1. Introduction

State-of-the-art display technologies leverage many benefits of laser sources over conventional incoherent sources to achieve high brightness and high contrast ratios for large-format projection. The benefits of laser sources for projection include larger color gamut, higher efficiency, shorter turn-on times, and longer lifetimes [1,2]. The challenge is the lack of cost-effective, high-power and high-efficiency laser sources available for key wavelength ranges of interest. This is particularly true for green wavelengths in the range of 520-550 nm that are required for 3D projection (using 6 primary colors) and for an optimized color gamut [1]. Although progress has been made [3,4], green laser diodes have been difficult to realize with the wavelengths and power levels necessary for projectors.

Second-order nonlinear optical processes allow for the generation of coherent light with wavelengths across the entire visible spectrum. In particular, as a relatively simple and cost-effective approach, second-harmonic generation (SHG) in periodically poled lithium niobate (PPLN) and periodically poled lithium tantalate (PPLT) can be used with many commercially available laser diodes to generate high power green light [5,6].

Such an approach has been realized commercially based on arrays of infrared VCSEL chips with intracavity SHG in bulk PPLN crystals [7]. These lasers cover the green wavelengths of interest. However, individual lasers produce limited power (about 150 mW) and have narrow linewidth that lead to speckle issues. The solution is to combine many laser beamlets in a module that produces a total output power of about 3W. The lasers are also binned for wavelength resulting in an increased combined spectrum. Nevertheless, multiple beamlets in the output of each module make it difficult to manage the output, leading to challenges with integration into a projector.

Single-mode, multi-Watt-power, low-cost green sources based on SHG of laser diodes would be beneficial for cost-effective and power-efficient laser projectors. To mitigate speckle issues in this case, conversion of a larger bandwidth input in a single beam configuration can be achieved with aperiodic poling designs consisting of chirped and apodized grating, hence creating a spectrally broad output [8].

SHG processes can be realized in many different configurations. The use of optical waveguides (WGs) in nonlinear crystals has important advantages: 1) increased interaction lengths and controllable mode areas, leading to more efficient nonlinear conversion [9], 2) favorable mode overlap between different edge-coupled devices without free-space optics, thus enabling sophisticated integrated optical system architectures, 3) existence of several fabrication approaches, including reverse-proton-exchange [10], dicing [11], etching of thin-film material layers [12], heterogeneous integration of thin film nonlinear materials with Si₃N₄ waveguides [13], and laser micromachining with ultrafast lasers [14–19], to name a few.

Laser micromachining of WGs relies on the internal modification of a material by exposure to high-peak-power laser pulses. Although the processing modifies the material, most of the optical mode remains in unmodified material and therefore can take advantage of the nonlinear and power handling properties of the substrate material. This approach is very attractive due to its fabrication simplicity: a single laser-exposure step followed by annealing. This compares favorably to other fabrication approaches that often require several often difficult-to-control steps involving masking, etching, or chemical processing. Laser micromachining of WGs is typically done in a serial fashion that limits the process speed for large integrated photonic systems. However, recent demonstrations of parallelized multi-beam fabrication promise to increase the process speed dramatically [20].

The laser micromachining process consists of focusing a pulsed laser through a fixed objective into the bulk of an optical material creating a localized region of modified material within the focal volume. By translating the sample under the fixed objective (or vice versa), repeated modified volumes with locations corresponding to each laser pulse are created, thus forming a track of modified material. Multiple tracks are then situated and grouped together to build up an index distribution necessary for optical guiding.

The physical mechanisms for laser material modification are complicated. They have been investigated by many research groups along with various processes for fabricating different WG geometries [21–28]. Here we provide only a brief overview.

