Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ Ⅳ:Pressure-Induced Shifts of R1 Line, R2 Line, and U Band at 300 K

By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts of R2 line, and U band of GSGG:Cr3+ at 300 K have been calculated, respectively. The calculated results are in good agreement with all the experimental data. Their physical origins have also been explained. It is found that the mixingdegree of \t22(3T1)e4T2> and \t322E> base-wavefunctions in the wavefunctions of R1 level of GSGG:Cr3+ at 300 K is remarkable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the and the PS of R1 line (or R2 line) due to EPI are quite different. It is the combined effect of them that gives rise to the total PS ofR1 line (or R2 line). In the range of about 15 kbar ～ 45 kbar, the mergence and/or order-reversal between t22(3T1)e4T2 levels and t32 2 T1 levels take place, which cause the fluctuation of the rate of PS for t22(3T1)e4T2 (or t3 2 2T1)with pressure. At 300 K, both the temperature-dependent contribution to R1 line (or R2 line or U band) from EPI and the temperature-independent one are important.     

Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ Ⅲ:Pressure-Induced Shift of R1 Line at 70 K

By means of both a theory for pressure-induced shifts (PS) of energy spectra and a theory for shifts ofenergy spectra due to electron-phonon interaction (EPI), the "pure electronic" PS and the PS due to EPI of R1 line ofGSGG:Cr3+ at 70 K have been calculated, respectively. Their physical origins have been revealed. It is found that theremarkable under the normal pressure, and the degree of the admixture rapidly decreases with increasing pressure. Thechange of the degree of the admixture with the pressure plays a key role for not only the pure electronic PS of R1 line butalso the PS ofR1 line due to EPL The detailed calculations and analyses show that the pressure-dependent behaviors ofthe pure electronic PS of R1 line and the PS of R1 line due to EPI are quite different. It is the combined effect of themthat gives rise to the total PS of R1 line, which has satisfactorily explained the experimental data (including a reversal ofPS of R1 line). In contributions to PS of R1 line due to EPI at 70 K, the temperature-independent contribution is muchlarger than the temperature-dependent contribution. The former results from the interaction between the zero-pointvibration of the lattice and localized electronic state.     

Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+ I: Theory

A theory for shifts of energy spectra due to electron-phonon interaction (EPI) has been developed. Both thetemperature-independent contributions and the temperature-dependent ones of acoustic branches and optical brancheshave been derived. It is found that the temperature-independent contributions are very important, especially at lowtemperature. The total pressure-induced shift (PS) of a level (or spectral line or band) is the algebraic sum of its PSwithout EPI and its PS due to EPI. By means of both the theory for shifts of energy spectra due to EPI and the theoryfor PS of energy spectra, the total PS of R1 line of tunable laser crystal GSGG:Cr3+ at 70 K as well as the ones of itsR1 line, R2 line and U band at 300 K will be successfully calculated and explained in this series of papers.     

Pressure Effects on Spectra of Tunable Laser Crystal GSGG:Cr3+Ⅱ:Energy Spectra at Normal Pressure, Low and Room Temperatures

With the strong-field scheme and trigonal bases, the complete d3 energy matrix in a trigonally distorted cubic-field has been constructed. By diagonalizing this matrix, the normal-pressure energy spectra and wavefunctions of GSGG:Cr3+ at 70 K and 300 K have been calculated without the electron-phonon interaction (EPI), respectively. Further, the contributions to energy spectra from EPI at two temperatures have also been calculated, where temperatureindependent terms of EPI are found to be dominant. The sum of aforementioned two parts gives rise to the total energy spectrum. The calculated results are in good agreement with all the optical-spectral experimental data and the experimental results of g||(R1) and g⊥(R1). It is found that the contribution from EPI to R1 line of GSGG:Cr3+ with taking into account spin-orbit interaction (Hso) and trigonal field (Vtrig) is much larger than the one with neglecting Hso and Vtrig, and accordingly it is essential for the calculation of the EPI effect to take first into account Hso and Vtrig. The admixture of base-wavefunctions, |t32 2E) and |t22(3T1)e4T2 ), the average energy separation △＝ E[t22 (3T1)e4T2]-E[t32 2E] and their variations with temperature have been calculated and discussed.     

Pressure-Induced Shift of R-Line of MgO:Cr3+ with Electron-Phonon Interaction Effect

By means of improved ligand-field theory, the "pure electronic" pressure-induced shift (PS) and the PS due to electron-phonon interaction (EPI) of R-line of MgO:Cr3 have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R-line of MgO:Cr3 and the PS of its R-line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R-line, which has satisfactorily explained the experimental results. The comparison between the feature of R-line PS of MgO:Cr3 and that of R1-line PS of ruby has been made.     

