Characterisation of nonlinear conversion and crystal quality in Nd- and Yb-doped YAB

Variable crystal quality affects the laser performance of many self-frequency doubling crystals, particularly those of the yttrium aluminum borate family. In this report we characterize nonlinear frequency conversion in Yb:YAB and demonstrate a simple non-destructive technique for measuring crystal quality. By imaging the nonlinear conversion using a CCD camera we observe phase matching characteristics similar to that obtained in quasi-phase-matched crystals. These effects are attributed to stacking faults in the structure of the YAB crystal during crystal growth. We believe that such defects cause the large variability in self-doubled performance reported for Ndor Yb-doped YAB and that our technique may be used as a nondestructive measurement of crystal quality. 2004 Optical Society of America OCIS codes: (190.2620) Nonlinear optics, frequency conversion; (140.3380) Laser Materials. References and links 1. F. Mougel, K. Dardenne, G. Aka, A. Kahn-Harari, and D. 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Wang, "Coupled-cavity, single-frequency, yellow microchip tunable cw Yb:YAB laser," Opt. Commun. 207, 315-320 (2002). 7. P. Dekker, P.A. Burns, J.M. Dawes, J.A. Piper, J. Li, X.B. Hu, and J.Y. Wang, "Widely tunable yellow-green lasers based on the self-frequency-doubling material Yb:YAB," J. Opt. Soc. Am. B 20, 706-712 (2003). 8. P. Dekker, J.M. Dawes, and J.A. Piper, "2.27W Q-switched Self-doubling Yb:YAB laser with controllable pulse length," J. Opt. Soc. Am. B (to be published), (2004). 9. J. Bartschke, R. Knappe, K.J. Boller, and R. Wallenstein, "Investigation of Efficient Self-Frequency-Doubling Nd:YAB Lasers," IEEE J. Quantum Electron. 33, 2295-2300 (1997). 10. G. Lucas-Leclin, F. Auge, S.C. Auzanneau, F. Balembois, P. Georges, A. Brun, E. Mougel, G. Aka, and D. Vivien, "Diode-pumped self-frequency-doubling Nd:GdCa4O(BO3)3 lasers: toward green microchip lasers," J. Opt. Soc. Am. B 17, 1526-1530 (2000). 11. G. Aka, A. Kahnharari, F. Mougel, D. Vivien, F. Salin, P. Coquelin, P. Colin, D. Pelenc, and J.P. Damelet, "Linearand Nonlinear-Optical Properties of a New Gadolinium Calcium Oxoborate Crystal, Ca4GdO(BO3)3," J. Opt. Soc. Am. B 14, 2238-2247 (1997). 12. H.-F. Pan, P. Wang, X.-F. Fan, R.-H. Wang, and B.-S. Lu, "Effects of Lu doping on optical properties and laser performances of NYAB crystal," Chinese Phys. Lett. 13, 602-605 (1996). 13. P. Dekker, Y.J. Huo, J.M. Dawes, J.A. Piper, P. Wang, and B.S. Lu, "Continuous Wave and Q-Switched DiodePumped Neodymium, Lutetium Yttrium Aluminium Borate Lasers," Opt. Commun. 151, 406-412 (1998). 14. A. Brenier, C.Y. Tu, M.W. Qiu, A.D. Jiang, J.F. Li, and B.C. Wu, "Spectroscopic properties, self-frequency doubling, and self-sum frequency mixing in GdAl3(BO3)4:Nd ," J. Opt. Soc. Am. B 18, 1104-1110 (2001). 15. A. Peter, K. Polgar, and E. Beregi, "Revealing growth defects in non-linear borate single crystals by chemical etching," J. Crys. Growth 209, 102-109 (2000). 16. X.B. Hu, S.S. Jiang, X.R. Huang, W.J. Liu, C.Z. Ge, J.Y. Wang, H.F. Pan, J.H. Jiang, and Z.G. Wang, "The growth defects in self-frequency-doubling laser crystal NdxY1-xAl3(BO3)4," J. Crys. Growth 173, 460-466 (1997). (C) 2004 OSA 29 November 2004 / Vol. 12, No. 24 / OPTICS EXPRESS 5922 #5590 $15.00 US Received 27 October 2004; revised 14 November 2004; accepted 15 November 2004 17. X.B. Hu, J.Y. Wang, J.Q. Wei, Y.G. Liu, R.B. Song, M.H. Jiang, Y.L. Tian, and J.H. Jiang, "Growth twins in self-frequency doubling laser crystal YbxY1-xAl3(BO3)4," Prog. Crys. Growth Chara. Mat. 40, 57-61 (2000). 18. S.R. Zhao, J.Y. Wang, D.L. Sun, X.B. Hu, and H. Liu, "Twin structure in Yb:YAl3(BO3)4 crystal," J Appl. Cryst. 34, 661-662 (2001). 19. Y.L. Lee, C.S. Jung, Y.C. Noh, M.Y. Park, C.C. Byeon, D.K. Ko, and J. Lee, "Channel-selective wavelength conversion and tuning in periodically poled Ti:LiNbO3 waveguides," Opt. Express 12, 2649-2655 (2004). 20. M. Asobe, O. Tadanaga, H. Miyazawa, Y. Nishida, and H. Suzuki, "Multiple quasi-phase-matched LiNbO3 wavelength converter with a continuously phase-modulated domain structure," Opt. Lett. 28, 558-560 (2003). 21. A. Brenier, C. Tu, Z. Zhu, and B. Wu, "Red-green-blue generation from a lone dual-wavelength GdAl3(BO3)4:Nd 3+ laser," Appl. Phys. Lett. 84, 2034-2036 (2004). 22. W. Koechner, Solid-State Laser Engineering. 5th ed. Springer Series in Optical Engineering. Vol. 1. 1999, Berlin: Springer-Verlag. 23. R.M. Vazquez, R. Osellame, M. Marangoni, R. Ramponi, E. Dieguez, M. Ferrari, and M. Mattarelli, "Optical properties of Dy doped yttrium-aluminium borate," J. Phys. Conden. Matt. 16, 465-471 (2004).


