1. Introduction

Of all the nonlinear optical materials used for quasi-phase matching (QPM) [1] KTiOPO₄ (KTP) is considered to be one of the most suitable for frequency generation in the green-blue spectral region at room temperature because of its low susceptibility to photorefraction. Besides its high nonlinearity [2] and high damage threshold, its excellent mechanical and thermal properties, KTP has a large anisotropy in the ferroelectric domain propagation velocities along the different crystal axes [3] facilitating the fabrication of short-period domain gratings [4], which are necessary for generation of short wavelengths by frequency doubling. Indeed KTP is one of the few materials that could be used for fabrication of QPM structures for second harmonic generation (SHG) at wavelengths below 400 nm. For low-intensity fundamental beams (below ~300 MW/cm²) the shortest wavelength, where periodically poled KTP (PPKTP) could be used is given by the bandgap of about 3.5 eV. For ultrashort pulses with higher peak intensity, where nonlinear absorption becomes important, the short wavelength range is further restricted. The effects of two-photon absorption in KTP can be compounded by free-carrier absorption and absorption due to induced color-centers, also, known as gray-tracks [5–8]. Recently, significant efforts have been made to improve the properties of KTP. An example is the so-called “gray-track resistant” KTP (GTR-KTP) [9], a flux-grown crystal with reduced iron impurities, which promises better resistance to photochromatic damage and is now becoming commercially available. However, as we show in this work, the performance of this material in the regime of frequency doubling of high-peak intensity pulses into the blue spectral region is unsatisfactory.

Another promising example is bulk Rb-doped KTP (RKTP). With less than 1% of Rb⁺ substituting K⁺ ions in the crystal, this material shows two orders of magnitude lower ionic conductivity, which is beneficial for fabrication of high-quality QPM structures. Switching of the spontaneous polarization in RKTP was first reported by Jiang et al. [10], and later Wang et al. [11] demonstrated periodic poling with a period of 5.27 µm. Recently, we achieved consistent periodic poling in 5 mm-thick crystals with a grating of 38.86 µm demonstrating high-energy optical parametric frequency conversion [12], as well as periodic poling of sub-µm domain gratings [4]. The low dopant concentration in the crystal suggests that the transmission and nonlinear optical properties of RKTP are very similar to those of undoped flux grown KTP. Nevertheless, the susceptibility to gray-tracking in this material needs to be assessed and its performance as a QPM frequency converter in the visible region has not yet been evaluated.

In this work we investigate the performance of PPKTP and periodically poled RKTP (PPRKTP) with a poling periodicity of 3.18 µm, designed for frequency doubling of 796 nm fundamental wavelength. First, we show that due to substantially reduced ferroelectric domain broadening in RKTP, the PPRKTP offers substantially higher effective nonlinearity, determined by the quality and homogeneity of the periodic domain structures. In the PPRKTP crystal a normalized conversion efficiency of 1.79%W⁻¹cm⁻¹, uniformly distributed over the whole crystal aperture was achieved. Furthermore, SHG of femtosecond pulses in the high-peak intensity regime was investigated. In this regime nonlinear crystals typically experience both nonlinear absorption and induced color-center formation as well as associated increased thermal loading. Under such conditions all possible adversary effects come into play and the difference in performance of seemingly very similar crystals becomes starkly evident. These measurements clearly show that among the investigated crystals, PPRKTP is by far the best in terms of low susceptibility to gray-tracking, high effective nonlinearity and high optical damage threshold. The high damage threshold in PPRKTP allowed investigating the SHG regime in which nonlinear-absorption induced thermal loading pushes the interaction into detuned SHG regime where instantaneous (Kerr-like) and delayed (Raman-like) [13] cascaded χ⁽²⁾:χ⁽²⁾ nonlinearities play an important role in frequency shifting and reshaping the fundamental pulse spectrum.

