We demonstrated a laser-diode-pumped, electro-optically internal-Q-switched laser system radiating at 1.085 µm fabricated using a periodically poled Nd:MgO:LiNbO3 (Nd:MgO:PPLN) crystal. The Nd:MgO:PPLN is 17-mm long and has a 12-mm long, 13.6-µm period polarization-mode quasi-phase-matching (PM QPM) grating section functioning as the Q-switch of the laser system. When the Nd:MgO:PPLN Q-switch was driven by a 260-V voltage pulse train at 5 kHz, we obtained laser pulses of pulse energy >2.45 µJ and a pulse width of ~28 ns, corresponding to a laser peak power of ~88 W, from this internal-Q-switched laser system with 2% output coupling at an absorbed diode pump power of 0.61 W.
©2008 Optical Society of America
LiNbO3 is a popular optical substrate for the construction of various optical and photonic devices. This is because of its superior material properties which make it suitable to use in electro optics, acousto optics, nonlinear optics, piezoelectricity, etc. Furthermore, with the aid of the impurity doping or metal indiffusion technique, LiNbO3 can also become a promising host material for various laser ions, such as Nd3+, Er3+, and Yb3+. Thus, laser ion-doped or diffused LiNbO3 has now become a medium of particular interest for the implementation of monolithic self-functioned laser devices such as self-frequency-doubled or internal-Q-switched (also termed as “self-Q-switched”; we adopt “internal-” instead of “self-” in this terminology to avoid possible confusion with the passively Q-switching technique) lasers . The integration of such a medium with nowadays popular diode-pumping technique could be an attractive scheme for producing a miniature yet efficient multi-function all-solid-state laser system. Nd:MgO:LiNbO3 can be a promising candidate for such purposes, in that the adverse problem of pump induced photorefractive damage found in the early development of Nd:LiNbO3 lasers has been effectively alleviated by doping with ≥5 mol. % MgO in the crystal  and by using a near-infrared pump source .
The laser Q-switching technique has proven to be an effective way of producing repetitively high-energy laser pulses with greatly enhanced peak laser power. This technique has also allowed the generation of a peak power greater than several tens of watts in a miniaturized laser. Some typical examples can be found from recent developments in actively and passively Q-switched microchip lasers [4, 5]. In particular, Chen et al.  has incorporated a periodically poled lithium niobate (PPLN) crystal in a compact Nd:YVO4 laser to act as a low-voltage electro-optic (EO) Q-switch. In this study, we further integrated the functionalities of an Nd3+ laser medium and an EO PPLN Q-switch into a monolithic periodically poled Nd:MgO:LiNbO3 (Nd:MgO:PPLN) crystal to achieve an actively internal- Q-switched laser. In addition to improving system miniaturization, the monolithic integration of laser intracavity elements has the obvious advantages of reducing the cavity loss and the difficulties with laser alignment. Besides, quasi-phase-matching (QPM) crystals have already been successfully fabricated from MgO:LiNbO3 for the purpose of performing high-efficiency nonlinear frequency conversion with improved laser damage resistance . The use of a Nd:MgO:PPLN crystal to fabricate and demonstrate an internally Q-switched laser in this work may contribute to the realization of a novel internal-Q-switched self-frequency-conversion laser in a monolithic LiNbO3 chip.
