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Abstract
We report on a novel approach to fabricate channel (ridge) waveguides (WGs) in bulk crystals using precision diamond saw dicing. The channels feature a high depth-to-width aspect ratio (deep dicing). The proof-of-the-concept is shown for a Tm3+:LiYF4 fluoride crystal. Channels with a depth of 200 µm and widths of 10–50 µm are diced and characterized by confocal laser microscopy revealing a r.m.s. roughness of the walls well below 100 nm. The channels obtained possess waveguiding properties at ∼815 nm with almost no leakage of the guided mode having a vertical stripe intensity profile into the bulk crystal volume and relatively low propagation losses (0.20-0.43 dB/cm). Laser operation is achieved in quasi-CW regime by pumping at 780 nm. The maximum peak output power reaches 0.68 W at ∼1.91 µm with a slope efficiency of 53.3% (in σ-polarization). The proposed concept is applicable to a variety of laser crystals with different rare-earth dopants.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Fluoride crystals doped with rare-earth ions (RE3+) are attractive for development of efficient power-scalable waveguide (WG) lasers emitting in the Short Wavelength Infrared (SWIR) spectral range, an, in particular, at ∼2 µm and beyond) [1–5]. As host matrices, they provide good thermal properties (e.g., the thermal conductivity of undoped LiYF4, <κ> = 6.0 Wm-1K-1) [6], broadband transparency (0.15-7.5 µm for LiYF4), low refractive index (no = 1.443 and ne = 1.465 for LiYF4 at ∼1.9 µm) [7] and low phonon energies (hνph = 446 cm-1 for LiYF4) [8]. The latter determines weak non-radiative relaxation and long upper laser level lifetimes of the RE3+ ions [9]. An example of efficient fluoride laser material is RE3+-doped lithium yttrium fluoride crystal, LiYF4 [10–12]. This material belongs to the tetragonal crystal class (sp. gr. I41/a) and it exhibits natural birefringence [7]. It also offers a single rare-earth site (the Y3+ one) and can be doped with the RE3+ ions in high concentrations [13]. The technology of growth of bulk RE3+-doped LiYF4 crystals by the Czochralski (Cz) method is well-developed [14].
Nowadays, a common way to produce crystalline RE3+-doped LiYF4 WGs is the Liquid Phase Epitaxy (LPE) [15]. In this way, high optical quality thin crystalline films of RE3+:LiYF4 are achieved on undoped oriented bulk LiYF4 substrates resulting in a planar WG geometry [16]. Consequently, a microstructuring step is required to fabricate channel WGs with a well-defined transverse profile of the refractive index leading to the single-transverse-mode operation. One known method of microstructuring of LPE-grown crystalline films is the ion beam milling leading to relatively low propagation losses (δloss ∼0.11 dB/cm) [17]. However, it is rather complicated from the technological point of view. Recently, we demonstrated the suitability of precision diamond saw dicing for microstructuring of LPE-grown Tm3+-doped LiYF4 crystalline thin-films [18]. A Tm3+:LiYF4 channel WG laser generated 1.30 W at 1880 nm with a slope efficiency of 80% with respect to the absorbed pump power and a low laser threshold of 80 mW.
In the present work, we aimed to extend this technology to direct fabrication of optical WGs in bulk crystals. A special geometry of WGs with a high depth-to-width aspect ratio (referred as deep dicing) was selected. In this way, the mode confinement is expected to be provided by the refractive index contrast at the crystal / air interfaces and an additional refractive index variation due to the photo-elastic effects originating from stresses induced by mechanical dicing.