Energy Spectra of the Tunable Laser Crystal Gd3Ga5O12:Cr3+ and Their Pressure-Induced Shifts

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction (EPI), at 300 K, the `pure electronic' contributions and the contributions from EPI to R₁ line, R₂ line, and U band of GGG:Cr³⁺ as well as their PS have been calculated, respectively. The total calculated results are in good agreement with all the experimental data. Their physical origins have been explained. It is found that the mixing-degree of |t₂²(³T₁)e ⁴T₂> and |t₂³²E> base-wavefunctions in the wavefunctions of R₁ level of GGG:Cr³⁺ is considerable under normal pressure, and the mixing-degree rapidly decreases with increasing pressure. The change of the mixing-degree with pressure plays a key role for PS of R₁ line or R₂ line. At 300 K, both the temperature-independent contribution to R₁ line (or R₂ line or U band) from EPI and the temperature-dependent one are important. The remarkable difference between pressure-dependent behaviors of PS of R₁ lines of GGG:Cr³⁺ and GSGG:Cr³⁺ results from the differences of their microscopic properties. The features of emission spectra of GGG:Cr³⁺ at various pressures have satisfactorily been explained.     

Pressure-Induced Shifts of R, R', and B Line-Groups and Ground-State Zero-Field-Splitting of Ruby

By means of improved ligand-field theory, the “pure electronic” presure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of the R₁, R₂, B₁, B₂, B₃, and R'₃ lines and the ground-state zero-field-splitting of ruby have been uniformly calculated. The calculation results are in very good agreement with all the experimental data. At normal pressure, ruby is a crystal with very strong crystal field. Thus, the admixture of |t₂²(³T₁)e⁴T₂〉and |t³₂²E〉bases in the wavefunction of R₁ level of ruby is small at normal pressure, and it gradually decreases with increasing pressure, which causes the R₁-line PS of ruby to monotonously red shift with approximate linearity. The combined effect of the pure electronic PS of R₁ line and the PS of R₁ line due to EPI gives rise to the total PS of R₁ line. The analyses and comparisons among the features of R₁-line PS's of three laser crystals (ruby, GSGG:Cr³⁺ and GGG:Cr³⁺) have been made, and the origin of their difference has been revealed.     

Energy Spectrum of YAG:Cr3+ and Thermal Shifts of Its R Lines

Traditional ligand-field theory has to be improved by taking into account both “pure electronic“ contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R1, R2, R‘3, R′2, and Ri lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R1 line and R2 line of YAG:Cr3 have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr3 ion in YAG:Cr3 is compressed along the [111] direction. Thus, for YAG:Cr3 and ruby, the splitting of t23 4A2 (or t23 2E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R1 and R2 lines of YAG:Cr3 , the temperature-dependent contributions due to EPI are dominant.     

Energy Spectrum of YAG:Cr3+ and Thermal Shifts of Its R Lines

Traditional ligand-field theory has to be improved by taking into account both “pure electronic” contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, R₁, R₂, R'₃, R'₂, and R'₁ lines, U band, ground-state zero-field-splitting (GSZFS) and ground-state g factors as well as thermal shifts of R₁ line and R₂ line of YAG:Cr³⁺ have been calculated. The results are in very good agreement with the experimental data. In contrast with ruby, the octahedron of ligand oxygen ions surrounding the central Cr³⁺ ion in YAG:Cr³⁺ is compressed along the [111] direction. Thus, for YAG:Cr³⁺ and ruby, the splitting of t₂³⁴A₂ (or t₂³²E) has opposite order, and the trigonal-field parameters of the two crystals have opposite signs. In thermal shifts of R₁ and R₂ lines of YAG:Cr³⁺, the temperature-dependent contributions due to EPI are dominant.     

Pressure-Induced Shift of R-Line of MgO：Cr^3＋ with Electron-Phonon Interaction Effect

By means of improved ligand-field theory, the ＂pure electronic＂ pressure-induced shift （PS） and the PS due to electron-phonon interaction （EPI） of R-line of MgO：Cr^3＋ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R-line of MgO：Cr^3＋ and the PS of its R-line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R-line, which has satisfactorily explained the experimental results. The comparison between the feature of R-line PS of MgO：Cr^3＋ and that of R1-line PS of ruby has been made.     