Introduction
Self frequency doubling lasers are of great interest due to their simplicity, compactness and potential for true single crystal, microchip style, visible sources.Significant research effort from a number of laboratories has concentrated on the material hosts of GdCOB/YCOB [1,2], LiNbO 3 [3] and YAB [4][5][6][7][8].All of these host materials have been demonstrated to be capable of self-frequency conversion with either neodymium or ytterbium doping although only Yb:YAB has resulted in significant second harmonic (SH) powers.For example, in YAB 1.1 W of cw second harmonic output at 530 nm using 11 W of diode pump power has been obtained [5].Even higher second harmonic powers were obtained when Q-switched, with the same authors reporting 2.28 W of SH at 522 nm when operating at a pulse repetition frequency (prf) of 10 kHz [8].In comparison, 450 mW of second harmonic has been reported in the neodymium doped analogue (Nd:YAB) [9], albeit using a Ti:Sapphire pump source.In the oxoborate crystals a maximum self-frequency doubled output power of 245 mW was reported in Nd:YCOB [2] with a conversion efficiency of 6.5 % while in Nd:GdCOB a maximum of 115 mW [10], with a conversion efficiency of around 10 % was obtained.Conversion efficiencies in the ytterbium doped systems are typically less than in their neodymium doped analogs and in the case of Yb:YCOB or GdCOB have only been reported at the milliwatt level [1].In the case of Yb:YAB however, high conversion efficiencies are obtained due to a fortuitously strong pump absorption coupled with a narrow emission spectrum allowing high pump and laser intensities to be maintained over the crystal length.This coupled with only weak reabsorption losses at the laser wavelength, when optimizing for free-running self doubled operation (~1060 nm), has made it possible to obtain similar if not higher conversion efficiencies in the 3-level material.
Despite the relatively low second harmonic powers obtained in the oxoborates they have commanded the largest research effort as this material can be grown by the Czochralski technique in a short amount of time and reportedly with exceptionally high crystal quality [11].YAB on the other hand does not melt congruently and must be grown using a flux, typically taking around 1 month to grow a boule of 10x10x10 mm dimensions.The difficulties in crystal growth of YAB have been widely reported and often stated as the reason to search for other self-frequency doubling materials.Poor crystal quality has been attributed to the difference in size between neodymium and yttrium ions.One method by which the distortion can be reduced is by volume compensation, for example by co-doping with lutetium which has a smaller radius than Nd or Y, resulting in the material Nd:LYAB [12].Although crystal growth is reported to result in better quality crystals, laser experiments have shown large variations in the reported SH powers with little to no variation in the fundamental power [13].Alternatively Gd may be substituted for Y resulting the material Nd:GdAB.In this case higher quality crystals with improved ease of growth was also reported, [14].The closest matching between doped and host ion radii is obtained however when using ytterbium as the dopant.Crystal quality is once again reported to be much improved in this situation and indeed materials with little to no variation across the crystal's clear aperture in either fundamental or SH output powers have been grown [4].Despite the improved matching between doped and host ion radii there have been continued investigations into growth defects in this family of materials [15][16][17][18].Defects include growth zone boundaries, dislocation, inclusions, refractive index (RI) variations and twinning.Of these defects both twinning and RI variations can lead to variations in the generated SH power.The fact that few people have reported any variations in fundamental output power across the crystal surface implies that the density of the growth defects such as dislocations, inclusions and striations, for example, are low or can be relatively easily controlled.
