximum power at the injection ratio of 0.92 is that the gain distribution of 181 the semiconductor laser is affected by the optical injection, which causes the amplitudes 182 of the red-shifted cavity resonance component and the regenerated injection component 183 in the optical spectrum of P1 dynamic to change with the injection ratio. When the injec-184 tion ratio is about 0.92, the amplitudes of the red-shifted cavity resonance component and 185 the regenerative injection component are almost the same, therefore, the microwave 186 power reaches its maximum [28,48]. This phenomenon is similar to that in the DFB laser 187 and VCSELs, where there is a maximum microwave power for a fixed frequency detuning 188 [28,34]. The impact of Δf on the frequency and power of the generated microwave pho-189 tonic signal is investigated under two injection ratios: a lower injection ratio ξinj = 0.1, and 190 a higher injection ratio ξinj = 0.92, as shown in Figure 4(c, d). There is no surprise that the 191 microwave frequency increases with the increase of the frequency detuning because the 192 main contribution of the generated microwave is the frequency beating of the red-shift 193 cavity frequency and the regenerated injection frequency. The microwave power de-194 creases with the increase of the frequency detuning due to the decrease of nonlinear fre-195 quency mixing effect with increasing Δf The quality of the generated microwave in the optically injected DM laser is exam-201 ined by analyzing its linewidth and phase noise. A 3dB linewidth is adopted to quantify 202 the linewidth, and the phase noise is obtained by integrating single sideband power spec-203 trum offset from 3 MHz to 200 MHz of the fundamental frequency and then normalized 204 to the microwave power. The linewidth and phase noise of the generated microwave 205 shown in Figure 4(a) are calculated and displayed in Figure 5. We can see that the lin-206 ewidth and phase noise of the generated microwave decrease first with the increase of ξinj 207 until they reach their minimum values at an injection ratio ξinj of around 0.92, further in-208 creasing the injection ratio, the linewidth and phase noise of the microwave signal in-209 crease again. The minimum linewidth and phase noise of the generated microwave ob-210 tained at the injection parameters (Δf, ξinj) = (15 GHz, 0.92) are 1.8 MHz and 2.75 rad 2 , 211 respectively. The microwave linewidths produced in the optically injected DM lasers are 212 similar to those in DFB lasers [28], but narrower than those in VCSELs In order to stabilize the fluctuation of the generated microwave and reduce its lin-220 ewidth, the optical feedback technique used in DFB lasers and VCSELs [28, 43] is adopted. 221 In this experiment, only a single feedback loop is introduced. Figure 6 presents the power 222 spectra of the DM laser (a) without optical feedback and (b) with optical feedback at the 223 injection parameters of (Δf, ξinj) = (15 GHz, 0.92). At these injection parameters, the funda-224 mental frequency of the microwave is 17.2 GHz. As shown in Figure 6 (a), the linewidth 225 of the generated microwave photonic signal is 1.8MHz without optical feedback. After 226 introducing the optical feedback, the linewidth reduces. Figure 6(b) shows that the lin-227 ewidth narrows from 1.82 MHz to 0.52 MHz when the feedback ratio is -27.8dB and the 228 feedback round trip time is 96.15ns. Many side peaks equally separated by multiple of 229 10.4 MHz also appear in Figure 6(b), which corresponds to the external cavity modes' 230 frequencies. To quantify the side peaks in the power spectrum, a concept of side peak 231 suppression (SPS) is introduced and is defined as the ratio of the power at the fundamen-232 tal frequency to the maximum power of the side peaks [43]. The SPS is around 28 dB as 233 shown in Figure 6  The effect of the optical feedback ratio on the linewidth, phase noise and SPS of the 238 generated microwave in the optically injected DM laser is studied and shown in Figure 7. 