Optical Indicatrix Axes Research Articles

Use of the Laser Beam Deflection Technique for Thermo-Optic Coefficients Study in Gadolinium-Yttrium Oxyorthosilicate Doped with Erbium Ions

Results of use of the laser beam deflection technique for determination of thermo-optic coefficients (TOCs) of the Er3+-doped gadolinium-yttrium oxyorthosilicate crystal (Er3+:(GdY) SiO– Er:GYSO) are presented. A 0.1 at.% Er-doped gadolinium-yttrium oxyorthosilicate crystal was grown by the Czochralski method under nitrogen atmosphere. Raw materials such as Er2O3, Gd2O3, Y2O3, and SiO2 were weighed according to the formula (Er0.001Gd0.8995Y0.0995)2SiO5. Optical properties of the biaxial Er:GYSO crystal are described within the frame of the optical indicatrix with orthogonal principal axes Np , Nm , and Ng . To characterize the anisotropy of the TOCs a sample from the grown Er:GYSO crystal was prepared in a shape of a rectangular parallelepiped with dimensions of 7.0 (Np ) × 8.0 (Nm ) × 8.5 (Ng ) mm3. Each face of the sample is perpendicular to one of the optical indicatrix axes Np , Nm and Ng . For determination of the TOCs the laser beam deflection technique for a material with a linear temperature gradient is used. Measurements are performed at the wavelength of 632.8 nm. The thermal coefficient of the optical path (TCOP) for the Er:GYSO crystal measured at the wavelength of 632.8 nm at different light polarization E and propagation direction k were obtained. The TCOP values are positive for all directions of the light propagation k // Np , Nm , Ng . This means that the sign of the thermal lens which is directly related to the TCOP value will also be positive, and the positive thermal lens is then expected for Np Nm-, and Ng -cut Er:GYSO. Applying an analysis of the thermal lensing the dn /dT value for Yb:GYSO is estimated to be 6.5×10–6 K–1.

Universal Method for Determining the Principal Optical Indicatrix Axes in Triclinic Crystals

Determining the orientations of principal optical indicatrix axes is a key prerequisite for the applications of optical crystals, which is still an intriguing challenge for triclinic optical crystals due to the lowest symmetry. The prism method is one of the important ways to determine these directions, but no actual examples are available owing to the complexity and scarcity of the triclinic crystals so far. To solve this remaining problem among seven crystal systems, we proposed a universal method, the so-called “multiple prisms method,” to determine the orientations of principal optical indicatrix axes X, Y, and Z as well as the principal refractive index values nx, ny, and nz in triclinic crystals based on four prisms and demonstrated this method by employing triclinic Nd3+-doped La2CaB8O16 crystals, which is of great significance to the studies and applications of triclinic optical crystals in the future.

Anisotropy of thermo-optic properties of beryllium hexaaluminate crystal doped with chromium ions

We determined the thermo-optic coefficients of Cr3+-doped beryllium hexaaluminate crystal (Cr3+:BeAl6O10) for light polarizations E||Np, Nm, and Ng, and present the thermo-optic dispersion formulas for the principal thermo-optic coefficients of Cr3+:BeAl6O10. We also measured the linear thermal expansion coefficients for this crystal in the directions of optical indicatrix axes Np, Nm, and Ng. Finally, we modeled the thermo-optic dispersion data in accordance with theory, taking into account contributions both from the change of the electronic bandgap with temperature and from the volumetric thermal expansion coefficient.

935 nm-diode-pumped passively Q-switched Er:Yb:Sr3Gd2(BO3)4 pulse laser at 1.5–1.6 μm

Eye-safe 1.5–1.6 μm pulse laser passively Q-switched by a Co2+:MgAl2O4 crystal was realized in a Z-cut, 1.8 mm-thick Er:Yb:Sr3Gd2(BO3)4 crystal end-pumped by a 935 nm laser diode. A 1534 nm pulse laser with energy of 9.1 μJ, repetition frequency of 15.6 kHz, and duration of 29 ns was obtained at an absorbed pump power of 2.5 W. Polarization of the output laser beam was measured to be linear and parallel to the Y optical indicatrix axis. Benefited from a broad and flat absorption band between 920 and 950 nm, the Er:Yb:Sr3Gd2(BO3)4 crystal may be a good gain medium for 1.5–1.6 μm laser pumped by a common commercial diode laser around 940 nm.

