Modulation of the shape of the photon echo pulse by a pulsed magnetic field: Zeeman splitting in LuLiF4:Er3+ and YLiF4:Er3+

A spectroscopy method has been proposed involving a change in the time shape of the echo signal in the presence of a perturbation, which splits the frequencies of the transitions of two or more ion subgroups of the echo-active ions. This method has been applied to optical systems in which the Zeeman effect is manifested. The ion transition frequencies of ions are switched by a weak pulsed magnetic field acting during the time of the radiation of the photon echo pulse. The modulation of the photon echo signal shape was observed in LuLiF₄:Er³⁺ and YLiF₄:Er³⁺. The time interval between the two nearest minima corresponds to the accumulated phase of the electric dipole moment ?? and makes it possible to determine the difference of the g factors of the ground and excited ⁴ F _9/2(I) states of the Er³⁺ ion in the LuLiF₄ the YLiF₄ matrices for the known amplitude of the pulsed magnetic field. It has been shown that the echo response of the system can be programmed by the weak magnetic field pulses.     

Zeeman splitting factor of the Er3+ ion in a crystal field

Numerical computations are presented on the energy levels of the Er³⁺ ion in crystalline fields of cubic, trigonal, tetragonal and orthorhombic symmetry. Zeeman splitting factors were obtained from the level splitting in an additional magnetic field. For the quartet Γ₈ states in cubic symmetry the Zeeman effect is described by an effective Hamiltonian ℋ= gμ_BBJ+ uμ_BBJ³ with the parametersg andu calculated for mixed fourth- and sixth-order potentials. For the eight doublets in the lower symmetry of an axial trigonal or tetragonal crystal field the principalg tensor components g_∥ and g_⊥ were calculated. The results of such calculations for a ground-state doublet can exactly account for the experimental data obtained on around 70 erbium centers in various crystalline hosts. However, sometimes different sets of parameters give comparably good results. An empirical rule of constant trace g_∥ + 2g_⊥ is supported by the calculations. In contrast to analytical treatments the effect of the crystalline field can be followed over a continuous range of the crystal field parameters. This allows one to establish relations on the relative signs of tensor components. It is found that the measured trace of tensors |g_∥| + 2|g_⊥| is not always equal to their real trace g_∥ + 2g_⊥. In an exploratory calculation a nonaxial center was simulated in an orthorhombic field, with calculation of the three principal values g_x, g_y and g_z. A good agreement is obtained for the recently reportedg values of an erbium center in silicon.     

Er~(3+)∶YVO_4的频率上转换动力学分析

测量并分析了980nm抽运下Er3+∶YVO4晶体的上转换荧光,建立了描述Er3+离子跃迁的速率方程。通过求解速率方程并拟合1550nm,980nm和550nm的荧光衰减实验曲线,得到了4I13/2+4I13/2→4I15/2+4I9/2,4I11/2+4I11/2→4I15/2+4F7/2的频率上转换系数C22=9.221×10-17cm3s-1,C33=7.545×10-17cm3s-1。通过测量980nm抽运下的550nm荧光衰减谱,得到了4S3/2能级的主要上转换机制是以激发态吸收为主。     

Formation of stimulated photon echo in ytterbium vapours in a longitudinal magnetic field

Intensity and polarization are derived for stimulated photon echo produced in a longitudinal magnetic field by transitions between resonance levels with the angular momenta 0 and 1. It is shown that stimulated photon echo generated in a longitudinal magnetic field can be used to obtain spectroscopic data on the times of relaxation of population, orientation, and alignment of the level ³P₁ of a ¹⁷⁴Yb atom.     

Er^3＋：YAG晶体Er^3＋离子的浓度对电磁感应光透明的影响

在一个三能级模型中展示了Er^3 :YAG晶体中的Er^3 浓度对电磁感应光透明（EIT）的影响。没有耦合场时,Er^3 离子浓度在15％左右时吸收达到最大;存在共振耦合场时,Er^3 离子浓度在3％左右时透射有一个最优值。     

Observation of photon echo in Er(3+):YAG at 1.527 microm

We report what is to our knowledge the first experimental observation of two- and three-pulse echoes in Er(3+) :YAG at 1.527microm . The experiment was performed on the transition from the (4)I(15/2) ground state to the lowest Stark level of the (4)I(13/2) excited state. The corresponding homogeneous dephasing time was measured to be approximately 50ns at 1 and 7K. In addition, three-pulse echo decay indicated a lifetime of the spectral grating of ~30micros . Implications of these results for optical data storage and optical signal processing are discussed.     

