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Abstract
Effective manipulation of resonant mode, output power and modulation bandwidth of lasers are all of vital importance for practical application scenarios such as communication systems. We show that by breaking the parity-time (PT) symmetry, single mode operation lasing can be realized in an intrinsic multiple mode Fabry-Perot (FP) resonator. Two identical FP resonators are employed to establish a symmetric system and high output power can be achieved with lower fabrication difficulty and intracavity losses compared with ring resonators. The small-signal response and direct modulation of the PT-symmetric FP laser have also been demonstrated with electrical pumping. Our work opens new avenues for mode selection of high-performance FP lasers and provides a cost-effective candidate for practical applications such as communication systems.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mode control is an important topic in laser physics and integrated photonics and has been investigated intensively. By adjusting the inner parameter, mode control can manage the intensity of modes to select a desired single mode, which is important for applications such as high-speed optical communication systems and on-chip light control in integrated photonics devices. Fabry-Pérot (FP) cavity is one of the typical components of photonic integrated circuits, which is also an ideal candidate for integrated semiconductor lasers due to its simple structure and ease of fabrication. Unfortunately, the FP laser supports multiple longitudinal resonant modes within the broad gain bandwidth of semiconductors, which hinders its applications. At present, most of the single mode lasing approaches rely on the use of intra-cavity optical feedback, such as distributed Bragg mirrors [1,2], distributed feedback gratings [3–5], or extreme confinement of light in sub-wavelength structures using metallic cavities [6–8]. These lasers are widely used for their large sidemode suppression ratio (SMSR). However, these schemes have increased the complexity of design and the difficulty of fabrication. For example, the fabrication of DFB lasers usually involves one or more regrowth steps. In contrast, the FP cavity has a massive convenience in design and fabrication.
Lately, parity-time (PT) symmetry has raised considerable attention in photonics [9–12]. PT symmetry was first developed within quantum mechanics. In general, a nonconservative optical system with balanced gain-loss distribution is considered as an ideal platform for studying the fundamentals of PT symmetry. As indicated in a number of studies, gain and loss of different optical components can be integrated as nonconservative ingredients to create new effects such as coherent perfect absorption [13–16], unidirectional invisibility [17–19], chiral mode conversion [20–23], sensitivity enhancement at an exceptional point [24–26], etc. Explorations of PT symmetry also offer a unique pathway for mode manipulation in lasers [27–30]. Several promising experiments show that PT symmetry breaking can be employed to establish a single-mode operation with large SMSR in inherently multi-mode micro-ring lasers with optical or electrical pumping [27–30]. Apart from SMSR, optical power and direct modulation character are also of vital importance for application in optical communication systems. However, directly modulated PT symmetric single mode laser with high output power has not been demonstrated yet.
In this study, we propose and experimentally demonstrate a directly modulated PT symmetric single-mode FP laser for the first time to the best of our knowledge. Two FP resonators rather than micro-ring resonators are employed for their lower fabrication difficulty and intracavity losses. Single-mode selection is achieved by controlling the interaction between gain and loss in the two resonators. The gain–loss can be controlled independently by incorporating two isolated electrodes in each of the two FP resonators and changing the injection currents. Single-mode lasing with an output power of 1.7 dBm and an SMSR exceeding 24 dB is experimentally demonstrated. A 3-dB bandwidth of 7.9 GHz is achieved, and clear eye-openings are obtained for 5 Gbps NRZ operation over 10 km single-mode fiber.
2. Principle and method
2.1 Principle of the PT symmetric FP lasers
Figure 1(a) shows the schematic structure of the electrically pumped single-mode PT-symmetric FP semiconductor laser, which consists of two coupled structurally identical cavities. Two isolated P-side electrodes are employed and the gain-loss can be controlled independently by changing the injection currents on each independent electrode. According to the coupled mode theory, the eigenfrequencies $\omega _m^{({1,2} )}$ of the PT-symmetric laser are described as follows [27]:
Fig. 1. Principle of the PT symmetric FP lasers. (a) Schematic image and (d) scanning electron-microscope image of the proposed electrically pumped single mode PT-symmetric FP semiconductor laser. Simulated (b) the real and (c) the imaginary parts of the eigenfrequency versus mode loss in the loss waveguide without frequency detuning, simulated (e) the real and (f) the imaginary parts of the eigenfrequency versus mode loss in the loss waveguide with frequency detuning of 20 GHz.