Monoclinic zinc monotungstate Yb3+,Li+:ZnWO4: Part II. Polarized spectroscopy and laser operation

Monoclinic ytterbium-lithium codoped zinc monotungstate crystal (Yb3+,Li+:ZnWO4) is a promising material for laser opertation at ~1.06 μm. Absorption, σabs, and stimulated-emission, σSE, cross-sections are determined for light polarized along the optical indicatrix axes, E || Np, Nm and Ng. At room temperature, the maximum σSE amounts to 2.81 × 10−20 cm2 at 1055.6 nm (for E || Np) and the gain bandwidth reaches ~22 nm (for E || Ng). The radiative lifetime of the upper laser level is 0.37 ms. The Stark splitting of Yb3+ multiplets is resolved with low-temperature (6 K) spectroscopy revealing a relatively large total splitting of the ground-state, ΔE(2F7/2) = 804 cm−1, being remarkably high as compared to other Yb3+-doped tungstate crystals. A notable inhomogeneous broadening of the zero-phonon line is detected at 6 K. A continuous-wave diode-pumped 1.8 at.% Yb3+,Li+:ZnWO4 laser generated a maximum output power of 2.90 W at ~1059 nm with a slope efficiency of 57.9% and a linearly polarized output (E || Np). Yb3+,Li+:ZnWO4 is attractive for broadly tunable and mode-locked oscillators.

Polarization switching realized in the continuous-wave and acousto-optic Q-switched pulse Er:Yb:LaMgB5O10 lasers at 1556 and 1568 nm.

By using the natural birefringence of crystalline quartz, the switching of a 1568 nm laser with polarization parallel to the Z optical indicatrix axis to a 1556 nm laser with polarization parallel to the Y optical indicatrix axis was observed in both continuous-wave and acousto-optic Q-switched pulse lasers based on an X-cut Er:Yb:LaMgB5O10 crystal, when the alignment of the output mirror in a 976 nm diode-end-pumped plano-concave resonator was precisely tilted. For the continuous-wave regime, a 1568 nm laser with a maximum output power of 500 mW and slope efficiency of 16%, as well as a 1556 nm laser with a maximum output power of 400 mW and slope efficiency of 13.5% were realized, respectively. For the Q-switched regime, a 1568 nm pulse laser with an energy of 144 μJ and width of 300 ns, as well as a 1556 nm pulse laser with an energy of 168 μJ and width of 270 ns, were obtained respectively by precisely tilting the alignment of the output mirror, when the absorbed pump power was 4.0 W and pulse repetition frequency was 0.5 kHz.

Monoclinic Tm:MgWO4 crystal: Crystal-field analysis, tunable and vibronic laser demonstration

Tm3+-doped monoclinic magnesium monotungstate (MgWO4) is a promising material for lasers emitting at above 2 μm. Stark splitting of 3H6 to 1G4 Tm3+ multiplets in MgWO4 is determined using low-temperature spectroscopy, calculated within crystal-field theory modified for the case of an intermediate configuration interaction (ICI) and analyzed in terms of the barycenter plot. Tm3+:MgWO4 features a large Stark splitting of the ground-state (3H6), 633 cm−1, and high transition cross-sections for polarized light due to its low-symmetry structure. A unique feature of Tm3+:MgWO4 to provide a naturally polarized emission at >2 μm, as well as its suitability for broadly tunable and mode-locked lasers in this spectral range are argued. The first tunable and vibronic Tm3+:MgWO4 lasers are demonstrated, yielding a continuous tuning from 1897 to 2062 nm in the former case. A vibronic laser operated at even longer wavelengths up to 2093 nm due to electron-phonon coupling with low-energy phonons of the crystalline host. Moreover, the optical indicatrix axes of high-refractive-index biaxial MgWO4 are assigned.

