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Characteristics of optical parametric oscillator synchronously pumped by Yb:KGW laser and based on periodically poled potassium titanyl phosphate crystal
Optics Communications 410 (2018) 774–781
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Characteristics of optical parametric oscillator synchronously pumped by Yb:KGW laser and based on periodically poled potassium titanyl phosphate crystal Julius Vengelis a, *, Adomas Tumas a , Ieva Pipinyte˙ a , Migle˙ Kuliešaite˙ a , Viktorija Tamuliene˙ a , Vygandas Jarutis a , Rimantas Grigonis a,b , Valdas Sirutkaitis a a b
Laser Research Center, Vilnius University, Sauletekio ave. 10, Vilnius LT-10223, Lithuania Light Conversion Ltd., Keramiku st. 2, LT-10223 Vilnius, Lithuania
a r t i c l e
i n f o
Keywords: Nonlinear optics Optical parametric oscillator Synchronous pumping Periodically poled potassium titanyl phosphate crystal Yb:KGW laser
a b s t r a c t We present experimental data and numerical simulation results obtained during investigation of synchronously pumped optical parametric oscillator (SPOPO) pumped by femtosecond Yb:KGW laser (central wavelength at 1033 nm). The nonlinear medium for parametric generation was periodically poled potassium titanyl phosphate crystal (PPKTP). Maximum parametric light conversion efficiency from pump power to signal power was more than 37.5% at 𝜆𝑠 =1530 nm wavelength, whereas the achieved signal wave continuous tuning range was from 1470 nm to 1970 nm with signal pulse durations ranging from 91 fs to roughly 280 fs. We demonstrated wavelength tuning by changing cavity length and PPKTP crystal grating period and also discussed net cavity group delay dispersion (GDD) influence on SPOPO output radiation characteristics. The achieved high pump to signal conversion efficiency and easy wavelength tuning make this device a very promising alternative to Ti:sapphire based SPOPOs as a source of continuously tunable femtosecond laser radiation in the near and mid-IR range. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Optical parametric oscillators (OPO) have long been used as an efficient way to get tunable laser radiation in a broad spectral range. Near-IR and mid-IR radiation of such light sources can be used in various applications: as a source for further spectrum conversion [1,2], in nonlinear microscopy [3–5], spectroscopy [6,7], gas sensing [8], etc. Some applications require ultrafast tunable laser source working at high repetition rate. In order to fulfill these requirements, synchronously pumped optical parametric oscillators (SPOPO) are used. Synchronous pumping means that pump pulse repetition rate matches repetition rate of generated pulse so that the generated pulse meets with pump pulse in the nonlinear medium after each round trip [9]. Currently, quasi– phase-matched materials dominate in such near and mid-IR SPOPO systems due to the fact that in such crystals the highest possible nonlinear coefficient can be used. Due to high nonlinear coefficient 𝑑𝑒𝑓 𝑓 = 16 pm/V [10], periodically poled lithium niobate crystals (PPLN) or magnesium doped PPLN (MgO-PPLN) [9–16] remain the most popular nonlinear materials for infrared SPOPO. However, low
laser-induced damage threshold (LIDT) of these crystals limits the maximum usable power of the pump source, hence the SPOPO output power [9]. Good alternative could be periodically poled potassium titanyl phosphate crystal (PPKTP). Although it has smaller nonlinear coefficient 𝑑𝑒𝑓 𝑓 = 13.7 pm/V [17] compared to lithium niobate, it has higher LIDT so higher pump intensities can be used. Another advantage is no photorefractive effect and, hence, no need for crystal heating, which is important in case of PPLN [12]. First femtosecond SPOPO with PPKTP crystal was reported in 1998 [18]. The 22 % signal power conversion efficiency and 150 mW OPO generation threshold were observed in the 1000 nm–1235 nm spectral range using the Ti:sapphire laser (𝑓 = 76 MHz, 𝜆 = 758 nm, 𝜏 = 215 fs) as pump for this SPOPO. Up to now, demonstrated SPOPO experiments and commercial SPOPO systems based on PPKTP are pumped by Ti:sapphire lasers operating at 0.8 μm. Alternative for such pumping systems are ytterbium lasers operating around 1 μm. This pumping source can give some advantages because the absorption maximum of ytterbium ions is at 980 nm, therefore they are suitable
* Corresponding author.