Er3+:YVO4中Er3+的光谱参数计算

根据掺杂Er3+(0.5%)的YVO4样品的吸收光谱,用Jubb-Ofelt理论拟合出唯象强度参最Ωλ,并由此计算了激发能级的振子强度、自发辐射跃迁速率、荧光分支比和积分发射截面等光谱参量.并根据这些光学参量,分析了Er3+:YVO4晶体的应用价值.其中,特别是4I13/2→4I15/2, 2H11/2→4I15/2, 4S3/2→4I15/2和4F9/2→4I15/2等几个强发光能级具有较大的振子强度(大于10-6)和积分发射截面(大于10-18cm),分别分析了它们的应用前景,因此非常值得关注.并且,本文结果和Capobianco等所报道的Er3+(2.5 mol%):YVO4晶体强度参量结果很相近.而且,通过比较掺Er3+钒酸钇晶体和掺Er3+其他晶体的光学性能,可以看出钒酸钇晶体作为激光晶体的优点.最后,还根据Er3+在晶体中的对称性,利用群论讨论了Er3+在YVO4晶场中各能级的劈裂情况.     

Effect of magnetic field on the stimulated photon echo in ytterbium vapors

Polarization of the stimulated photon echo (SPE) at the 0 ? 1 transition in ytterbium vapors in the presence of a longitudinal magnetic field of 0–40 G is experimentally and theoretically studied. The SPE is generated using three light pulses with identical linear polarizations, so that the SPE polarization is the same at zero magnetic field. In the presence of a weak magnetic field, the SPE polarization vector rotates around the magnetic field vector and the depolarization of the SPE signal takes place. Each of the SPE polarization components exhibits biharmonic oscillations depending on the magnetic field. In the presence of a strong magnetic field, these oscillations vanish and the SPE becomes depolarized. The experimental data are in qualitative agreement with the results of the numerical calculations performed with the method of the evolution operator for the finite-duration excitation pulses. The application of the results for the processing of optical data is discussed.     

Energy transfer between Yb3+ and Er3+ ions in an Er,Yb:YAl3(BO3)4 crystal

The electron-excitation energy transfer between Er³⁺ and Yb³⁺ ions in Er,Yb:YAl₃(BO₃)₄ crystals has been investigated. Crystals with different concentrations of active ions have been grown, and their luminescence decay kinetics in the spectral range near 1 μm have been experimentally measured. The energy-transfer microparameters have been calculated. It is shown that, to correctly describe the energy transfer in Er,Yb:YAl₃(BO₃)₄ crystals, one must take into account the interactions of higher orders than dipole-dipole interactions.     

Effect of concentration of the Er3+ ion on electromagnetically induced transparency in Er3+:YAG crystal

We studied the effect of Er³⁺ concentration on electromagnetically induced transparency in two types of three-level schemes—the ladder and the Λ models in Er³⁺:YAG. The numerical calculations show that, under the same intensities of the probe and the coupling fields, the absorption and the dispersion were dramatically changed with Er³⁺ concentration.     

VUV-UV-visible luminescence of Nd3+, Er3+ and Tm3+ in LiLuF4 single crystal host

An overlook of absorption and luminescence characteristics of Nd³⁺, Er³⁺ and Tm³⁺ centers in LiLuF₄ single crystal is provided. Single crystal doped with the mentioned RE ions were prepared by micro-pulling-down technique in the form of few cm long rods with the diameter of about 2 mm. Excitation and emission spectra and fast decay kinetics in VUV spectral region were measured at SUPERLUMI station at synchrotron DESY, Hamburg and characterization was further completed in UV-visible region at conventional spectrophotometers. Observed absorption and emission peaks are ascribed to the 5d–4f and 4f–4f optical transitions in the doped rare earth ions. Concentration dependence of the decay kinetics is discussed.     

Oscillations of the photon echo intensity in a pulsed magnetic field: Zeeman splitting in LiLuF<Subscript>4</Subscript>:Er<Superscript>3+</Superscript>

A method of high-resolution time-resolved optical spectroscopy using oscillations of the photon echo intensity in the presence of a perturbation, which splits the optical frequencies of the transitions of two or more ion subgroups, has been proposed and demonstrated. This method has been applied to systems in which the Zee-man effect is manifested. The transition frequencies of ions are switched by a pulsed magnetic field. Oscillations of the photon echo intensity were observed in LiLuF₄:Er³⁺ and LiYF₄:Er³⁺. The first minimum corresponding to the accumulated phase of the electric dipole moment π/2 is reached in the pulsed magnetic field with an amplitude of ～2 G at a duration of 30 ns. The Zeeman splitting in this field is ～10 MHz, which is much less than the laser spectral width (0.15 Å ～ 9 GHz). The g factor of the ⁴ F _9/2(I) excited state of the Er³⁺ ion in the LiLuF₄ matrix has been determined in zero magnetic field. The comparison with the g-factor value found from the measurement of the absorption spectrum in a magnetic field of 8 kG has been performed.     

