Passive mode locking with slow saturable absorbers

We give a comprehensive overview on passive mode locking of solid-state lasers with slow saturable absorbers, based on analytical and numerical calculations. For picosecond lasers, we present a simple equation to estimate the obtained pulse duration and compare the results to those for mode locking with fast saturable absorbers. We also discuss how much shorter the pulse duration can be compared to the absorber recovery time and present a simple rule. The effect of self-phase modulation is found to be qualitatively different compared to the case of a fast saturable absorber, and the effect of phase changes in the absorber is also discussed. Finally, we discuss various issues concerning soliton mode-locked lasers. Received: 20 July 2001 / Revised version: 28 September 2001 / Published online: 7 November 2001     

Theoretical study of the operation of gated saturable absorbers

The operation of gated saturable absorbers is described by the classical space-time-dependent rate equation model considering both ground-state and excited-state absorption and stimulated emission. The effect of different molecular and cavity parameters on the transmitted pulse is shown.     

酞菁铜非共振反饱和吸收的稳态特性

酞菁铜溶液在波长532nm调Q激光作用下,实验获得反饱和吸收特性.在稳态条件下,用速率方程理论推得分别描述薄样品和厚样品的反饱和吸收特性的两个解析式,理论分析与实验结果一致.     

Doping-induced changes in the saturable absorption of monolayer graphene

Graphene is a broadband, fast saturable absorber well suited for passive mode-locking of lasers. The broadband absorption, ultra-short recovery time, and low cost of graphene absorbers compare favorably with traditional semiconductor saturable absorber mirrors (SESAMs). However, it remains difficult to tailor the parameters of a monolayer graphene absorber such as the modulation depth and the insertion loss; this limits the absorber??s design freedom, which is often required for mode-locking without Q-switching instability. We demonstrate in this work that, by hole-doping graphene chemically to various Fermi levels, the modulation depth and insertion loss are modified. Further control of graphene??s saturable absorption by electric-field gating and its application to active suppression of Q-switching in lasers is discussed.     

Ionization yield of two-step photoionization process in an optically thick atomic medium of barium

The kinetics of a two-step photoionization process in optically thick atomic medium of barium (Ba) is studied using the rate equation approach. In the first step, Ba atoms get resonantly excited by laser radiation from their ground state to an intermediate excited state and subsequently are ionized in the second step by another laser radiation. The absorption of exciting radiation is taken into account along its propagation direction (optically thick). However, the medium is assumed to be optically thin for the ionizing radiation. A numerical simulation is done to estimate the ionization yield for time-varying Gaussian shaped laser pulses. The required energy density of the laser pulse to saturate the excitation transition throughout the thick medium is calculated. The effect of optical delay between the laser beams on the ionization yield is simulated. The calculated ionization yield from the simulation is compared with the measured values.     

Two-beam interaction in saturable media

The dynamics of two coupled soliton solutions of the nonlinear Schrödinger equation with a saturable nonlinearity is investigated. It is shown by means of a variational method and by direct numerical calculations that two well-separated solitons can orbit around each other, if their initial velocity is equal to a certain critical velocity. For initial velocities below and above this critical velocity the solitons merge and separate, respectively. The analytical calculations are based on the assumption of a large separation distance, and under this assumption numerical simulations confirm the main results.     

On the description of quadratic and cubic optical effects of propagation of femtosecond pulses within the framework of the model of the saturable potential

It is shown that, for describing the simultaneous manifestation of nonlinear effects of different orders (quadratic, cubic, etc.) in propagation of high-intensity femtosecond pulses, it is sufficient to use the saturable potential of the restoring force. With the use of computer simulation, it is demonstrated that the spectrum of the response of a medium calculated on the basis of the Duffing equation with quadratic and cubic nonlinearity is in qualitative agreement with the spectrum calculated on the basis of the equation with a saturable restoring force. The dependence of the frequency corresponding to the maximum spectral radiance on the duration of the interacting pulse is discussed. It is noted that, for ultrashort pulses, even in the case of their propagation in a linear medium, the response can occur at the natural frequency rather than at the frequency of the propagating pulse.     

