Computer simulation of laser photon fluctuations: DFB lasers

This fourth paper of the Series is devoted to photon fluctuations in the light output of distributed feedback (DFB) lasers. Statistics on laser photon fluctuations are collected from numerical solutions of noise driven rate equations. The approximate formula for the variance of the photon fluctuations, presented earlier [1], is also applicable to the DFB laser. Compared to the single-cavity injection laser, the DFB laser has the following features. 1) The order of magnitude of the photon fluctuations of the single lasing mode of a DFB laser is comparable to the fluctuations of the total power output of a single-cavity laser. 2) Contrary to single-cavity lasers, which cannot be made to Operate in a single longitudinal mode even under idealized conditions if they are driven by short current pulses, DFB lasers will readily deliver a single, pulsed mode. Thus, if thermal effects and backreflection of scattered light can be controlled, there will be no mode jumping during pulsed operation.     

Computer simulation of laser photon fluctuations: Coupled-cavity lasers

This third paper of the series deals with photon fluctuations in the light output of coupled-cavity lasers. As before, statistics on laser photon fluctuations are collected from numerical solutions of noise driven rate equations. Compared to the single-cavity injection laser, the coupled-cavity laser is found to have the following advantages. 1) The coupled-cavity laser can be made to operate in a single mode by driving one of its sections above and the other below threshold. For a given amount of output power from the high-current end, fewer photon fluctuations occur if it is the longer laser section that is driven above threshold. 2) The order of magnitude of the photon fluctuations of the single lasing mode of a coupled-cavity laser is comparable to the fluctuations of the total power output of a single-cavity laser. 3) Contrary to single-cavity lasers, which cannot be made to operate in a single mode if they are driven by short current pulses, coupled-cavity lasers will readily deliver a single, pulsed mode. Thus, if thermal effects and backreflection of scattered light (for example, from an attached fiber) can be ignored, mode jumping need not occur.     

Effects of nonlinear gain on single longitudinal mode behavior of semiconductor lasers

The effects of nonlinear gain on the single longitudinal mode are analyzed by means of multilongitudinal mode and multitransverse mode rate equations and compared with the linear gain calculations and experments. It is shown that further suppression of the third order nonlinear gain on nonlasing modes always serves to accelerate the process of the single longitudinal mode operation and that results obtained with long cavity length are entirely contrary to those where only linear gain is considered. The experiments also show that single longitudinal mode lasers with even larger output power can be realized with long cavity length; and, with further proper reduction of the stripe width, single mode (single frequency) operation can be realized. But the results obtained from both gain considerations indicate that single longitudinal mode operation will be facilitated if the active layer is not too thin and the end face reflectivity is increased.     

Detailed model and investigation of gain saturation and carrier spatial hole burning for a semiconductor optical amplifier with gain clamping by a vertical laser field

A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the on-off state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser.     

Computer simulation of laser photon fluctuations: Theory of single-cavity laser

This paper is the first of a series devoted to theoretical studies of photon fluctuations in the light output of semiconductor injection lasers. Statistics on laser photon fluctuations are collected by means of a simulation of the dynamic behavior of the laser based on numerical solutions of noise driven laser rate equations. This first paper in the series introduces the noise driven rate equations for a single-cavity laser, explains the method used for their numerical solution, and discusses some approximate analytical results. The second paper presents results of photon counting statistics for the single-cavity laser collected from numerical solutions of the time dependent equations. Additional papers in this series will concentrate on coupled-cavity and distributed feedback lasers. Comparison of these statistical results will show clearly the advantage of coupled-cavity and distributed feedback laser designs over conventional single (Fabry-Perot) cavity injection lasers.     