Twinning on the other hand has been observed in YAB in the doped and undoped forms.Twinned crystals are defined as composite crystals of a single substance, in which the individual parts are related to one another in a definite crystallographic manner and are considered as a stacking fault in the material lattice.Twinned crystals can originate during crystal growth where the alternate arrangement contributes only a small increase in the total energy over that of the un-twinned form.Growth twins have been observed in BBO, LBO, LTB and doped and undoped YAB, and have been attributed to growth instability in the melt [15].In doped YAB crystals (either Nd or Yb doped) twinning has been observed with identical crystallographic orientations in each material [16][17][18].From differences in the orientations of etching pits [18] on the {10 11} crystallographic faces, the twin boundary has been determined to be reflection and perpendicular to the y-axis, (12 10) .Twins of this type are considered similar to Brazilian twins in quartz [17] and are characterized by twin pairs with opposite polar axis.In terms of second harmonic operation, the inversion twins will result in a vanishing of the crystal polarity and hence exactly cancel the nonlinear coupling, (given that the path length through the host and twin is identical).In practice however, the ratio of the twinned and host region thickness varies, depending on the thickness of the twin lamellae and distance between twin boundaries.
Twin defects have been widely observed in the differently doped YAB crystals, typically by chemical etching and atomic force microscopy (AFM) or synchrotron radiation mapping.Both these techniques are destructive and time consuming.
In this paper we characterize the nonlinear laser crystal YAB (either Nd or Yb doped) from the view-point of a laser engineer in terms of its nonlinear performance and phase matching characteristics, and in particular, we examine anomalies due to what we believe is twinning in this material.

Angular, temperature and wavelength acceptance in YAB
Typically nonlinear conversion acceptance bandwidths are determined from calculations based on Sellmeier equations fitted to refractive index dispersion data.For Nd-or Yb-doped YAB however, refractive indices have not been measured above 700 nm.This results in large variations in calculations of the phase matching acceptance bandwidths depending on the fit of the Sellmeier equations.For example, near 1.06 µm the calculated wavelength acceptance bandwidth for doubling ranges between 1-5 nm.cm.Clearly experimental determination is the most appropriate approach in this case.
The experimental arrangement used to measure the angular and temperature acceptance bandwidths is shown in Fig. 1.The probe source was a Nd:YAG laser operating at 1064 nm, Q-switched at 10 Hz, with a pulsewidth of ~6 ns and with up to several milli-joules of output although only micro-joules were incident on the nonlinear crystal.A precision rotation mount for both θ and φ was used to orient the crystal so that either axis could be varied independently.XY translation was also possible, enabling precise positioning of the probe beam on the surface of the nonlinear material.The angular acceptance bandwidth was measured for several Yb:YAB crystals and for several locations within each crystal resulting in an average value of ∆θ.l x ≈1.35 mrad.cm.
The measured phase matching curve is shown in Fig. 2(a) with a sinc 2 x function overlaid.
Variation in ∆θ.l x ranged from 1.2-1.45mrad.cmalthough larger deviations were also recorded in crystals with defects, described in the following section.The temperature acceptance was also measured using the arrangement described above although the crystal was additionally held in a temperature-controlled mount, capable of temperatures of up to 160 with 0.1 °C precision.The temperature acceptance was measured to be 28 °C.cm.To measure the wavelength acceptance bandwidth the phase mismatch angle was measured as a function of tuned wavelength while operating in an L-shaped cavity [7].An angular tuning coefficient (∆θ/∆λ) of 0.0011 mrad.nm - was measured, and, taking into account the measured angular acceptance, we obtain a wavelength acceptance of 1.23 nm.cm, [∆θ.l x /(∆θ/∆λ)].
Using the experimental approach described above we found somewhat surprisingly that within certain parts of the crystals, for either Yb:YAB, Nd:YAB or Nd:LYAB, that rather than obtain a single sinc 2 function for the angular acceptance we obtained multiply peaked functions.In this case the second harmonic intensity was much reduced.The results of such an experiment (using Yb:YAB) are shown in Fig. 2(b).
The angular acceptance in this case is reduced from 1.63 mrad.cm for the single peak to 1.3 mrad.cm for each of the doubly peaked outputs.Interestingly the second harmonic conversion intensity is approximately half of that obtained when operating with a single PM peak.
