Relaxation Oscillation Frequency Research Articles

Intensity noise and modulation dynamics of an epitaxial mid-infrared interband cascade laser on silicon

Interband cascade lasers typically have significantly lower threshold current and power consumption than quantum cascade lasers. They can also have advantages regarding costs and compactness with the photonic integration onto silicon substrates by epitaxial growth. This research introduces a novel examination of the relative intensity noise and the modulation dynamics of a silicon-based Fabry–Perot interband cascade laser emitting at 3.5 μm. The investigation delves into crucial parameters, such as relaxation oscillation frequency, differential gain, gain compression, and K-factor. The resonance patterns identified in relative intensity noise curves can provide essential insights for the thorough characterization of high-defect mid-infrared semiconductor structures intended for high-speed applications. Moreover, this study demonstrates the feasibility of reaching 10 Gbit/s free-space transmission using a silicon-based interband cascade laser in conjunction with an interband cascade infrared photodetector.

Broadband chaotic signal generation with a solitary microcavity laser

We have proposed and experimentally demonstrated a novel chaotic signal generator using a solitary deformed square microcavity laser. The carrier density in the microcavity laser exhibits periodic or chaotic oscillation due to the interaction between the cavity modes, as long as the frequency difference between the modes is comparable to the relaxation oscillation frequency of the laser. The oscillation of carrier density leads to the variation of the Fermi level and, consequently, the applied voltage. The electrical signal can then be extracted directly from the electrode of the microcavity laser without the need for optical-electrical conversion. The obtained chaotic signal has a standard bandwidth of 9.6 GHz, and physical random numbers can be generated from the temporal waveform with simple post-processing methods. The scheme demonstrated here requires simple hardware, making it a promising solution for chaotic signal generators in various applications.

Simultaneously enhancing capacity and security in free-space optical chaotic communication utilizing orbital angular momentum

Optical chaotic signals emitted from an external-cavity feedback or injected laser diode enable small-signal information concealment in a noise-like carrier for secure optical communications. Due to the chaotic bandwidth limitation resulting from intrinsic relaxation oscillation frequency of lasers, multiplexing of optical chaotic signal, such as wavelength division multiplexing in fiber, is a typical candidate for high-capacity secure applications. However, to our best knowledge, the utilization of the spatial dimension of optical chaos for free-space secure communication has not yet been reported. Here, we experimentally demonstrate a free-space all-optical chaotic communication system that simultaneously enhances transmission capacity and security by orbital angular momentum (OAM) multiplexing. Optical chaotic signals with two different OAM modes totally carrying 20 Gbps on–off keying signals are secretly transmitted over a 2 m free-space link, where the channel crosstalk of OAM modes is less than −20 dB, with the mode spacing no less than 3. The receiver can extract valid information only when capturing approximately 92.5% of the OAM beam and correctly demodulating the corresponding mode. Bit error rate below the 7% hard-decision forward error correction threshold of 3.8×10−3 can be achieved for the intended recipient. Moreover, a simulated weak turbulence is introduced to comprehensively analyze the influence on the system performance, including channel crosstalk, chaotic synchronization, and transmission performance. Our work may inspire structured light application in optical chaos and pave a new way for developing future high-capacity free-space chaotic secure communication systems.

Tunable microwave frequency comb generation via periodic relaxation oscillation in directly modulated laser

In this paper, a novel and simple generation scheme based on a directly modulated laser (DML) is proposed for tunable microwave frequency combs (MFCs). When the input modulated RF power is intentionally controlled to be sufficiently high to drive the DML into its nonlinear operating region periodically, relaxation oscillations will be excited in the same period. The modulated light from the DML is subsequently detected by a photodetector, and a special kind of microwave signal source can be optically produced and shows up in the form of MFC in the frequency domain. In the proof-of-concept experiment, tunable MFCs are demonstrated with the bandwidth of more than 25 GHz, the comb spacing of 0.5 ∼ 3 GHz, and the flatness of less than ± 2 dB with the frequency from 3 GHz to 18 GHz. The bandwidth of the generated MFC is in accordance with the relaxation oscillation frequency of the DML. The comb spacing is strictly equal to the frequency of the modulated RF signal and thus flexibly adjustable. The carrier-to-noise ratio can be up to 48 dB, and the single-sideband phase noise is measured to be lower than − 90 dBc/Hz@1 kHz for MFCs with comb spacings of 0.7 ∼ 3 GHz.