Figure 1(b) and (c) show the profile of the real and imaginary parts of eigenvalues evolution curves versus the loss in the loss waveguide based on Eq. (1). The solid and dashed lines denote the principal mode (m = 0) and next-strongest competing resonance mode (m = 1), respectively. When ${\gamma _{diff}} < {\kappa _m}$, the real part is splitting, and the imaginary part is consistent, implying that two eigenvalues of this non-Hermitian system can be entirely real-valued with a frequency difference, and the two supermodes experience the same gain or loss. However, when ${\gamma _{diff}} > {\kappa _m}$, the real parts are coalescent and the imaginary parts are split, indicating that the PT symmetry is spontaneously broken, and a conjugate pair of lasing and decaying modes emerge. In the PT symmetry region, the gain differential is a constant and determined by gain spectrum and free spectral range of the FP laser. By contrast, the maximum achievable gain differential can be greatly increased by the selective breaking of PT symmetry (28). Therefore, with appropriate gain-loss contrast and coupling coefficient, a single-mode operation is accomplished. Figure 1(e) and (f) are the profile of the real and imaginary parts of eigenvalues evolution curves versus the loss in the loss waveguide when the frequency detuning is considered. The real part and image part of the eigenfrequencies evaluate similarly with the case of no frequency detuning. The difference is that PT symmetry breaking is thresholdless due to the frequency detuning.
2.2 Fabrication of the PT symmetric FP lasers
To meet the needs of the proposed laser’s fabrication, an InAlGaAs/InP structure is grown on an n-doped InP substrate by MOCVD, whose structure is shown in Fig. 2(a). The coupled waveguides are defined by standard photolithography process and etch processes of inductively coupled plasma etching and wet etching. The fabrication process of sample is shown in Fig. 2(b). First of all, the SiO2 layer is deposited by PECVD as a hard mask for the subsequent etching. After that, the positive resist is spun onto the SiO2. Furthermore, the pattern of the hard mask is defined by ICP etching. The next step is etching two kinds of FP cavities. Both shallow and deep etching use dry-etching (ICP) and wet-etching (HCL and H3PO4) to fabricate two ridge waveguides and the entire etching depth is 2.9 μm. After the etching, the SiO2 hard mask is removed from the top of the wafer. Then a new SiO2 isolate layer is deposited by PECVD to provide electrical isolation. After that, the ICP etching is used again to open windows on the twin ridge waveguides. A p-contact electrode layer consisting of Ti/Pt/Au is deposited by Sputter. Two independent electrodes are fabricated by a lift-off process. In the end, the n-contact electrode consisting of AuGeNi/Au is deposited after the thinning of the substrate to about 130μm. The finished sample wafer is cleaved into bars and chips for the following experiments.
Fig. 2. Fabrication of the PT symmetric FP lasers. a The epitaxial structure of the components in the proposed FP laser. b Schematic of the sample fabrication process.
3. Experiments and results
3.1 Experiments setup
The PT symmetric FP laser is fabricated by standard photolithography and etch processes, and no regrowth step and electron-beam lithography are required, which reduces the complexity and cost of the fabrication process. A 150 μm long laser with waveguide width of 2.5 μm, gap of 3.2 μm, front facet reflectivity of 30% and rear reflectivity of 92% is fabricated.
Several testing platforms are built to investigate the proposed laser. As shown in Fig. 3(a), the electrically driven laser test platform is used to get the real-time output power and optical spectra. The LD sample with microstrip is driven by two laser diode controllers and two microwave probes. The emission is directed into a lensed fiber adjusted by the six axes stage. An optical power meter is used to make sure the lensed fiber is collecting almost all output optical power. An optical spectrum analyzer is used to get the spectrum of the LD sample. Besides, the near field is also tested in this platform. The laser emission is collected by a 100X objective lens and is directed to an IR camera to capture the optical field patterns. A band-pass filter is applied to remove visible light, and the density filter can adjust optical power to protect the CCD. The distance between the laser and the objective can be precisely adjusted. When the object distance exceeds the focal length of the objective lens, the laser is directly imaged on the CCD, and the near field can be captured. As shown in Fig. 3(b), eye diagram and bit error rate are tested. The random signal sequence generated by a Pattern Generator is amplified to obtain an appropriate modulation amplitude. A DC bias (23 mA) is generated by the Current Source for the single longitudinal mode operation of the laser. The two parts of the signal are superimposed together through Bias-T and loaded onto the laser chip through a high-speed RF probe. The emission of laser is coupled into a high-speed photodetector through a lensed fiber, and the eye diagram and bit error rate are tested by a Digital Serial Analyzer and Bit Error Rate Tester, respectively. An optical spectrum analyzer is applied for spectrum monitoring in real-time.
