Study of Nd³⁺ ion as a Dopant in YAG and Glass Laser

Kireet Semwal*, S. C. Bhatt

Department of Physics, G.B. Pant Engineering College, Pauri (Garhwal), India

Abstract: Trivalent neodymium (Nd³⁺) is the most successful type of active ion for solid-state lasers and thus far has been made to lase in more types of crystal and glass hosts than any other ion. It can operate as either a pulsed or continuous-wave laser with a sharp emission line. The most common emission wavelength is near 1μm, but there are several possible laser transitions in the near-infrared spectral region, and in addition a near-ultraviolet laser line. Although the effects of different host environments on the spectroscopic properties of Nd³⁺ are more subtle than those for transition-metal ions, they can cause significant differences in lasing characteristics through changes in physical processes such as radiative transition strength, radiationless decay probabilities, excited-state absorption, and cross relaxation quenching. The Nd ion when doped into a solid-state host crystal produces the strongest emission at a wavelength just beyond 1μm. The two host materials most commonly used for this laser ion are yttrium aluminium garnet (YAG) and glass. At room temperature the 1.064μm radiative transition is homogeneous broadened with a narrow emission line width of 0.45nm and the upper level lifetime is 230μs. Nd can be doped to very high concentration in glass. The outstanding practical advantage compared to crystalline materials is the tremendous size capability for high-energy applications. The fluorescent lifetime is approximately 300μs, and, the emission line width is 18-28nm.

Keywords: Nd³⁺, Nd:YAG laser, Nd:Glass laser

Received December 31, 2012; Revised March 05, 2013; Accepted March 10, 2013

Citation: Kireet Semwal, S. C. Bhatt, Study of Nd³⁺ ion as a Dopant in YAG and Glass Laser. International Journal of Physics, 1 (1). 15-21. January 2013. doi:10.12691/ijp-1-1-3

1. Introduction

Materials for laser operation must possess sharp fluorescent lines, strong absorption bands, and reasonably high quantum efficiency for the fluorescent transition of interest. These characteristics are generally shown by solids (crystals or glass) which incorporate in small amount of elements in which optical transitions can occur between states of inner, incomplete electron shells. Thus the transition metals, the rare earth (lanthanide) series, and the actinide series are of interest in this connection. It is possible to co-dope many of these elements within solid-state host, chosen to obtain the desired long lifetime as well as other suitable laser properties. The sharp fluorescent lines in the spectra of crystals doped with these elements result from the fact that the outer shells from the surrounding crystal lattice shield the elements involved in transitions in the optical regime [4]. The host material must possess good optical properties as well good mechanical and thermal properties. Poor optical properties include variations in index of refraction, which lead to irregular beam quality in the laser output and impurities, which lead to scattering and undesired absorption of pump light or laser beam output. Poor mechanical and thermal properties lead to material deformation or fracturing of the host when the laser is operated under such high pulse-repetition rate or high steady state pumping. The host must also be able to accept the dopant material in a way that will not distort the desired properties of the dopant i.e. a long lifetime and an appropriate line shape. The host must also be capable of being grown in size, with a uniform distribution of the dopant that is required for laser gain media [5].

The rare earth ions are natural candidates to serve as active ions in solid-state laser materials because they exhibit a wealth of sharp fluorescent transitions representing almost every region of the visible and near-infrared portions of the electromagnetic spectrum. It is a characteristic of these lines that they may be very sharp, even in the presence of the strong local fields of crystals, as a result of the shielding effect of the outer electrons. The outermost electrons of these ions from a complete rare gas shell, which is the xenon shell with two 5s and six 5p electrons. This shell is optically inactive. Next inside the xenon shell is the 4f shell, which is filled successively in passing from one element to the next. Trivalent cerium, Ce³⁺, has one 4f electron, and trivalent ytterbium, Yb³⁺, has 13. As long as the 4f shell is not completely filled with 14 electrons, a number 4f levels are unoccupied, and electrons already present in the 4f shell can be raised by light absorption into these empty levels. The sharp lines observed in rare earth absorption and emission spectra are ascribed to these transitions, and the sharpness of the lines is explained by the fact that the electrons making the transition lie inside the xenon shell and thus interact only weakly with outside ions Table 1 shows the population of the outermost electron shells of the rare earths [4]. Rare earth ions usually exist in solids in either the trivalent or the divalent state. A divalent rare earth ion is formed when the atom gives up its outermost 6s electrons. When a trivalent ion is formed the atom also loses its 5d electron if it has one; otherwise, one of the 4f electrons is lost. The rare earth ions generally have a number of sharp emission lines due to the atomic like character of the radiating 4f state. They usually exist in solids in the trivalent form. Rare earth triple ions include neodymium (Nd³⁺), erbium (Er³⁺), holmium (Ho³⁺) and thulium (Tm³⁺) etc.