So far, precision diamond saw dicing was used for fabrication of optical WGs in various optical materials, Table 1. Chen et al. applied this method for fabrication of ridges in polymer films deposited on SiO2/Si wafers and doped with fluoride nanoparticles (Er3+,Yb3+:NaYF4); optical gain at ∼1.5 µm was reported [19]. Waeselmann et al. patterned Nd3+:α-Al2O3 (sapphire) thin films produced by pulsed laser deposition (PLD). Laser operation was achieved: the WG laser generated 322 mW at 1092 nm with a slope efficiency of ∼12% probably due to the high losses of ∼6 dB/cm [20]. Earlier, Jia et al. fabricated ridge WGs in bulk Nd3+:Y3Al5O12 single-crystals subjected to swift heavy ion irradiation and extracted 84 mW of output power at 1064 nm with a slope efficiency of 43% corresponding to lower δloss = 1.7 dB/cm [21]. Kifle et al. structured LPE-grown anisotropic Tm:KY1-x-yGdxLuy(WO4)2 thin films and generated 262 mW at 1833 nm with a high slope efficiency of 82.6% and moderate δloss = 1.1 dB/cm [22]. Finally, WGs in irradiated LiNbO3 and KTiOPO4 crystals were also fabricated by diamond saw dicing [24,25], featuring WG propagation losses of ∼1 dB/cm. These structures were used for second-harmonic generation leading to green emission.
Table 1. Optical waveguides produced by diamond saw dicing.
Note that all the previous studies [19-24] focused on near-surface dicing (with the depth not exceeding few tens of µm) corresponding to small aspect ratios (depth / width, or y/x) of about unity or much less. High aspect ratio (e.g., top width: 1 µm, depth: 500 µm) WGs were reported only in lithium niobate [25], however, reasonably low propagation losses of 0.5 dB/cm were observed for less exaggerated structures, cf. Table 1.
2. Fabrication of waveguides
2.1 Diamond saw dicing
As a reference material for proof-of-the-concept, we selected the tetragonal Tm3+:LiYF4 crystal. It was grown by the conventional Czochralski (Cz) method and doped with 4.0 at.% Tm (the actual ion concentration: NTm = 5.50×1020 cm-3). A rectangular sample was cut for light propagation along the crystallographic a-axis (a-cut) with a thickness (t) of 7.0 mm and an aperture of 3.5(c)×10 mm2. The input and output faces and the top surface of the sample were polished to laser quality and remained uncoated.
Then, the top surface was subjected to precision diamond saw dicing resulting in fabrication of surface channels (ridges) with a depth of 200 µm along the c-axis and a varied width of 10–50 µm (with a step of 10 µm), Fig. 1. Such widths are similar to those achieved in LPE films or single crystals by other micro-structuring methods, such as ion beam milling or fs direct laser writing. The step of 10 µm was selected from the point of view of convenience in discriminating the guides from each other, there were no technical limitation for this. The channels propagated through the whole length of the sample. For this purpose, very low grit size blades were selected and calibration processes occurred to ensure the dimensions of the ridges. The channels were separated by about 500 µm, which is sizable but comes from the use of a large blade: it enforces a better stability and minimize vibrations during deep dicing. The end-facets of the crystal sample were not repolished after the dicing, but the dicing process may additionally improve the end-facet quality by cutting the material orthogonally to the ridge thus reducing roughness and ensuring a good verticality of the input/output surfaces.
The quality and geometry of channels were inspected with a confocal laser microscope (Sensofar S-neox) equipped with a blue light-emitting diode (LED, λ = 405 nm), Fig. 2. First, we studied one of the end-facets of the sample, showing vertical “pillows” separated by diced regions, Fig. 2(a). No cracks propagating into the guides nor into the bulk crystal volume are observed (the dark lines are due to the polishing of the end-facet of the sample before dicing and they are enhanced because of the observation geometry in reflected light which is sensitive to the surface quality). A close view on one of the fabricated guides (with an intermediate width of 30 µm), Fig. 2(b), reveals vertical walls within about 3/4 of its height. The flatness of the input facet of the guide is similar to that of the bulk crystal, so that no repolishing is required. In the bottom part of the same guide (at about 1/4 of its height), Fig. 2(c), (a) rounding is observed and it is asymmetric from left and right diced areas. In this part, small bright spots with a size <0.1 µm are visible and they are interpreted as writing debris. Such rounding in the bottom part of the channels is characteristic for diamond saw dicing and it was also observed in guides diced at small depths [18,22].
