This work reports on a beam quality and dynamic behaviors of a mirror-coated highly-doped YAG (Y3Al5O12) microchip ceramic laser possessing an increased number of grain boundaries. The degradation of beam quality factor in transverse patterns due to spatial inhomogeneity across the beam, multiple split-mode operations, violation of antiphase dynamics and high-speed intensity modulations due to the interference between non-orthogonal transverse modes were observed in a laser-diode end-pumping scheme.
©2004 Optical Society of America
Laser-diode- (LD-) pumped solid-state lasers (DPSSLs) have attracted much attention as compact, highly efficient light sources for a variety of applications. Recent progress in DPSSL technology including developments of new materials and high-power LDs led to high-power and tunable solid-state lasers. Among many advantages of DPSSLs, stable oscillations in the lowest-order transverse and a small number of longitudinal modes are attractive to achieve highly coherent diffraction-limited laser beams.
Thin-slice microchip platelet lasers with coated dielectric mirrors on both end surfaces in an LD end-pumping scheme by using the thermal lens effect  are the most simple and promising device configuration for practical uses if the high beam-quality is ensured. However, in contrast to DPSSLs with well-designed external cavity configurations, in which stable transverse eigenmodes are formed, transverse eigenmodes are formed through the pump-dependent thermal-lens effect in thin-slice platelet DPSSLs with end-mirrors, which depends on thermal properties of laser materials . Therefore, the beam quality strongly depends on thermal properties of laser media (e.g., thermal conductivity, thermal expansion coefficient, thermal coefficient of refractive index, thermal birefringence), heat dissipation design and the transverse beam quality of pump beam.
A wide variety of materials has been studied to develop more efficient and high power microchip lasers. In end-pumping schemes, in particular, materials with a short absorption length for the LD pump beam are strongly anticipated for highly efficient operations because of the excellent match between the mode and pump beam profiles. Early studies on Nd-stoichiometric lasers, such as NdP5O14 , LiNdP4O12 (LNP) , and NdAl3(BO3)O4, with high Nd concentrations, were along this research line. On the other hand, a simple sintering method led to the development of polycrystalline Nd:YAG ceramics that have transparency comparable to Nd:YAG single crystals [5,6]. High doping of Nd ions into the YAG ceramics has been successfully attained to overcome the short absorption length in Nd:YAG single crystals and 2.3 times higher output power than a 0.9 at. % Nd:YAG single-crystal laser has been reported in a 3.4 at. % Nd:YAG ceramic laser, for instance . Similar to Nd stoichiometric lasers like LNP, Nd:YAG ceramic lasers with high Nd concentrations (i.e., short absorption length for the LD pump light) are promising for microchip DPSSLs with coated end-mirrors without using an external cavity. Systematic studies of Nd:YAG ceramic lasers for different doping levels such as fabrication process, optical properties and thermal properties have been reported [5–9]. It has been shown that if we dope Nd3+-ions higher than 4 at. %, it is difficult to keep the large grain size, although the thermal conductivity is unchanged. Then, the number of grain boundaries will increase within the same path length and the cavity loss increases accordingly.
In this paper, we report on oscillation properties, including oscillation spectra, noise characteristics, dynamic effects observed in a highly Nd-doped Nd:YAG ceramic thin-slice laser with coated end-mirrors, together with beam quality, which provide a new insight into laser physics in ceramic lasers.
2. Spatial inhomogeneity and transverse beam quality
In order to make use of the short absorption length (i.e., high pump efficiency) for LD end-pumping of highly-doped Nd:YAG ceramic laser and make the simplest laser device, a micro-cavity configuration without external mirrors is promising. From the practical point of view, however, we have to investigate its beam quality of the oscillating mode which is formed according to the pump-power dependent thermal-lens effect itself, while stable Gaussian transverse eigenmodes are formed in the case of external cavity resonators in general, which ensure the diffraction-limited beam with beam-quality factor of M2 =1. The thermal-lens effect makes the unpumped ‘unstable’ plane-parallel Fabry-Perot resonator act as a stable resonator if the thermally-induced gradient refractive-index profile satisfies the stability condition of laser resonators .
Such effect depends on the pump-beam focusing condition, e.g., beam spot size and profile, and thermal properties of the laser material Therefore, the stability condition of optical resonators is not always ensured and the degradation of beam quality factor is expected even if the laser goes into oscillation, particularly in highly-doped Nd:YAG ceramics which include many grains across the lasing beam diameter.