A micromachining laser within the transparency range of the crystal must be used to prevent linear absorption. As short laser pulses are focused into the bulk of the material, the high peak intensity leads to nonlinear absorption through multiphoton absorption and/or field-ionization effects, depending on the laser wavelength and field strength. For the parameters used here, a combination of both effects is likely which leads to an initial population of free carriers. The presence of free carriers gives rise to run-away free-carrier absorption leading to a significant density of carriers with kinetic energies larger than the bandgap. These energetic carriers break chemical bonds and modify the crystalline structure. Typically, the pulse duration used is shorter than the characteristic relaxation time of the lattice, allowing for full energy deposition of the pulse prior to significant coupling of hot electrons to phonon modes. The process has been demonstrated in many optical materials, including fused silica [29], Si [30], polymers [31], Nd:YAG [32,33], Ti³⁺:sapphire [34], lithium niobate and lithium tantalate [14–19].

Here, we report on the use of femtosecond-laser micromachining processes to fabricate WG structures in MgO-doped periodically poled stoichiometric lithium tantalate (MgO:PPSLT) bulk crystals. Optimization of the WG fabrication process is discussed, where control of beam parameters, focusing conditions, and laser powers were first varied to create appropriate building blocks for WG geometries. We describe recipe development by more narrowly varying machining parameters to achieve low-loss designs for depressed cladding and stress-induced WGs. The recipe development was aided by strain-optic simulations which confirmed the guiding mechanism and provided insight into design optimizations. These designs were then used for further studies of WG SHG experiments. The robustness of the nonlinear optical material properties after the WG machining process was investigated by SHG conversion efficiency studies for various WG designs. The SHG efficiency was also measured under varying conditions of the pump laser linewidth, power, and polarization, the grating uniformity and aperiodicity, as well as crystal length.

2. Recipe development and waveguide fabrication

The WGs reported in this paper were fabricated in 10-to-30-mm-long Z-cut MgO:PPSLT chips obtained from Oxide Corporation. Their + Z surface was optically polished to minimize distortions and scattering during the machining process. Both X-propagating and Y-propagating WG geometries were tested. However, X-propagating was the preferred geometry due to the standard poling process in PPSLT that creates ferroelectric domain walls with the normal along the X-direction. For recipe development purposes, we also used single domain (unpoled) material with uncoated optically polished X facets for inspection of the internal structures after micromachining. Although, the WGs supported both TE and TM modes, TM guided modes (vertically polarized) in Z-cut crystals were focused on and the analysis throughout the text describes results for this polarization.

To fabricate WGs and achieve precise control over the variability of relative modified material track placements, we used a high-precision commercial micromachining system (LASEA LS5) [35]. The system contained an Amplitude Satsuma laser operating at 1030 nm. A motorized beam expander allowed to vary the beam size entering a Mitutoyo 20x Plan APO NIRB (0.4 NA) focusing objective. Typically, the expander was set to produce 12-15 mm 1/e² beam diameter, overfilling the ~8-mm aperture of the objective to approximate plane-wave illumination.

The LS5 system contained very precise opto-mechanical assemblies and was engineered to isolate and temperature stabilize the processing area from environmental factors. The overall mechanical design of the system and the use of precise linear stages (Aerotech ANT series) allowed for high-precision track profiles and their relative placements in three dimensions. The system incorporated a confocal sensor system to allow for accurate determination of the top crystal surface, an important consideration for fabricating WG geometries with tightly controlled mode locations. The included vision system, the confocal sensing channel, and the laser beam path through the objective were all coaxial. It also incorporated a position-synchronized output (PSO) feature for accurate triggering of laser pulses based on encoder feedback from the stages. This allowed for selection of the spatial distance between consecutive pulses (pulse-to-pulse spacing) along the stage direction independent of repetition rate and stage velocity. Therefore, the temporal and spatial overlap of pulses could be varied separately in a very repeatable way to evaluate these important effects.