239 The parameters in Figure 7 are the same as those in Figure 6(b) except for the optical feed-240 back ratio. Figure 7(a) shows that the linewidth first decreases as the feedback ratio in-241 creases. When the feedback ratio is increased to -35.7dB, the linewidth remains almost 242 constant as the feedback ratio is further increased until the feedback ratio reaches -25.7dB. 243 Further increasing the optical feedback ratio, the linewidth increases again. This variation 244 trend is different from that in the DFB laser and VCSEL [28,35], but is similar to that in 245 the DFB laser with filter feedback at some frequency detuning [44]. The relationship be-246 tween the phase noise and the feedback ratio is similar to that of the linewidth. As the 247 feedback ratio increases, the phase noise first decreases, then remains constant at around 248 0.3 rad 2 , and then increases again. Figure 7 (c) presents SPS as a function of feedback ratio. 249 When the feedback ratio is -42.7dB, the SPS is 30.3 dB. The SPS starts to decrease first when 250 the feedback strength increases, which is similar to that in the DFB laser and VCSEL [28, 251 35]. But after the feedback ratio increases to -35.8 dB, further increasing the feedback ratio, 252 the SPS remains almost constant at a value of about 28.3dB until the feedback ratio reaches 253 -25.7dB. Beyond the aforementioned feedback ratio, the SPS decreases sharply. This is be-254 cause the DM laser is about to leave P1 dynamic. Figure 7 shows that the SPS remains 255 above 25dB within the feedback ratios where the linewidth and phase noise are kept to 256 their minimum. The results indicate that a high SPS can be maintained over a wide feed-257 back ratio range in the optically injected DM laser with a single optical feedback loop. The 258 different variations shown in Figure 7 compared to those in DFB lasers and VCSELs may 259 attribute to the filtering effect caused by the structure of the DM laser, but further study 260 is needed to fully understand the characteristics of DM lasers.
where E(t) is the slowly varying complex amplitude of the electric field, Einj is the 271 injection field amplitude. N(t) represents the carrier number, α is the linewidth-enhanced 272 factor, g is the differential gain coefficient, N0 is the transparency carrier number and ε is 273 the gain saturation factor, τp is the photon lifetime, τext is the feedback round trip time of 274 optical feedback loop, ω is the angular frequency of the laser, η denotes the injection 275 strength, κ denotes feedback strength from optical feedback loop, I is the injection current, 276 e is the electron charge, A is the non-radiative modulus, B is the spontaneous modulus, C 277 is the Auger recombination modulus. The parameter values used in [46] are adopted, 278 where α = 3, g = 1.48 × 10 4 s -1 , I = 30 mA, N0 = 1.93 × 10 7 , ε = 7.73 × 10 -8 , τp = 2.17 ps, A = 2.8 × 279 10 8 s -1 , B = 9.8 s -1 , and C = 3.84 × 10 -7 s -1 . The relaxation oscillation frequency of the free-280 running laser is approximate fr=(gE 2 /τp) 1/2 /2π = 6.2 GHz. Eqs. (1), (2) are solved using the 281 second-order Runge-Kutta algorithm. 282 The dynamical map of the DM laser in the parameter space of frequency detuning Δf 283 and injection strength η is presented in Figure 8(a). The result qualitatively consistent with 284 the experimental measurements in Figure 3. To validate the model used in the simulation, 285 we also simulated the dynamical map of the DFB laser using the model and parameters 286 of [47] and the results are shown in Figure 8(b). Figure 8(b) shows only one small non-P1 287 island within the P1 region above the Hopf bifurcation line, which is different from the 288 experimental observation. Therefore, the nonlinear carrier recombination is necessary to 289 be included for the investigation of the nonlinear dynamics of the optically injected DM 290 laser. The SPS as a function of feedback strength for the generated MWP signal in the opti-296 cally injected DM laser and DFB laser with single optical feedback is calculated and dis-297 played in Figure 9. The injection parameters (Δf, η) are set at (15 GHz, 8ns -1 ), and the feed-298 back round trip time is 10ns. Figure 9 shows that for the DM laser, the SPS is ~17.1 dB at 299 the feedback strength of 0.32ns -1 . When the feedback strength is increased, the SPS starts 300 to drop, and when the feedback strength reaches 0.4ns -1 , the SPS decreases to ~14.1dB. But 301 further increasing the feedback strength, the SPS remains almost unchanged until the 302 feedback strength reaches 0.5ns -1 . Increase the feedback strength further, the SPS starts to 303 deteriorate again. However, for the DFB laser, the SPS decreases monotonically with the 304 increase of the feedback strength. These results are qualitatively consistent with our ex-305 perimental results in the DM laser and the reported results in the DFB laser, which indi-306 cates that single optical feedback is sufficient to achieve a narrow microwave linewidth in 307 the optically injected DM laser.  