Table 1. Electronic structure of elements 59 to 71

Trivalent neodymium (Nd³⁺) is the most successful type of active ion for solid-state lasers and thus far has been made to lase in more types of crystal and glass hosts than any other ion. It can operate as either a pulsed or continuous-wave laser with a sharp emission line. The most common emission wavelength is near 1μm, but there are several possible laser transitions in the near-infrared spectral region, and in addition a near-ultraviolet laser line. The two host materials most commonly used for this laser ion are yttrium aluminium garnet (YAG) and glass. When doped in YAG, the Nd: YAG crystal produces laser output primarily at 1.064μm; when doped in glass, the Nd: glass medium lases at wavelengths ranging from 1.054 to 1.056μm, depending upon the type of glass used. Nd ions in YAG crystals are limited to a maximum concentration of 1.0 - 1.5 % [1]. Higher concentration leads to increased collision decay, resulting in a reduced upper laser level lifetime. At room temperature the 1.064μm radiative transition is homogeneous broadened with a narrow emission line width of 0.45nm and the upper level lifetime is 230μs. Nd:YAG rods have good heat conduction properties, which make them desirable for high-repetition rate laser operation. These have a disadvantage, however, in that they are limited by crystal growth capabilities to small laser rods, of the order of up to 1 cm in diameter and lengths of the order of 10cm. doping YAG with neodymium results in a blue to violet crystal. Because the material becomes strained at atomic percentages greater than approximately 1.5%, the majority of Nd:YAG crystals are doped at approximately 1%. Is generally accepted that higher doped material (1 to 1.4 %) is better for Q-switched laser performance (due to the higher energy storage) while lower doped material (0.5 to 0.8%) is better to cw (steady-state) laser performance where optical beam quality is important [6].

Nd can be doped to very high concentration in glass. Many types of phosphates and silicate glasses have been used for the lasers. The outstanding practical advantage compared to crystalline materials is the tremendous size capability for high-energy applications. For Nd: glass laser gain media, very large-size laser materials have been produced. It can be fabricated into special laser configurations such as slabs and fibers as well as standard rod designs. Rods of up to 2m long and 0.75m in diameter and disks of up to 0.05m thick have been successfully demonstrated. The optical quality can be excellent, and beam angles approaching the diffraction limit can be achieved. Glass, of course, is easily fabricated and takes a good optical finish. The fluorescent lifetime is approximately 300μs, and, the emission line width is 18-28nm. This is wider than for Nd:YAG by factor of 40 to 60. This increased emission line width (inhomogeneous broadening) in effect reduces the laser gain. The drawback of Nd: glass laser materials is their relatively poor thermal conductivity, which restricts these lasers to relatively low pulse repetition rates for pulsed lasers and a lower operating power for cw lasers [2,3,7]. Therefore, the laser thresholds for glass lasers have been found to run higher than their crystalline counterparts. This leads to thermally induced birefringence and optical distortion in glass laser rods when they are operated at high average powers. Therefore crystalline laser hosts generally offer as advantages over glasses their higher thermal conductivity, narrower fluorescence linewidth, and, in some cases, greater hardness. However, the optical quality and doping homogeneity of crystalline hosts are often poorer, and the absorption lines are generally narrower. A summary of the host crystals used for laser systems is given in Table 2 [8,9,10].