Er3+:GdVO4中Er3+离子的光谱参数计算和晶场中能级分裂的讨论

对Er3+:GdVO4样品的光谱参数以及Er3+在晶场中能级的分裂情况进行了研究.首先对样品进行了吸收光谱的测量,接着用Judd-Ofelt理论拟合出了Er3+在GdVO4晶体中的强度参量Ωt,并由此计算了跃迁的振子强度、自发辐射跃迁速率、荧光分支比和积分发射截面.通过计算结果可以发现有较多能级之间的跃迁都有大于10-6的振子强度和大于10-18 cm的积分发射截面,并且具有较高的荧光分支比,特别是2H11/2→4I15/2,4S3/2→4I15/2,4F9/2→4I15/2和4I13/2→4I15/2等几个强发光能级除了具有较大的振子强度和积分发射截面外还有很好的应用前景,因此也更加值得关注.最后还利用群论讨论了Er3+离子在GdVO4晶场中各能级的分裂情况并对各Stark子能级的Jz混杂情况进行了分析.     

Contributions to crystal field parameters for Er3+: Au from ligand electrons and nuclei

A pseudo-point charge model has been found from a calculation of the 4f/ligand charge penetration effects, in Er³⁺: Au within a more general recently developed many-body theory for crystal fields in metals. In this particular system contributions to crystal field parameters (CFP) directly from neighbours may be described in terms of a Coulomb interaction using different effective total charges on the ligands for the fourth order and sixth order components of the crystal field. It has been found that the penetration effects considerably enhance the CFP with respect to their point charge model (PCM) values. The sixth order CFP is much more affected than the fourth CFP by such effects. The calculation of these effective charges is presented in the absence of any contributions from 5d virtual bound states.     

Crystal growth and luminescence properties of Pr-doped LuLiF4 single crystal

0.1, 1, and 3% Pr (with respect to Lu) doped LuLiF₄ (Pr:LuLiF₄) single crystals were grown by the micro-pulling-down (μ-PD) method. Transparency of the grown crystals was higher than 70% in the visible wavelength region with some absorption bands due to Pr³⁺ 4f-4f transitions. Intense absorption bands related with the Pr³⁺ 4f-5d transitions were observed at 190 and 215 nm. In radioluminescence spectra, Pr³⁺ 5d-4f emissions were observed at 220, 240, 340, and 405 nm. In the pulse height spectra recorded under ¹³⁷Cs γ-ray excitation, the Pr 3% doped sample showed the highest light yield of 2050 photons/MeV and the scintillation decay time of it exhibited 23 and 72 ns also excited by ¹³⁷Cs γ-ray.     

Record performance from a Q-switched Er3+:Yb3+:YVO4 laser

A diode-pumped Yb³⁺, Er³⁺:YVO₄ laser was Q-switched by the rotating prism method and record performance obtained. Pulse energies of up to 0.2 mJ and pulse durations as short as 60 ns were demonstrated. A model based on a system of rate equations is also described and used to explain the observed behaviour.     

Phonon-assisted energy up-conversion process of Er3+ ions doped in KY F4 crystal

Er³⁺ ions doped in KY F₄ crystal emit blue photoluminescence around 406 nm by energy up-conversion process when excited by 532 or 488 nm laser. By measuring the temperature dependence of up-converted luminescence, we found that the up-conversion process is enhanced with increasing temperature, which is an indication that phonons are assisting the process. This observation is supported by the fact that the energy transfer responsible for the up-conversion involves two transitions that have an energy mismatch.     

Polarization operator of a photon in a magnetic field

The polarization operator of a photon in a static uniform magnetic field has been studied at photon energies both above and below the threshold of electron–positron pair production by a photon. In the first order of the fine-structure constant α, expressions for the refractive index of a photon with a certain polarization in both low and high fields as compared to the critical field H₀ = 4.41 × 10¹³ G have been obtained. Both the purely quantum range of photon energies, where the particles of a pair are produced at the lowest Landau levels, and the region of applicability of the semiclassical approximation in the case of the population of high energy levels have been considered. A general spectral integral formula has been obtained with divergent threshold terms separated in an explicit form.