Fig. 3. Schematics of test platforms. a Optical spectrum and near field measurement setup. b Eye diagram and bit error rate measurement setup. CCD, charge-coupled device; PD, photodetector; DSA, digital serial analyzer; BERT, bit error rate tester.
3.2 Single-mode operation based on PT-symmetry
The optical spectra and field distribution of a single FP laser and the proposed PT-symmetric FP laser are shown in Fig. 4. For a traditional single waveguide FP laser, a standard multi-modes spectrum with low SMSR is observed (Fig. 4(a)). For the double-waveguide FP laser, an emission spectrum with multiple modes is observed and the coupling-induced mode splitting can be seen when two waveguides are electrically even pumped with the same currents (Fig. 4(b)). The near field is evenly distributed between the gain and loss waveguides when the double waveguides are evenly pumped. Once the PT symmetry is broken by tuning the injection currents of two waveguides, the near field of the laser predominantly resides in the waveguide of gain and single-mode lasing with an SMSR of 24 dB at 1329 nm occurs (Fig. 4(c)). The injection currents are 23 mA and 0 mA. The wavelength of the PT-symmetric FP laser can be tunable by adjusting the temperature. The SMSR is larger compared with the single FP laser, indicating the increment of gain differential due to PT symmetry breaking.
Fig. 4. Experimental characterization of the PT symmetric FP laser. Optical spectrum under three arrangements of (a) single waveguide, (b) evenly pumped double waveguide, (c) PT symmetric and (d) Characteristic light-current curves for three arrangements. The insets are the corresponding near field patterns.
The characteristic light-current curves for three arrangements of evenly pumped double waveguide, PT symmetric and single waveguide is shown in Fig. 4(d). The current is the sum of the injection currents of the two electrodes, and the light from the laser is coupled out of the chip using a lensed fiber. The PT-symmetric arrangement has the performance similar to that of single-waveguide arrangement, and appears greater slope efficiency and smaller threshold current than those of evenly pumped arrangement, indicating that the presence of the lossy waveguide only serves to suppress the unwanted modes without necessarily decreasing the overall efficiency. An output power of 1.7 dBm is achieved.
The transition of the system by a nonuniform pump distribution has also been studied. The injection current in the gain waveguide maintains 23 mA, and the injection current in the loss waveguide changes from 28 mA to 14 mA with a step of 2 mA. Figure 5(a)-(h) show the corresponding evolution of the output spectra. As the loss increase, the frequency spacing of the two resonant peaks associated with the two supermodes first increases and then decreases. There is some difference in the corresponding evolution of the output spectra between our electrically pumped laser and the optically pumped microring laser in previous study [32]. Those differences come from frequency detuning $({\omega _{am}} \ne {\omega _{bm}})$ due to the carrier dispersion effect and thermal effect introduced by electrical pumping. Figure 5(i) and (j) are the profiles of the simulated real and imaginary part of eigenvalues evolution curves versus the injected current in the loss waveguide considering frequency detuning. In the simulation, the coupling coefficient is $2\textrm{\; }c{m^{ - 1}}$ and a gain difference ($6\textrm{\; }c{m^{ - 1}}$) between two resonators exists considering the reflectivity difference between two resonators. When the injection current in the loss waveguide is 28 mA (line A), the frequency detuning is zero (${\omega _{am}} = {\omega _{bm}}$) and ${\gamma _{diff}} > {\kappa _m}$. In this way, eigenfrequencies $\omega _m^{({1,2} )}$ of the PT-symmetric degenerate and the frequency spacing ($\mathrm{\Delta \omega }$) of the two supermodes is zero, which is consistent with the experimental result (Fig. 5(a)). As the injected current in the loss waveguide decrease and larger than the threshold current, frequency detuning and the frequency spacing ($\mathrm{\Delta \omega }$) of the two supermodes gradually increases (Fig. 5 k), which also match well with the experimental results (Fig. 5(b)-(g)). In our electrically pumped FP laser, PT symmetry breaking