Optimization of the pulse energy of GaAs saturable absorber Q-switched lasers

By taking into account the single-photon absorption (SPA) and two-photon absorption (TPA) processes of GaAs, the Gaussian spatial distributions of the intracavity photon density and the initial population-inversion density, and the pumping and the spontaneous emission during the pulse formation, the new normalized rate equations of a GaAs saturable absorber Q-switched laser are solved. The key parameters of an optimally coupled GaAs saturable absorber Q-switched laser are determined, including the optimal normalized coupling parameter and the optimal normalized GaAs saturable absorber parameters, which can maximize the pulse energy, and a group of general curves are generated for the first time, which clearly show the dependence of the optimal key parameters on the parameters of the gain medium, the GaAs saturable absorber, and the resonator. In addition, the influence including the space variation, the pumping and the spontaneous emission is also shown. Sample calculations for a diode-pumped Nd³⁺:YVO₄ laser with a GaAs saturable absorber are presented to demonstrate the use of the curves and the relevant formulas.     

Dynamic study of gated saturable absorbers

The capability of gated saturable absorbers for single-pulse selection is studied theoretically using the classical space-time-dependent rate-equation model. The dynamics of operation is followed experimentally by the well-known pump—probe technique. Comparing the theoretical and experimental results, it is found that gated saturable absorbers can efficiently be used for pulse forming and pulse selection of pulses longer than picosecond.     

饱和吸收体实现波长转换的理论模型分析

作为自动交换光网络中的核心器件,全光波长转换器在网络中发挥着重要作用。基于半导体激光器速率方程,提出了新的基于饱和吸收体实现全光波长转换器的理论模型;并针对该理论模型,采用小信号分析方法讨论了波长转换的频率调制响应特性;数值求解了不同偏置电流、码速、输入信号光功率对波长转换性能的影响,对于实现和优化基于饱和吸收体的全光波长转换器有理论指导作用。     

Theory of passive mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers

Mode locking of solid-state lasers using metal nanocomposites as slow saturable absorbers (SAs) is studied theoretically. The derived equation for the transient nonlinear response of metal nanocomposites is based on the semiclassical two-temperature model. The model is confirmed experimentally by pump-probe measurements on Au nanoparticles (NPs). The theory was applied to study passive mode locking of a solid-state laser containing Au NPs as SA in the green spectral range. Pulse durations as short as 100 fs are predicted, and design criteria of metal NP SAs are derived.     

Recent development of saturable absorbers for ultrafast lasers [Invited]

As one of the greatest inventions in the 20 th century, ultrafast lasers have offered new opportunities in the areas of basic scientific research and industrial manufacturing. Optical modulators are of great importance in ultrafast lasers, which directly affect the output laser performances. Over the past decades, significant efforts have been made in the development of compact, controllable, repeatable, as well as integratable optical modulators(i.e., saturable absorbers). In this paper, we review the fundamentals of the most widely studied saturable absorbers, including semiconductor saturable absorber mirrors and low-dimensional nanomaterials. Then, different fabrication technologies for saturable absorbers and their ultrafast laser applications in a wide wavelength range are illustrated. Furthermore, challenges and perspectives for the future development of saturable absorbers are discussed and presented. The development of ultrafast lasers together with the continuous exploration of reliable saturable absorbers will open up new directions for the mass production of the nextgeneration optoelectronic devices.     

The multiwave regime of light diffraction and focusing effect in volume phase gratings

Some pecularities of multiwave light diffraction in optically thin and thick phase unslanted gratings have been considered. An approximate solution of the wave equation is derived by the eiconal method. The solution is valid for gratings which are both optically thin and thick. This is verified by comparison of approximate solutions with numerical calculations. A range of parameters is found where the solution gives a reliable result. It has been found that the phase grating has the property of focusing light in planes with a maximum value of refractive index if the grating thickness is close to the focal distance introduced.     

Low power phase conjugation in thin films of saturable absorbers

Organic dyes with high triplet yield are used as saturable absorbers with very low saturation intensity. Phase conjugation is performed in a thin film by a cw laser. The theory of degenerate four wave mixing in saturable absorbers is verified and imaging capabilities are demonstrated.     