A self-locking structure for quantum dot DFB and FP lasers based on optical feedback

This paper presents a self-coherent optical feedback system that achieves resonance between the external cavity mode and the relaxation oscillation frequency of distributed feedback (DFB) laser and the repetition frequency of Fabry–Perot (FP) laser, all in an effort to achieve optical feedback self-locking. Results using this system show that for FP lasers, feedback is able to reduce the 3 dB radio frequency linewidth from 2 MHz to 600 kHz. In the case of DFB lasers, an electric frequency comb with an external cavity repetition rate of 17.25 MHz is achieved. This research presents a significant step toward the improvement of the performance of quantum dot lasers in optical communication systems.

Parameter Optimization for Modulation-Enhanced External Cavity Resonant Frequency in Fiber Fault Detection

Fiber fault detection is crucial for maintaining the quality of optical communication, especially in well-established optical access networks with extended distances and a growing number of subscribers. However, the increasing insertion loss in fiber links presents challenges for traditional fault-detection methods in capturing fault echoes. To overcome these limitations, we propose a modulation-enhanced external-cavity-resonant-frequency method that utilizes a laser for fault echo reception, providing improved sensitivity compared to traditional photodetector-based methods. Our previous work focused on analyzing key parameters, such as sensitivity and spatial resolution, but did not consider practical aspects of selecting optimal modulation parameters. In this study, we develop a model based on Lang–Kobayashi rate equations for current-modulated optical feedback lasers and validate it through experimental investigations. Our findings reveal that optimal detection performance is achieved with a modulation depth of 0.048, a frequency sweeping range of 0.6 times the laser relaxation oscillation frequency, and a frequency sweeping step of 0.1 times the external cavity resonant frequency.

Wideband chaos synchronization using discrete-mode semiconductor lasers.

Optical chaos communication encounters difficulty in high-speed transmission due to the challenge of realizing wideband chaos synchronization. Here, we experimentally demonstrate a wideband chaos synchronization using discrete-mode semiconductor lasers (DMLs) in a master-slave open-loop configuration. The DML can generate wideband chaos with a 10-dB bandwidth of 30 GHz under simple external mirror feedback. By injecting the wideband chaos into a slave DML, an injection-locking chaos synchronization with synchronization coefficient of 0.888 is realized. A parameter range with frequency detuning of -18.75 GHz to approximately 1.25 GHz under strong injection is identified for yielding the wideband synchronization. In addition, we find it more susceptible to achieve the wideband synchronization using the slave DML with lower bias current and smaller relaxation oscillation frequency.

Uncooled 100-GBaud Directly Modulated Membrane Lasers on SiC Substrate

We investigate the temperature dependence of the dynamic characteristics of a 1.3-μm InGaAlAs-based directly modulated membrane laser on a SiC substrate. The laser is fabricated by combining direct wafer bonding of SiC and InP substrates using a very thin (∼10 nm) oxide layer and epitaxial regrowth of a membrane InP layer on the InP/SiC template. The membrane laser structure on SiC with a high thermal conductivity (490 Wm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ) and a moderate refractive index (∼2.6) ensures both high thermal dissipation and a large optical confinement factor in the active region, which are ideal for increasing the relaxation oscillation frequency even at high operating temperatures. We further leverage the optical feedback effect from the output facet of a waveguide to enhance the bandwidth and enable signal modulation at 100 GBaud and beyond. Owing to the high relaxation oscillation frequency and the photon-photon resonance effect, it is possible to obtain a flat frequency response at temperatures ranging from 25 to 85°C. The fabricated membrane laser on SiC with an active-region length of 50 μm exhibits 3dB bandwidths of >110, 97, and 74 GHz at 25, 55, and 85°C, respectively. We successfully demonstrate 2-km transmissions of 100-Gbit/s NRZ signals under uncooled conditions (25 to 85°C). Furthermore, the laser is capable of 112-Gbit/s NRZ modulation at 85°C.