To create effective WG geometries, a symmetric track shape was required to build up the geometry created from a repeated ordering of the tracks. The aim of the initial recipe development was to accomplish a desired track shape. Many system parameters can affect the shape of tracks including wavelength, pulse energy, pulse duration, polarization, numerical aperture, spatial separation of adjacent pulses along the machining path, order of tracks, and adjacent track placement. During recipe development, these effects were systematically varied to understand their influences and their interplay. These are the system parameters used: 0.375 – 1 µJ pulse energy (75 mW – 200 mW average power), 200 kHz rep rate, 300 fs pulse duration, 1 µm pulse-to-pulse spacing, 150 µm depth, and 200 mm/s stage velocity. Dueto the large stage velocity used, the stage velocity was monitored and verified to be constant prior to the laser encountering the crystal. While the laser micromachining process is in general polarization dependent, we did not observe a strong polarization dependence. Therefore, all tracks and WGs shown in this report were written using circular polarization.

As annealing has been shown to improve the loss characteristics of these types of WGs by removing residual type-I regions [36], an annealing step in an open-air oven was conducted after wrapping the nonlinear crystal in aluminum foil to electrically ground the + Z and -Z surfaces and prevent charge buildup. The annealing step was investigated by starting with typical numbers found in literature (150 °C annealing temperature with a one-hour dwell) [37], and then moving to higher temperatures and longer dwell times. Annealing temperatures up to 500°C and dwell times up to six hours were investigated, but we found that above a certain temperature threshold (200 °C and one-hour dwell) there was no measurable improvement to the loss after annealing. However, there were also benefits to the SHG performance due to annealing (discussed in section 4) and this led to a standard annealing step of 350 °C with a one-hour dwell which was used for all of the WGs in this report.

We observed that aside from the formation of a single ellipsoidal modified region centered around the geometric focus that one would expect to see, a secondary modification appeared with a consistent vertical offset from the geometric focus. This secondary modification, shown in Fig. 1(a), was pulse energy and numerical aperture dependent. Starting from low pulse energy and keeping all other system parameters constant, the secondary modification was first distinctly observed 10-15 µm above the geometric focus. For these low pulse energies, a faintly visible filamentation was also observed in the geometric focal volume, which disappeared after the annealing step, leaving only the secondary modification visible. Due to the vanishing of the filament, it was attributed to a thermally unstable type I modification (local increase in refractive index) while the secondary modification was attributed to a stable type II modification (local reduction in refractive index) [14,21]. As the pulse energy was increased, the size of the secondary modification increased prior to a track appearing within the geometric focal volume. These two modified zones were consistently spatially separated up to pulse energies which would destroy the integrity of the crystal. Since suppressing this secondary modification likely requires more complex techniques such as adaptive optics or spatial beam filtering, and this modification had a very repeatable and predictable offset from the geometric focus, it was used as the building block for the WG technology presented here.

 

Fig. 1 Laser-written track building blocks and representative fabricated WG geometries and accompanying mode images (at 1064 nm). (a) Cross-sectional microscope image of laser-written tracks for various pulse energies (0.375 – 1 µJ), for constant depth, repetition rate, pulse-to-pulse spacing and scan speed. As the pulse energy is increased, a modification above the geometric focus is initially observed, followed by a modification at the geometric focus for further increases in pulse energy. (b)(c) Optimized depressed cladding WG geometries and mode profiles. (d) Stress-induced WG geometry and mode profile; the WG consists of two stress regions each of which contain four rows and four columns of laser-written tracks. All scale bars are 10 µm.

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The origin of the secondary modification was investigated, with multiple potential mechanisms of linear and nonlinear optical origin considered. Spherical aberration occurs due to focusing of a beam with a curved wavefront through a planar surface with a refractive-index difference, where extreme rays on the edge of the beam have a different incident angle from those close to on axis [38]. Spherical aberration will lead to beam energy being spread out continuously along different depths, but not the two separate distinct spots. Double focus effects also exist, associated with the birefringence of the material, where rays with off-axis wave-vectors have polarization components along both the ordinary and extraordinary axes. These effects lead to separate focal spots occurring for each polarization [39], but a simple estimate of the spread from the double focusing effect gives a number of less than one micron, which is much smaller than the observed effect. These effects depend on the crystal orientation, but the secondary modification also appeared to be very similar when machining through a Y-cut crystal surface.

