Broadband Optical Frequency Comb Generation Utilizing a Gain-Switched Weak-Resonant-Cavity Fabry–Perot Laser Diode under Multi-Wavelength Optical Injection

Abstract

We propose and experimentally demonstrate an approach for generating a wideband optical frequency comb (OFC) featuring multiple comb lines and wavelength tunability based on a gain-switched weak-resonant-cavity Fabry–Perot laser diode (WRC-FPLD) under multi-wavelength optical injection. The longitudinal mode interval of the utilized WRC-FPLD is about 0.28 nm (35.0 GHz), and its relaxation oscillation frequency is about 2.0 GHz at 1.15 times the threshold current. Under current modulation with a power of 20.00 dBm and a frequency of 2.0 GHz, the WRC-FPLD is driven into the gain-switched state. By further introducing multi-wavelength injection light (MWIL) containing four power equalization comb lines with an interval of 0.56 nm, a wideband OFC featuring multiple comb lines and wavelength tenability can be obtained. The experimental results demonstrate that by gradually increasing the injection’s optical power, the number of produced OFC lines initially increases and then decreases. By meticulously adjusting the wavelengths of the MWIL and carefully selecting the matched injection power, the broadband OFC can be tuned across an extensive spectral range. Under optimized operation parameters, an OFC with 147 lines, and a bandwidth of approximately 292 GHz within a 10 dB amplitude, variation is achieved. In this case, the measured single-sideband phase noise at the fundamental frequency is about −115 dBc/Hz @ 10 kHz, indicating that the comb lines possess good stability and strong coherence.

1. Introduction

Optical frequency combs (OFCs) [1], serving as a source of multi-wavelength light, are characterized by a series of discrete and coherent spectral lines that are uniformly spaced in the frequency spectrum. Concurrently, in the time domain, the OFC manifests as a train of pulses with consistent time intervals. The OFC’s unique properties allow it to be applied in various fields, including spectroscopy [2,3], atomic clocks [4,5], optical communication [6,7], and arbitrary waveform generation [8,9]. The main methods for producing an OFC include mode-locked lasers [10,11], electro-optic modulation [12,13], and optical injection-locked gain-switched (OI-GS) laser diodes [14,15]. Among these methods, the OFC-generated schemes based on OI-GS laser diodes receive additional attention due to their exceptional performances in terms of stability, tunability, and phase correlation [16,17,18].

The Fabry–Perot laser diode (FP-LD) possesses a relatively wide gain spectrum, which gives an OI-GS FP-LD the potential to generate a wideband OFC [19]. In recent years, various experimental schemes utilizing OI-GS FP-LDs to generate broadband OFCs have been reported. In 2011, Zhou et al. experimentally generated an OFC using an OI-GS FP-LD and subsequently expanded its bandwidth to about 160 GHz (16 comb lines) via a phase modulator [20]. In 2015, Pascual et al. demonstrated an OFC with a bandwidth exceeding 325 GHz (52 comb lines) by simultaneously injecting and locking two modes of a gain-switched (GS) FP-LD [21]. In 2021, Jain et al. reported an OFC with a bandwidth of approximately 100 GHz (nine comb lines), where the comb spacing and central wavelength can be tuned [16]. In 2023, Lakshmijayasimha et al. reported an OFC with a bandwidth exceeding 275 GHz (44 comb lines) via a GS FP-LD under multi-wavelength optical injection, where the multi-wavelength injection light (MWIL) contains 13 wavelength components, which is provided by an OI-GS distributed feedback semiconductor laser (DFB-SL) [22]. However, the aforementioned schemes face a challenge due to the relatively large mode spacing of the utilized FP-LDs, which makes it difficult for the injected light, at a specific wavelength, to effectively stimulate the adjacent longitudinal modes. As a result, both the bandwidth and the number of comb lines (NCL) of the generated OFCs are restricted. Compared to traditional FP-LDs, the weak-resonant-cavity Fabry–Perot laser diode (WRC-FPLD) possesses a longer cavity length and lower front-facet reflectivity [23,24], which leads to more compact mode spacing and a flatter gain spectrum. As a result, based on an OI-GS WRC-FPLD, it is expected that an OFC with a wider bandwidth and a greater NCL can be achieved.