光纤光栅外腔半导体激光器的理论和实验分析

从耦合模理论出发,结合激光原理,研究了光纤光栅外腔半导体激光器(FBG-ECL)的理论模型．得到光纤光栅反射率的解析解。利用速率方程理论讨论FBG-ECL的高频响应特性。根据等效腔模型．讨论了耦合系数对FBG-ECL阈值特性的影响。指出存在最佳光纤光栅反射率．使得激光器不仅功率输出大,而且边模抑制比高。最后实测了不同反射率情况下激光器的激射光谱。     

Rate equation model of a coupled-cavity laser

We derive a novel rate equation system for a laser consisting of two coupled cavities arranged in tandem. The derivation of the photon rate equations is based on classical electromagnetic theory, while the rate equations for the electrons are written down heuristically in analog with the conventional laser rate equations. This paper discusses the initial numerical evaluation of our coupled-cavity laser model which indicates that the laser tends to oscillate more readily in a single longitudinal mode than a single-cavity laser of comparable length. The enhanced mode selectivity stems from the constructive and destructive interference of the fields in the two coupled cavities. Suppression of secondary longitudinal modes by more than 20 dB is readily obtainable. The coupled-cavity laser maintains single-wavelength operation even if the peak of the gain profile shifts over a certain wavelength range. However, when it finally responds to a sufficiently large shift of the gain profile, it does so by jumping discontinuously to a new (single) operating wavelength. Further investigations of frequency tuning by means of the injection current as well as studies of the frequency instability due to temperature and refractive index variations will be reported in a separate publication.     

Picosecond pulse analysis of gain-switched 1.55 µm InGaAsP laser

Results of computer simulation of gain-switched pulses from InGaAsP lasers emitting at 1.55 μm are reported. Multimode rate equations are solved for short triangular current pulses of large amplitude superimposed on a dc bias close to threshold. Lasers of conventional length (200μm) and with short cavity (50 μm) are analyzed. The effect of wavelength chirp on time-resolved and the time-averaged multimode spectra is demonstrated. Optical pulses as short as 10 ps are predicted for short-cavity lasers with reflective coatings. While the number of longitudinal modes in gain-switched spectrum is efficiently reduced for short-cavity lasers, the dynamic linewidth of each mode remains of a similar magnitude (up to 140 GHz) as for standard-cavity lasers. It is expected that gain saturation effects could reduce the calculated values of dynamic linewidth.     

Two-segment cavity theory for mode selection in semiconductor lasers

A simple three-mirror composite laser cavity is analyzed and optimum structures proposed in terms of the position of the central reflector and the value of its reflectivity in order to give single longitudinal mode operation. Two optimum structures are discussed, the first corresponding to relatively long cavities where a large period in the gain modulation is required in order to avoid a jump to the next mode with a high effective reflectivity, usually in a second mode group (as defined by a neighboring period of the gain modulation). The second corresponds to shorter lasers where jumps to neighboring modes should be avoided, since the spectral gain variation prevents jumps to other mode groups. The effects of mode discrimination due to external feedback have been analyzed and minimum values of reflectivity for the third mirror derived in order to preserve the internal mode selectivity.     

基于重叠光栅和啁啾光栅的双波长光纤激光器

研究光寻址电位传感器(LAPS)的器件噪声特性 。通过对LAPS半导体场效应器件的结构分析,建 立LAPS的理论模型,并进一步分析LAPS器件噪声信号的来源、种类及特性。以 pH缓冲液中H离子 浓度为检测对象,搭建基于NI采集卡和Labview环境的LAPS测试系统,对影响LAPS信号噪声 特性的光源 波长、光源调制频率、光源强度和Si衬底厚度等因素进行了仿真和实验研究。结果表明,增 大光源波长和光源强度 是提高输出信号幅值和信噪比(SNR)的最有效方法。     

The power spectrum of injection lasers: The theory and experiment on a nonlinear model of lasing