The most likely dominant effect is self-focusing based on the optical Kerr effect, a ${\chi }^{(3)}$ process which is numerical aperture and pulse energy dependent, where an intensity-dependent refractive index leads to modification of the propagating beam. The pulse energy required for modification is well above simple estimations of the critical power for self-focusing, which we have estimated to be ~0.35 MW (0.1 µJ) using the nonlinear index of lithium niobate as a reference for estimation [40]. Based on this estimation, it is likely that the optical power near the center of the beam produces the secondary modification, with the intensity exceeding the damage threshold before reaching the geometric focus, and the power in the wings of the beam creates the modification at the geometric focus being undisturbed by the secondary modification.

The parameter space determined above was used to create WG geometries which fell into two categories: stress-induced WGs and depressed cladding WGs. For both categories the initial recipe development was focused on creating low-loss WG structures. We used unpoled MgO:PPSLT substrates with uncoated X-facets. The loss was then measured using a Fabry-Perot interference method [41].

Depressed cladding WG geometries, as shown in Fig. 1(b), were investigated with varying internal diameters, number of tracks in each ring, numbers of ring cladding layers, spatial and angular offset of tracks in each ring and adjacent rings, pulse-to-pulse spacing and pulse energy. Depressed cladding WGs have been previously demonstrated in Nd:YAG [42]. The depressed cladding WGs rely upon the index contrast between the center of the tracks and the unmodified core of the WG, which has been shown to be between −0.0075 and −0.01 in literature [18,43], depending on the machining conditions. While the center of tracks always contains a negative index change, the tracks also create a local index distribution change which extends out into the crystal by a few µms and can exhibit an index change of either sign. Optimized recipes for depressed cladding WGs rely on maximizing the confinement by increasing the index contrast and the overlap of tracks in the cladding while still minimizing the influence of the stress-induced index. This is confirmed by strain-index simulations in the following sections.

Seeming to follow this logic, WG loss decreased with increasing pulse energy and reduced pulse-to-pulse spacing, but there was a clear minimum in the laser power which can be partially understood as follows. With low pulse energies and large pulse-to-pulse spacing (low spatial overlap) there is weaker confinement and the mode size is larger, leading to larger radiative losses and scattering losses. As the pulse energy is increased the confinement increases and the mode energy is pushed away from the tracks leading to reduced loss. However, as the pulse energy is increased further a point is reached where another loss mechanism starts to dominate and therefore the loss starts to rise. It is possible that scattering losses from the tracks themselves increases or the stress-induced index perturbation region surrounding the tracks extends far enough into the WG core to significantly contribute to losses. For the depressed cladding WGs, a pulse energy of 0.6 µJ (measured after the objective) and a pulse-to-pulse spacing of 1 µm was used.

In general, the loss of the depressed cladding WGs decreased with increasing number of cladding layers. This is to be expected due to the relatively thin cladding ~1 µm compared to the size of the mode. A minimum loss of 1.01 dB/cm (1064 nm) was observed for an optimized single ring WG with a 30-µm diameter, while an optimized 30-µm three-ring WG achieved a loss of 0.52 dB/cm. Prior to annealing, the single ring and three-ring WGs exhibited loss numbers of 2.36 dB/cm and 1.28 dB/cm, respectively. The optimized three-ring WG geometry is shown in Fig. 1(b); the mode-field diameter was measured to be 22 µm (1/e² intensity). For this large diameter, the number of tracks in each consecutive ring was held constant and the tracks in each consecutive ring were radially offset by half the track-to-track radial distance to complete the cladding. However, further increasing the number of cladding layers for this diameter did not further reduce the loss.