In this work, based on a GS WRC-FPLD under multi-wavelength optical injection, we propose a scheme for generating an OFC with a wide bandwidth, multiple comb lines, and tunability. For such a scheme, via the four-wave mixing (FWM) effect in a DFB-SL under continuous light injection [25,26], a light source containing four wavelength components with an interval of 0.56 nm (twice the longitudinal mode spacing (0.28 nm) of the WRC-FPLD) is obtained and taken as the MWIL after undergoing power equalization. By inspecting the performances of the generated OFC under different injection parameters, the influences of the injection parameters on the performances of the generated OFC are revealed. Under optimized injection conditions, an OFC comprising 147 lines with a bandwidth of approximately 292 GHz under a free spectral range (FSR) of 2 GHz is obtained. Based on this proposed scheme, the generated OFC has some unique virtues including a small FSR, a large bandwidth, and tunability, and it possesses application prospects in a variety of fields such as high-density optical communication and spectroscopy.

2. Experimental Setup and Theory

Figure 1 is the schematic diagram of the experimental system. A WRC-FPLD is powered by the combination of two currents through a T-type bias tee (BST, Picosecond, 5541A, 80 kHz–26 GHz, OH, USA), where one is a DC bias provided by a laser diode controller (LDC1, ILX-Lightwave, LDC-3724C, CA, USA) and the other is a sinusoidal modulation current at a frequency of f_a supplied by a microwave frequency synthesizer (MFS, Agilent E8257C, Santa Clara, CA, USA). The WRC-FPLD adopts the compact and simple design of a TO-56-can package, which uses a set of a designed copper mount and a thermistor to reduce the influence of temperature variation on the laser [27,28,29]. Throughout the entire experimental process, the temperature of the WRC-FPLD is maintained at 17.15 °C by LDC1. The continuous light wave from a tunable laser (TL, Santec TSL-570, 1480–1640 nm, Aichi, Japan) is injected into a DFB-SL via an optical circulator (OC1). The DFB-SL is driven by another laser diode controller (LDC2, ILX-Lightwave, LDC-3908, CA, USA). Based on the FWM effect in the DFB-SL cavity, four coherent comb lines can be observed, for which there exist significant differences in the power amplitudes among the four comb lines. Subsequently, by sending them to a fiber Bragg grating filter (FBGF, ExFOXTM-50, QC, Canada) combined with an erbium-doped fiber amplifier (EDFA, Wuhan, China), power-balanced MWIL containing four comb lines can be obtained through selecting suitable operating parameters. The MWIL successively passes through a variable attenuator (VA), a polarization controller (PC), a 10:90 fiber coupler (FC1), and an optical circulator (OC2), and is then injected into the WRC-FPLD. The injection light power is monitored via a power meter (PM, Thorlabs, PM100D, NJ, USA). The optical signal output from the WRC-FPLD is split into two branches by a 50:50 fiber coupler (FC2). One branch is connected to an optical spectrum analyzer (OSA, Aragon Photonics BOSA lite+, 20 MHz resolution, Zaragoza, Spain) for spectral analysis. The other branch is further divided into two paths by another 50:50 fiber coupler (FC3). One path is sent to an electrical spectrum analyzer (ESA, Rohde & Schwarz FSW, 67.0 GHz bandwidth, Munich, Germany) after being converted to an electrical signal by a photodetector (PD1, U2T-XPDV2150R, 50.0 GHz bandwidth, Sunnyvale, CA, USA). The other path is connected to another photodetector (PD2, New Focus 1544B, 12.0 GHz bandwidth, CA, USA) and is then sent to a digital storage oscilloscope (DSO, Agilent X91604A, 16.0 GHz bandwidth, Santa Clara, CA, USA) for time-series measurement.

Based on the multi-mode rate equations describing the FP-LD [30], the theory model for a GS WRC-FPLD under multi-wavelength optical injection can be established after further considering the effects of current modulation and optical injection. The rate equations for a GS WRC-FPLD under multi-wavelength optical injection can be described as

$$\begin{array}{l}{\displaystyle \frac{\mathrm{d}{E}_{\mathrm{m}}(\mathrm{t})}{\mathrm{dt}}}={\displaystyle \frac{1}{2}}(1+\mathrm{i}\mathsf{\alpha })[G_m-\mathsf{\gamma }]E_{\mathrm{m}}(\mathrm{t})+{\displaystyle \sum _{j=1}^4{k}_{\mathrm{m}, \mathrm{j}}{E}_j^{inj}\exp (-i\mathsf{\Delta }{\mathsf{\omega }}_{\mathrm{m}, \mathrm{j}}\mathrm{t})}\\ +\sqrt{2\mathsf{\beta }N(t)}{\mathsf{\zeta }}_{\mathrm{m}}(\mathrm{t})\end{array},$$