E-mail address: [email protected] (J. Vengelis). https://doi.org/10.1016/j.optcom.2017.11.057 Received 9 October 2017; Received in revised form 15 November 2017; Accepted 20 November 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
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Optics Communications 410 (2018) 774–781
for direct pumping by InGaAs diodes. More than that, the difference between pump and emitted radiation wavelengths is very small for ytterbium lasers compared to Ti:sapphire lasers – this allows creating more compact, efficient and less expensive laser systems. However, up to now, no studies of femtosecond SPOPO based on PPKTP and pumped by ultrafast ytterbium lasers were reported. In this paper we present, for the first time to the best of our knowledge, a detailed experimental investigation of femtosecond SPOPO based on PPKTP and pumped by Yb:KGW laser oscillator emitting 1033 nm radiation. We achieved more than 26 % conversion efficiency in the 1470 nm–1970 nm spectral range with maximum conversion efficiency of 37.5% at 𝜆𝑠 = 1530 nm wavelength, which is a promising result of such device for its further development and application. A numerical model is also presented and its results are compared with the experimental data. 2. Experiment results and discussion 2.1. Experimental setup Fig. 1. Principal experimental setup of femtosecond PPKTP SPOPO: M – highly reflective (at 1000 nm–1060 nm range) mirror, L1, L2 – lenses (𝑓 = 125 mm and 𝑓 = 25 mm respectively) for beam expansion, L3 – focusing lens (𝑓 = 100 mm) for SPOPO, 𝜆∕2 – 𝜆∕2 phase plate, BrPol – Brewster type polarizer, BD – beam dump, MN – curved mirror (𝑅 = −100 mm), BM – broadband mirror, OC – output coupler (𝑇 = 15%).
The experimental setup of SPOPO based on PPKTP crystal is shown in Fig. 1. The pump source for the SPOPO was a mode-locked Yb:KGW laser oscillator providing pulses at 76 MHz repetition with average power of 5.5 W at central wavelength of 𝜆 = 1033 nm. Measured (before SPOPO cavity) pump pulse duration was 155 fs. It is important to note that laser pulses reaching the SPOPO cavity were slightly chirped during propagation through some optical components before SPOPO cavity. The 𝜆∕2 phase plate and Brewster-type polarizer were used as attenuator to control pump power. Pump power for SPOPO under our focusing conditions (the diameter of the focused pump beam in the crystal was 38 μm at 1∕𝑒2 level) was limited to 1 W due to highly probable laser induced damage at greater pump powers. Since we had only one PPKTP crystal, we could not perform laser induced damage threshold (LIDT) measurements and specify and exact LIDT value for PPKTP crystal. However, we did measure LIDT for periodically poled lithium niobate (PPLN) crystal under the same experimental conditions: the measured LIDT corresponds to 3 W pump power. Since PPLN has higher 𝑑𝑒𝑓 𝑓 , we believe that LIDT for PPKTP should be somewhat higher than for PPLN. As there is a general recommendation that for any optical element maximum used laser intensity should be several (5–10) times less than LIDT of that element, so choosing 1 W maximum pump power for our SPOPO is a fairly accurate and safe limit. The SPOPO cavity was folded and consisted of two curved mirrors (MN) with 100 mm radius of curvature, three plane broadband mirrors (BM) and 15% transmittance (in 1500 nm–2000 nm spectral range) output coupler (OC). The resonator length was adjusted by moving the output coupler mirror which was mounted on high precision (1.25 μm step) translation stage. Nonlinear medium for parametric generation was 1 mm thick periodically poled KTP crystal (from ‘‘Eksma Optics’’) with eight gratings of periods ranging from 32 μm to 38.8 μm with 1 μm step (Fig. 2a). It was also AR-coated (𝑅 < 2%) for 1350 nm–1750 nm spectral range. PPKTP crystal was mounted on a translation stage for adjusting the grating period used for parametric generation. Wavelength tuning was achieved by changing the grating period and by adjustment of cavity length. Calculated theoretical quasi-phase matching curve for PPKTP crystal pumped with 1033 nm radiation is depicted in Fig. 2(b). Wavelength tuning by adjusting resonator length will be discussed in detail in the results section. In order to achieve the best stability, we constructed singly resonant optical parametric oscillator. Therefore, all cavity mirrors were coated with high reflection (HR) broadband coatings for 1500 nm–2000 nm spectral range which roughly matches the entire signal wave tuning range. In this way we ensured that only signal wave oscillates in the cavity. The idler wave in such case does not oscillate in the cavity since
(a)
(b)
Fig. 2. Principal view of PPKTP crystal geometry (a), calculated theoretical quasi-phase matching curve for PPKTP crystal pumped with 1033 nm wavelength (b). Sellmeier coefficients for calculation were taken from [19].