is thresholdless due to the frequency detuning. Therefore, the imaginary parts of two supermodes are not strictly equal even the injection current in the loss waveguide is larger than the effective phase transition point (Fig. 5(j)), which match well with the intensity difference between the two supermodes (Fig. 5(b)-(g)). Once the injection current in the loss waveguide is smaller than the effective phase transition point, the difference between the imaginary parts of two supermodes sharply increases (line B) and only one mode experiences sufficient amplification and lases. Figure 5 h shows the corresponding experimentally measured spectrum of line B, and the measured frequency spacing (Δω) of the two supermodes is zero for only one supermode lases. In addition, PT symmetric laser in Fig. 5 h just passes the effective phase transition point and goes into the PT broken phase, which shows no obvious SMSR because the gain-gap between two adjacent longitudinal modes is too small to meet the needs (shown in Fig.1f).
Fig. 5. Phase transition character. a-h Evolution of the emission spectra of the PT-symmetric FP laser with a constant gain in the gain waveguide and decreased loss in the loss waveguide. (i) the real and (j) the imaginary parts of eigenvalues evolution curves versus the injected current in the loss waveguide considering frequency detuning. k the experimental measured (blue line) and simulated (red dash) frequency spacing of the two supermodes.
3.3 Direct modulation character
Figure 6(a) shows the small-signal response of the evenly pumped double-waveguides laser with injection currents of 23 mA and 23 mA, PT symmetric laser with injection currents of 23 mA and 0 mA, and single-waveguide laser with injection currents of 23 mA. To observe the impact of PT symmetry on bandwidth, both PT symmetric laser and single-waveguide laser have same material, structure and cavity length which are major factors in bandwidth. The 3 dB bandwidth of the PT-symmetric laser is 7.9 GHz. With the increases in injection currents, the PT symmetric laser demonstrates the same 3 dB bandwidth as the single-waveguide laser, indicating that PT symmetry breaking has little impact on the small-signal response of lasers (Fig. 6(b)). According to the PT symmetric and coupling differential equations, PT broken phase in resonators provides mode selection but no bandwidth enhancement, which fits small-signal response results. The response intensity in Fig.6a has little difference between the broken PT symmetric laser (23 mA-0 mA with a SMSR) and single ridge FP laser (23 mA with no SMSR) which also means the broken PT symmetry has little effect on response performance of lasers.
Fig. 6. Direct modulation character. a small-signal response for three arrangements of evenly pumped double waveguides, PT symmetric and single waveguide, b small-signal response for different injection currents for PT symmetric and single waveguide arrangements. c eye diagrams in BTB and 10 km SMF transmission configuration for 5 Gbps NRZ signal. d BER characteristics as a function of received optical power in both BTB and 10 km SMF transmission configuration for 5 Gbps NRZ signal.
We also directly modulate the PT-symmetric FP laser with a 5 Gbps NRZ signal in both back-to-back (BTB) and the 10-km single-mode fiber (SMF) transmission configuration. A clear eye opening is obtained (Fig. 6(c)). The bit error rate (BER) measurement for 5 Gbps signals in both BTB and 10-km SMF transmission configuration is also performed. The bias current of the PT symmetric FP laser is set to 23 mA and 0 mA, the same as the single-mode lasing condition. Figure 6(d) shows the characteristics of the BERs as a function of the optical power received in both the BTB and 10-km SMF transmission configuration. The BER after the 10 km transmission is large than that of the BTB configuration due to the dispersion effect of the SMF, and the near error-free operation is still obtained for 10-km SMF transmission. The BERs’ characteristics of the PT-symmetric FP laser are better than the single waveguide FP laser for both the BTB and the 10-km SMF transmission configuration (Fig. 6(d)) because the broken PT phase in resonators provides a higher SMSR which means the mode competition in PT cavities is stabler with less jitter compared with multi-modes in single FP laser.
