Fluctuations of Single-Mode Laser Driven by Two Different Kinds of Colored Noise

A single-mode laser with coupling between additive and multiplicative noise terms is investigated when the multiplicative noise and the coupling between two noise terms are colored fluctuations with finite correlation times T1 and T2. Combining the unified colored noise approximation （UCNA） and the functional analysis, the stationary probability distribution （SPD） and the variance of the laser intensity is derived. It is found that the colored nature of multiplicative noise and the coupling strength between two noise terms can affect both the structure and the height of the SPD, while the colored nature of the coupling between two noise terms can only affect the height of the SPD. The multiplicative noise can enhance the intensity fluctuations while the additive noise can reduce the fluctuations in a laser system. Numerical simulations are presented and consistent to the analytical results.

Stochastic resonance in a single-mode laser driven by frequency modulated signal and coloured noises

By adding frequency modulated signals to the intensity equation of gain noise model of the single-mode laser driven by two coloured noises which are correlated, this paper uses the linear approximation method to calculate the power spectrum and signal-to-noise ratio （SNR） of the laser intensity. The results show that the SNR appears typical stochastic resonance with the variation of intensity of the pump noise and quantum noise. As the amplitude of a modulated signal has effects on the SNR, it shows suppression, monotone increasing, stochastic resonance, and multiple stochastic resonance with the variation of the frequency of a carrier signal and modulated signal.

Stochastic Resonance in Linear Region of a Single-Mode Laser: Effects of Amplitude Modulation of Signal

A single-mode laser noise model driven by quadratic colored pump noise and amplitude modulation signal is proposed. The real and imaginary parts of the pump noise are assumed to be cross-correlation. The effect of cross- correlation of noise and amplitude modulation of signal on laser statistical properties is studied by using the linearized approximation. The analytic expression of signal-to-noise ratio （SNR） is calculated. It is found that the phenomena of stochastic resonance （SR） respectively exist in the curves of the SNR versus the noise cross-correlation coefficient λ and the SNR versus the pump parameter a, as well as the SNR versus the signal frequency ω in our model. It is shown that there are three different typies of SR in the model： the conventional form of SR, the SR in the broad sense, and the bona fide SR.

Time-Delayed Feedback Control in a Single-Mode Laser System

The effects of time-delayed feedback control in a single-mode laser system is investigated.Using the smalltime delay approximation,the analytic expression of the stationary probability distribution function of the laser field isobtained.The mean,normalized variance and skewness of the steady-state laser intensity are calculated.It is found thatthe time-delayed feedback control can suppress the intensity fluctuation of the laser system.The numerical simulationsare in good agreement with the approximate analytic results.

The statistical fluctuation of a single-mode laser system driven by coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts

Using the linear approximation method, this paper studies the statistical property of a single-mode laser driven by both coloured pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, and calculates the steady-state mean normalized intensity fluctuation and intensity correlation time. It analyses the influences of the modulation signal, the net gain coefficient, the noise and its correlation form on the statistical fluctuation of the laser system respectively. It is found that the coloured pump noise modulated by the signal has a great suppressing action on the statistical fluctuation of the laser system; the pump noise self-correlation time and the specific frequency of modulation signal have the result that the statistical fluctuation tends to zero. Furthermore, the ＇colour＇ correlation of pump noise has much influences on the statistical fluctuation of the laser system. Increasing the intensity of pump noise will augment the statistical fluctuation of the laser system, but the intensity of quantum noise and the coefficient of cross-correlation between its real and imaginary parts have less influence on the statistical fluctuation of the laser system. Therefore, from the conclusions of this paper the statistical property can be known and a theoretical basis for steady operation and output of the laser system can be provided.