2. Nd:YAG Crystal

The Nd:YAG laser is the most commonly used type of solid-state laser at the present time, perhaps surpassing in number the ruby laser. Nd:YAG (Neodymium-doped yttrium aluminium garnet Y₃Al₅O₁₂:Nd³⁺) is clear (colourless), optically isotropic, of good optical quality, hard material, whose most familiar application is as a diamond replacement in jewelry. YAG is optically isotropic crystal, of good optical quality, and has a high thermal conductivity (0.14 W/cm-K). YAG is also nonhygroscopic, melts at 1970 ⁰C, and has a Knoop hardness of 1215 (around 8.2 on the Moh’s hardness scale), which makes it one of the most durable of the common laser crystals [3,7]. It possesses a cubic structure characteristic of garnets with space group Ia3d. The cubic structure of YAG favours a narrow fluorescent linewidth, which results in high gain and low threshold for laser operation. The YAG structure is stable from the lower temperatures up to the melting point, and no transformations have been reported in the solid phase. The strength and hardness of YAG are lower than ruby but still hard enough so that normal fabrication procedures do not produce any serious breakage problems [1,4]. In the garnet crystal structure the yttrium ion is surrounded by eight oxygen ions in the shape of a distorted cube. In Nd:YAG about 1% of Y³⁺ is substituted by Nd³⁺. The radii of the two rare earth ions differ by about 3%. The larger size of the Nd³⁺ ion results in polyhedra with sides that are greater in length than those of the Al³⁺ polyhedra. This distorts the lattice and thus limits the maximum doping concentration to several atomic weight percent. Therefore, with the addition of large amounts of neodymium, strained crystals are obtained-indicating that either the solubility limit of neodymium is exceeded or that the lattice of YAG is seriously distorted by the inclusion of neodymium. Doping introduces a lattice strains and distorts the properties of the optical spectra. The local site symmetry is D₂. Since the Nd:YAG crystal has good optical quality and high thermal conductivity, making it possible to provide pulsed laser output at repetition rates of up to 100Hz. Nd glass laser is restricted to the repetition rates less than 5Hz by the limitation of the laser material above that repetition rate, however, the performance plummets and the second and most widely used solid-state-laser system.

Table 2. Laser Host Materials

The Nd laser incorporates a four-level system and consequently has a much lower pumping threshold than that of the ruby and other lasers. The upper laser lifetime is relatively long (2.30μs for Nd: YAG and 320μs for Nd: glass) so population can be accumulated over a relatively long duration during the pumping cycle when the laser is used either in the Q-switching mode or as an amplifier. The emission and gain linewidths are 0.45nm for YAG and 28nm for glass. The Nd:YAG crystal produces laser output primarily at 1.064 μm. At room temperature, this 1.064μm radiative transition is homogeneously broadened with a narrow emission linewidth of 1.2 X 10¹¹ Hz (Δλ = 0.45nm) and the upper level lifetime is 230μs. Nd: YAG rods have good heat conduction properties, which make them desirable for high-repetition rate laser operation. They have a disadvantage, however, in that they are limited by crystal growth capabilities to small laser rods, of the order of up to 1cm in diameter and lengths of the order of 10cm. thereby limiting the power and energy output capabilities of this laser. The optical quality of such rods is normally quite good and comparable to the best quality of Czochralski ruby or optical glass [4]. Commercially available laser crystals are grown exclusively by the Czochralski method. Growth rates, dopants, annealing procedures, and final size generally determine the manufacturing rate of each crystal. The boule axis or growth direction is customarily in the <111> direction. The high manufacturing costs of Nd:YAG are mainly caused by the very slow growth rate of Nd:YAG, which is of the order of 0.5mm/hr. Typical boules of 10 to 15cm in length require a growth run of several weeks. In specifying Nd:YAG rods, the emphasis is on size, dimensional tolerance, doping level, and passive optical tests of rod quality. Cylindrical rods with flat ends are typically finished to the following specifications: end flat to λ/10, ends parallel to ± 4 arc seconds, perpendicularity to rod axis to ± 5 minutes, rod axis parallel to within + 5⁰ to <111> direction. Dimensional tolerances typically are ± 0.5 mm on length and ± 0.025mm on diameter.