Fig. 2. Confocal laser microscope images of the Tm3+:LiYF4 crystal subjected to precision diamond-saw dicing: (a-c) the end-facet view showing (a) (from left to right) 40 µm, 30 µm, 20 µm and 10 µm wide WGs, (b) a close view in the 30 µm WG and (c) the bottom part of the 30 µm WG; (d-f) the top surface view on (d) (from left to right) 40 µm, 30µm, 20 µm and 10 µm WGs, (e,f) the input facet of (e) 30 µm and (f) 10 µm WG. Reflection mode, λ = 405 nm.
Furthermore, the top surface of the sample was observed, Fig. 2(d). The fabricated guides are straight and there are no cracks preventing the light propagation through the whole length of the sample. A lose view on the top surface of two guides (with a width of 30 µm and 10 µm) is shown in Figs. 2(e) and 2(f). The ridges have smooth side walls. The r.m.s. surface roughness of the channel walls is well below 100 nm (this value is an upper estimation, limited by the precision of the used method). According to the studies of ridges in lithium niobate, even lower roughness down to ∼5 nm is expected.
2.2 Waveguiding properties
The passive waveguiding properties of the fabricated channels were studied at the wavelength of ∼815 nm. It is close to the pump wavelength for Tm3+:LiYF4 (780 nm, the 3H6 → 3H4 Tm3+ transition). The power of the pump beam was maintained to be low (∼20 mW) to operate in the small-signal regime avoiding bleaching of the Tm3+ absorption. As a laser source, we used a Ti:sapphire laser (3900S, Spectra Physics). Its output (beam quality parameter: M2 ≈ 1) was focused into the WGs using an uncoated CaF2 lens (focal length: f = 40 mm) resulting in a measured spot size 2wP of 30 ± 5 µm (at the 1/e2 level). The mode profile at the output facet of the waveguide was reimaged to a CCD camera (BladeCam-XHR, DataRay Inc.) using a short focal length CaF2 lens (f = 15 mm). The scale calibration for the camera was performed by illuminating the WGs with a known size using a near-IR light source (LED) placed before the focusing lens. The obtained calibration images well matched those obtained with the confocal microscopy yielding an estimated scaling error of less than 3 µm. The polarization of the laser beam in the crystal corresponded to π (E || c, vertical). This polarization was selected because it corresponds to higher absorption and stimulated-emission cross-sections for Tm3+ ions in LiYF4.
In the first set of experiments, the pump was focused in the central part (with respect to the height) of each guide. The guided modes had a vertical stripe intensity profile well confined within the cross-section of the channel (representing a kind of a rotated planar WG geometry immersed in the air), Fig. 3. The pump modes were spatially multimode for all the guides. For example, for the 10 µm and 20 µm wide WGs, the pump modes were assigned as TM1,0 and TM2,0, respectively. The appearance of high-order modes was justified by the M2 measurement along the vertical direction. For wider WGs (30–50 µm), the beam was spatially multimode also along the horizontal direction and an asymmetry in the mode was detected: the maximum of light intensity was localized near one of the side walls, Figs. 3(b) and 3(c). This is attributed to the slight asymmetry of the waveguide cross-section induced by dicing, see Figs. 2(b) and 2(c) for example. No leakage of the guided modes into the bulk crystal volume was detected.
Fig. 3. 2D intensity profiles of the guided pump mode at the output WG facet: the WG width is (a) 10 µm, (b) 30 µm and (c) 50 µm. While lines showing the crystal surface are drawn as guides for eyes. λP = 815 nm. Pumping in the central part of the input facet. The laser polarization (π) is vertical.
We studied the same WG (with a width of 10 µm) focusing the pump beam in different positions (along the vertical axis) of the input facet, Fig. 4. When focusing the pump near the top of the WG, a vertically extended TM0,0 mode was observed, Fig. 4(a). By shifting the position of the pump spot to the center of the guide, the mode extended in the vertical direction corresponding to TM1,0, Fig. 4(b). Still, almost no leakage of the pump into the bulk volume was observed. Only when focusing the pump close to the bottom part of the guide, see Fig. 4(c), the modal profile was distorted strongly leaking into the bulk, and a small nearly-circular mode guides under the “pillow” was visible. This distortion is due to the asymmetric rounding of the guide described above.