Improved Ligand-Field Theoretical Calculation of R-Line Pressure-Induced Shift of MgO:V2+

By means of an improved ligand-field theory, the “pure electronic” PS and the PS due to EPI of R line of MgO:V²⁺ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R line of MgO:V²⁺ and the PS of its R line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R line, which has satisfactorily explained the experimental results. The mixing-degree of |t₂²(³T₁)e⁴T₂〉and |t₂^{3 2}E〉 in the wavefunction of R level and its variation with pressure have been calculated and analyzed. The comparison between the feature of R-line PS of MgO:V²⁺ and that of MgO:Cr³⁺ has been made.     

Energy Spectrum of La3Lu2Ga3O12:Cr3+ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced shifts (PS) of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction (EPI), the normal-pressure energy spectra of α andβ centers of Cr3 ions for LLGG:Cr3 and the PS‘s of R1 lines and U band of these centers have been calculated at 10 K, respectively.The total calculated results are in very good agreement with the experimental data. For LLGG:Cr3 , the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Relmix (2E- 4T2) [mixing-degree of |t22(3T1)e4T2) and |t322E) base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line.The comparison between R1-line PS‘s of GSGG:Cr3 and LLGG:Cr3 has been made. It is found that a peak of R1-line PS appears at Relmix (2E - 4T2) ≈ 0.08.     

Energy Spectra,g Factors and Their Pressure-Induced and/or Thermal Shifts of SrTiO3:Cr3+ and SrTiO3:Mn4+ III: R-Line Thermal Shifts of SrTiO3:Mn4+

By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d³ electronic configuration, the values of the parameters in the expressions of thermal shift (TS) from EPI for the ground level, R level and R line of SrTiO₃:Mn⁴⁺ have been evaluated; the R-line TS and various contributions to it have been calculated in the low-temperature region. It is found that all the three terms of R-line TS from EPI relevant to the lattice vibration are red shifts. The Raman term is the largest, the neighbor-level term is the second, and the optical-branch term is very small over the range of T≤80 K. The contribution to R-line TS from thermal expansion has been approximately neglected in this work. The very strong EPI relevant to its lattice vibration for SrTiO₃:Mn⁴⁺ causes its R-line TS to be an unusually large red-shift. Only by taking into account the strong softening of the low-frequency acoustic modes of the lattice vibration at low temperatures, can we successfully explain the variation of R-line TS of SrTiO₃$:Mn⁴⁺ with temperature.     

Pressure-Dependent Base-Wavefunction Admixture and Lifetime of R1 State of La3Lu2Ga3O12:Cr3+

As a key factor leading to the pressure-dependent R₁-line-shift reversal and R₁-state lifetime, at 10 K, the pressure-dependent variation of mixing-degree of |t₂²(³T₁)e⁴T₂〉 and |t₂³² E〉base-wavefunctions in the wavefunction of R₁ state of LLGG:Cr³⁺ has been calculated and analyzed. From this, the physical origin of the pressure-dependent R₁-line-shift reversal has been revealed. Furthermore, by using the pressure-dependent values of the sum of all square mixing-coefficients of |t₂²(³T₁)e⁴T₂〉in the wavefunction of R₁ state, the lifetimes of R₁ state of LLGG:Cr³⁺ at various pressures have been calculated, which are in good agreement with observed results. The quantum anticrossing effect between t₂³²E and t₂²(³T₁)e⁴T₂ levels due to both spin-orbital interaction and electron-phonon interaction is remarkable, which is related to the admixture of |t₂²(³T₁)e⁴T₂〉and |t₂³² E〉as well as the low-high crystal-field transition.     

Improved Ligand-Field Theoretical Calculation of R-Line Pressure-Induced Shift of MgO：V^2＋

By means of an improved ligand-field theory, the ＂pure electronic＂ PS and the PS due to EPI of R line of MgO： V^2＋ have been calculated, respectively. The calculated results are in very good agreement with the experimental data. The behaviors of the pure electronic PS of R line of MgO：V^2＋ and the PS of its R line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R line, which has satisfactorily explained the experimental results. The mixing-degree of ｜t2^2（^3T1）e^4T2〉 and ｜t2^3 ^2E〉 in the wavefunetion of R level and its variation with pressure have been calculated and analyzed. The comparison between the feature of R-line PS of MgO：V^2＋ and that of MgO：Cr^3＋ has been made.     