2. Laser design and construction
We fabricated QPM grating of 13.6-µm period in a 17-mm long, 1-mm wide, and 1-mm thick z-cut Nd:MgO:LiNbO3 crystal by using the high-temperature (170°C) electric-field poling technique . The characterized coercive field of this crystal was around 1.4 kV/mm. The co-doping concentrations of Nd and MgO in the Nd:MgO:LiNbO3 crystal are 0.4- and 5-mol. %, respectively. The 13.6-µm grating period for the Nd:MgO:PPLN crystal is designed to phase-match the 1st-order EO polarization-mode QPM (PM QPM) process  for a 1.085-µm light at 40°C. The working principles of such an EO PM QPM device have been reportd , so shall not be discussed here. Figures 1(a) and (b) show two typical cross-sectional photographs of the HF-etched y surface of the fabricated Nd:MgO:PPLN crystal taken near the former +z surface and at the depth of around 600 µm from the former +z surface, respectively. The photographs indicate that a uniform periodicity is maintained from the crystal surface to a ~600 µm depth. The reason for the occurrence of this earlier domain termination or merging can be attributable to the peculiar resistance reduction problem found in electric-field domain-polarity switching of a MgO:LiNbO3 crystal . Nevertheless, a Nd:MgO:PPLN crystal with a ~600-µm clear aperture is already sufficient for current applications (see below). The average domain duty cycle estimated from the periodically poled region is ~30%/70%. The first 5-mm length of this Nd:MgO:PPLN crystal by design serves as the diode end-pump region where the diode pump power is predominantly deposited due to the exponential absorption law. This mitigates the thermo-optic effects in the downstream 12-mm long EO PM QPM device (for this work, we named thereinafter the device as “EO Nd:MgO:PPLN”) whose performance is sensitive to changes in the crystal birefringence and refractive indices. The two y faces of the 12-mm long EO Nd:MgO:PPLN device were sputtered with NiCr layers as side electrodes. The device functioned as a Pockels cell  and served as the laser’s Q-switch in this work.
We then constructed a compact diode end-pumped, internally Q-switched Nd3+ laser based on the fabricated monolithic Nd:MgO:PPLN device, as schematically shown in Fig. 1(c). The pump laser was an 808-nm fiber-coupled diode laser with an emission polarization ratio of 2.5:1. The 808-nm wavelength is coincident with a σ-polarized wave absorption band of a Nd:MgO:LiNbO3 crystal . A coupling lens set was used to collimate and focus (with an effective focal length ~20 mm) the pump beam into the Nd:MgO:PPLN crystal near the front surface. The pump waist radius was ~190 µm. The lower halves of both crystal end faces (x surfaces) have been blocked to ensure lasing through the upper 600-µm periodically poled region (see Figs. 1(a) and (b)). Both of the crystal end faces have the anti-reflection (AR) coatings for dual wavelengths at 808 and 1085 nm. The Nd:MgO:PPLN crystal was first mounted in a copper heat sink whose temperature was stabilized by a thermal-electric cooler (TEC) unit, then placed in a laser resonator. The resonator was composed of a 15-cm radius-of-curvature (ROC) meniscus (zero power) dielectric mirror (M1) having >99% reflectance at 1.085 µm and ~95% transmittance at 808 nm and a 20-cm ROC plano-concave mirror (M2) having 98% reflectance at 1.085 µm as the laser output coupler. The cavity length of the constructed Nd:MgO:PPLN laser was as compact as 3.4 cm. The Nd:MgO:PPLN laser radiates at π-polarized 1.085 µm through the 4F3/2 → 4I11/2 transition. The measured cw threshold absorbed pump power and slope efficiency for this laser were 318 mW and ~11%, respectively. The laser output mode was in a slightly elongated shape with an eccentricity of ~0.3. The characterized M2 values approached 1 for both the vertical and horizontal beam-divergence directions. These results can be attributable to the geometry of the intracavity Nd:MgO:PPLN crystal (~600 µm in clear aperture and 17 mm in length as aforementioned) that poses the emission of an elongated TEM00 beam. The ratio of the peak emission cross sections of the π-polarized to the σ-polarized lines of the 4F3/2 → 4I11/2 transition in Nd:MgO:LiNbO3 crystal is ~3.5 , which is quite close to that (~3.8) of the same transition in a Nd:YVO4 crystal (note, however, the cross-section values of Nd:YVO4 are more than one order of magnitude larger than those of Nd:MgO:LiNbO3 for that transition). This large gain ratio between the two polarizations facilitates the efficiency of operation of an EO PPLN device as a laser Q-switch [6, 9].