(1)

$${\displaystyle \frac{\mathrm{d}N\left(\mathrm{t}\right)}{\mathrm{dt}}}={\displaystyle \frac{I_{bias}(1+a\sin (2\mathsf{\pi }{f}_{\mathrm{a}}\mathrm{t}))}{\mathrm{q}}}-{\displaystyle \frac{1}{{\mathsf{\tau }}_{\mathrm{n}}}}N(t)-{\displaystyle \sum _{m=1}^M{G}_m|E_m(t){|}^2},$$

(2)

where E_m(t) and N(t) are the slow variable field amplitude for the mth longitudinal mode and carrier number, respectively. $E_j^{inj}$ is the slow variable field amplitude of the jth injection light, and k_m,j is the injection strength for the mth longitudinal mode subject to the jth injection light. I_bias is the bias current, α is the linewidth enhancement factor, and γ is the cavity decay rate. Δω_m,j is the frequency detuning between the frequency of the mth longitudinal mode and the jth injection light. Here, we assume that the injected light contains four wavelengths. β and ζ_m represent the spontaneous radiation factor and spontaneous radiation noise, respectively. a is the modulation amplitude, and f_a is the modulation frequency. q represents the charge of an electron, and τ_n is the photon lifetime. M represents the total mode number that needs to be considered. G_m is the gain of the mth longitudinal mode, which can be described as

$$G_{\mathrm{m}}={\displaystyle \frac{{\mathrm{g}}_{\mathrm{c}}(N(t)-N_0)}{1+\epsilon {\displaystyle \sum _{m=1}^M|E_m(t){|}^2}}}[1-{({\displaystyle \frac{m-m_c}{\mathsf{\Delta }{\mathrm{f}}_{\mathrm{g}}}}\mathsf{\Delta }{\mathrm{f}}_{\mathrm{L}})}^2],$$

(3)

where g_c and ε are the differential gain coefficient and gain saturation coefficient, respectively. N₀ is the transparency carrier number. m_c is the order of the strongest longitudinal mode, Δf_L is the longitudinal mode spacing of the laser, and Δf_g represents the gain bandwidth.

Based on Equations (1)–(3), the output characteristics of a GS WRC-FPLD under multi-wavelength optical injection can be analyzed numerically.

3. Results and Discussion

First, we analyze the fundamental properties of the WRC-FPLD utilized in this work. Figure 2 illustrates the P-I curve of the free-running WRC-FPLD, along with its optical spectrum under a bias current of 52.00 mA. As shown in Figure 2a, the threshold current (Ith) for the WRC-FPLD is approximately 45.00 mA. Under the bias current (I_bias) set at 52.00 mA (~1.15 Ith), the output power reaches 0.409 mW, and the corresponding optical spectrum is presented in Figure 2b. The peak wavelength is located at 1547.0899 nm, and the optical spectrum covers approximately 40 nm (from 1525 nm to 1565 nm). The wavelength spacing (Δλ_w) between two adjacent longitudinal modes is about 0.28 nm (corresponding to a frequency spacing Δν_W ~35 GHz), which is determined by the optical length of the active region in the WRC-FPLD. Through accurately designing the optical length of the active region combined with precisely controlling its temperature, the frequency spacing between two adjacent longitudinal modes in the WRC-FPLD can be matched with the telecom channel standards. In this work, we take the WRC-FPLD biased at 52.00 mA as an example to demonstrate the generation of the OFC after introducing current modulation and multi-wavelength optical injection. Through experimental measurement, it was found that the relaxation oscillation frequency of the WRC-FPLD biased at 52.00 mA is approximately 2.0 GHz. As a result, a modulation signal with a frequency of 2.0 GHz is employed to drive the WRC-FPLD into a GS state.