More than three cladding layers showed a stronger influence when the WG diameter was reduced to 20 µm. For this diameter, five cladding layers and an increased number of tracks in each consecutive ring were required to achieve a similar loss number of 0.56 dB/cm. Figure 1(c) shows the optimized five-ring WG design. It is believed that the cladding was more completely enclosed in this case. There was a limit to how small the depressed cladding WGs could be made without introducing significant loss. Reducing the diameter below 20 µm lead to significant loss increases and was avoided. Figure 2 shows representative data collected from propagation loss measurements, comparing the fringe contrast for single ring and three-ring depressed cladding WGs. For this measurement, a TM polarized laser was coupled into the WG and the transmitted power was collected as a function of wavelength (current tuned over a mode-hop free range). A repeatable loss number was observed for WGs written with the same parameters, and therefore WGs written into crystals with AR coatings were assumed to have the same propagation losses, since it was not directly measurable.

 

Fig. 2 Interference fringes from propagation loss measurement of typical depressed cladding waveguides. The method was based on a Fabry-Perot interference method where the loss value was extracted from the fringe contrast. The loss shown is for TM propagating modes at 1064 nm. Results for a three ring WG geometry (a) and a single ring geometry (b).

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To investigate WGs with smaller mode areas, the stress-induced WG geometry was utilized. The guiding effect in these WGs relies on the stress-induced region around the tracks being large enough to significantly overlap and create a long-range effect which encompasses the guiding center. Some demonstrations of this WG type in literature typically have used long single tracks very closely spaced to achieve guiding but creating a larger group of stress centers with multiple tracks closely spaced was seen to further improve the desired effects [16]. The optimized design consisted of two groups of 16 tracks, each of which consisted of four rows and four columns spaced 1 µm horizontally and 6 µm vertically. The dominating stress effect was also observed to be temperature dependent, where the guided mode had optimal loss and symmetry at a specific temperature. The WGs had a slight multimode nature (at 1064 nm), but a symmetric mode profile could easily be achieved with manipulation of the input coupling.

The stress-induced WGs showed the lowest loss when the pulse-to-pulse spacing was reduced, by lowering the stage velocity to 100mm/s, to achieve stronger pulse overlap which is believed to create a more uniform index modification along the WG axis. Since the dosage is increased with the reduced pulse-to-pulse spacing, the pulse energy is roughly the same as that used for the depressed cladding WGs. Since the index distribution in the core of the stress-induced WG is larger than the surrounding crystal and therefore also much larger than the index in the track itself, the mode is more confined within the core and away from the tracks which are believed to be lossy. It is believed that this is the reason for the smaller attainable mode size with this WG type. Figure 1(d) shows an optimized stress-induced WG design.

3. Strain-optic simulations

Simulations were conducted using COMSOL Multiphysics to help predict and interpret the outcomes of the WG fabrication process due to the large parameter space with many potential spatial and laser system parameters. COMSOL provides a convenient simulation solution for the considered effects, by allowing for seamless integration of mechanical and optical simulations. COMSOL has been previously demonstrated to be an effective tool to predict the behavior of laser written WGs, where complicated 3D WG geometries have been simulated in lithium niobate [43,44]. First a mechanical simulation is conducted to solve for the stress and strain tensor in the crystal. The change in the index tensor can then be computed based on Eq. (1), where ${\sigma }_{kl}$ and ${\epsilon }_{kl}$ are the stress and strain tensors, ${\pi }_{ijkl}$ and $P_{ijkl}$ are the stress and strain-optic tensors and n is the unmodified bulk material index. LiTaO₃ has 3m crystalline symmetry leading to six unique non-zero elements for both the stress and strain-optic tensors [45], and the analysis can be simplified further by using the condensed Voigt notation as in Eq. (2). Built-in strain in the tracks is used in the simulation to vary the stress/strain and index tensors in the crystalline region surrounding the tracks. The simulated change in index for

 