Based on the pumping scheme and the TEC temperature controlling system specifications, we investigated the thermo-optic effect on the fabricated monolithic Nd:MgO:PPLN device of performing an EO internal Q-switch. Figure 2(a) shows the isosurfaces of the temperature inside the crystal calculated by a finite-element method software, Comsol Multiphysics®, under an absorbed pump power of 0.61 W and a TEC stabilizing temperature of 40°C. It was estimated that ~31% of the incident 808-nm pump power is converted to heat due mainly to the Stokes shift (ηS~ 0.74) and pump quantum efficiency (ηQ~ 0.93) of a Nd:MgO:LiNbO3 laser . We considered all the absorbed power turned into the sum of deposited thermal power and laser power. Therefore, the calculation result in Fig. 2(a) is overestimated since the fluorescence loss was also considered as the thermal load [12, 13]. It can be clearly seen from Fig. 2(a) that the temperature change due to this thermal deposition in the crystal is mainly located at the very first 5 mm of the crystal. The red line indicates the optical axis of the laser system. The minimum temperature is ~39.8°C located at the far end of the crystal and the maximum temperature is ~48.8°C located at about 1 mm from the crystal front surface, corresponding to the focus of the pump beam. Figure 2(b) shows the temperature distribution (solid curve) along the optical axis in the Nd:MgO:PPLN crystal. The corresponding distributions of the refractive index change of the crystal for 1.085-µm σ-polarized and π-polarized waves (dotted and dashed curves, respectively) are also plotted in Fig. 2(b) using the Sellmeier equations of a MgO:LiNbO3 . Since the EO Nd:MgO:PPLN Q-switch works on the basis of the EO PM QPM condition which is a function of the crystal birefringence as aforementioned, the influence of the existence of refractive indices variations in the Nd:MgO:PPLN crystal on the device performance should be clarified. Assuming for an incident π-polarized wave, the efficiency of an EO PM QPM device can be evaluated by its single-pass polarization-mode conversion efficiency, defined by
where Aσ(L, E) and Aπ(0) are the field amplitude envelopes of the converted σ-polarized wave after traversing the crystal of length L under an applied electric field E and the input π- polarized wave, respectively. For an EO PPLN device, the electric field E is applied along the PPLN crystallographic y axis . To find the T(E) for our Nd:MgO:PPLN device having a nonuniform temperature distribution as exhibited in Fig. 2, we can assume the crystal is composed of N crystal blocks, each with a thickness of Δx≪lc=λ 0/2(nσ-nπ), where lc is the coherence length of the prescribed EO PM QPM process , λ 0 is the wavelength of the incident wave in vacuum, and nσ and nπ are the refractive indices of the σ- and π-polarized waves in Nd:MgO:LiNbO3, respectively. For λ0=1.085 µm, the lc=6.8 µm at 40°C. We chose Δx=0.34 µm for this work. In such a small crystal thickness, a low-conversion limit and a uniform temperature across the block can be assumed. Accordingly the coupled wave equations describing the EO PM QPM coupling process  can be recast for waves in the j-th crystal block as
where i is the imaginary unit , xj = jΔx represents the position of the j-th block of the Nd:MgO:PPLN for j = 1, 2, 3…N, Δk = kσ-kπ is the wave-vector mismatch between the two polarization modes, and κ(xj) is the coupling coefficient at position xj, defined by
In Eq. (3), r51 is the relevant Pockels coefficient and the sign function s(xj)=±1 denotes the ±z domain polarity of the Nd:MgO:PPLN crystal block at position xj. Under the initial condition of Aπ(0)=1 and Aσ(0)=0, the Aσ(L, E), and therefore the conversion efficiency T(E) according to Eq. (1), can then be obtained by iteratively solving Eq. (2) through the N blocks (L=NΔx). Figure 3 compares the calculated electric-field tuning curves of the polarization-mode conversion efficiency T(E) of the Nd:MgO:PPLN device. The solid curve shows the calculated conversion efficiency assuming the temperature distribution across the whole crystal is uniform at 40°C while the dashed curve was calculated using the temperature distribution obtained from Fig. 2(b). These two curves coincide closely, which indicates the thermo-optic effect has introduced minor effect on the performance of the Nd:MgO:PPLN internal Q-switch in current monolithic design (see Fig. 1(c)).