Next, we examine the output characteristics of the WRC-FPLD under current modulation. Figure 3 gives the optical spectra (first column), time series (second column), and power spectra (third column) of the WRC-FPLD output under current modulation with a frequency f_a = 2.0 GHz and different power levels. For a modulation power P_m = 0 (Figure 3(a1–a3)), the WRC-FPLD operates at a free-running state. A series of longitudinal modes emerge in the optical spectrum, and the time series displays randomness and irregularity. Moreover, the power spectrum is close to the noise level except for a peak at around 2.0 GHz, corresponding to the relaxation oscillation frequency of the WRC-FPLD. For P_m = 0.00 dBm (Figure 3(b1–b3)), the longitudinal modes in the optical spectrum are broadened without discernible comb lines. The time series manifests as pulses with a repeat period of T = 0.5 ns (=1/f_a) and random fluctuations in peak power. The power spectrum reveals the presence of beat frequency signals, originating from the periodic nature of the modulation signal. Additionally, the continuous noise level is elevated due to incoherent time jitter between pulses caused by varying spontaneous emission during the pulse recovery period [31]. These characteristics indicate that the WRC-FPLD begins to enter the GS state. The GS state refers to repeated toggling of the gain “on” and “off” states in a laser under a high-frequency alternating current, which results in the output power switching between “on” and “off” states. As a result, the output of the laser is in the form of pulses [32]. For P_m = 20.00 dBm (Figure 3(c1–c3)), the optical spectrum becomes flatter, and the time series manifests as pulses with a stronger peak power. Meanwhile, much higher-order harmonics appear in the power spectrum, and the continuous noise level is obviously enhanced. Under this case, the WRC-FPLD exhibits the typical characteristics of the GS state. In the following, we will utilize the WRC-FPLD in a typical GS state to generate a high-quality OFC through introducing multi-wavelength optical injection.

In order to simultaneously lock multiple modes of the WRC-FPLD for generating an OFC with a wide bandwidth, the spacing between the comb lines of the MWIL is required to be an integer multiple of the longitudinal mode spacing Δλ_w (=0.28 nm) of the WRC-FPLD. Our previous research has demonstrated that the NCL of the OFC generated by a GS WRC-FPLD under single-wavelength light injection varies periodically with the injected light wavelength, and the period is the same as the spacing between longitudinal modes [33]. Meanwhile, the bandwidth of the generated OFC can exceed the longitudinal mode spacing of the WRC-FPLD. Therefore, it is appropriate that the comb line spacing (Δλ_D) of the MWIL is set at double the mode spacing (2Δλ_w = 0.56 nm). In this work, the MWIL is generated via the four-wave mixing (FWM) effect in a DFB-SL under optical injection and subsequently undergoes power equalization. Based on our previous experimental investigations [33], the injection light is best placed close to the strongest mode of the WRC-FPLD. Considering that the wavelength of the strongest longitudinal mode of the WRC-FPLD is located at 1547.0899 nm, the central wavelength of the DFB-SL (λ_D) is set at 1547.0294 nm. In this case, the optical spectrum of the free-running DFB-SL is given in Figure 4a. The CNR is greater than 60 dB. To obtain MWIL with Δλ_D = 2Δλ_w (0.56 nm), the wavelength detuning between the tunable laser (TL) and the DFB-SL should be set at Δλ_D (=2Δλ_w). Adopting continuous light with a power of 10.00 dBm and a wavelength of λ_D + Δλ_D to inject into the DFB-SL, a light source containing multiple comb lines with wavelength spacing of Δλ_D can be achieved based on the FWM effect, and its optical spectrum is provided in Figure 4b. Obviously, the amplitudes of the four comb lines differ significantly, which is not conducive to generating an OFC with high flatness. Further adopting an FBGF combined with an EDFA to implement power equalization, high-quality MWIL can be obtained, whose optical spectrum is given in Figure 4c. The four comb lines possess comparable power levels, and the CNR is approximately 40 dB.

Then, the high-quality MWIL is injected into the GS WRC-FPLD operating at the state shown in Figure 3(c1–c3). Through adjusting the gain of the EDFA and the attenuation rate of the VA, the injection power (P_inj) can be controlled. Under P_inj = 4.982 μW, the optical spectrum of the GS WRC-FPLD under multi-wavelength optical injection with λ_D = 1547.0294 nm is displayed in Figure 5. The generated OFC consists of 147 comb lines with a CNR greater than 20 dB, and its bandwidth is approximately 292 GHz. The reason for generating a broadband OFC through introducing MWIL is as follows. On one hand, the interaction between MWIL and the cavity’s longitudinal modes facilitates the coupling among adjacent modes, which can maintain a stable phase relationship among them. Therefore, the overall stability of the laser output is improved, and the comb lines with a high CNR can be achieved. On the other hand, the enhanced FWM effect, stimulated by the interaction of multiple wavelengths, broadens the output optical spectrum. As a result, through introducing MWIL to achieve the locking of ten adjacent longitudinal modes, an OFC with a bandwidth of approximately 292 GHz within a 10 dB amplitude variation is generated. It should be pointed out that when maintaining comb line wavelength spacing of 0.56 nm and tuning the wavelengths of MWIL, quasi-continuous tuning of the OFC’s central wavelength in the range of 1525 nm to 1565 nm can be realized.