Optimization of diode-pumped passively Q-switched mode-locked c-cut Nd:GdVO4 laser with a GaAs saturable absorber

By considering the single-photon absorption (SPA) and two-photon absorption (TPA) processes in the GaAs saturable absorber, the coupled rate equations for a diode-pumped passively Q-switched and mode-locked (QML) laser with GaAs coupler under Gaussian approximation are given. The key parameters of an optimally coupled passively QML laser can be obtained by numerically solving these equations. These key parameters include the parameters of the gain medium, the saturable absorber and the resonator, which can maximize the pulse energy of singly Q-switched envelope. Sample calculations for a diode-pumped passively Q-switched mode-locked c-cut Nd:GdVO₄ laser with a GaAs saturable absorber are presented to demonstrate the optimal method applicable.     

Optical characterization of semiconductor saturable absorbers

Semiconductor saturable absorber mirror (SESAM) devices have become a key component of ultrafast passive mode-locked laser sources. Here we describe in more detail how the key SESAM parameters such as saturation fluence, modulation depth, and nonsaturable losses are measured with a high accuracy. These parameters need to be known and controlled to obtain stable pulse generation for a given laser. A high-precision, wide dynamic range setup is required to measure this nonlinear reflectivity of saturable absorbers. The challenge to measure a low modulation depth and key measures necessary to obtain an accurate calibration are described in detail. The model function for the nonlinear reflectivity is based on a simple two-level travelling wave system. We include spatial beam profiles, nonsaturable losses and higher-order absorption, such as two-photon absorption and other induced absorption. Guidelines to extract the key parameters from the measured data are given. PACS 07.60.Hv; 42.65.Re; 42.70.Nq     

Optimization of pulse width of double passively Q-switched lasers with GaAs and Cr-doped saturable absorbers

Compared with a single passively Q-switched laser, a double passively Q-switched laser with a GaAs saturable absorber and a Cr⁴⁺-doped saturable absorber can produce more symmetric and shorter pulses with high pulse peak power. New normalized coupled rate equations for a double passively Q-switched laser with both a GaAs saturable absorber and a Cr⁴⁺-doped saturable absorber are solved numerically, where the single-photon absorption (SPA) and two-photon absorption (TPA) processes of GaAs are combined. The Gaussian spatial distributions of the intracavity photon density and the initial population-inversion density are considered. The optimization of a double passively Q-switched laser to obtain the shortest pulse width is performed, and a group of general curves are generated for the first time. The curves clearly show the dependence of the optimal normalized parameters on the parameters of the gain medium, the GaAs saturable absorber, the Cr⁴⁺-doped saturable absorber and the spatial distributions of the intracavity photon density. Sample calculations for a diode-pumped Nd³⁺:YVO₄ laser with both a GaAs saturable absorber and a Cr⁴⁺:YAG saturable absorber are presented to demonstrate the use of the curves and the related formulas.     

Quasi-stable propagation of vortices and soliton clusters in saturable Kerr media with square-root nonlinearity

Analytical and numerical investigation of the propagation of optical beams in Kerr-like saturable photorefractive media is carried out, utilizing a novel model for the local isotropic part of the space-charge field generated in the medium. Using a variational technique, optimal propagation parameters for the most stable propagation of otherwise unstable single Gaussian, single vortex, and optical soliton cluster beams are determined. Analogy between a ring of identical weakly overlapping solitons and a vortex of the same topological charge is explored.     

有机材料反饱和吸收特性分析

从能级角度出发,结合入射激光脉宽对粒子吸收方面的影响,用速率方程模拟了各能级粒子数的瞬时变化关系,给出了激光脉宽与能级寿命可比拟时反饱和吸收的动态解,表明粒子在能级上的分布情况。用C60和HITCI(1,1′,3,3,3′,3′hexa methyl lindo tricarbocyanine Iodide)的实验参数理论模拟了激发态吸收截面大于基态吸收截面时透射率随光强的变化关系,用以说明大的上能级吸收截面可以抑制光强过大时引起的饱和吸收,增强材料的非线性光限幅特性。