Table 3. Material Properties of Nd: YAG

Table 4. Thermal properties of Nd: YAG

Table 5. Index of refraction and reflectance of Nd:YAG

An energy-level diagram for Nd³⁺ doped in a YAG host material is shown in Figure 1 (a). The relevant laser levels are slightly lowered for doping in glass as compared to YAG, as shown in below Figure 1 (b). The upper laser level is shifted downward by 112cm⁻¹ and the lower laser is shifted downward by 161cm⁻¹, producing a net decrease in the laser wavelength for glass. The excitation bands occur in the blue and the green. The pump energy then transfers nonradiatively (collisionally) to the upper laser level ⁴F3/2. The laser terminates on the ⁴I11/2 lower level, from which collisional decay takes the population back to the ground state. Two other radiative transitions in the Nd ion are also used as laser transitions. They originate from the same upper laser level as the 1.064μm transition anddecay to the ⁴I13/2 level radiating at 1.35μm and to the ⁴I9/2 level producing 0.88-μm radiation. These transitions have lower gain than the 1.064μm transition and therefore are not as easily made to lase [12,13,14].

Figure 1. Comparison of energy levels of the laser transition for Nd doped in YAG and glass

Table 6. Typical Nd: YAG and Nd: Glass Laser Parameters

2.1. Energy Levels of Nd³⁺

The electronic configuration for the 60 electrons of a neodymium atom is:

1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶4d¹⁰4f⁴5s²5p⁶5d⁰6s². The first nine sets of orbitals make up the filled core, while the optically active electrons are in the partially filled 4f orbitals. The latter are shielded by the electrons in the outermost 5s through 6s orbitals. The trivalent neodymium ion has given up three electrons, two from the outer 6s orbitals and one from the 4f orbitals, leaving a configuration of Xe (4f ³5s²5p⁶). The three 4f electrons are the ones that play the dominant role in determining the optical properties of the ion. Although the transitions giving rise to the optical spectra take place between different levels of the 4f3 configuration, it is also important to know the positions of the energy levels of the 4f N-15d configurations since configuration interaction is critical in determining spectral line strengths. The Russell-Saunders coupling approach can be used to determine the electronic terms of the free ion with three electrons, each having quantum numbers n = 4 and l =3. Due to the shielding of the outer-shell electrons, the crystal-field splitting is always treated in the weak-field limits, so spin-orbit coupling is applied first to determine free-ion multiplets. The types of spectroscopic terms available for Nd³⁺ ions can be determined by using appropriate combinations of single-electron orbitals and applying the Pauli’s exclusion principle. Since all of the optically active electrons have same values of n and l, there are only certain combinations of the quantum numbers ml and ms that are allowed. Since l =3 for each of the electrons, the largest value of the total angular momentum quantum number could be 9 so ML should run from 0 to ± 9 in integer steps. However, the only way for the orbitals angular momenta of the three electrons to couple to give L = 9 would result in two of the electrons having an identical set of quantum numbers, which is not allowed. The spin angular momenta of the three electrons can couple to give quartets or doublets, so MS = ± 3/2, ± 1/2. A table of single-electron states that contribute to the multielectron terms can be constructed and the results are shown in Table 7. Only the positive ML - positive MS quarter of the table is shown since the table is symmetric and thus all of the required information can be obtained from this quarter. Here the single-electron states are represented by (ml₁±, ml₂±, ml₃±) where the + or – superscript designates spin up or spin down, respectively. These are placed in the ML row and MS column of an appropriate term. Since the largest values of ML and MS equal L and S, respectively, for a given term, Table 7 can be used to determine the spectroscopic terms of a 4f³ ion. The highest ML row in the table has single-electron states occupying only the cells in the MS = ± 1/2 columns. Since this cell represents ML = 8, these must belong to a ²L term. One of the single-electron states occupying only the cells in the MS = ± 1/2 columns will also belong to this term thus can be eliminated. This leaves the highest occupied cells those with ML = L = 7 and MS = ± 3/2. The states in these cells belong to a ⁴I term with additional states in all the remaining cells. This procedure can be followed until all of the single-electron states have been associated with multielectron terms resulting in the identification of 17 terms: ²L, ²K, ⁴I, ²I, ²H, ²H, ⁴G, ²G, ²G, ⁴F, ²F, ²F, ⁴D, ²D, ²D, 2P, ⁴S. Next these terms must be placed in order to ascending energy. Using Hunds’s rule, implies that the ⁴I term is the ground state, and the energies of the other terms with respect to the ground state must be determined. As with transition-metal ions, perturbation theory is used to determine the energy levels with the zero-order perturbation being the electrons in the 4f orbital moving independently of each other in the central field of the nucleus and the inner-shell electrons. Under these conditions, all energy levels of a given 4fn configuration are degenerate. The Coulomb interaction between the optically active electrons is treated as one perturbation and the spin-orbit interaction of the electrons is treated as another perturbation. This gives a good approximation for calculating the energy levels. However, for rare-earth ions the interactions between electrons in different configurations can also be important in some cases.