The symmetry of the results show that, for certain positions inside the crystal, the phase matching angle needs to be detuned in order to obtain maximum second harmonic output.Consider for the moment the singly peaked data shown in Fig. 2 mismatch reduces the coherence length, to less than the crystal length for only small changes in the phase matching angle.For example, a phase mismatch of 0.13° reduces the coherence length to 0.3 cm compared to 100 cm at θ pm .At this point power flows out of the second harmonic polarization wave back into the fundamental with the final conversion efficiency depending on the coherence length (l c ) to crystal length (l x ) ratio (l c /l x ).If however there is a twin crystal, (for example, covering half the crystal length of 0.4 cm) then reducing the coherence length to less than the crystal length allows a fraction of the inverted section of the crystal to convert to the second harmonic.This is similar to quasi-phase matched operation in ferro-electric crystals such as LiNbO 3 , except in this case, we use a combination of birefringent phase matching and domain inversion to arrive at the net second harmonic conversion efficiency.Double or multiple peaked second harmonic conversion efficiency curves are also often observed in PPLN, and are attributed to fabrication faults such as non-uniform periodicity of the quasi-phase matched grating or inhomogeneity of the refractive index along the waveguide, [19].In fact, by introducing a continuous phase difference of a periodic domain structure it has been shown that multiply peaked second harmonic tuning curves can be engineered, [20].Peculiar phase matching characteristics have also been observed in Nd:GdAB [21], where for a fixed crystal alignment simultaneous (although non optimized) self-frequency doubled operation at 532 and 669 nm as well as sum frequency mixing (SFM) of pump and fundamental at 1062 nm has been observed.Although not examined in the work presented here crystal twinning may in this case improve the nonlinear conversion by increasing the effective wavelength acceptance bandwidth similarly to the multiple peak angular acceptance curves obtained in Yb:YAB as shown in Fig. 2(b).
To verify the possibility that in Yb:YAB the multiple peak tuning curve is a consequence of domain reversal, we calculated the coherence length, , as a function of detuning angle and then calculated the second harmonic conversion using Equation 1, [22].For the coherence length calculations the refractive index (RI) data of Dy:YAB [23] was used due to the availability of RI data past 1 µm and noting that there is little difference in RI data between the differently doped borates.It was also assumed at this point that only a single inversion existed with the domain thickness taken as being equal to the calculated coherence length for either peak of the measured data.To account for the twinned regions the second harmonic was summed in each of the inverted domains assuming only a single pass, which is appropriate for extracavity conversion.The nonlinear coupling coefficient (K), fundamental power (P ω ) and mode area (A) were taken as constant and the singly peaked function used to normalize the model to the data.The results of this calculation along with the experimental data are shown in Fig. 3.As expected, the detuning curve follows a sinc 2 function when a single domain position is found in the crystal.The doubly peaked curve cannot be fitted to a sinc 2 function but does however fit reasonably well to the calculated second harmonic intensity assuming a twin and host crystal thickness of 1.85/2.15mm respectively.The discrepancies between model and experiment are not unexpected as morphology studies [18] show that twins grow parallel to the rhombic planes with twin regions criss-crossing the sample.Only with a low density of twins is a simple detuning curve such as that shown in Fig. 3  To verify the experimental approach used, detuning experiments were also performed for several other borates including Nd:YAB, LBO, BiBO and Yb:GdCOB (as well as other samples of Yb:YAB).Of these materials both Nd:YAB and Yb:YAB resulted in multiple PM peaks within certain positions across the crystal, while LBO, BiBO and Yb:GdCOB showed no such irregularities.Clearly phase matching irregularities are common in both Nd and Yb:YAB.

Phase matching maps
Optimized second harmonic operation was obtained, in many Yb:YAB crystals, by angular detuning of the phase matching from the calculated peak in order to counteract the effects of growth twins.In the same way, by changing the crystal temperature inside the nonlinear material or by slightly shifting the probe wavelength, a sufficient phase mismatch could be obtained.Clearly non-uniformities in the nonlinear conversion in YAB place limitations on its potential as a nonlinear host and thus needs to be investigated further.However, in order to determine if twins are present and to estimate their density in all of the crystals available to us, a more systematic way of mapping the crystal surface is required.Comprehensive examination can be made by chemical etching and AFM or synchrotron topography, although this approach is destructive and cannot be made in most laser laboratories.Imaging the generated nonlinear intensity of a relatively low power probe laser is however possible and is the approach used here.In contrast, these defects were not observed using a polarizing microscope or for example using a point diffraction interferometer.