Efficient diode-pumped Er:KLu(WO4)2 laser at ∼1.61 μm.

We report on an efficient diode-pumped continuous-wave erbium-doped monoclinic double tungstate laser. It is based on a 1at.% Er3+:KLu(WO4)2 (Er:KLuW) crystal cut along the Ng optical indicatrix axis. The Er:KLuW microchip laser, diode pumped at 0.98μm, generates 268mW at 1.610μm with a slope efficiency of 30%. The output is linearly polarized (E||Nm), and the laser beam is nearly diffraction limited (Mp,m2<1.1). Spectroscopic properties of Er3+ in KLuW are also presented. The stimulated-emission cross-section σSE is 0.46×10-20 cm2 at ∼1.609 μm for E||Nm. The microchip Er:KLuW laser outperforms the commercial Er,Yb:glass.

Thermal stress and end-bulging in monoclinic crystals: the case study of double tungstates.

An analytical description of the thermal stress and end-bulging component of thermal lensing is presented for monoclinic laser crystals, taking into account the anisotropy of their optical, thermal, and elastic properties for the first time, to the best of our knowledge. The geometry of longitudinal diode-pumping (plane stress approximation) is considered. The developed approach is applied to the monoclinic double tungstates (MDTs), Yb:KGW, Yb:KYW, and Yb:KLuW, yielding values of normal and shear stresses, tensile stress, and the end-bulging term. We show that for low-symmetry crystals, end-bulging is responsible for the astigmatism of the thermal lens. The geometry of this astigmatism is explained in terms of the principal meridional planes. We show that the crystal cut of the MDTs along the optical indicatrix axis Ng (propagation direction) provides low thermal stress and a purely positive and weakly astigmatic thermal lens, which is a key condition for power scaling and diffraction-limited laser output.

Temperature-dependent spectroscopy and microchip laser operation of Nd:KGd(WO4)2

High-resolution absorption and stimulated-emission cross-section spectra are presented for monoclinic Nd:KGd(WO4)2 (Nd:KGW) laser crystals in the temperature range 77–450 K. At room-temperature, the maximum stimulated emission cross-section is σSE = 21.4 × 10−20 cm2 at 1067.3 nm, for light polarization E || Nm. The lifetime of the 4F3/2 state of Nd3+ in KGW is practically temperature independent at 115 ± 5 μs. Measurement of the energy transfer upconversion parameter for a 3 at.% Nd:KGW crystal proved that this was significantly smaller than for alternative hosts, ∼2.5 × 10−17 cm3/s. When cut along the Ng optical indicatrix axis, the Nd:KGW crystal was configured as a microchip laser, generating ∼4 W of continuous-wave output at 1067 nm with a slope efficiency of 61% under diode-pumping. Using a highly-doped (10 at.%) Nd:KGW crystal, the slope efficiency reached 71% and 74% when pumped with a laser diode and a Ti:Sapphire laser, respectively. The concept of an ultrathin (250 μm) Nd:KGW microchip laser sandwiched between two synthetic diamond heat-spreaders is demonstrated.

Thermal Lensing and Multiwatt Microchip Laser Operation of Yb:YCOB Crystals

Thermal lensing is studied in monoclinic Yb:Ca 4YO(BO 3) 3 (Yb: YCOB) oxoborate crystals cut along the optical indicatrix axes. For all orientations, the thermal lens is positive. In the $Z$ -cut crystal, the sensitivity factors of the thermal lens are $M_{Z-X} = 2.4$ and $M_{Z-Y} = 2.8 \text{m}^{-1}/\text{W}$ (for $E \| X$ ), and the astigmatism degree is as low as $S/M = 14\%$ . The positive thermal lens in Yb:YCOB is related to the large thermal expansion and strong photoelastic effect. Microchip lasers are realized with 3-mm-long $X$ , $Y$ , and $Z$ -cut 15 at.% Yb:YCOB crystals. With a $Z$ -cut crystal, maximum output power of 8.35 W is achieved at ∼1040 nm with slope efficiency of 70%. Using various crystal cuts and output coupler transmissions, multiwatt emission in the spectral range of 1033–1091 nm is demonstrated.