In order to achieve an ideal symmetric pumping, a CW Ti: Sapphire laser operating at 808 nm was employed as a pump source at first. We used a 900μm-thick Nd:YAG ceramic sample with 5 at. % Nd concentration having dielectric mirrors coated on end surfaces (99.9% and 99% reflectivities at 1064 nm). Here, an absorbed threshold pump power was 100 mW and the slope efficiency was 40%, in which the absorption coefficient was 44 cm-1. M2 value of the Nd:YAG ceramic laser was measured as a function of the absorbed pump power using the beam quality evaluating system, Shack-Hartman wave front sensor (WaveFront Science, CLAS-2D), in which intensity and phase distribution across the transverse electric field were measured simultaneously. Example distributions are shown in Fig. 1, in which phase distribution shows the curvature of the constant phase. Except for the limited low pump power region, field profiles show strongly non-Gaussian distributions and the distortions are pronounced as the pump power is increased. The measured beam-quality factor, M2 value, along x- and y-axis are shown as a function of the output power in Fig. 2. Such strong deformations of the lasing field distribution in Nd:YAG ceramic laser is considered to arise from the spatial inhomogeneity across the lasing beam due to smaller grain sizes inherent in highly doped Nd:YAG ceramics.
As a reference laser with a high Nd concentration, we replaced the Nd:YAG ceramics by a 1-mm-thick mirror-coated LNP laser, in which the output coupling was 1%. The absorbed threshold pump power was 30 mW and the slope efficiency was 50%, where the absorption coefficient was 115 cm-1, yielding the absorption length of 87 μm. In this case, the stable single transverse mode and single-frequency operation on multiple transitions , which was free from dynamic instability described below, was observed. The measured M2 values along x- and y-axis are shown as a function of the output power in Fig. 3, in which M2 values below 3 were obtained in the entire pump power region.
The surface view of the Nd:YAG ceramic used in the experiment measured with a Zygo NewView is shown in Fig. 4. A random terrace-like structure which appeared reflecting the crystal-axis dependent polishing rate due to random distributions of single-crystalline grains, whose directions of crystal axes are independent, is seen. Such random grain distribution also contributes to the deformation of field distributions through the birefringence effect because the thermal birefringence (i.e., depolarization) strongly depends on the direction of crystal axes of the grain and thus phase distortions occur over transverse directions with increasing the pump-power. Averaged gain size was measured to be smaller than 50 μm from the view of etched surface as shown later. Therefore, the present Nd:YAG ceramic laser acts as an active medium consisting of randomly-distributed multiple single-crystal grains surrounded by grain boundaries, namely ‘lasing in random media’ .
3. Dynamics of a highly-doped Nd:YAG microchip ceramic laser
3.1 Oscillation spectra and noise property
Next, we replaced the Ti:Sapphire laser by a laser diode and examined oscillation properties. The experimental setup is shown in Fig. 5. A collimated elliptical-shape pump beam from the LD was passed through a pair of anamorphic prisms to transform the elliptical shape into circular one, and then it was focused onto the surface of the Nd:YAG ceramic laser or the LNP laser by a microscope objective lens (NA = 0.25).
The threshold pump power and the slope efficiency were almost the same as those for the Ti:Sapphire laser pumping. Example far-field patterns and three-dimensional intensity profiles, measured by a CCD camera, is shown in Fig 6.
In order to extract generic features in highly-doped ceramic lasers (i.e., ‘random media’ ), we measured global optical spectra and detailed oscillation spectra by using a multi-wavelength meter (HP-86120B; resolution: 20GHz) and a scanning Fabry-Perot interferometer (Burleigh; SAPLUS; free spectral range: 2GHz; resolution: 6MHz), respectively. A typical result is shown in Fig. 7.
The global oscillation spectrum in Fig. 7(a) indicates that the laser oscillates in a single longitudinal mode. The single-mode oscillation was maintained in the entire pump-power region in the experiment, where adjacent longitudinal modes separated by λ2/2nL= 0.35 nm (n=1.82: refractive index, L=0.9mm: thickness) were not observed. However, the scanning Fabry-Perot interferometer measurement clearly indicated that such a ‘single-mode’ oscillation consisted of closely-spaced multiple field components, which fluctuates over times, as shown in Fig. 7(b). In short, the laser field from the Nd:YAG ceramic laser is considered to be composed of closely-spaced unstable multiple modes emitted from composite single-crystal grains. It is reasonable that such incoherent superposition of multiply split modes results in the deformation of field distributions and the increase of M2 values as shown in Fig. 2.
Such multiple split-mode operations in the highly-doped Nd:YAG ceramic laser strongly affected intensity noise properties. The inherent antiphase dynamics in homogeneously-broadened single-crystalline solid-state lasers with spatial hole-burning  does not hold in this case. The inherent antiphase dynamics implies that N relaxation oscillation noise peaks appeared in power spectra for N modal intensities, while lower-frequency noise peaks are strongly suppressed by the inherent antiphase dynamics and only the highest relaxation oscillation noise peak at f1 remains for the overall output intensity. An example rf power spectrum of the overall output intensity of the Nd:YAG ceramic laser, measured with an rf spectrum analyzer (ADVANTEST R3131A; 9kHz-3GHz), is shown in Fig. 8, in which lower relaxation oscillation components are not suppressed. Therefore, the antiphase dynamics is violated. The observed noise property implies that multiple split-modes arise from the spatial inhomogeneity, but not from spatial hole-burning effect in the longitudinal direction.