The spin-orbit interaction is the same order of magnitude as the Coulomb interaction for the rare-earth ions and therefore must be treated before treating the crystal-field perturbation. The qualitative splitting of the terms into multiplets follows the description of angular momentum coupling. The values of the J quantum numbers for the multiplets of a term with quantum numbers L and S run in integer steps from L – S to L + S. Thus the ground term of Nd³⁺ has the four multiplets ⁴I9/2, ⁴I11/2, ⁴I13/2, and ⁴I15/2 with the first of these being lowest in energy because the electronic configuration of this ion is less than a half-field shell. The four multiplets of the metastable state range from ⁴F3/2 to ⁴I9/2. Some of these splitting is shown in Figure 2 [15,16].

Table 7. Single-electron states for a 4f³-electron configuration

2.2. Laser Transitions in Nd: YAG

The Nd:YAG laser is a four-level system as depicted by a simplified energy level diagram in and Figure 2. The 1.064 and 1.061-μm transitions, provide the lowest threshold laser lines in Nd:YAG. The main laser transition occurs at 1064nm due to the ⁴F3/2 – ⁴I11/2 transition, originates from the R2 component of the ⁴F3/2 level and terminates at the Y₃ component of the ⁴I11/2 level. The width of the laser transition is 4.5 A⁰ and the stimulated emission cross section is 6.5 10⁻¹⁹cm². The index of refraction at the wavelength of the laser transition is 1.82, and the scattering loss coefficient for a typical laser crystal is 0.002cm⁻¹. At room temperature only 40% of the ⁴F3/2 population is at level R₂; the remaining 60% are at the lower sublevel R₁ according to Boltzmann’s law, i.e. at room temperature the 1.064μm line R₂→Y₃ is dominated, while at low temperatures the 1.061 μm R₁→Y₁ has the lower threshold [17]. If the laser crystal is cooled, additional laser transitions are obtained, mostly the 1.839 μm line and the 0.946 μm line. Lasing takes place only by R₂ ions whereby the R2 level population is replenished from R₁ by thermal transitions. The ground level of Nd:YAG is the ⁴I9/2 level. There are a number of relatively broad energy levels, which together may be viewed as comprising pump level 3. Of the main pump bands shown, the 0.81μm and 0.75μm bands are the strongest. The terminal laser level is 2111 cm⁻¹ above the ground state and thus the population is a factor of exp (ΔE/kT) ≈ exp (-10) of the ground state density. Since the terminal level is not populated thermally, the threshold condition is easy to obtain.