Fig. 4. 2D intensity profiles of the guided pump mode at the output WG facet: focusing of the pump beam in (a) the top part, (b) the medium part and (c) bottom part of the 10 µm wide WG. While lines showing the crystal surface are drawn as guides for eyes. Red dashed circles indicate the position of the pump beam at the input facet. λP = 815 nm. The laser polarization (π) is vertical.
Let us discuss the guiding mechanism of the fabricated channels. Tetragonal LiYF4 is an optically uniaxial crystal; its optical axis is parallel to the c-axis [7]. There are two principal light polarizations, denoted as π (E || c) and σ (E ⊥ c) and corresponding to the principal refractive indices ne and no. Both polarizations are available for the selected crystal cut (a-cut). From the side walls and the top surface, the guiding is provided by the very high refractive index contrast between the crystal (for undoped LiYF4, ne = 1.4724 at 815 nm) and the air.
The pump geometry (M2 ≈ 1, 2wP = 30 µm) corresponded to a Rayleigh length zR of 1.28 mm in the crystal. Thus, at the output facet of the WG, the pump beam would have a diameter of (2wP)out ∼ 165 µm which agrees with our observations. However, this does not explain the modal profile of the pump along the vertical direction. For the mode confinement of the pump radiation along the vertical direction, we propose two mechanisms: (i) a refractive index variation (increase) in the guide due to the photoelastic effect (a change of the refractive index owing to permanent stresses, in our case, induced by dicing) and (ii) the absorption at the pump wavelength which is stronger for the “wings” of the pump mode which are not able to saturate the Tm3+ ions [26]. For Tm3+:LiYF4, the absorption cross-section at 815 nm σPabs is 0.41×10−21 cm2 in π-polarization corresponding to a small-signal absorption loss in the studied WGs of 0.7 dB (in a single-pass).
In a similar manner, one may explain the guiding of the laser mode. Note that the 3F4 → 3H6 laser transition of Tm3+ ions represents a quasi-three-level laser scheme with reabsorption. For example, for lasing in π-polarization, the stimulated-emission (SE) cross-section at the peak emission wavelength of ∼1880 nm σSE is 4.0×10−21 cm2 and the reabsorption cross-section σLabs is 0.41×10−21 cm2. Thus, the gain-guiding (the reabsorption in the non-pumped areas of the WG) can be in part responsible for the mode confinement along the vertical direction [27,28]. The second possible reason is the photo-elastic effect. In Fig. 5, we analyzed the 10 µm wide WG using a mode calculator (a variational mode solver based on quasi-analytical vectorial slab mode expansion) [29]. The minimum refractive index variation (increase) in the upper part of the WG with respect to its bottom part and the bulk volume Δn which can support the fundamental mode (TM0,0) at 1880 nm is ∼2.5×10−3, Fig. 5(b). The corresponding pump mode at 780 nm (TM1,0) is shown in Fig. 5(a) in agreement with the experiment.
Fig. 5. Simulated 2D intensity mode profiles in the 10 µm wide WG at the light wavelength of (a) 780 nm (pump, TM1,0 mode) and (b) 1880nm (laser, TM0,0 mode). The light polarization is vertical. The refractive index increase in the guide Δn is ∼2.5×10−3, ne = 1.4728 (780 nm) and ne = 1.4652 (1880nm).
The WG propagation losses δloss at 815 nm were estimated by observing the top surface of the sample with a CCD camera and detecting the intensity of the scattered pump light along the WG (in the longitudinal direction). An example of this evaluation for the 20 µm and 50 µm wide WGs is shown in Fig. 6. The on-axis intensity of the pump radiation changed according to the equation I(z) = I0×exp(-δtotz), where δtot = αabs + δloss is the total loss coefficient, αabs = σPabsNTm = 0.23 cm-1 is the small-signal absorption coefficient at the pump wavelength and z is the axial coordinate. The origin of strong dispersion of the data points in the end of the guides is non-uniform reflection of scattered light from the silver paint used for mounting the sample. The δloss monotonously increases for more narrow WGs, from 0.20 ± 0.03 dB/cm for the 50 µm wide WG to 0.43 ± 0.04 dB/cm for the 10 µm wide one, Table 2. This is explained by stronger interaction of the pump mode with the side walls of the WGs containing small defects causing light scattering.