2. Experimental results and discussion

The commercial GTR-KTP [14] crystals unfortunately could not be periodically poled. Nevertheless, in order to assess the photochromic damage properties, we compared the blue light-induced infrared absorption dynamics in single-domain flux-grown KTP, RKTP and GTR-KTP crystals. The RKTP crystals are grown with 1.4 mol% Rb added to the growth melt, which results in 0.3% Rb concentration in the as-grown crystals [15]. For the induced absorption measurements all crystals had dimensions of 10 × 6 × 1 mm³. The output of a Ti:sapphire regenerative amplifier providing 800 nm, 1 ps pulses at a repetition rate of 1 kHz was frequency doubled using a type-I BBO crystal. The generated second harmonic (1 μJ) and remaining fundamental (40 μJ) beams were superimposed with a CW He-Ne (632 nm) beam and focused into the sample to a beam radius of 220 μm. The blue and infrared light was polarized parallel and perpendicular to crystal z-axis, respectively. The peak intensities at 800 nm and 400 nm were 26.3 GW/cm² and 0.66 GW/cm², respectively, large enough to generate nonequillibrium charge carriers by nonlinear absorption process. The capture of these electrons by local defect centers results in color-center formation and gray-tracking. The color-center concentration dynamics in the samples after starting the exposure to the picosecond pulses was determined by measuring changes in the transmission of the He-Ne beam. Figure 1 shows the gray-tracking dynamics of the investigated RKTP, KTP and GTR-KTP crystals.

 

Fig. 1 Induced absorption dynamics in RKTP, KTP and GTR-KTP.

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From the results in Fig. 1 it is clear that RKTP presents the highest resistance to gray-tracking. This can be tentatively attributed to the fact that RKTP has a reduced effective mobility of the potassium vacancies, V(K⁺), which are partially responsible for the color-center formation [5–9,16]. Rb⁺ has higher activation energy (0.45 eV) than K⁺ (0.33 eV), which reduces the overall hoping rate of the remaining K⁺ and V(K⁺) ions in the lattice. Surprisingly, in the blue spectral region GTR-KTP appears to be the most susceptible to gray-tracking. Owing to the proprietary process of the crystal growth, however, we do not have enough information to determine the physical reasons of this strong photochromic damage in GTR-KTP.

Periodic poling was done in 1 mm-thick RKTP crystals of dimensions 10 × 6 × 1 mm³ (corresponding to a × b × c crystallographic axes, respectively). The crystals were patterned on their c^- faces with a QPM period of Λ = 3.18 µm by employing standard photolithographic techniques. The periodic aluminum electrode had a duty cycle of 18%. Liquid electrodes were used to contact the crystals to an external circuit. The poled area had dimensions of 6.5 × 3 mm² determined by the electrode geometry.

The crystals were periodically poled at room temperature by applying a 5 ms-long symmetric triangular pulse of 7.76 kV/mm magnitude. Figure 2 shows the resulting domain structure revealed on the polar faces after selective chemical etching on (a) the patterned face and (b) the unpatterned face of the periodically poled RKTP crystal. The obtained ferroelectric-domain duty cycle close to 47% on both faces ensues from poling in the high field regime, which increases the domain broadening and therefore enables us to use the same lithographic mask as that for KTP. In fact, applying lower field pulses (7.4 kV/mm) produces a domain pattern in RKTP which faithfully replicates the mask. Obviously, in this case, the resulting structures would not be suitable for efficient SHG.

 

Fig. 2 Micrographs of the domain structure revealed by chemical etching on (a) patterned face, (b) unpatterned face of RKTP, and (c) patterned face and (d) unpatterned face of KTP.

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For comparison, flux-grown KTP samples were also patterned with the same period and periodically poled applying 5 ms-long symmetric triangular pulses of 6.0 kV/mm magnitude. Figures 2(c) and 2(d) show the resulting domain structure on the patterned and unpatterned faces of periodically poled KTP (PPKTP) crystal, respectively. In this case the domain structure did not propagate homogeneously through the crystal bulk. This difference in domain-propagation characteristics can be explained by the fact that the two-orders of magnitude lower conductivity in RKTP results in lower electric-field screening and, thus, in improved domain-propagation along the c-direction.

A continuous wave (CW) SHG of Ti:sapphire laser emitting at 795.7 nm was employed to test the quality of the fabricated structures. The z-polarized pump light was launched along the x-direction of the crystals and focused to a beam waist of 23 μm radius (1/e² intensity) with a 50 mm focal length lens. A waveplate-polarizer arrangement was used to control the pump power. The crystals were uncoated and the experiments were performed at room temperature. Figure 3 compares the second harmonic (SH) efficiencies of PPKTP and periodically poled RKTP (PPRKTP) crystals for different pump powers.

 

Fig. 3 Second harmonic power (open symbols) and efficiencies (solid symbols) for PPRKTP (squares) and PPKTP (circles) as a function of the CW Ti:sapphire pump power.