To image the nonlinear conversion we substituted the photodiode shown in Fig. 1 with a CCD camera.At the same time we used several lenses to spatially filter and collimate the probe beam as well as using a 100 mm focal length lens to image the second harmonic conversion using a 2f imaging arrangement onto a CCD camera.In the same way as the angular detuning experiments, the generated second harmonic was imaged for a range of incident angles close to the optimum phase matching angle.The results using this approach with the same Yb:YAB crystal as used in Fig. 2(b) are shown in Fig. 4.
Near optimum phase matching, (labeled H in Fig. 4) approximately 25 % of the crystal's clear aperture generates second harmonic power.At this point there are also large areas in the crystal with no net second harmonic conversion.Twisting the crystal away from optimum phase matching results in reduced second harmonic intensity in the previously brightest region while simultaneously increasing in others.Following the phase matching maps either side of the optimum phase matching point, it is evident that certain areas in the material phase-match twice and with lower intensity than regions that only phase-match once.The series of phase matching maps shown in Fig. 4 shows that only around 25 % of the clear aperture results in the maximum possible generated second harmonic output.Twinning in this sample thus significantly reduces the usable area in this crystal.To investigate the density of the twin-host crystal regions in Yb and Nd doped YAB all of the available ytterbium and neodymium samples (10) available in our laboratory were tested, a selection of which are shown in Fig. 5.All of the crystals were twisted around their optimum phase matching angle with the generated second harmonic recorded at each point.The percentage of clear area on each of the crystals varied from 94 %, to as low as 25 %, clearly indicating the large variability between samples.It is also apparent that all of the samples showed some degree of phase matching irregularity, which we believe is due to twin crystal formation.The same approach to mapping of the nonlinear crystal quality was used for Yb:GdCOB, LBO and BiBO.No phase matching irregularities or anomalies were observed at any point in these crystals.In this case uniform nonlinear conversion is obtained across the entire crystal surface as shown for the case of Yb:GdCOB in Fig. 6.The results presented above show that effects such as twinning are not common in all nonlinear materials and in fact have only been observed by these authors in Yb:YAB and Nd:YAB.Despite this, other workers [15] have also observed twinning in BBO, LBO and LTB to name a few, indicating these effects do arise in other relevant nonlinear laser materials.

Conclusions
We have measured the phase matching acceptance bandwidths in Yb:YAB as a function of angle (∆θ.l x ≈1.35 mradcm) , temperature (∆T.l x ≈28°Ccm) and wavelength (∆λ.l x ≈1.23 nmcm) allowing the laser designer more accurate calculation of possible conversion efficiencies in this material.We have also identified defects that limit nonlinear conversion applicable to any self-frequency converting system based on this material.The principle effect in this case is believed to be due to crystal twinning which results in cancellation of the nonlinear polarisability due to a reversal in piezo-electric domains between twinned pairs.In this case optimum second harmonic power is obtained by introducing a phase mismatch, from the expected phase matching peak, in order to maximize the nonlinear interaction in this quasiphase matched like structure.Conversion efficiencies are at best half that obtained from the completely birefringently phase matched crystal.The material defects in YAB, (either Yb or Nd doped) require further investigation in order to more closely determine the exact mechanism for the density of the twin domains.The approach used to measure the second harmonic conversion efficiency across the full aperture of the crystal may allow the crystal grower a quick-check for twin or inversion defects, compared to chemical etching and AFM or synchrotron radiation mapping.The nondestructive purely optical technique described gives unique and valuable information on phase matching and crystal quality for the grower or laser engineer.Despite the defects observed, high second harmonic conversion efficiencies were obtained in Yb:YAB when optimizing the fundamental beam position within the crystal.For example using an uncoated crystal (top right in Fig. 5) we obtained 1.1 W of cw green output with 10 % conversion from the pumpto-green and 25 % from the optimized fundamental-to-green [5].

Fig. 1 .
Fig. 1.Schematic of arrangement used to measure angular and temperature acceptance in YAB.

Fig. 2 .
Fig. 2. Angular acceptance curves for phase matched Yb:YAB in crystals without (a) and with (b) twinning.In both cases φ was orientated normal to the probe beam. Photodiode

Fig. 4 .
Fig. 4. Second harmonic phase matching maps in Yb:YAB, (3x3x4.1mm)as a function of phase mismatch.Red/white areas signify high intensities while blue-purple low intensity.Angle in top right hand corner indicates phase-mismatch angle from θ pm (external angle).
2004 OSA 29 November 2004 / Vol. 12, No. 24 / OPTICS EXPRESS 5929 Fig. 3. Calculated and measured second harmonic intensity as a function of detuning angle in different regions in a Yb:YAB crystal.Model normalized to singly peaked data.