3.4 Tunable wavelength by tuning the temperature
Single-mode operation with tunable wavelength is of vital importance for applications in wavelength division multiplexing communication systems. We also experimentally demonstrate the wavelength tuning characteristic of the PT-symmetric FP laser by adjusting the temperature. The PT-symmetric FP laser is mounted on a copper heat sink, and the temperature is controlled by a thermoelectric cooler (TEC). As shown in Fig. 7(b), a tuning range of 8 nm and tuning step of 2 nm is obtained by tuning the temperature from 15℃ to 35℃, and a high SMSR above 16 dB is maintained simultaneously by fine tuning of injection currents. As shown in Fig. 7(a), the central wavelength of the PT-symmetric FP laser is almost the same as the single waveguide laser because only the mode with the highest gain reaches the PT-symmetric breaking threshold. The central wavelength is linearly related to the temperature at about 0.4 nm/℃.
Fig. 7. Experimental results of the tunable single-mode lasing under PT-symmetry condition. a central wavelength under different temperatures for the PT symmetric laser and single waveguide laser and b optical spectrum of the PT symmetric laser under different temperatures.
3.5 Influence of structure parameters on the laser performance
To further investigate the influence of cavity length, facet reflectivity, and electrical isolation between two P-side electrodes on the side mode suppression ratio and output optical power, several kinds of PT-symmetric FP laser with different structures are fabricated. As shown in Fig. 8(a), the average SMSR is 14 dB for the 200 μm long PT-symmetric FP lasers with front facet reflectivity of 30% and rear reflectivity of 92%, and 10 dB for front facet reflectivity of 30% and rear reflectivity of 30%. The better performance of higher facet reflectivity is due to the higher quality factor. As shown in Fig. 8(d), the PT-symmetric FP lasers with higher facet reflectivity also show higher output power due to smaller mirror loss. PT-symmetric FP lasers with shorter cavity lengths have also been demonstrated. As shown in Fig. 8(b), lasers with shorter cavity length show a slight improvement for SMSR. The measured free spectral ranges (FSR) are 1.18 nm and 1.59 nm for lasers with cavity lengths of 200 μm and 150 μm, respectively. The small increase in FSR contributes to the slight improvement of SMSR. Finally, two kinds of electrical isolation are considered. The first one is accomplished just by two separated electrodes on the P side, and the measured resistance is only 1 kΩ. The second method is the deep etching, and the measured resistance reaches 60 kΩ. As shown in Fig. 8(c), the average SMSR is 15 dB and 18 dB for the first and second methods, respectively. Deep etching demonstrates some advantage in terms of high SMSR but at the sacrifice of output power for large cavity loss. As a result, etching depth and cavity length parameters can be adjusted to meet the needs of different output power and SMSR.
Fig. 8. Effect of structure parameters on the laser performance. a-c Side-mode suppression ratio, and d-f characteristic light-current curves for PT symmetric FP lasers with different facet reflectivity, cavity length, and electrical isolation, respectively.
4. Conclusions
In this paper, we propose and experimentally demonstrate an electrically pumped FP semiconductor laser that supports single-mode lasing, high output power, high-speed direct modulation and tunable wavelength based on PT symmetry for the first time to the best of our knowledge. Single-mode lasing with an output power of 1.7 dBm and an SMSR exceeding 24 dB is experimentally demonstrated. A 3 dB bandwidth of 7.9 GHz is achieved, and clear eye-openings were obtained for 5Gbps NRZ operation over 10-km single-mode fiber. An experimental result of the tunable single-mode lasing under the PT-symmetry condition has been demonstrated with a tuning range of 8 nm and a step of 2 nm. Compare to commercial DFB and FP lasers, the proposed PT-symmetric FP laser reaches an applicable SMSR without grating layers, which successfully combines device performance and process cost. Moreover, the tunableness and high-speed direct modulation ability of proposed laser provide a brand new and more economical candidate for short reach and wavelength division multiplexing optical communication system, have great potential in commercial application.
Funding
National Key Research and Development Program of China (2018YFB2201500); National Natural Science Foundation of China (61835010); Strategic Priority Research Program of Chinese Academy of Sciences (XDB43000000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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