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The PPRKTP crystal generated 2.15 mW of blue light when pumped with the maximum available fundamental power of 430 mW, which corresponds to a normalized conversion efficiency of 1.79%/Wcm. This would give the nonlinear coefficient d₃₃ = 13 pm/V, which is somewhat lower than 15.7 pm/V reported in a single domain KTP [2]. Slightly lower effective nonlinearity could be expected due to the fact that the duty cycle of the domain structure deviates from the perfect 50%. Nevertheless, this result is very good indeed for frequency doubling of 800 nm radiation. It is worth noting that the conversion efficiency of the PPRKTP was homogeneous over the whole crystal aperture. As expected from non-uniform structure in PPKTP (Figs. 2(c) and 2(d)) the SHG efficiency was not homogeneously distributed along the z-direction. The highest normalized efficiency of 1.1%/Wcm was achieved when the fundamental beam was propagating close to the patterned crystal face.

Translating the high normalized conversion efficiency observed with PPRKTP in CW SHG regime into high conversion efficiency by scaling up intensity of the fundamental wave, e.g. by using femtosecond pulses, is not straightforward in this spectral region. Apart from linear effects such as group-velocity mismatch, and linear absorption at the second harmonic wavelength, which can be mitigated by appropriate QPM structure design, at high peak intensities one has to take into account nonlinear absorption, the resulting increase in thermal loading and dephasing which, in turn, leads to cascaded χ⁽²⁾:χ⁽²⁾ interactions. Under conditions of group-velocity mismatch, the non-stationary cascaded interactions lead to Raman-like frequency shift and spectral reshaping of the fundamental pulses [13].

In order to evaluate the performance of the PPKTP and PPRKTP crystals at higher intensities we used femtosecond Ti:sapphire laser operating at 76 MHz repetition rate. To compare the relatively long, 6.5 mm, crystals we used the fundamental beam waist radius of 50 µm and the pulse length was adjusted to 138 fs by narrowing down the spectral width by adjusting intracavity dispersion. The calculated wavelength acceptance bandwidth of 6.5 mm long PPKTP crystals was 0.17 nm. The crystals were placed in a temperature-stabilized holder at a temperature of 25°C. The generated second harmonic average powers and efficiencies in both materials are shown in Fig. 4(a) . The efficiency in PPRKTP is substantially higher than in PPKTP, as could be expected due to higher quality of the PPRKTP structures. More striking, however is the observation of strong gray-tracking in PPKTP at the fundamental peak intensities of 0.5 GW/cm². The process clearly requires the presence of both the intense near-infrared and the generated SH. By increasing further the fundamental average power the nonlinear absorption-induced gray-tracking eventually leads to runaway thermal loading and breakdown of the crystal. Under the same pumping conditions, PPRKTP did not show gray-tracking even at the peak intensities of 0.77 GW/cm². In Fig. 4(b) we show the time-dependence of the conversion efficiencies over two hours of continuous operation in both materials. The peak intensity here was 0.4 GW/cm². The result clearly indicates the long-term color-center accumulation effect in PPKTP, which is not observed in PPRKTP.

 

Fig. 4 SH average power (open symbols) and SHG efficiency (solid symbols) in 6.5 mm-long PPKTP (circles) and PPRKTP (squares) for 138 fs fundamental pulses at 796 nm, (a). Long-term variation of the SHG efficiency at 0.4 GW/cm², (b).

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Higher conversion efficiency for femtosecond pulses, when group velocity mismatch is large, can normally be achieved by employing short nonlinear crystals and tight focusing to reduce the characteristic nonlinear interaction length. For instance, such paradigm was successfully employed for reaching frequency doubling above 50% for femtosecond oscillator pulses at 1040 nm [17]. However, it is not obvious that the same paradigm could help to increase the SHG efficiency for frequency doubling femtosecond pulses at 800 nm where simultaneous absorption of the fundamental and second harmonic photons $(\hslash {\omega }_F+\hslash {\omega }_{SH})$can create free charge carriers with associated free-carrier absorption and increased thermal loading. It should be noted that the energy of the fundamental frequency photon is smaller than the half of the RKTP bandgap, therefore the two-photon absorption at the fundamental frequency is not efficient.

In order to investigate these and other limiting effects on SHG under high-peak intensity and the two-photon absorption conditions, we reduced the length of PPRKTP crystals to 1 mm and the fundamental pulse length down to 85 fs. The wavelength acceptance bandwidth of 1 mm long PPRKTP crystals was estimated to be 1.1 nm.

The measurement results shown in Fig. 5 reveal that the SHG efficiency in the shorter crystals is actually lower than in the longer ones and the efficiency is promptly diminishing for the fundamental peak intensities above 1 GW/cm². Again, no visible gray-tracking could be seen in PPRKTP crystals even after operation at peak intensities of 1.5 GW/cm².