The upper laser level, ⁴F3/2, has a fluorescent efficiency greater than 99.5% [12] and a radiative lifetime of 230 μs. The branching ratio of emission from ⁴F3/2 is as follows [18]: ⁴F3/2→⁴I9/2 =0.25, ⁴F3/2→⁴I11/2 = 0.60, ⁴F3/2→⁴I13/2 = 0.14, and ⁴F3/2→⁴I15/2< 0.01. This means that almost all the ions transferred from the ground level to the pump bands end up at the upper laser level, and 60% of the ions at the upper laser level cause fluorescent output at the ⁴I11/2 manifold. Figure 3 shows the absorption spectrum for the Nd-ions in YAG. Under normal operating conditions the Nd:YAG laser oscillates at room temperature on the strongest ⁴F3/2→⁴I11/2 transition at 1.064 μm, which is homogeneously broadened by thermally activated lattice vibrations. The values of stimulated emission cross-section for the extensively measured 1.06-μm line ranges from 2.7 to 8.8 10⁻¹⁹cm² [11,18]. It is possible, however, to obtain oscillation at other wavelengths by inserting a dispersive prism in the resonator, by utilizing a specially designed resonator reflector as an output mirror [19], or by employing highly selective dielectrically coated mirrors [20]. These elements suppress laser oscillation at the undesirable wavelength and provide optimum conditions at the wavelengths desired. With this technique over 20 transitions have been made to lase in Nd:YAG. The effective cross section at room temperature of the important transitions and the measured relative thresholds of those transitions at which room-temperature cw oscillation have been observed are given in Table 8 [4]. There is a second prominent laser transition for Nd:YAG that originates on the same metastable state but terminates on the ⁴I13/2 level. This occurs at 1.338μm and has a cross section that is about four times smaller than that of the main laser line [21]. The slope efficiency of this laser transition is somewhat less than that of the main laser line which is consistent with the lower energy of the photons involved in the transition. The threshold for lasing is higher; the gain lower, and the maximum output power is lower for the 1.338-μm emission as compared to 1.034-μm emission. Both lasing transitions can be operated in cw, pulsed, and Q-switched operation, the 1.064-μm line typically provides pulses with temporal widths between about 12 and 75 ns while the 1.338-μm line typically provides pulses between about 100 and 400 ns [23,24,25,26].

Figure 2. Energy level diagram of Nd: YAG

Figure 3. Absorption Spectrum of Nd: YAG

Table 8. Main transitions in Nd:YAG

Conclusion

Trivalent neodymium (Nd³⁺) is the most successful type of active ion for solid-state lasers and thus far has been made to lase in more types of crystal and glass hosts than any other ion. It can operate as either a pulsed or continuous-wave laser with a sharp emission line. The two host materials most commonly used for this laser ion are yttrium aluminium garnet (YAG) and glass. When doped in YAG, the Nd: YAG crystal produces laser output primarily at 1.064μm; when doped in glass, the Nd: glass medium lases at wavelengths ranging from 1.054 to 1.056μm, depending upon the type of glass used. Nd ions in YAG crystals are limited. At room temperature the 1.064μm radiative transition is homogeneous broadened with a narrow emission line width of 0.45nm and the upper level lifetime is 230μs. Nd can be doped to very high concentration in glass. The outstanding practical advantage compared to crystalline materials is the tremendous size capability for high-energy applications. The fluorescent lifetime is approximately 300μs, and, the emission line width is 18-28nm.