A comprehensive treatment of the theory and experiment on a nonlinear model of injection lasers develops a general way to find the order underlying the complexities of the emission spectrum of lasers operated far above threshold by describing the emission in terms of a few measurable parameters of the cavity and material. The theory is largely unpublished, while the experimental work covers publications fortified with more recent studies and considerable new work. The laser is described by rate equations in which the gains and losses are approximated as prorated averages over one round trip. The gain contains an explicit nonlinearity described by a critical power at which the gain begins to saturate. The steady state solution at low level is the linear theory. At high level, the excited power in each cavity mode is an explicit function of its particular gain and loss coefficients. To express the characteristics of the radiation in terms of observables, the dependence of gain and loss coefficients on mode number are deduced by modeling. The unsaturated gain is taken as parabolic in frequency, while the loss coefficients are deduced by decomposing each cavity mode into three independent sets of waveguide modes. For a cavity with sawed side walls, this gives a scattering loss proportional to the square of the lateral mode number, which determines the shape of the lateral profile of the beam. The summation of the modal powers over all cavity modes expresses the lateral profile, the frequency spectrum, and the total power in terms of an overdrive parameter X associated with the dynamical state of the laser, which is an implicit function of the population inversion. Relating X to the spontaneous emission at short wavelength gives a set of equations, involving only observables, which determines all the parameters in the summation. The equations reveal previously unknown relations between power, spontaneous emission, beam width, spectral width, and polarization. The critical power is expressed from first principles in terms of phenomenological optical constants.The experiments examine the relation by pulsed studies at room temperature of wide lasers with sawed sides or stripe contacts. It is shown that many of the lasers have the dispersion of box modes assumed in the summation of the distribution function. At high enough power that a statistical average over the excited modes is meaningful, the general predictions are verified. The lateral profile has the correct shape to about 10 dB below the peak, its width grows as $\text{(X)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, and it's peak as $\text{(X)}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$. The power dependence of the polarization ratio follows quantitatively the predicted shape, and the total power is quadratic in X. Extensive records of 21 lasers with a wide variety of internal structures are intercompared, showing that all have a similar coefficient of side wall loss, that the curvature of gain against wavelength varies widely, and that the critical power $\text{P}{}^1$ seems to be a general constant of the predicted magnitude, independent of internal structure, cavity geometry, and facet area. The same constant is also found for wide cavities with Hermite-Gaussian modes and one narrow stripe cavity. There is a discussion of geometries not yet covered, including lasers with many transverse modes and narrow stripe and cw lasers.     

Tailoring characteristics of DFB lasers with low- and high-reflection facets by using sampled gratings

Tailorability of distributed-feedback (DFB) laser characteristics by sampled grating has been pursued for DFB lasers with low- and high-reflection facets. This is based on the finding that there exists close correlation between the threshold gain difference and the axial photon distribution of the main and side modes. An effective-index transfer matrix method is used. This finding enables us to tailor DFB laser characteristics, and shows the futility of an attempt to relieve longitudinal spatial hole burning by making similar the axial photon distribution of the main and side modes. The threshold gain difference is shown to be improved by more than 15% by simple changing the arrangement of the sampled regions.     

Mode partition in semiconductor lasers with optical feedback

The authors point out that random noise processes induce mode partition fluctuations in semiconductor lasers. Mode partition depends on laser parameters and modulation current. However, external optical feedback can also increase mode partition noise. Here, a numerical solution of multimode noise-driven rate equations with time-delayed terms is utilized to investigate mode partition in semiconductor lasers with reflecting feedback. Photon statistics of the main and side modes in semiconductor lasers under both CW operation and dynamic operation are considered. Probability-density curves for the main and side modes are shown. The feedback-induced change of photon statistics of the main and side modes is clearly seen. Numerical results indicate that, if the laser used is exposed to reflections, a more stringent mode discrimination requirement for suppressing the buildup of laser-cavity longitudinal side modes may result. If mode discrimination is insufficient for avoiding the excitation of side modes, the feedback-induced power penalty depends on the fiber dispersion     

低压驱动复合腔电光调Q微晶片激光器

复合腔电光调Q微晶片激光器是一种集成化的固体激光器,具有体积小、基横模、单纵模、线偏振运转,输出脉冲重复频率高,脉宽窄的优点,是高重复频率、高光束质量的主振荡功率放大器(MOPA)激光系统的理想种子源。进行了低压驱动复合腔电光调Q微晶片激光器的实验与理论研究。根据理论分析,增加电光晶体长度和提高端面反射率可减小标准具透射谱半宽度,进而降低驱动电压。设计了两套激光器实验方案。实验中激光增益介质和电光晶体分别选用Nd:YVO4和LiTaO3,谐振腔尺寸小于3 mm×3 mm×2.5 mm。方案1主要研究增加电光晶体长度后的激光器输出特性,在抽运功率184 mW,240 V驱动电压下,可实现300 kHz激光脉冲输出,脉冲宽度10 ns,峰值功率9.4 W。在方案2中,通过进一步提高端面反射率,在短时间内可输出1 MHz脉冲。     