 

Fig. 5 SH average power (solid symbols) and SHG efficiency (open symbols) in 1 mm-long PPRKTP for 85 fs fundamental pulses at 796 nm and 1/e² beam waist radius of 50 µm.

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The saturation of the SHG efficiency and the apparently lower saturated efficiency in shorter crystals cannot be explained solely by thermal effects, which should be much more pronounced in longer crystals. The group velocity dispersion effects, although they are not of major importance here, are also reduced in shorter crystals. For frequency doubling of 796 nm high-peak power pulses we found that the strongest process limiting the generated second harmonic and transmitted fundamental is the two photon absorption (TPA), $\hslash {\omega }_F+\hslash {\omega }_{SH}.$The effect of the TPA is clearly seen in an open aperture z-scan measurements shown in Fig. 6 .

 

Fig. 6 Normalized total transmission (solid squares) and the ratio of the SH and fundamental power after the crystal (open squares) as a function of crystal position with respect to the beam waist. Maximum intensity at the beam waist 5.8 GWcm⁻², PPRKTP crystal length 1 mm, pulse length 85 fs.

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Here the solid symbols show total power transmission as a function of the 1-mm-long PPRKTP position with respect to the beam waist. The beam waist radius was 13 µm and the crystal was kept at a constant nominal temperature of 25°C corresponding to the most efficient SHG in CW experiments. The total power transmission (fundamental plus second harmonic) decreases by 53% when the crystal is at the beam waist position. At this position about 50% of the total transmitted power is actually in second harmonic. Moreover, such reduction of the transmitted power was not observed in the unpoled RKTP crystals.

It is clear, therefore, that the above mentioned TPA involving both the fundamental and the second harmonic photons is the main source of losses which in turn limits the obtainable SHG efficiency in this extreme SHG regime. As a result, the SHG efficiency at 796 nm as normalized to the incident fundamental power does not exceed 20% even for short PPRKTP crystals and for tight focusing in strong contrast to the femtosecond SHG at 1 µm or CW SHG at 846 nm, where the TPA process is absent or significantly reduced [17, 18]. It should be mentioned that the above experiments could not be performed with PPKTP due to crystal damage associated with increased absorption by induced color-centers.

The significant power absorbed by the crystal due to TPA and linear absorption will eventually be released as heat causing thermal dephasing. One direct result of this will be shifting of the maximum of SHG to longer wavelengths as shown in Fig. 7(a) . From the measurement of the SHG peak shift observed at the fundamental peak intensity of 4.4 GWcm⁻² we estimate that the mean temperature along the beam at this intensity has increased from 25°C to 73°C, calculated using Sellmeier equations by evaluating the SHG wavelength peak shift from 398 nm to 399 nm. The temperature increase has important consequences also for the fundamental spectrum. As can be seen in Fig. 7(b), the fundamental pulse spectrum acquires a sideband at longer wavelengths and the peak of the fundamental pulse spectrum is shifted to higher frequencies. It is well known that the phase mismatched second order interactions lead to cascaded nonlinear phase shifts emulating optical Kerr effect which can be used e.g. for mode-locking different lasers [19–21].

 

Fig. 7 The measured normalized pulse spectra of the second harmonic (a) and fundamental (b) at different fundamental peak intensities. The input fundamental pulse length was 85 fs; different intensities were obtained by moving PPRKTP crystal with respect to the beam waist without adjusting the laser. Dashed lines on the fundamental spectra indicate the positions of exact quasi-phase matching for both intensities.