it is not reflected by cavity mirrors. Therefore, it leaves the cavity and is directed to the beam dump element (as depicted in Fig. 1). We can note that in order to achieve tunable femtosecond radiation in the idler spectral region, one would need to use different cavity mirrors which would reflect idler wavelengths (roughly 2000 nm–3500 nm). From Fig. 2(b) one can see that signal wave tuning range is slightly broader 775
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Optics Communications 410 (2018) 774–781
Fig. 3. Normalized PPKTP SPOPO output signal spectra across the tuning range. Spectral widths at FWHM are (from left): 30 nm, 53 nm, 62 nm, 39 nm, 157 nm and 52 nm.
than HR mirror bandwidth. We could not choose broader bandwidth cavity mirrors due to the fact that the manufacturer of highly reflective mirrors could not achieve broader bandwidth without avoiding large group delay dispersion (GDD) oscillations in the required spectral range. Using broadband mirrors with high GDD oscillations complicates signal wavelength tuning for SPOPO, therefore we decided to use HR mirror with bandwidth limits in the aforementioned spectral range. Pre-alignment of femtosecond SPOPO was complicated due to very small tolerance to cavity misalignment and synchronous pump condition – the period of signal wave round-trip in the cavity must match the period of pump wave round-trip in laser cavity which in reality means that laser and SPOPO cavity lengths must be practically equal with up to a few micrometer accuracy (which corresponds to the pump pulse temporal length). For precise cavity pre-alignment we used a semiconductor laser operating at 1550 nm (which matches one of the signal wavelengths) and after correct alignment we adjusted the resonator length to meet the synchronous pumping condition and achieved parametric oscillation. Final alignment was conducted by measuring the output power and observing the spatial mode of the signal beam. The highest output power and lowest order transverse mode (TEM00 ) corresponded to the best SPOPO cavity alignment. 2.2. Results and discussion In this section we present experimental data and discuss SPOPO operation features when using periodically poled crystal as nonlinear medium. We achieved signal wave tuning in a broad wavelength range: from 1470 nm to roughly 1970 nm. Examples of PPKTP SPOPO signal wave spectra are shown in Fig. 3. As seen from the results, spectral bandwidths (at FWHM) ranged from 30 nm to 157 nm. Such variations of signal wave spectral bandwidth are related to the fact that parametric amplification bandwidth increases as signal wavelength approaches point of degeneracy (𝜆𝑠 = 𝜆𝑖 ). Wavelength tuning was realized by changing the PPKTP crystal grating period (Fig. 2b) and by adjusting cavity length. It is important to note that cavity length adjustment allowed wavelength tuning in a very broad spectral range. Fig. 4 depicts cavity wavelength tuning characteristics at various fixed PPKTP crystal grating periods. We can see that minimum wavelength tuning ranges exceed 100 nm and can be more than 300 nm. Moreover, cavity length tuning limits are also different at different grating periods. These peculiar features can be explained considering the specifics of SPOPO operation. Tuning any optical parametric generator or oscillator by changing the periodically poled nonlinear crystal grating period
Fig. 4. Examples of PPKTP SPOPO wavelength tuning characteristics at various fixed periodically poled crystal grating periods as a function of relative resonator length change. Note that point of zero cavity length change is a relative notation with respect to maximum signal spectrum intensity which is different for each grating period.
means changing the signal and idler wavelengths for which the phase matching is perfect (𝛥𝑘 = 0). In case of synchronously pumped optical parametric oscillator (which is our case), there is another condition that has to be satisfied for this device to operate – synchronous pumping condition. Therefore, it is possible for SPOPO to operate at signal/idler wavelengths that have small phase mismatch, but perfectly satisfy synchronous pumping condition as long as parametric gain outweighs losses – this enables signal/idler wavelength tuning in SPOPO by adjusting cavity length. Adjusting resonator length means changing the 776
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(a) Fig. 5. PPKTP resonator net GDD dependence on wavelength.