Dual-HR-FBG based single-frequency fiber laser at 1030 nm

We demonstrate a single-frequency fiber laser operating at 1030 nm with a distributed Bragg reflector cavity consisting of two high-reflectivity fiber Bragg gratings (HR-FBGs). By proper thermal adjustment, the gain bandwidth of the fiber laser is significantly compressed through the spectral overlap near the edges of the reflection band of two HR-FBGs, and the single-longitudinal-mode lasing is achieved. The effective cavity length of the fiber laser with the proposed cavity configuration is calculated, and its variation with the temperature difference between two HR-FBGs is also verified through the observation of the relaxation oscillation frequency shift. The measured laser linewidth is about 4.45 kHz at a temperature difference of 48.2 °C. The single-frequency output power of 14.4 mW is achieved at a pump power of 540 mW.

Stimulated Emission Cross-Section Measurement for Laser Crystals of High-Power Solid-State Lasers Using Relaxation Oscillation Frequency

We demonstrate a new method for measuring the stimulated emission cross-section (σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>s</i></sub> ) of laser crystals for high-power solid-state lasers at working state using the relaxation oscillation frequency (ROF). The method is implemented by measuring the ROF of the laser together with making the relation curve between the ROF and σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>s</i></sub> of the laser. The stimulated emission cross-section of the laser crystal can be obtained when the ROF in the relation curve equals to that of the measured value. Employing the method, the actual σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>s</i></sub> of the Nd:YVO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> crystals with doping concentrations and pumping powers of 0.2 at.% and 51.5 W at 808 nm, 0.8 at.% and 80 W at 888 nm, and 0.8 at.% and 113 W at 888 nm are measured upon considering the influence of concentration quenching and energy transfer upconversion of the lasers. The measured results are 23.34 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-19</sup> , 23.77 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-19</sup> , and 23.42 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-19</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively. The results are further compared and analysed with considering the temperature gradient of the laser crystals. It is found that the anomalous temperature gradient of the laser crystal at working state can induce an inhomogeneous gain spectral broadening, which can severely impact σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>s</i></sub> of the laser crystal.

Ultra-Narrow-Bandwidth Single-Frequency Self-Sweeping Ytterbium-Doped Fiber Laser

The sterling merits of single-frequency self-sweeping fiber laser in linewidth, compact design, wavelength and pulse dynamics make it a promising tool for laser measurement. In this letter, we proposed an ultra-narrow-bandwidth ytterbium-doped self-sweeping fiber laser by using a reflector including collimator and mirror. The self-sweeping state was achieved by a 2 m long fiber saturable absorber, and was confirmed by the unique pulse intensity. The central wavelength of laser located at 1065.382 nm along with a self-sweeping range within 2 pm. The radio frequency spectrum observed the relaxation oscillation and beat frequency signals. Especially, the nonlinear saturable absorption feature was confirmed by fitting the intervals of beat frequency signals. The behaviors of relaxation oscillation peaks were summarized and fitted by the empirical formula. This work provides a new self-sweeping laser tool with a narrow bandwidth and can be applied in laser ranging and tunable microwave signal generation.

Alternate method to measure transmission and internal losses in non-planar ring oscillator laser

The transmission T and internal losses L of a non-planar ring oscillator (NPRO) laser are measured using a unique approach. Measurement of slope efficiency, axial mode separation, and relaxation oscillation frequency as a function of NPRO output power are all used in this procedure. T was assessed to be 2.3%, which was significantly higher than the supplier’s given value of 1.7% for a 32-deg angle of incidence at the NPRO output coupler at 1064 nm. The estimated value of internal loss was 4.2%.

Wide-waveguide high-power low-RIN single-mode distributed feedback laser diodes for optical communication.