Fig. 6. (a) Longitudinal distribution of the intensity of pump radiation at 815 nm in the 20 µm and 50 µm wide WGs: symbols – experimental data, curves – their exponential fits using a total loss coefficient δtot = αabs + δloss; (b) The corresponding 2D intensity map from a CCD-camera for the 50 µm wide WG.
Table 2. Pump coupling efficiency, propagation losses and pump absorption in the studied WGs.
Under pumping at 780 nm, the channels provided an intense polarized luminescence at ∼1.9 µm due to the 3F4 → 3H6 Tm3+ transition. The spectral properties were similar to those of the bulk crystal.
3. Laser operation
3.1 Laser set-up
The scheme of the WG laser is shown in Fig. 7. As a pump source, we used a CW Ti:Sapphire laser delivering about 3.2 W of linearly polarized output at 780 nm in a fundamental mode (M2 ≈ 1). This wavelength corresponded to the local peak in the absorption spectrum of Tm3+:LiYF4 crystal (the 3H6 → 3H4 Tm3+ transition). The pump polarization was set to be vertical (π-polarization in the crystal). The incident pump power was varied by a rotatory λ/2 plate and a Glan-Taylor polarizer. The pump beam was focused by an uncoated CaF2 lens (f = 40 mm, T = 93.8%) providing a pump spot diameter at the input face of the WG 2wP of 30 ± 5 µm. For quasi-CW pumping, the pump beam was modulated using a mechanical chopper (frequency: 10 Hz, duty cycles ranging from 1:2 to 1:12).
Fig. 7. (a) Scheme of the waveguide laser set-up: λ/2 – half-wave plate, P – Glan-Taylor polarizer, FL and CL – focusing and collimating lenses, respectively, PM – pump mirror, OC – output coupler, F – cut-off filter; (b) top view photograph of the 50 µm wide WG pumped at 780 nm, Pinc = 1.0 W, the bright trace corresponds to Tm3+ upconversion luminescence.
The Tm3+:LiYF4 crystal with the surface guides was mounted on a Cu-holder using a silver paste to improve the thermal contact from the bottom part of the sample. The holder was passively cooled. The crystal was placed in a simple linear plano-plano cavity. It was formed by a flat pump mirror (PM) coated for high transmission (HT, T = 99.4%) at ∼0.78 µm and for high reflection (HR, R > 99.9%) at 1.60-2.02 µm, and a set of flat output couplers (OCs) with a transmission at the laser wavelength TOC ranging from 2% to 50%. Both cavity mirrors were gently pressed towards the WG end-facets. No index-matching liquid was used to avoid damaging the optical surfaces. The geometrical cavity length was 7.0 mm. The pump beam was focused into the WGs through the PM.
To filter out the residual (non-absorbed or non-coupled) pump after the OC, a long-pass filter (FEL900, Thorlabs) was used. The laser emission spectra were measured using an optical spectrum analyzer (AQ6375B, Yokogawa).
To determine the pump coupling efficiency, we coupled into the WGs the laser beam from the Ti:Sapphire laser tuned to 830 nm (out of the Tm3+ absorption) and monitored the power at the output facet. The pump coupling ηcoupl = Plaunch/Pinc (Plaunch is the launched pump power) was calculated excluding the propagation losses δloss estimated in Section 2.2. The ηcoupl value includes Fresnel losses at the uncoated input facet of the crystal (TFr = 96.4%, as calculated using a refractive index of LiYF4: ne = 1.4722 at 830 nm). It is in the range of 80.5–46.1% for the 50-10 µm wide WGs and it is relatively close to the value obtained considering only the Fresnel losses and the geometrical overlap of the WG end-facet and the pump beam. As expected, ηcoupl decreased for smaller widths of the guides.