3. Laser performance measurement and discussion
To operate the laser in Q-switching mode, the EO Nd:MgO:PPLN section was first driven with a 5-kHz voltage pulse train 260 V in amplitude and 300 ns in pulse width. This 260-V driving voltage corresponds to a normalized value of 0.31 V×d (µm)/L (cm), where d (=1000 µm for the present device) is the electrode separation and L (=1.2 cm for the present device) is the electrode length. The demand of a higher driving voltage than that for an undoped PPLN (<0.18 V×d (µm)/L (cm))  can be attributable to the lower domain poling quality obtained with our current technical capability for implementing a uniform periodicity and 50%-duty-cycle Nd:MgO:PPLN crystal. At 0.61-W absorbed pump power, we obtained laser pulses of pulse energy >2.45 µJ and a pulse width <30 ns, corresponding to a laser peak power of ~88 W. Figure 4 shows the variation of the measured pulse width (solid circles) and pulse energy (solid triangles) with the absorbed pump power. The pulse width decreased from 152 to 28 ns and the pulse energy increased from 0.52 to 2.45 µJ as the absorbed pump power increased from 0.4 to 0.61 W. The inset shows the measured Q-switched laser pulse. By using the material properties of a Nd:MgO:LiNbO3 crystal  (absorption coefficient α=0.002 cm-1, upper level lifetime τf~100 µs, and emission cross section σs~2×10-19 cm2 at λL=1.085 µm), the aforementioned cavity geometric and coating parameters, and the measured pump threshold and slope efficiency (ηsl) from the cw laser output, we calculated the theoretical fittings (solid and dash-dotted curves, respectively) for the two measurements plotted in Fig. 4 according to the model we have used to predict the output performance of an EO PPLN Q-switched Nd:YVO4 laser . We also measured the peak power and pulse width as a function of the Q-switch repetition rate with the EO Nd:MgO:PPLN laser system operated at an absorbed pump power of 0.57 W; indicated in Fig. 5 by the solid triangles and circles, respectively. The pulse width increased from 33 to 160 ns and the peak power decreased from 59.3 to 1.6 W as the Q-switch repetition rate increased from 5 to 35 kHz. In this figure, the solid and dash-dotted curves represent the theoretical fittings of the two measurements, obtained using the aforementioned system parameters and calculation model. It can be seen from Figs. 4 and 5 that the experimental data agrees reasonably well with the theoretical predictions. This agreement implies that the 2% output coupling used in this work is close to the optimum value for the present laser system in the applied diode pump power range . To further enhance the output performance (e.g., the pulse width reduction and pulse energy extraction) of this internal-Q-switched laser, the increase of the output coupler transmittance is necessary. To optimize the Q-switched laser system with a higher output coupling value, the pump threshold of the system has to be lowered accordingly . This can be done by reducing the dissipative loss of the resonator and/or the pump beam size (it is ~380 µm with current setup) . To reduce the pump beam size in the Nd:MgO:PPLN crystal, a more compact design of the laser system might be helpful. For example, one can directly apply a high-reflectivity mirror coating on the input end of the Nd:MgO:PPLN crystal to save the mirror M1 (refer to Fig. 1(c)).
We also observed few-watt (peak power) non-phase-matched second harmonic generation (542 nm) from this laser system. No photorefractive effects were observed in the experiment. This appreciable amount of generation originates in the high intracavity fundamental peak power (~4.4 kW). This observation suggests the laser system has the potential to develop as an interesting internal-Q-switched self-frequency-conversion laser if an additional QPM wavelength-conversion section can be monolithically integrated into the current Nd:MgO:PPLN crystal.
We have successfully fabricated and demonstrated a laser-diode-pumped, actively internal-Q-switched laser system using a 17-mm long, 13.6-µm period monolithic Nd:MgO:PPLN crystal. We obtained 28-ns, 2.45-µJ Q-switched laser pulses, corresponding to a laser peak power of ~88 W, from this miniature 1.085-µm laser system with 2% output coupling when driven by a 5-kHz 260-V voltage pulse train and pumped at 0.61-W absorbed diode power. The characterized output performance of this laser system agreed reasonably well with the theoretical calculations.
This work was supported by the National Science Council (NSC) of Taiwan under NSC Contract Nos. 96-2120-M-001-005 and 96-2221-E-008-042 and partially supported by the Technology Development Program for Academia (TDPA) with Project Code 95-EC-17-A-07-S1-011.
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