Figure 10. We can see that for 316 the DFB laser, the fundamental frequency variation with the injection strength is similar 317 to the report [48], where the frequency change rate for the lower injection strength is 318 smaller compared to that for a higher injection strength. But for the optically injected DM 319 laser, the fundamental frequency increases linearly with the injection strength. This linear 320 relationship implies that DM lasers may be a better candidate for frequency-modulation 321 continuous-wave microwave generation based on P1 dynamic.

326
In the experiment, due to the limitation of the bandwidth of the spectrum analyzer and 327 the maximum output power of the ML, only the injection parameters with the injection 328 ratio ≤ 1 and the frequency detuning ≤ 26 GHz are investigated. The experimental results 329 show that the fundamental microwave frequency increases linearly with the increase of 330 the frequency detuning and injection ratio. It has been reported that the generated micro-331 wave frequency at strong injection ratio still increases linearly with the injection ratio in 332 other types of lasers [34,48]. The properties of the MWP signal generation in the DM laser 333 at larger frequency detuning and stronger injection power will be investigated in future 334 studies. The linewidth of the generated microwave is related to the linewidth of the ML 335 and SL, therefore, the generated microwave linewidth in the DM laser is comparable to 336 that in the DFB laser, and narrower than that in the VCSEL. In the experiment, the micro-337 wave linewidths produced in the optically injected DM lasers with and without optical 338 feedback are still in the range of hundreds of kilohertz to several megahertz. The linewidth 339 of the generated microwave in the DFB laser can be reduced to a few hertz or even milli-340 hertz by optical modulation sideband injection locking or opto-electronic feedback [49, 341 50]. Therefore, further reduction of the generated microwave linewidth in the DM laser 342 will be undertaken in our next investigation. In addition, the relationship between the 343 linewidth of the generated microwave and the feedback strength in an optically injected 344 semiconductor laser subject to filtered optical feedback is related to the injection parame-345 ters [44], so it is worth further study the relationship between the linewidth and the feed-346 back strength in the DM laser at other injection parameters. 347

348
In summary, we experimentally and theoretically investigate MWP signal generation 349 based on P1 dynamic of an optically injected DM semiconductor lasers. The experimental 350 results show that the frequency of the generated microwave can be tuned by changing 351 optical injection ratio or frequency detuning. The results also show that the linewidth of 352 the generated microwave in the DM laser is comparable to that in DFB lasers and narrower 353 compared to that in VCSELs, which may be due to the narrow linewidth of the DM laser. 354 In addition, by introducing optical feedback, the relationship between the linewidth and 355 the feedback ratio in the DM laser is similar to that in the DFB laser with filter feedback, 356 which can attribute to the filtering effect caused by the structure of the DM laser. Further-357 more, a SPS of > 25 dB can remain over a wide range of the feedback ratio, this suggests 358 that single optical feedback is sufficient for reducing the linewidth of the generated mi-359 crowave in the DM laser. Numerical simulations with the consideration of the nonlinear 360 carrier recombination confirms that high SPSs can be maintained over a wide range of 361 optical feedback strength, which is in good agreement with the results obtained in the 362 experiment.