We present an 8-µm-wide 800-µm-long high-power, single-mode and low RIN DFB laser using a dual-waveguide structure. The introduced passive lower waveguide has weakenes the lateral optical confinement for the ridge waveguide, and thus reduces losses caused by the p-doped layers and maintains single mode stability of the laser. The fabricated laser exhibited an output power higher than 170 mW and a relative intensity noise (RIN) below -157 dB/Hz along with a side-mode suppression-ratio (SMSR) over 55 dB. The temperature tuning from -10°C to 60°C allows an 8.6 nm wavelength tunability with a variation coefficient of 0.12 nm/K. The relaxation oscillation frequency is around 8 GHz, and the linewidth is about 250 kHz at 100 mW output power for the fabricated laser. The characteristics of the proposed high-power laser, including high slope efficiency, single mode stability and low noise, make it a suitable candidate for optical communication.

Experimental investigation of the dependence of compact optical frequency comb generated by direct modulation of semiconductor laser on the modulation waveform and mode

Optical frequency combs (OFCs) generated by direct injection modulation of semiconductor lasers are attractive for their compactness, simplicity, and low cost. We investigated the dependence of the performance of this type of OFC on the modulation waveform and mode on a distributed feedback laser diode (DFB-LD). OFCs can be achieved with various modulation waveforms (sinusoidal, triangular, sawtooth, and sinc) in continuous wave (CW) mode without the limitation of modulation frequency higher than the relaxation oscillation frequency (ROF). In gain-switching (GS) mode, however, this limitation can be avoided by narrow-pulse modulation with frequency lower than the ROF for high spectral resolution, and have a better performance than that in CW mode. We experimentally demonstrated that OFCs generated by pulse modulation have the best performances over various modulation waveforms mentioned above. Specifically, the OFC parameters improvements of carrier-to-noise ratio (CNR) and spectral width by pulse modulation over common used sinusoidal modulation are 37% and 30% respectively. Further, the OFC performance becomes better with increasing modulation frequency in GS mode. We also evaluated the spectral linewidth of OFC being very closed to that of constant operation, which is the absolute highest limit of spectral resolution of an OFC whether in CW or GS mode. Thus, the requirement for high OFC performance of spectral resolution, CNR, and spectral width could be a simple compromising of modulation waveform, frequency, and working mode on a semiconductor diode laser with our investigation. Optimizing of OFCs performance is achieved by changing the waveform or parameters of the modulating signal during gain-switched laser. This method not only reduces the system cost and complexity, but also improves the flexibility of the system.

Sensing by Dynamics of Lasers with External Optical Feedback: A Review

External optical feedback (EOF) has great impacts on the properties of lasers. It influences the stable operation of lasers. However, various applications based on lasers with EOF have been developed. One typical example is self-mixing interferometry technology, where modulated steady-state laser intensity is utilized for sensing and measurement. Other works show that laser dynamics can also be used for sensing, and the laser in this case is more sensitive to EOF. This paper reviews the sensing technology that uses the dynamics of lasers with EOF. We firstly introduce the basic operating principles of a laser with EOF and discuss the noise properties of and intensity modification in lasers induced by EOF. Then, sensing applications using laser dynamics are categorized and presented, including sensing by frequency-shifted optical feedback, relaxation oscillation frequency, and dynamics with self-mixing interferometry signals and laser optical chaos. Lastly, we present an analysis of the transient response waveform and spectrum of a laser with EOF, showing its potential for sensing.

Analysis and Suppression of Laser Intensity Fluctuation in a Dual-Beam Optical Levitation System.

Levitated micro-resonators in vacuums have attracted widespread attention due to their application potential in precision force sensing, acceleration sensing, mass measurement and gravitational wave sensing. The optically levitated microsphere in a counter-propagating dual-beam optical trap has been of particular interest because of its large measurement range and flexible manipulation. In this system, laser intensity fluctuation directly influences the trap stability and measurement sensitivity, which makes it a crucial factor in improving trapping performance. In this paper, a time-varying optical force (TVOF) model is established to characterize the influence of laser intensity fluctuation in a dual-beam optical trap. The model describes the relationship between the laser intensity fluctuation, optical force and the dynamic motion of the micro-sized sphere. In addition, an external laser intensity control method is proposed, which achieved a 16.9 dB laser power stability control at the relaxation oscillation frequency. The long-term laser intensity fluctuation was suppressed from 3% to 0.4% in a one-hour period. Experiments showed that the particle’s position detection sensitivity and the stability of the relaxation oscillation could be improved by laser intensity fluctuation suppression.