For the 4.0 at.% Tm3+:LiYF4 crystal, the small-signal pump absorption ηabs,0 at 780 nm is close to unity. Indeed, ηabs,0 = 1 – exp(–σPabsNTmt) = 96.2%, where σPabs = 0.85×10−20 cm2 is the absorption cross-section at the pump wavelength λP for π-polarized light. The pump absorption under non-lasing conditions, ηabs,NL = Pabs/Plaunch (Pabs is the absorbed pump power) was determined from the pump-transmission (end-fire) measurements, see Fig. 8 for the example of the 20 µm and 50 µm wide WGs. The ηabs,NL slowly decreased with the incident pump power due to the ground-state bleaching. At very small pump powers, ηabs,NL ≈ ηabs,0. For estimating the absorbed pump power under lasing conditions Pabs, we have taken the ηabs,NL value at the laser threshold (for each of the studied OCs). For example, for the 50 µm wide WG, the pump absorption slightly decreased from 94.5% for TOC = 2% down to 93.9% for the highest studied TOC = 50%. The pump saturation for the WG with a smaller width (20 µm) was stronger, as expressed by smaller values of ηabs,NL for the same pump level, which is due to the higher light intensity in the guide. The values of pump absorption for the same TOC = 50% and different WG width are compared in Table 2.
Fig. 8. Measured pump absorption under non-lasing conditions, ηabs,NL, in the 20 µm and 50 µm wide ridge WGs in 4 at.% Tm3+:LiYF4 as a function of the incident pump power. Blue circle – small-signal pump absorption.
3.2 Laser performance
The laser operation was achieved for all the WGs when focusing the pump beam in the upper part of each of the guides. No laser emission was detected when the pump was focused in the bulk part of the sample. The experiments were performed in quasi-CW regime (duty cycle: 1:2) to diminish the thermal effects in thin passively-cooled ridges. The input-output dependences for the largest studied WG (width: 50 µm) are shown in Fig. 9(a). For TOC = 50%, the laser generated a maximum output peak power of 381 mW at 1901-1929 nm (a broad emission spectrum) with a slope efficiency η of 42.2% with respect to the absorbed pump power Pabs. The laser threshold was at Pabs = 0.25 W and the optical-to-optical efficiency ηopt was 18.6% (as calculated vs. the pump power incident on the guide). For smaller output coupling, the laser threshold gradually decreased reaching Pth = 0.16 W for TOC = 2%. For Pabs exceeding ∼1 W, a thermal roll-over was observed in the input-output dependences. Thus, Pabs was limited to about 1.5 W to avoid thermal fracture of the guides.
Fig. 9. Deep-diced Tm3+:LiYF4 ridge waveguide laser: (a,c) input-output dependences, η – slope efficiency; (b,d) typical laser emission spectra measured at (b) Pabs ∼ 1.0 W and (d) Pabs ∼ 0.6 W. Quasi-CW regime of operation with a duty cycle of 1:2. The channel width is (a,b) 50 µm and (c,d) 20 µm. The laser polarization is (a,b) σ and (c,d) σ or π.
The typical spectra of laser emission for the 50 µm wide WG and various transmissions of the output coupler are shown in Fig. 9(b). For all the OCs, the laser emission was linearly polarized (σ); the polarization was naturally selected by the gain anisotropy. The emission occurred at around ∼1.91 µm for all the studied OCs in agreement with the gain spectra of Tm3+:LiYF4 for σ-polarization and small inversion ratios (see below).
For the sake of comparison, in Figs. 9(c) and 9(d), we show the input-output dependences and the typical spectra of laser emission for the smaller guide (width: 20 µm). The best performance for this WG corresponded to a maximum output peak power of 153 mW at 1884-1888 nm (in π polarization) with lower η = 25.3% and higher laser threshold Pth = 0.29 W (as compared to the 50 µm wide WG, for TOC = 50%). The optical-to-optical efficiency was thus only 2.9%.
The spectral behavior of the 20 µm wide WG laser was different from the 50 µm wide one, Fig. 9(d). For small output coupling, the laser operated in σ-polarization corresponding to the emission at ∼1.91 µm (e.g., 1906-1911 nm for TOC = 5%). For intermediate TOC = 7–30%, two polarizations coexisted within the whole studied range of the absorbed pump power. As a result, the spectra contained emission lines within several regions (e.g., 1878-1882 & 1912-1918 nm for TOC = 10%, with the short wavelength emission in π-polarization and the long-wavelength one in σ-polarization). Finally, for high TOC = 50%, only π-polarized emission occurred.