Fig. 3 Strain-optic simulations for WG geometries discussed in this report. For all plots a Z-cut orientation is assumed with the WG propagation direction along the crystalline X-direction. (a)-(c) Stress-induced WGs where the extraordinary (ordinary) index can be seen to increase (decrease) in between the two groups of laser-written tracks. Simulated guided mode with a predominant polarization along the Z direction and an effective index slightly larger than the bulk index. (d)-(f) Depressed cladding-style WGs. For this geometry, the strain induced index has a negligible effect in the core (center of WG) due to symmetry and length scale effects. The simulated guided mode has an effective index which is lower than the bulk material index, confirming the depressed cladding guiding mechanism; (a)-(c) are scaled uniformly as are (d)-(f), and the scale bars shown in (c) and (f) are 5 and 10 µm, respectively.

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The stress-based index change exhibits slight off-axis directionality which can be seen by the contour lines in Fig. 3(b). This is due to in-plane asymmetry in the compliance tensor and off-diagonal element contributions. To confirm this, Y-propagating (Z-cut) geometries were also simulated which showed very symmetric index distributions around the track groups. Representative values for the built-in strain inside of the tracks of 1.5(10⁻³) and 7.5(10⁻³) were used for the shown stress-induced and depressed cladding simulation results, respectively. The full anisotropic compliance tensor of lithium tantalate was used in the simulations for the surrounding crystalline material, leading to an anisotropic strain in the crystal surrounding the track. These values are used to represent the strain in the crystal but in the real case the tracks themselves have a reduced index and density. The crystalline area surrounding the tracks has a higher density and is stressed outward by the tracks. The plane-strain 2D approximation was used for these simulations.

The full stress-dependent index tensor is then used in to solve for guided modes in COMSOL wave-optics simulations. For the wave-optics simulation, the index modification inside the tracks themselves is assumed to be 10⁻² based on empirical data from literature [18,40]. The bulk index for the simulation was defined to be n_e, n_o = 2.1295, 2.1265 and the simulation wavelength was 1050 nm. The stress-induced structure supports a slightly asymmetric mode (following the index distribution) in between the large track groups with an effective index slightly higher than the bulk index, due to the strain-induced index. The equal index values between the core and crystalline area outside the cladding for the depressed cladding structure can complicate the mode solver analysis. The simulated structure supports many spurious modes requiring many modes (~10-100) to be solved for and post processing done in order to find appropriate mode distributions. For the depressed cladding structure, the step index of the unmodified core to cladding supports guiding without the influence of the strain-induced index. This is verified due to the effective index value of the fundamental mode which is slightly smaller than the bulk index. The large size of the ring geometry supports many higher-order modes which were also observed in the simulation.

4. Second-harmonic generation

A necessary requirement for using the fs laser micromachining process for fabricating frequency conversion devices is that the nonlinearity and poled domain structure of the crystal not be modified. Laser micromachining of WGs in PPLN has been demonstrated previously and the process has been shown to preserve the nonlinearity [47,48]. However, this experiment was done due to the varying parameters used and the sensitive nature of the micromachining process. For depressed cladding WGs, the tracks are far from the optical mode, but power from the laser does pass through the WG core during machining. To confirm that the nonlinearity in the WG core was not affected we characterized the wavelength dependence of the SHG process after WG fabrication using a tunable CW laser. The response was then compared with the calculated case for bulk. Figure 4(a) shows the measured and calculated wavelength tuning curve for a depressed cladding WG written in a 20-mm-long crystal with a grating period of 7.61 µm and 50% duty cycle, indicating no strong deviation from the bulk nonlinearity. For SHG studies, AR coatings (AR for IR and second harmonic (SH)) were deposited on the X-facets of the chips prior to the micromachining process. Inspection and testing after the machining process did not show any noticeable change to the properties of the AR coating. Further low power and CW (narrow linewidth) SHG studies were conducted and showed clear enhancement of the nonlinear interaction over bulk, as one would expect from a guide-wave interaction. For the stress-induced WG in Fig. 1(d) (20-mm uniform grating) a normalized efficiency of 11.6%/W/cm² was measured, following the definition in Eq. (3).