Influence of Signal and Noise on Statistical Fluctuation of Single-Mode Laser System

On the basis of calculating the steady-state mean normalized intensity fluctuation of a signal-mode laser system driven by both colored pump noise with signal modulation and the quantum noise with cross-correlation between its real and imaginary parts, we analyze the influence of modulation signal, noise, and its correlation form on the statistical fluctuation of the laser system. We have found that when the amplitude of modulation signal weakens and its frequency quickens, the statistical fluctuation will reduce rapidly. The by reducing the intensity of pump noise and quantum noise. statistical fluctuation of the laser system can be restrained Moreover, with prolonging of colored cross-correlation time, the statistical fluctuation of laser system experiences a repeated changing process, that is, from decreasing to augmenting, then to decreasing, and finally to augmenting again. With the decreasing of the value of cross-correlation coe~cient, the statistical fluctuation will decrease too. When the cross-correlation form between the real part and imaginary part of quantum noise is zero correlation, the statistical fluctuation of laser system has a minimum. Compared with the influence of intensity of pump noise, the influence of intensity of quantum noise on the statistical fluctuation is smaller.

Stationary properties of a single-mode laser system with non-Gaussian and Gaussian noise

A single-mode laser system with non-Gaussian and Gaussian noise is investigated. The stationary mean value and the normalized variance of the laser intensity are numerically calculated under the condition that the stationary probability distribution function （SPDF） is derived. The SPDF as a function of the laser intensity exhibits a maximum, The maximum becomes smaller with the increase of the correlation intensity or the non-Gaussian parameter, where the later is a measure of the deviation from the Gaussian characteristic. The maximum becomes larger as the correlation time increases. The laser intensity stationary mean value decreases with the increase of the correlation intensity or the non-Gaussian parameter while increases with the correlation time increasing. The laser intensity normalized variance increases with the increase of the correlation intensity or the non-Gaussian parameter while decreases as the correlation time increases.

Laser patterning of large-scale perovskite single-crystal-based arrays for single-mode laser displays

Lead halide perovskites have attracted considerable attention as potential candidates for high-performance nano/microlasers,owing to their outstanding optical properties.However,the further development of perovskite microlaser arrays(especially based on polycrystalline thin films)produced by the conventional processing techniques is hindered by the chemical instability and surface roughness of the perovskite structures.Herein,we demonstrate a laser patterning of large-scale,highly crystalline perovskite single-crystal films to fabricate reproducible perovskite single-crystal-based microlaser arrays.Perovskite thin films were directly ablated by femtosecond-laser in multiple low-power cycles at a minimum machining line width of approximately 300 nm to realize high-precision,chemically clean,and repeatable fabrication of microdisk arrays.The surface impurities generated during the process can be washed away to avoid external optical loss due to the robustness of the single-crystal film.Moreover,the high-quality,large-sized perovskite single-crystal films can significantly improve the quality of microcavities,thereby realizing a perovskite microdisk laser with narrow linewidth(0.09 nm)and low threshold(5.1µJ/cm2).Benefiting from the novel laser patterning method and the large-sized perovskite single-crystal films,a high power and high color purity laser display with single-mode microlasers as pixels was successfully fabricated.Thus,this study may offer a potential platform for mass-scale and reproducible fabrication of microlaser arrays,and further facilitate the development of highly integrated applications based on perovskite materials.

Strange Attractors in the Resonance Interaction of Two-State Atoms with Single-Mode Laser Field

The resonance interaction of two-state atoms with single mode field is described theoretically by using the semi-classical theory and Jaynes-Cummings model. The nonlinear characteristics of this system are calculated by using FFT and Runge-Kutta methods. The chaotic strange attractors in this system are obtained from the numerical results.

Relative phase locking of a terahertz laser system configured with a frequency comb and a single-mode laser