Such polarization-switching is common for optically anisotropic (birefringent) laser crystals which exhibit similar gain cross-sections for two orthogonal principal light polarizations [30,31]. The switching between two polarizations can be promoted by change of the total intracavity losses (e.g., via the output coupling) or by polarization-dependent thermal lensing affecting the mode overlap efficiency or cavity stability. As a result, there may exist such levels of the cavity losses or pump powers for which two polarizations coexist leading to dual-wavelength (or multi-color) emission.
As pointed out above, the 3F4 → 3H6 laser transition is a quasi-three-level scheme. The gain cross-sections, σgain = σSE – (1 – β)σabs, where β = N2(3F4)/NTm is the inversion ratio and N2 is the population of the upper laser level (3F4), are thus calculated to conclude about the selected polarization and, consequently, the laser wavelength. Such a calculation for Tm3+:LiYF4 and π and σ polarizations is performed in Fig. 10. For small inversion ratios β < 0.20, the gain in σ-polarization is higher. A local peak in the gain spectra is found at ∼1.91 µm and it is relatively broad (the gain bandwidth, determined as full width at half maximum, FWHM, Δλg is ∼60 nm for β = 0.20). For intermediate 0.20 < β < 0.30, the peak gain cross-sections at ∼1.91 (σ) and ∼1.88 µm (π) are close. Finally, for high inversion ratios of β > 0.35, π-polarization corresponds to higher gain. The local peak at ∼1.88 µm is narrower (as expressed by Δλg ∼35 nm).
Fig. 10. Gain cross-sections, σgain = σSE – (1 – β)σabs, for the 3F4 ↔ 3H6 transition of Tm3+ in LiYF4 crystal for π and σ light polarizations. β = N2(3F4)/NTm is the inversion ratio, N2 is the population of the upper laser level (3F4).
These observations well explain the observed spectral behavior for narrow (20 µm) WG, considering that higher output coupling will lead to higher β. We believe that polarization-switching in such WGs can be controlled via a precise control of the propagation losses which can be reached, e.g., by managing the cross-section profile of the guides or optimizing the dicing conditions.
The waveguide propagation losses for the 20 µm and 50 µm wide WGs were estimated by means of the Caird analysis [32]: inverse of the slope efficiency, 1/η, was plotted as a function of inverse of the output-coupling losses, 1/γOC, where γOC = –ln(1 – TOC). The experimental points were fitted using the equation (1/η) = (1/η0)(1 + 2γ/γOC) [33], where η0 is the intrinsic slope efficiency and γ = –ln(1 – L), L is the single-pass passive loss, see in Fig. 11. The best-fit values yields the propagation losses δloss = 4.34×L/t = 0.32 ± 0.2 dB/cm (20 µm WG) and 0.13 ± 0.2 dB/cm (50 µm WG).
Fig. 11. Caird analysis: a plot of inverse of the slope efficiency, 1/η, vs. inverse of the output-coupling losses, 1/γOC, for 20 µm and 50 µm wide WGs: symbols – experimental data, lines - their fits for the determination of the propagation losses δ.
The determined values of δloss agree well with the estimations (cf. Table 2) from the pump-propagation measurements considering the difference in the light wavelength and modal profile (less transverse modes are expected for the laser emission because of much longer λ). We also confirm that the losses tend to increase for smaller guides.
In Fig. 12, we compare the laser performance for all the guides (10–50 µm) and the same output coupling (TOC = 50%). The output power and the slope efficiency gradually decreased and the laser threshold increased for the smaller guides. For example, the 10 µm wide WG laser generated a peak power of 15 mW at 1878-1886 nm with η = 4.4% and a high laser threshold of 0.31 W. There exist several factors affecting the laser performance of smaller guides. First, the WG propagation losses increase as described above leading to both decreased η and higher Pth. Second, narrow guides exhibit severe thermal problems, so that the thermal roll-over in the output dependences occurs earlier. Finally, smaller guides provide higher intracavity laser intensities which, together with higher inversion needed to compensate for the higher passive losses, enhances the upconversion. Energy-transfer upconversion in Tm lasers is known to have a serious effect on the laser threshold [10]. Indirectly, it further enhances the heat dissipation.