YAG晶体中Cr4+和Yb3+的光谱和荧光特性研究

报道了（Ｃｒ＾４＋,Ｙｂ＾３＋）：ＹＡＧ晶体的吸收光谱和荧光光谱特性。在室温下,（Ｃｒ＾４＋,Ｙｂ＾３＋）：ＹＡＧ晶体在９３７ｎｍ和９６８ｎｍ处存在两个吸收带,能与ＩｎＧａＡｓ激光二级管有效耦合：而且在１０３０ｎｍ处有一Ｃｒ＾４＋吸收峰,可以实现对Ｙｂ＾３＋的自调Ｑ激光输出。（Ｃｒ＾＋,Ｙｂ＾３＋）：ＹＡＧ 荧光光谱与Ｙｂ＾３＋：ＹＡＧ晶体一样,发光中心也是位于１０２９ｎｍ,但其强度比Ｙｂ＾３＋：     

Microscopic Theoretical Calculations of R—Line Thermal Shifts and Broadenings of MgO：Cr^3＋

By taking into account all the irreducible representations and their components in the electron-phonon interaction (EPI) as well as all the levels and the admixtures of basic wavefunctions within d^3 electronic configuration,the values of all the parameters in the expressions of thermal shift (TS) and thermal broadening (TB) due to EPI for the ground level,R level and R line of MgO:Cr^3 have microscopically been evaluated;and then,TS and TB of R line and various contributions to them have uniformly been calculated.The results are in very good agreement with the experimental data.It is found that all the three terms of TS due to EPI are red shifts;the Raman term is the largest one,and the optical-branch term and neighbor-level term are important for TS;the contribution to TS from thermal expansion is blue shift,which is also important.The R-line TS of MgO:Cr^3 comes from the first-order term of EPI.The elastic Raman scattering of acoustic phonons plays a dominant role in R-line TB of MgO:Cr^3 .For both TS and TB,it is very important to take into account all the admixtures of basic wavefunctions within d^3 electronic configuration.     

Energy Spectrum of La3Lu2Ga3O12：Cr^3＋ and Its Pressure-Induced R-Line-Shift Reversal

By means of both the theory for pressure-induced Shifts （PS） of energy spectra and the theory for shifts of energy spectra due to electron-phonon interaction （EPI）, the normal-pressure energy spectra of α and β centers of Cr^3＋ ions for LLGG：Cr^3＋ and the PS＇s of R1 lines and U band of these centers have been calculated at 10 K, respectively. The total calculated results are in very good agreement with the experimental data. For LLGG：Cr^3＋, the pressureinduced low-high crystal-field transition and the reversal of R1-line PS take place. The pressure-dependent variation of Rmix^ei （2E - 4T2） [mixing-degree of （t2^2 （^3T1）e^4T2） and （t2^3 E） base-wavefunctions in the wavefunction of R1 state without EPI] plays a key role for the reversal of R1-line PS. The behavior of the pure electronic PS of R1 line is quite different from that of the PS of R1 line due to EPI. It is the combined effect of them that gives rise to the total PS of R1 line. The comparison between R1-line PS＇s of GSGG：Cr^3＋ and LLGG：Cr^3＋ has been made. It is found that a peak of R1-line PS appears at Rmix^ei （^2E - ^4T2） ≈ 0.08.     

Cr3+:Al2(WO4)3晶体的生长和光谱特性

采用顶部籽晶法从Na2WO4助熔剂体系生长出优质的Cr^3 ：Al2(WO4)3晶体,测定了吸收和荧光光谱,结果表明：Cr^3 离子在晶体中有两个宽且强的吸收带和一个微弱的吸收线,两宽带中心波长分别为422和595nm,还有两个较弱的吸收峰,其荧光峰值分别为684和663nm。其荧光宽带和一个较弱的荧光线峰并存,宽带范围为650～820nm,峰值波长为740nm,荧光线峰波长约为680nm,其强度较强。计算了晶场强度和Racah参数,其Dq／B=2．42,晶体属于中阶场介质。研究表明,Cr^3 ：Al2(WO4)3晶体具备可调谐激光晶体的基本光谱要求,且有良好的物化性能,可以实现宽频带可调谐激光输出。     

Cr3+：MgAl2O4晶体EPR参量及其电子精细光谱的研究

考虑了SS(Spin-Spin)作用和SOO(Spin-Other-Orbit)作用，采用完全对角化方法，结合自旋Hamiltonian理论，研究了Cr³⁺∶MgAl₂O₄晶体EPR参量及其吸收光谱，理论与实验符合甚好. 在此基础上，进一步研究了⁴A₂(3d³)离子EPR参量的微观起源. 研究表明，EPR参量起源于四种微观机制：(1) SO(Spin-Orbit) 耦合机制；(2) SS耦合机制；(3)SOO耦合机制；(4) SO～SS～SOO总联合作用机制. 在这些机制中，SO机制是最主要的.