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Unlike in natural Kerr effect, the sign of the effective cascaded Kerr nonlinearity can be controlled by controlling the sign of the phase mismatch $\Delta k=k_{2\omega }-2k_{\omega }-2\pi /\Lambda ,$where $k_{2\omega },k_{\omega },\Lambda$are the second harmonic, fundamental wavevectors and the QPM grating period, respectively. At high fundamental intensities the TPA-induced temperature change moves the position of $\Delta k=0$ to longer wavelengths as shown by the dashed markers on Fig. 7(b). Therefore at high peak intensities the bulk of the fundamental pulse spectrum has positive phase mismatch and experiences negative effective nonlinear index. Therefore the beam experiences self-defocussing cascaded Kerr nonlinearity. The cascaded interaction is driven by the relative phase lag between the fundamental and the second harmonic and thus happens within a single cycle of the fundamental wave and therefore can be termed as “instantaneous” or stationary. It results in broadening of the fundamental pulse spectrum [21] as well as in modification of the spatial phase front curvature. For short pulses and long nonlinear crystals the group velocity mismatch becomes appreciable and imparts additional relative delays between the fundamental and the second harmonic envelopes. Under the conditions of cascading, $\Delta k\ne 0,$this results in delayed or nonstationary cascaded second order interaction, which in spectral domain manifests itself by spectral shifting of the fundamental spectrum [13, 22]. The sign of the frequency shift is governed by the sign of the product of the phase mismatch and group velocity mismatch (GVM) [13], $\Delta k{L}_{GVM}\equiv \Delta k\tau /(n_{\omega ,g}-n_{2\omega ,g}),$ where $\tau ,n_{\omega ,g},n_{2\omega ,g}$are the fundamental pulse length, the fundamental and the second harmonic group indices, respectively. At fundamental peak intensity of 4.4 GWcm⁻² the peak of the fundamental spectrum acquires a phase mismatch of about Δk = 25 cm⁻¹ owing to the TPA, thus under conditions of normal dispersion the peak of the fundamental spectrum will be blue-shifted as observed in the experiment. On the other hand the low-frequency parts of the fundamental spectrum where Δk < 0 will be red-shifted. Numerical simulations of the phase mismatched SHG under conditions of group-velocity mismatch, shown in Fig. 8 , reproduce well the experimental observations. Here two situations are shown, (a) quasi-phase matched SHG, Δk = 0, in 1 mm PPRKTP employing 138 fs pulse with peak intensity of 0.187 GWcm⁻² (dashed lines) and (b) phase mismatched SHG, Δk = 25 cm⁻¹, using 85 fs pulse with a peak intensity of 5.8 GWcm⁻². For the simulations we used an effective nonlinearity of 9.8 pm/V and the phase and group indices were calculated from the Sellmeier equations of Ref. 23.

 

Fig. 8 Calculated spectra of the fundamental and the second harmonic after SHG in 1 mm of PPRKTP crystal. Central wavelength of the fundamental corresponding to 0 THz frequency is 796 nm. Dashed lines: spectra for 138 fs pulse with the peak intensity of 0.187 GWcm⁻² and Δk = 0. Solid lines: spectra for 85 fs pulse with peak intensity of 5.8 GWcm⁻² and Δk = 25 cm⁻¹.

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As shown above, the TPA-associated temperature increase and associated dephasing of the SHG process shifts the phase matching point to longer wavelengths.

At high peak-powers and high repetition rates the thermal lens created by the temperature distribution due to nonlinear absorption is then compensated by the negative cascaded Kerr lens. Indeed, as the phase matching point is now at longer wavelengths, the bulk of the spectrum of the fundamental pulse experiences Δk > 0. It might be tempting to compensate for the phase mismatch by lowering the crystal temperature or/and by slightly tuning the central wavelength of the fundamental pulse. This will also change the cascaded Kerr lens which might become self-focusing instead and will immediately lead to crystal damage. Obviously by carefully adjusting the crystal temperature and the distance from beam waist it is possible to find operating conditions where the phase curvature of the fundamental beam as well as the effect of the thermal lens are compensated by the cascaded Kerr lens and the beam propagates without spreading.

3. Conclusions

In conclusion, we have demonstrated that RKTP is more resistant to gray-tracking in the blue region than flux-grown KTP and even than GTR-KTP. We have shown periodic poling of 1 mm thick RKTP with a QPM grating period of 3.18 µm. The PPRKTP has a high quality domain-grating over the whole crystal aperture with a normalized conversion efficiency of 1.79%/Wcm. The crystal has been used to frequency-double fs pulses with 20% efficiency at fundamental peak-intensities of 560 MW/cm² without gray-tracking. The conversion efficiency is stable during our two-hour test. Resistance to the induced color-center formation in PPRKTP allowed investigating high-peak power and high-repetition rate SHG of 796 nm, the regime where standard PPKTP invariably fails. We showed that the predominant mechanism limiting SHG efficiency in this spectral range is the TPA process involving the fundamental and the second harmonic photons. In the SHG regime, where TPA is strong, it leads to modifications of the fundamental pulse spectrum well accounted for by nonstationary cascaded second order interaction. Owing to above mentioned processes, 20% SHG efficiency for femtosecond pulses at 796 nm and optical damage threshold of PPRKTP are low compared to other nonlinear materials, e.g. BBO, however comparison of performance of different nonlinear materials is beyond the scope of this publication.