Analysis of vertical-cavity surface-emitting laser multimodebehavior

This paper investigates problems associated with multimode oscillation in vertical-cavity surface-emitting lasers (VCSELs). The multimode rate equations for transverse mode were formulated. These equations take into account carrier diffusion and gain nonuniformity in the lateral direction. It was shown that multimode transverse mode excitation is due to carrier spatial hole burning, but many factors affect the number of lasing modes. The role of gain nonuniformity distribution, carrier diffusion, and modal loss compared with mirror loss in a cavity were demonstrated by numerical solution of the multimode rate equations     

增益导引折射率反导引大模场光纤激光器特性分析

为了研究增益导引折射率反导引光纤激光器的功率分布及输出特性,根据此类光纤的结构原理和特点,建立了端面抽运的增益导引折射率反导引光纤激光器的基模光速率方程,推导了避免激发高阶模的增益阈值判决条件,并运用弦切法和Runge-Kutta法数值求解了该速率方程,分析了光纤长度、腔镜反射率等参量对基模输出功率的影响.采用芯径为1...     

Modeling temperature effects and spatial hole burning to optimizevertical-cavity surface-emitting laser performance

Two-dimensional physical models for single-mode index guided vertical cavity surface emitting lasers (VCSELs) are developed and compared with experimental measurements on state-of-the-art devices. Starting with the steady-state electron and photon rate equations, the model calculates the above threshold light-current (LI) characteristics. Included are temperature effects, spatial hole burning effects, carrier diffusion, surface recombination, and an estimation of optical losses. The model shows that the saturation of output power in the experimental devices is due to carrier leakage over the heterojunction and not simply the shifting of the gain peak relative to the cavity mode. Using the verified model new designs are analyzed, showing that output powers greater than 15 mW and power efficiencies above 20% should be achievable with existing processing technology     

DBR单纵模光纤激光器波长温度调谐

报道了采用DBR方式,利用8 mm的高浓度掺Yb3+单模光纤,实现了波长为1 064 nm的单纵模调谐激光稳定输出的实验结果。该DBR谐振腔有效腔长为16 mm,输出最大功率为7.4 mW,通过半导体制冷器温控改变谐振腔的温度,实现了0.824 nm的单纵模无跳模调谐。采用光纤外差法,并利用低损耗环形器和光纤反射镜倍增延迟线长度提升测量精度的方式,测量得到激光最大线宽为4.4 kHz。单纵模激光的弛豫震荡峰位于900 kHz处,其相对强度噪声为-110 dB/Hz,当频率大于1.5 MHz时相对强度噪声为-145 dB/Hz。     

A quantum amplifier model for predicting temporal variations in theoutput power from a semiconductor laser on a picosecond time scale

A new model for simulating temporal fluctuations in the power emitted by a semiconductor laser is described. Light in the cavity is assumed to circulate in the form of traveling photon packets, in which the photon number fluctuates due to the processes of spontaneous emission, stimulated emission, absorption, scattering, and reflection. The dipole dephasing time T plays a critical role in modeling the interaction of the photon packets and gain medium. The Monte Carlo method is used to simulate the temporal behavior of a continuously pumped Fabry-Perot laser. The laser output power is found to exhibit periodic fluctuations at the cavity transit time frequency (longitudinal mode beat frequency). The amplitude of these fluctuations, as well as the relaxation oscillation, which occurs at a much lower frequency, is strongly influenced by the magnitude of T. The results of these simulations are related to the temporal behavior expected from a conventional FP laser     

The influence of power level on injection laser linewidth andintensity fluctuations including side-mode contributions

The contribution of side modes to the main-mode line-width is calculated as function of power output using analytic relations and verified using a series of Monte Carlo calculations. For well-behaved lasers having photon lifetimes of 0.88 and 1.57 ps and gain compression of 10% or less, it is found that the total linewidth decreases monotonically with increasing power output. These lasers have main-mode to side-mode ratios in the range 100-300 at 3 mW output; they exhibit side-mode contributions to main-mode linewidth of 17 and 57% respectively at a power level of 10 mW and modal ratios of 940 and 390. When the gain compression exceeds 10% as it may in lasers running at 10 mW or more, the linewidth can reach a minimum and then increase with increasing power level, in accordance with laboratory observation on some lasers