Stable operation is one of the most important requirements for a laser source for high-precision applications.Many efforts have been made to improve the stability of lasers by employing various techniques,e.g.,electrical and/or optical injection and phase locking.However,these techniques normally involve complex experimental facilities.Therefore,an easy implementation of the stability evaluation of a laser is still challenging,especially for lasers emitting in the terahertz(THz)frequency range because the broadband photodetectors and mature locking techniques are limited.In this work,we propose a simple method,i.e.,relative phase locking,to quickly evaluate the stability of THz lasers without a need of a THz local oscillator.The THz laser system consists of a THz quantum cascade laser(QCL)frequency comb and a single-mode QCL.Using the single-mode laser as a fast detector,heterodyne signals resulting from the beating between the singlemode laser and the comb laser are obtained.One of the heterodyne beating signals is selected and sent to a phase-locked loop(PLL)for implementing the relative phase locking.Two kinds of locks are performed by feeding the output error signal of the PLL,either to the comb laser or to the single-mode laser.By analyzing the current change and the corresponding frequency change of the PLL-controlled QCL in each phase-locking condition,we,in principle,are able to experimentally compare the stability of the emission frequency of the single-mode QCL(f s)and the carrier envelope offset frequency(f CEO)of the QCL comb.The experimental results reveal that the QCL comb with the repetition frequency injection locked demonstrates much higher stability than the single-mode laser.The work provides a simple heterodyne scheme for understanding the stability of THz lasers,which paves the way for the further locking of the lasers and their high-precision applications in the THz frequency range.

Phase-locked single-mode terahertz quantum cascade lasers array

We demonstrated a scheme of phase-locked terahertz quantum cascade lasers(THz QCLs)array,with a single-mode pulse power of 108 mW at 13 K.The device utilizes a Talbot cavity to achieve phase locking among five ridge lasers with first-order buried distributed feedback(DFB)grating,resulting in nearly five times amplification of the single-mode power.Due to the optimum length of Talbot cavity depends on wavelength,the combination of Talbot cavity with the DFB grating leads to better power amplification than the combination with multimode Fabry-Perot(F-P)cavities.The Talbot cavity facet reflects light back to the ridge array direction and achieves self-imaging in the array,enabling phase-locked operation of ridges.We set the spacing between adjacent elements to be 220μm,much larger than the free-space wavelength,ensuring the operation of the fundamental supermode throughout the laser's dynamic range and obtaining a high-brightness far-field distribution.This scheme provides a new approach for enhancing the single-mode power of THz QCLs.

Integrated lithium niobate single-mode lasers by the Vernier effect

Microcavity lasers based on erbium-doped lithium niobate on insulator(LNOI),which are key devices for LNOI integrated photonics,have attracted significant attention recently.In this study,we report the realization of a C-band single-mode laser using the Vernier effect in two coupled erbium-doped LNOI microrings with different radii under the pump of a 980-nm continuous laser.The laser,operating stably over a large range of pumping power,has a pump threshold of about 200μW and a side-mode suppression ratio exceeding 26 dB.The high-performance LNOI single-mode laser will promote the development of lithium niobate integrated photonics.

The phenomenon of stochastic resonance in a single-mode laser system with an input periodical signal

Using the linear approximation method, we study a single-mode laser system driven by colored pump noise and quantum noise with coupling between the real and imaginary parts when the laser is operated well above threshold. The steady state mean intensity fluctuation C(0) and signal-to-noise ratio (SNR) are calculated. It is found that there is a maximum in SNR when there is a minimum in the fluctuation of laser system if the coupling coefficient between real and imaginary parts of the quantum noise equals zero.

Effecfs of Cross-Correlation Between Real Noise in Transient Process of Single-Mode and Imaginary Parts of Colored Pump Laser

A two-dimensional single-mode laser model with cross-correlation between the real and imaginary parts of the colored quadric pump noise is investigated. A novel laser amplitude Langevin equation is obtained, in which the cross-correlation λp between the real and imaginary parts of the pump noise appears. The mean, variance, and skewness of first-passage-time are calculated. It is shown that the mean, variance, and skewness of first-passage-time are strongly affected by λp.

Stochastic resonance for signal-modulated pump noise in a single-mode laser

By adopting the gain-noise model of the single-mode laser in which with bias and periodical signals serve as inputs. combining with the effect of coloured pump） noise, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio （SNR） of the laser intensity under the condition of pump noise and quantum noise cross-related in the form of δ function. It is found that with the change of pump noise correlation time. both SNR and the output power will occur stochastic resonance （SR）. If the bias signal α is very small, changing the intensities of pump noise and quantum noise respectively does not lead to the appearance of SR in the SNR： while α increases to a certain number, SR appears.