3.2 Dynamic instability
In end-pumped microchip thin-slice DPSSLs with coated end-mirrors, the pump-beam profile is important for the thermally-induced refractive-index confinement of transverse modes. We have demonstrated that the asymmetric LD pump beam profile results in the formation of complicated transverse patterns, in which non-orthogonal transverse modes are created as eigenmodes, and transverse field-interference induced high-speed modulations occur, as demonstrated in the 300-μm-thick LNP laser with an LD asymmetric end-pumping and reproduced by numerical simulation [13,14]. Contrary to the previous experiment [13,14], in the present experiment the symmetric end-pumping was maintained along the longitudinal direction by the use of a pair of anamorphic prisms. Even in such a symmetric pumping, due to spatial inhomogeneity and an increased number of grain boundaries, the mode orthogonality among transverse modes formed in a random medium shown in Fig. 4 is not always ensured. As a result, formation of non-orthogonal transverse mode pairs and associated high-speed modulations through transverse-field interference are expected to take place. In the case of the LNP laser with the symmetric pumping, no instability occurred.
Example results indicating high-speed modulations are shown in Fig. 9, where 9(a) indicates the detailed optical spectrum measured by the scanning Fabry-Perot interferometer, 9(b) the intensity wave form measured by a digital oscilloscope, and 9(c) the corresponding rf power spectrum. Here, the entire output beam was focused onto the photo-detector. Note that a frequency separation of mode pairs in 9(a), indicated by fB, fluctuated over times in the Nd:YAG ceramic laser unlike that for asymmetrically-pumped LNP laser [13,14], however, the averaged value coincided with the beat-frequency among modes (i.e., pulsation frequency) in the power spectrum, shown in 9(c). Another example wave form and the corresponding power spectrum, indicating ‘breather mode’, which features two pulsation frequencies fB1, fB2 due to two closely-spaced pairs of non-orthogonal modes [13,14], is shown in Fig. 10.
4. Summary and discussion
We studied stationary and dynamic properties of a highly-doped Nd:YAG ceramic laser with directly coated mirrors, which is attractive for the simplest LD-pumped microchip laser configuration using thin-slice samples.
From the systematic laser experiment, the following results were obtained. Firstly, although the efficiency of Nd:YAG ceramics is good enough for practical microchip laser applications, the high Nd-doping (e.g., 5 at. %) results in the degradation in the beam quality factor M2 especially in the high pump-power regime, featuring multiple split-mode operations and violation of antiphase dynamics in noise spectra. Secondly, the spatial inhomogeneity due to increased grain boundaries results in the formation of non-orthogonal transverse modes and resultant high-speed modulations through the field interference of non-orthogonal transverse modes. Oscillation spectra, noise property, and dynamic effects observed in the experiment would be new indicators for evaluating ceramic lasers in terms of spatial inhomogeneity and its link with laser oscillations in random active media.
Typical reflection microscopic photographs of Nd:YAG ceramics with different doping levels, taken after thermal etching, are shown in Fig. 11 . These pictures indicate that the specimen consists of grains measuring several tens of micrometers with perfect pore-free structure. However, in general the grain size becomes much smaller for >5 at. % doping level because of the small effective segregation coefficient of elemental neodymium for the YAG single crystal of ~0.2, as reported in various papers. A systematic study of the effect of optical quality and grain size of ceramics on the formation of transverse patterns is under progress by using samples of different doping levels.
From a practical point of view toward more efficient and stable high power operations of LD-pumped highly-doped thin-slice Nd:YAG,, without annoying dynamic behaviors, a further improvement in the sintering method (purity of starting powder, soaking time, temperature) is needed, particularly in the coated-mirror resonators whose cavity modes are formed through the pump-dependent thermal-lens effect in ceramics.
Meanwhile, a stable external cavity design is another way to overcome the problem in highly-doped samples reported in the present study. Indeed, by the use of an external short cavity, in which the lasing beam diameter of a well-defined TEM00 eigenmode profile within the sample was designed to be not much larger than grain sizes independently of the pump-power level. Mx2=1.01 and My2=1.09 were obtained in a LD-pumped 3.4 at. % doped 847-μm-thick Nd:YAG ceramic laser consisting of a 50-mm-long semi-confocal resonator. Measured position-dependent beam radii near the focus are shown in Fig.12. Stable operations  without mode splitting, which were free from dynamic instability, were achieved
The authors are indebted to Yoich Sato of Institute for Molecular Science for measuring the absorption coefficient of the Nd:YAG ceramics. They also wish to thank A. Ikesue of Japan Fine Ceramic Center for providing us with surface photographs of Nd:YAG ceramics, Fig. 11.
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