References

[1]   | K. J. Kuhn; Laser Engineering, Prentice Hall Pub., 1998.
[2]   | L. R. Marshall, A. D. Hays, H. J. Kasinski, and R. Burnham; “Highly efficient optical parametric oscillators”, SPIE, 1419: 141-152, 1991.
[3]   | R. D. Stultz, D. E. Nieuwsma, E. Gregor; SPIE, 1419: 64-74, 1991.
[4]   | Walter Koechner, Solid State Laser Engineering, 5rh ed., Springer Berlin, 1999.
[5]   | Willium T. Silfvast, Laser Fundamentals, Cambridge University Press, 1991.
[6]   | V. J. Corcoran; “High-repetition-rate eyesafe rangefinders” SPIE, 1419: 160-163, 1991.
[7]   | J. A. Skidmore, M. A. Emanuel, R. J. Beach, B. L. Freitas, N. W. Carlson, C. D. Marshall, W. J. Benett, R. W. Solaz, D. P. Bour, and D. W. Treat; “New diode wavelengths for pumping solid state lasers”, SPIE Proceedings, 2382: 106-116, 1997.
[8]   | J.E. Geusic, H.M. Marcos, L.G. Van Uitert; “LASER OSCILLATIONS IN Nd‐DOPED YTTRIUM ALUMINUM, YTTRIUM GALLIUM AND GADOLINIUM GARNETS”, Appl. Phys.Letters 4(10): 182, 1964.
[9]   | Z. J. Kiss and R. J. Pressley; “Crystalline solid lasers”, Proc. IEEE 54(10): 1236, 1966.
[10]   | Z. J. Kiss and R. J. Pressley; “Crystalline Solid Lasers”. Appl. Opt., 5(10): 1474-1486, 1966.
[11]   | R. V. Alves, R. A. Buchanan, K. A. Wickersheim, E. A. C. Yates; “Neodymium‐Activated Lanthanum Oxysulfide: A New High‐Gain Laser Material”, J. Appl. Phys. 42(8): 3043, 1971.
[12]   | T. Kushida, J. E. Geusic; “Optical Refrigeration in Nd-Doped Yttrium Aluminum Garnet”, Phys. Rev. Letters, 21(16): 1172, 1968.
[13]   | W. F. Krupke, M. D. Shinn, J. E. Marion, J. A. Caird, and S. E. Stokowski; “Spectroscopic, optical, and thermomechanical properties of neodymium- and chromium-doped gadolinium scandium gallium garnet”, J. Opt. Soc. Am. B, 3(1): 102, 1986.
[14]   | R. C. Powell, S. A. Payne, L. L. Chase and G. D. Wilke; “Index-of-refraction change in optically pumped solid-state laser materials”, Opt. Lett., 14(22): 1204-1206, 1989.
[15]   | G.H. Dieke and H.M. Crosswhite; “The Spectra of the Doubly and Triply Ionized Rare Earths”, Appl. Opt., 2(7): 675, 1963.
[16]   | B. R. Judd; “Optical Absorption Intensities of Rare-Earth Ions”, Phys. Rev., 127(3): 750, 1962.
[17]   | M. Birnbaum; “Stimulated emission cross section at 1.061 μm in Nd:YAG”, J. Appl. Phys., 44(6): 2928, 1973.
[18]   | T. Kushida, H. M. Marcos, J. E. Geusic; “Laser Transition Cross Section and Fluorescence Branching Ratio for Nd³⁺ in Yttrium Aluminum Garnet”. Phys. Rev., 167(2): 289-291, 1968.
[19]   | H. F. Mahlein; IEEE J. Quant. Electr. QE-6: 529, 1970.
[20]   | C. G. Bethea; IEEE J. Quant. Electr. QE-9: 254, 1973.
[21]   | N.P. Barnes, D.J. Gettemy, L. Esterowitz, and R.E. Allen; IEEE J. Quant Elect. QE-23, 1434, 1987.
[22]   | F. J. Duarte, Tunable Laser Optics, Elsevier-Academic, New York, 2003.
[23]   | D. Y. Shen et al., “Highly efficient in-band pumped Er:YAG laser with 60 W of output at 1645 nm”, Opt. Lett. 31(6): 754-756, 2006.
[24]   | Li Chaoyang et al., “106.5 W high beam quality diode-side-pumped Nd:YAG laser at 1123 nm”, Opt. Express 18(8): 7923-7928, 2010.
[25]   | X.Delen et al, “34 W continuous wave Nd:YAG single crystal fiber laser emitting at 946 nm”, Appl. Phys. B 104(1): 1, 2011.
[26]   | H.C. Lee et al., “Diode-pumped continuous-wave eye-safe Nd:YAG laser at 1415 nm”, Opt. Lett. 37(7): 1160, 2012.