Nearly 70 Gbit/s NRZ-OOK encoding of a dual-mode 850 nm VCSEL with a highly In-doped and small Zn-diffused emission area

By pre-emphasized encoding of a dual-mode 850 nm vertical-cavity surface-emitting laser (VCSEL), the nearly 70 Gbit/s on–off keying (OOK) transmission performance is performed for the ultrafast data link. This VCSEL is designed with a new structural configuration, including 6 μm oxidized aperture and 4 μm Zn-diffused emission aperture, which exhibits dual-mode lasing with a threshold current of 0.75 mA, a nonsaturated power of 2.2 mW at 8 mA, and a differential quantum efficiency of 0.38 under a lensed OM4 multimode fiber (MMF) coupling scheme. In particular, the high indium (In) dopant density in the quantum well increases its differential gain coefficient to upshift the relaxation oscillation frequency, which effectively broadens the modulation bandwidth to high-speed data transmission. For the back-to-back transmission, the VCSEL coupled with a lensed OM4-MMF (1 m) for short-reach link reveals an NRZ-OOK transmission at 66 and 69 Gbit/s with a corresponding bit-error ratio (BER) of 5.9 × 10 − 10 and 10 − 5 for error-free decoding after forward-error correction. When employing graded-index single-mode fiber (GI-SMF) with 100 m length as the transmission segment, the VCSEL linked to the GI-SMF connected with a lensed OM4-MMF (1 m) collimator can provide the pre-emphasized NRZ-OOK transmission at 51 Gbit/s with a BER of 4.5 × 10 − 10 and SNR of 14.1 dB.

Chaotic microlasers caused by internal mode interaction for random number generation

Chaotic semiconductor lasers have been widely investigated for generating unpredictable random numbers, especially for lasers with external optical feedback. Nevertheless, chaotic lasers under external feedback are hindered by external feedback loop time, which causes correlation peaks for chaotic output. Here, we demonstrate the first self-chaotic microlaser based on internal mode interaction for a dual-mode microcavity laser, and realize random number generation using the self-chaotic laser output. By adjusting mode frequency interval close to the intrinsic relaxation oscillation frequency, nonlinear dynamics including self-chaos and period-oscillations are predicted and realized numerically and experimentally due to internal mode interaction. The internal mode interaction and corresponding carrier spatial oscillations pave the way of mode engineering for nonlinear dynamics in a solitary laser. Our findings provide a novel and easy method to create controllable and robust optical chaos for high-speed random number generation.

Period-One Laser Dynamics for Photonic Microwave Signal Generation and Applications

Due to the advantages of rich dynamics, small size, and easy integration, semiconductor lasers have many applications in microwave photonics. With a proper perturbation to invoke period-one (P1) nonlinear laser dynamics, a widely tunable microwave signal can be generated. In this paper, we concentrate on the realization and application of photonic microwave signal generation based on the P1 oscillation state of semiconductor lasers. Recent developments in P1 dynamics-based tunable microwave signal generation techniques are reviewed with an emphasis on the optical injection system, which has a large frequency tuning range that is far beyond the intrinsic relaxation oscillation frequency. In order to improve the spectral purity and stability of the generated microwave signal, two typical approaches are introduced, i.e., microwave modulation stabilization, and delayed feedback stabilization. Various applications of the P1 dynamics-based microwave signal generator in diverse signal generation and photonic microwave signal processing are described. Development trends of the P1 dynamics-based photonic microwave signal generator are also discussed.

Wideband chaotic tri-mode microlasers with optical feedback.

A tri-mode micro-square laser under optical feedback is proposed and demonstrated to generate chaos with the broadband flat microwave spectrum. By adjusting lasing mode intensities, frequency intervals, and optical feedback strength, we can enhance the chaotic bandwidth significantly. The existence of two mode-beating peaks makes the flat bandwidth much larger than the relaxation oscillation frequency. Effective bandwidth of 35.3 GHz is experimentally achieved with the flatness of 8.3 dB from the chaotic output spectrum of the tri-mode mode laser under optical feedback.