 

Fig. 4 (a) Transfer function for a depressed cladding WG written in a 20mm uniform grating confirming the maintained material nonlinearity and poling integrity after micromachining. (b) Measured second-harmonic power as function of input fundamental pump power for the depressed cladding WG geometry shown in Fig. 1(b) written in a 30-mm-long crystal with a uniform grating. (c) Normalized SHG efficiency as a function of input power. The efficiency can be seen to decrease as the pump power is increased likely due to temperature detuning.

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To characterize the high-power SHG performance of the WGs, a CW 400-W 1070-nm fiber laser (IPG Photonics, YLR-LP) was used. The spectral bandwidth of the laser scaled with the laser output power, so the laser was set to a fixed output power of 100 W, resulting in a bandwidth of ~1 nm FWHM. The laser output was then attenuated using a half-wave plate and two Brewster's angle reflecting polarizing beam splitters, directed through a high-power large-aperture isolator, and then coupled into the WG by a plano-convex spherical lens AR coated for IR and with a focal length chosen to properly mode match to the WG mode. Coupling out of the WG was achieved using a shorter focal length (35 mm) spherical lens with AR coating for both ~532 nm and 1064 nm. Multiple cascaded dichroic mirrors (green reflecting) allowed for full separation of the fundamental (FH) and SH beams. The SH spectrum was also sampled with an OSA. A crystal oven constructed from gold-plated copper was used to stabilize the crystal temperature, the crystal was wrapped in indium foil to aid in thermalization.

As was previously noted, the demonstrated WGs had a multimode nature which is more prevalent at the SH wavelength since it is shorter by a factor of two. The multimoded behavior allows for SHG at several temperatures relating to phase matching conditions between the fundamental mode of the FH, the fundamental mode of the SH and high-order SH modes. This behavior has recently been clearly demonstrated for similar WGs in MgO:PPSLT, where efficient phase matching conditions were found relating to various SH modes [47]. In this report we discuss SHG results for optimal phase matching between the fundamental FH and fundamental SH modes.

High-power measurements were conducted for many different WG geometries and recipe skews. Maxima in the SHG efficiency were observed for various processing parameters, but clear correlations between parameter variation and high-power SHG performance was more challenging to determine than for the low-power case. Overall, the best high-power SHG performance was observed with the depressed cladding WG geometries. Figure 4(b) shows the SH power as a function of FH input power with a maximum of 8.5W generated using 45 W of input FH power. The SHG measurements shown were conducted on a depressed cladding WG written with the same parameters as those used to write the WG shown in Fig. 1(b). To the best of our knowledge, this is the highest demonstrated CW SH power in a guided wave configuration to date. However, the SH power was seen to quickly deviate from the expected quadratic scaling as the FH power is increased. Beyond 10 W of FH power, the SH power scales closer to linear, demonstrated by the linear fit to the rest of the data. If quadratic scaling was achieved throughout, an estimate of 17 W of SH power could be achieved. The normalized SHG efficiency (%/W/cm²) as a function of input pump power is plotted in Fig. 4(c).

Although this efficiency is with a broadband pump, the value is already much smaller than that observed for the low power CW case. The efficiency can also be seen to decrease quickly as pump power is increased, instead of staying constant as would be expected. The reduction of the efficiency with FH power was observed for all WG types and geometries. However, smaller mode areas typically showed a quicker reduction in normalized efficiency, opposite to the low-power CW case. It is believed that the reduced efficiency is due to thermal dephasing effects in the WG due to non-uniform absorption along the axis of the WG and inside the WG cross-section [49]. The thermo-optic effect is outlined in the following discussion.