Influence of the net gain on characteristic of stochastic resonance in a single-mode laser system

The phenomenon of stochastic resonance (SR) is found in a single-mode laser system driven by the colored pump noise with signal modulation and the quantum noise with cross-correlation between the real and imaginary parts. When the net gain a0 changes, it is found that, 1) the shape of the curve of the signal-to-noise ratio (SNR) versus the pump noise self-correlation time τ exhibits a changing process of multiform SR, from single-peak SR, to simultaneous existence of resonances and suppressions; 2) the curve of SNR. versus signal frequency Ω experiences a complicated changing process from the monotonous descending to the simultaneous appearances of a maximum and a minimum, and finally to monotonous descending; 3) the curve of SNR versus cross-correlation coefficient between the real and imaginary parts of the quantum noise λq appears an acute single-peak SR. Therefore, the net gain ao greatly influences the characteristic of SR of laser system.

A novel hybrid Ⅲ–Ⅴ/silicon deformed micro-disk single-mode laser

A novel hybrid III-V/silicon deformed micro-disk single-mode laser connecting to a Si output wave- guide is designed, and fabricated through BCB bonding technology and standard i-line photolithography. Com- pared to a traditional circular micro-disk in multi-longitudinal-mode operation, unidirectional emission and single longitudinal-mode output from a Si waveguide are realized. In the experiments, an output power of 0.31 mW and a side-mode suppression ratio of 27 dB in the continuous-wave regime are obtained.

Single-mode low threshold current multi-hole vertical-cavity surface-emitting lasers

A multi-hole vertical-cavity surface-emitting laser （VCSEL） operating in stable single mode with a low threshold current was produced by introducing multi-leaf scallop holes on the top distributed Bragg-refleetor of an oxidation- confined 850 nm VCSEL. The single-mode output power of 2.6 mW, threshold current of 0.6 mA, full width of half maximum lasing spectrum of less than 0.1 nm, side mode suppression ratio of 28.4 dB, and far-field divergence angle of about 10% are obtained. The effects of different hole depths on the optical characteristics are simulated and analysed, including far-field divergence, spectrum and lateral cavity mode. The single-mode performance of this multi-hole device is attributed to the large radiation loss from the inter hole spacing and the scattering loss at the bottom of the holes, particularly for higher order modes.

Widely tunable single-mode lasers based on a hybrid square/rhombus-rectangular microcavity

Hybrid square/rhombus-rectangular lasers(HSRRLs) consisting of a Fabry–Perot(FP) cavity and a square/rhombus microcavity(SRM) are proposed and demonstrated for realizing single-mode lasing with a wide wavelength tuning range. The SRM is a deformed square microcavity with a vertex extended to the FP cavity to control the coupled mode field pattern in the FP cavity. Single-mode operation with a side-mode suppression ratio(SMSR) over 45.3 dB is realized, and a wide wavelength tuning range of 21 nm with SMSR >35 dB is further demonstrated by adjusting the injection currents of the SRM and the FP cavity simultaneously. Furthermore, a 3-dB modulation bandwidth of 14.1 GHz and an open-eye diagram at 35 Gb/s are demonstrated for the HSRRL.

Single-Mode Fabry-Pérot Quantum Cascade Lasers at λ ~10.5 μm

In this paper, we report a single-mode Fabry-Pérot long wave infrared quantum cascade lasers based on the double phonon resonance active region design. For room temperature CW operation, the wafer with 35 stages was processed into buried heterostructure lasers. For a 4 mm long and 13 μm wide laser with high-reflectivity (HR) coating on the rear facet, continuous wave output power of 43 mW at 288 K and 5 mW at 303 K is obtained with threshold current densities of 2.17 and 2.7 kA/cm2. The lasing wavelength is around 10.5 μm. Single mode emission was observed for this particular device over the whole investigated current and temperature range.