Optical studies of the ferroelastic phase transitions in KFe(MoO4)2

ABSTRACTThe ferroelastic phase transitions in KFe(MoO4)2 have been studied by means of polarized light microscopy. The crystal undergoes a sequence of ferroelastic phase transitions. It has been found that the second transition consists of two transitions separated by the temperature interval of about 0.4 K. Both these transitions are of the first order and are evidenced through a phase front passing, without the domain structure rebuilding. The disposition of optical indicatrix axes ng, nm has been established, and the birefringence has been measured in the plane (0001) in the temperature range covering all ferroelastic phases. From temperature studies of the morphic birefringence, a critical exponent of the order parameter has been estimated.

Ferroelastic phase transition in KIn(WO4)2

ABSTRACTIt has been found that structural phase transition in KIn(WO4)2 occurs at the temperature 499 K that is much higher than reported in literature. Temperature observations of the crystal in a polarised light reveal the ferroelastic domain structure consistent with the monoclinic symmetry. An orientation of optical indicatrix axes corresponding to refractive indices ng and nm has been found and optical birefringence has been measured in (0001) plane. Based on electron paramagnetic resonance studies of Gd3+ ions and the disposition of optical indicatrix axes the monoclinic symmetry C2/c has been suggested for the ferroelastic phase of KIn(WO4)2.

Complex ferroelastic domain patterns of K1-xRbxSc(MoO4)2 crystals

ABSTRACTThe K0.97 Rb0.03Sc(MoO4)2 single crystal cross-section (0001) has been studied with an optical microscopy to determine temperature changes of domain configuration through the ferroelastic phases. The domain pattern found in the lowest ferroelastic phase is not fully consistent with the monoclinic symmetry. Four domain types observed differ in the orientation of optical indicatrix axes as well as in the value of birefringence. It has been suggested that in the third ferroelastic phase monoclinic and triclinic systems coexist in K0.97 Rb0.03Sc(MoO4)2.

Anisotropy of laser emission in monoclinic Nd:ScYSiO5 crystals cut along the optical indicatrix axes

In this Letter, we demonstrate the anisotropy of laser emission in disordered Nd:ScYSiO5 (Nd:SYSO) crystals cut along the optical indicatrix axes. High-powered lasers with different oscillation wavelengths and polarizations are realized by using different oriented crystals as gain media. For Y-cut crystals, the dual-wavelength laser vibration direction is found to be along the X axis and a maximum output power of 9.43 W is obtained, giving an optical-to-optical conversion efficiency of 48.8% and a slope efficiency of 51.3%. For X- and Z-cut crystals, 1075 and 1078 nm lasers operating orthogonally polarize oscillate with total output powers of 7.07 and 8.43 W, respectively. The experimental results reveal that the intrinsic anisotropy for the monoclinic disordered laser crystals could make laser design flexible and controllable.

Athermal directions and their dispersion in KGd(WO4)2 and KLu(WO4)2 crystals

An analysis of the existence of athermal properties for optically biaxial crystals KGd(WO4)2 and KLu(WO4)2 is performed and compared with that of KY(WO4)2 for monolithic and laser cavity configurations. Short-wavelength limits for athermal behavior in the principal planes of optical indicatrix are found. In KGd(WO4)2 they lie near or in the absorption band. In KLu(WO4)2, one of the two isonomal waves and both isonomal waves in the Np–Nm principal plane of KGd(WO4)2 for the laser cavity configuration have also long-wavelength limits. It is shown that for some wavelengths (one or two in the visible spectrum) and light wave polarization, the optical indicatrix axes can be athermal. In KLuW, for the monolithic configuration, the Np axis is athermal at three wavelengths, two of which lie in the IR region (0.843 and 1.975μm). All-space athermal directions are determined for KLu(WO4)2 at 2μm. For the monolithic configuration, they form a cone with its axis parallel to the Np axis and oval cross-section.