Fig. 12. Effect on the guide width on the laser performance of the deep-diced Tm3+:LiYF4 ridge waveguide laser: (a) input-output dependences, η – slope efficiency; (b) typical laser emission spectra measured at intermediate Pabs. Quasi-CW regime of operation with a duty cycle of 1:2. TOC = 50%. The laser polarization is σ or π.
The spectral behavior of the WGs lasers, Fig. 12(b), agrees with these considerations and the gain spectra. For small guides (10-20 µm) with higher passive losses, the laser operated in π-polarization and for broader guides (30-50 µm) – in σ-polarization. The difference in the gain bandwidths also explains broader laser emission in the latter case.
To verify our consideration about the thermal effects in the guides, we studied the laser performance of the 50 µm WG with the same output coupling (TOC = 50%) but under different pump regimes, ranging from true CW to quasi-CW with various pump duty cycles (between 1:2 to 1:12), Fig. 13. The CW laser generated only 34 mW and the lasing was ceased for Pabs > 0.5 W. For the quasi-CW operation regimes with decreasing the duty cycle down to 1:12 (thus reducing the heat loading), the input-output dependence gradually approached the linear one, so that the power scaling was limited only by the available pump. For the 1:12 duty cycle, the maximum peak output power reached 684 mW with η = 53.3%. Note that the laser threshold was almost independent on the pump modulation.
Fig. 13. Evidence of thermal effects in deep-diced Tm3+:LiYF4 ridge waveguide laser: input-output dependences measured for true CW and quasi-CW operation regimes. WG with a width of 50 µm, TOC = 50%. η – slope efficiency for the duty cycle of 1:12.
The determined value of the slope efficiency exceeds the Stokes limit under lasing conditions, ηSt,L = λP/λL = 40.8% (λL ∼1910 nm is the laser wavelength) indicating the action of cross-relaxation for adjacent Tm3+ ions increasing the pump quantum efficiency [26].
4. Conclusions
To conclude, we report on a novel approach to fabricate ridge WGs with a large surface area (high depth-to-width aspect ratio, well above 1) in bulk fluoride crystals based on precision diamond saw dicing. This method has the following advantages: (i) it is relatively simple from a technological point of view, (ii) it provides an appropriate precision, an easy control of the geometrical profile and a fast writing speed, (iii) it ensures strong guiding both in the passive and laser-active regimes of light propagation without leakage of the modes in the bulk volume, (iv) it provides low roughness of the guide walls and, consequently, relatively low passive losses, potentially down to 0.1 dB/cm, and (v) it can be applied for a wide variety of materials with different RE3+ dopants. A single-transverse-mode laser operation is expected with a proper design of the geometrical profile of the channels; it will be also facilitated by the gain guiding in the case of quasi-three-level lasers. Further studies are however needed to clarify the nature and the absolute value of the expected refractive index variation in the guides with respect to the bulk volume.
In the particular case of deep-diced Tm3+:LiYF4 WGs, the main limitation for power scaling is the thermal issues. It can be overcame by better thermal management, e.g., by applying active cooling. Other strategies may involve using higher Tm3+ doping levels for more efficient cross-relaxation reaching a pump quantum efficiency of 2 (for the conventional pumping at ∼780 nm) or employing in-band pumping directly to the 3F4 upper laser level. Bulk Tm3+:LiYF4 crystals of laser quality with high doping levels (7–15 at.% Tm) are easily accessible. An optimization of the writing depth may also greatly improve the thermal behavior of the guides.
Funding
Agence Nationale de la Recherche (CEPAGE ANR-AAP-CE2, LabEx EMC ANR-10-LABX-09-01, SPLENDID2 ANR-19-CE08-0028); Conseil Régional de Haute Normandie; European Community Funds (FEDER NOVAMAT).
Acknowledgments
This work was partly supported by the French RENATECH network and its FEMTO-ST technological facility.
Disclosures
The authors declare no conflicts of interest.
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