Figure 5 is obtained under P_inj = 4.982 μW. Our experimental results demonstrate that the number of comb lines in the output of the OI-GS WRC-FPLD is dependent on the injection power. Figure 6a presents the number of comb lines (NCL) of OFC output from the OI-GS WRC-FPLD varied with the injection power under λ_D = 1547.0294 nm. It should be noted that the values are obtained from five sets of measurements taken after completely shutting down and restarting the experimental system. As shown in Figure 6a, with the increase in injection power, the number of OFC comb lines shows a trend of increasing first and then decreasing. However, the variation in the number of comb lines is relatively small. When P_inj = 4.982 μW, the number of comb lines in the OFC reaches its maximum value at 147, and its optical spectrum is shown in Figure 5. Figure 6b shows the power variation of different comb lines of the generated OFC with the injection power. With the increase in injection power, the power of different comb lines gradually rises. From this diagram, it can also be observed that the power fluctuations from multiple measurements for each of the comb lines are relatively small, which indicates that our proposal for generating an OFC possesses good reproducibility.

Finally, we discuss the characteristics of the frequency spectrum for the OFC in Figure 5, which is presented in Figure 7. From the power spectrum (Figure 7a), it can be seen that compared to the GS state shown in Figure 3(c3), the continuous noise level at higher frequencies has been suppressed. Moreover, much higher-order beat frequency signals can be observed. As a result, after introducing MWIL, the coherence among pulses has been enhanced. As previously mentioned, the “off” state in GS lasers causes the pulses to be completely disconnected, and each new pulse established by spontaneous emission of photons possesses a random initial phase. However, after introducing MWIL, the externally injected photons serve as a seed from which the pulses are derived. Such a specific phase correlation between successive pulses leads to noise suppression effects [34]. To characterize the coherence and stability of the obtained OFC, we measure the spectral distribution near the center frequency of the fundamental signal in the power spectrum and the single-sideband (SSB) phase noise of the fundamental signal, which are given in Figure 7b,c, respectively. As shown in Figure 7b, the CNR is greater than 60 dB and the 3 dB linewidth is approximately 1 Hz. The SSB phase noise of the fundamental signal (shown in Figure 7c) is approximately −115 dBc/Hz @ 10 kHz. Therefore, the OFC generated based on the OI-GS WRC-FPLD exhibits high coherence and stability. Figure 7d gives the SSB phase noise of the fundamental signal at a 10 kHz frequency offset as a function of the observing time. Over a 30 min observation window with an interval of 5 min, the SSB phase noise maintains at a fluctuation below 2.22 dBc/Hz, which means that the generated OFC possesses long-term stability.

For comparison,

Table 1. Summary of OI-GS FP-LD acquisition of OFC.

Ref.	Year	Key Expansion Component	Number of Wavelengths Contained in Injected Light	OFC FSR (GHz)	OFC Bandwidth (GHz)	NCL
[20]	2011	OI-GS FP-LD + phase modulator	1	10	~160	16
[21]	2015	OI-GS two-mode FP-LD	1	6.25	~325	52
[16]	2021	OI-GS FP-LD	1	12.5	~100	9
[22]	2023	MWIL introduction to GS FP-LD	13	6.25	~275	44
This work	2024	MWIL introduction to GS WRC-FPLD	4	2	~292	147

summarizes the related experimental schemes for generating the broadband OFC based on the OI-GS FP-LD. It can be found that the OFC generated in this work possesses a larger NCL and a smaller FSR.

4. Conclusions

In summary, we experimentally demonstrated broadband OFC generation utilizing a gain-switched WRC-FPLD under multi-wavelength optical injection. Utilizing the FWM effect of the DFB-SL under continuous light injection, coherent MWIL with spacing that is twice the mode spacing of the WRC-FPLD is generated. After undergoing power equalization, the MWIL is introduced to lock multiple modes of the GS WRC-FPLD for generating the broadband OFC. The experimental results show that with the increase in MWIL power, the number of comb lines of the generated OFC exhibits a trend of increasing first and then decreasing. Under optimized operating parameters, an OFC with 147 comb lines and a bandwidth of approximately 292 GHz is generated, for which the 3 dB linewidth of the beat signal fundamental frequency is approximately 1 Hz, and the SSB phase noise is around −115 dBc/Hz @ 10 kHz. Since the generated OFC based on this proposed scheme possesses some special advantages, it is expected that this scheme has potential applications in some fields, such as high-density optical communication and spectroscopy.