Ho:KLuW microchip laser intracavity pumped by a diode-pumped Tm:KLuW laser

A compact intracavity-pumped microchip Ho laser is realized using stacked Tm:KLuW/Ho:KLuW crystals pumped by a laser diode at 805 nm; both crystals are cut for light propagation along the N g optical indicatrix axis and emit with polarization along the N m axis. Maximum CW output power of 285 mW is achieved at a wavelength of 2080 nm for 5.6 W absorbed pump power in the Tm:KLuW crystal with a maximum slope efficiency of 8.3 %. Maximum total (Tm3+ and Ho3+ emission) output of 887 mW with a slope efficiency of 23 % is achieved. Laser operation is obtained in the 1867–1900 nm spectral range corresponding to the Tm emission, while Ho emits at 2078–2100 nm, depending on the output coupling. The microchip Ho laser generates a near-circular output beam with M 2 < 1.1. The compact laser setup with plane–plane cavity provides automatic mode-matching condition for the Tm and Ho laser modes.

Prospects of monoclinic Yb:KLu(WO_4)_2 crystal for multi-watt microchip lasers

The concept of Yb-doped double tungstate microchip lasers is verified and scaled to the multi-watt power level. The active element is a 2.6 mm-thick Yb:KLuW crystal cut along the Ng optical indicatrix axis. Maximum continuous-wave output power of 4.4 W is extracted at 1049 nm with a slope efficiency of 65% and an optical-to-optical efficiency of 44% with respect to the absorbed pump power. The laser emission is linearly polarized and the intensity profile is characterized by a near-circular TEM00 mode with M2x,y < 1.1. Due to low intracavity losses of the microchip laser, laser operation at wavelengths as long as 1063 nm is achieved. The mechanism of the thermal mode stabilization in the microchip cavity is confirmed. At very low resonator losses polarization-switching between E || Nm and Np oscillating states is observed and explained on the basis of spectroscopic and thermal lens characteristics.

Microchip laser operation of Tm,Ho:KLu(WO₄)₂ crystal.

A microchip laser is realized on the basis of a monoclinic Tm,Ho-codoped KLu(WO₄)₂crystal cut for light propagation along the Ng optical indicatrix axis. This crystal cut provides positive thermal lens with extremely weak astigmatism, S/M = 4%. High sensitivity factors, M = dD/dP(abs), of 24.9 and 24.1 m(-1)/W for the mg- and pg- tangential planes are calculated with respect to the absorbed pump power. Such thermo-optic behavior is responsible for mode stabilization in the plano-plano microchip laser cavity, as well as the demonstrated perfect circular beam profile (M(2) < 1.1). Maximum continuous-wave output power of 450 mW is obtained with a slope efficiency of 31%. A set of output couplers is employed to achieve lasing in the spectral range of 2060-2096 nm. The increase of output coupler transmission results in deterioration of the laser performance attributed to the increased up-conversion losses.

Thermal lensing in Yb:KLu(WO4)2 crystals cut along the optical indicatrix axes

Thermal lensing is studied in Yb:KLu(WO4)2 crystals cut along the three optical indicatrix axes, Np, Nm and Ng. The cut along the Ng-axis is the only one that provides a pure positive thermal lens with the sensitivity factors M = 3.5 and 2.8 m−1 W−1 (wp = 100 μm) for the mg- and pg-planes, respectively, and a low astigmatism degree, S/M < 20%. Both Np-cut and Nm-cut crystals produce different-signed lens with at least six-times stronger astigmatism. This behavior is related to the anisotropy of the photo-elastic effect. A CW Yb:KLu(WO4)2 microchip laser delivering a maximum output power of 992 mW at 1051 nm with a slope efficiency of 40%, and possessing low spatial distortions of the laser beam and M2 < 1.1, is realized on the basis of Ng-cut crystal.