For each input power, the phase-matching temperature was adjusted to maximize the SH output power, starting from a temperature very close to bulk as the WG effective index matches very closely to the bulk index (see strain-optic simulations). The optimized phase-matching temperature, plotted in Fig. 5(a), slowly deviates at low power but then starts to quickly decrease. A reduction in the effective phase-matching temperature is consistent with a heating mechanism being present in the WG.

 

Fig. 5 (a) Optimized phase matching temperature as a function of pump power. (b) Second harmonic (SH) spectral output for increasing input pump power. The SH spectral width broadens with increasing pump power, due to thermo-optic effects. The self-convolution of the pump spectrum (INL) is also shown. The broadening of the SH spectrum appears to be bounded by the INL spectrum. (c) Qualitative comparison of the calculated SH spectrum including a temperature gradient of 28 K/cm and the measured output for 45 W of pump power, showing a similar bandwidth.

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Along with the reduction in the phase matching temperature, the presence of temperature gradients in the WG is evidenced by the change in the SH spectrum as the input power is scaled. Figure 5(b) shows the SH spectrum for various pump powers, where broadening of SH spectrum occurs as the pump power is increased. This broadening seems to increase to that close to the self-convolution of the pump spectrum (I_NL) (also plotted in Fig. 5(b)). A temperature gradient present in the WG could lead to broadening of the spectral output by effectively inducing a non-uniformity into the grating due to thermo-optic changes along the length of the WG propagation axis. To understand the potential influence of an axial temperature gradient, we calculated the expected output spectrum with an axial temperature gradient and a corresponding change to refractive index. Figure 5(c) shows the calculated output spectrum with a temperature gradient of 28 K/cm present along the WG. Plotted as a comparison, is the measured output spectrum for 45 W of input pump power, which exhibits a similar spectral width. This temperature gradient is very large and seems unrealistic considering that the phase matching temperature only reduces by 16K up to 45W of pump power. This discrepancy points to another factor playing a role in the observed spectral broadening. It is likely that cross-sectional temperature gradients and index fluctuations are also present due to the expected intensity dependence of heating mechanisms in the WG. This type of index fluctuation could also play a role in reducing the SHG efficiency, since the optimal phase matching temperature would only be experienced by a portion of the optical mode. It is likely that the observed reduction in efficiency with temperature is due to a combination of both axial and cross-sectional temperature instabilities.

The heating effect in the WG is likely due to absorption, but the absorption mechanism is difficult to pin down. Linear absorption effects are negligible in bulk LiTaO₃ at the wavelengths of interest due to the large bandgap and associated transparency window. However, green-induced infrared absorption (GRIIRA) effects are well known to be present in high-power SHG processes in LiNbO₃ and LiTaO₃, but GRIIRA has been shown to have a very small influence in MgO:PPSLT [50]. Non-linear (e.g. two-photon) absorption has also been observed to have a degrading effect in other nonlinear crystals [51]. It is also possible that the laser micromachining process chemically and structurally modifies the material in the tracks in such a way that changes the suppression of linear or non-linear absorption processes. The crystalline integrity of the material is modified during the micromachining process which may lead to different optical properties in the tracks.

5. Conclusions

A quick and effective method for fabricating WGs in non-linear crystals using fs laser systems was discussed. The method was optimized to create low-loss WGs with varying geometries and structures. The laser micromachining technique was complimented by strain-optic simulations used to understand and predict the different guiding mechanisms and the dominating effects for both WG types. The simulations were a very useful tool to aid in the search of effective geometrical arrangements. The SHG performance attainable with these structures at low and high-power levels was investigated. Low-power CW performance similar that seen with other technologies in PPLN was observed. Although a high SH power of 8.5 W was achieved, scaling trends observed at low power were not observed at high power with thermal dephasing leading to a smaller overall efficiency. Further investigation and optimization around the absorption effects and induced temperature gradients could be very beneficial for optimizing the SHG efficiency in these WGs and may lead to higher overall output powers.