signal/idler wavelength for which synchronous pumping condition is satisfied. In Fig. 4 the highest intensity points correspond to wavelengths that both have smallest phase mismatch and perfectly satisfy synchronous pumping condition. The signal wavelength tuning limits increase with increasing grating period can be explained in the following way. From Fig. 2(b) it follows that signal wavelengths increase with increasing grating period. Since parametric amplification bandwidth increases as signal wavelength approaches point of degeneracy, cavity length tuning limits for bigger PPKTP grating periods also become broader. From Fig. 4 one can also notice that wavelength tuning characteristics have somewhat different and dependencies. This is due to group delay dispersion (GDD) oscillations of cavity ultrabroadband dielectric coatings. Fig. 5 shows net cavity GDD dependence on wavelength determined by summing single cavity mirror reflection GDD according to the number of reflections from certain mirror and adding calculated PPKTP crystal GDD. We need to note that the depicted GDD estimation is not strictly accurate because signal beam angle of incidence at certain cavity ultrabroadband mirrors is slightly more than zero degrees, therefore the GDD for these mirrors is somewhat different from the value at 0 degrees of incidence – the angle at which ultrabroadband mirror GDD was measured and used in net GDD calculations. Since net cavity GDD determines the temporal delay of signal pulses when they propagate in SPOPO cavity, its oscillations mean that wavelength tuning by cavity length adjustment step (𝛥𝜆𝑠 per 𝛥𝐿) will be different for different wavelengths. As a result, at different PPKTP crystal grating periods wavelength tuning colormaps are different. The difference depends on the amplitude of GDD oscillations which in our case is relatively small at the region of signal wavelength tuning. The ideal case would be to have ultrabroadband mirrors with no oscillation, however, this is impossible due to technological limitations related to ultrabroadband dielectric coatings. PPKTP SPOPO output power (at maximum pump power) dependence at various signal wavelengths, when cavity length tuning is applied, and maximum pump to signal conversion efficiencies for different crystal grating periods are depicted in Fig. 6. It is important to point out that due to high nonlinearity of PPKTP crystal multiple cascaded nonlinear processes (such as second harmonic generation of pump and signal wavelengths, sum-frequency of pump and signal generation, etc.) also occur in the crystal. Although SPOPO cavity mirrors are highly reflective for only 1500 nm–2000 nm radiation, some light from these cascaded processes may still come through the output coupler. Therefore, in order to make sure that only signal wave power is measured we additionally used filters which allow only signal wavelength to pass. As seen from Fig. 6, maximum SPOPO output power exceeds 225 mW for any PPKTP crystal grating period and may be as high as 375 mW.
(b)
Fig. 6. PPKTP SPOPO output power dependence on wavelength (a) and maximum pump to signal conversion efficiency for different PPKTP grating periods (b).
This corresponds to maximum pump-signal conversion efficiency of 37.5%. Maximum output power/conversion efficiency dependence on wavelength can be explained considering signal/pump photon energy ratio, pump and signal wave group velocity mismatch in PPKTP crystal (Fig. 7a), crystal’s nonlinearity coefficient dependence on wavelength and net cavity losses dependence on wavelength (Fig. 7b). At shortest signal wavelengths (34 μm grating period) pump and signal energy ratio and GVM are smallest, but there are two sharp peaks (at 1440 nm and 1507 nm) in cavity losses in this spectral region which limit maximum output power/conversion efficiency. Therefore, maximum pump to signal conversion efficiency is achieved for longer wavelengths (35 μm grating period) after spectral region of sharp peaks in cavity losses. For even longer signal wavelengths, output power/conversion efficiency decreases due to lower signal/pump photon energy ratio, increasing pump-signal GVM, decreasing nonlinearity coefficient of PPKTP crystal and increasing cavity losses (for longest signal wavelengths). Within single PPKTP crystal grating output power dependence on wavelength is additionally related to the phase matching conditions – for a single grating period perfect phase matching can be achieved at certain signal/idler wavelength, so output power dependence has to have a peak at wavelength which experiences perfect phase matching. Another important energy characteristic of any SPOPO is parametric oscillation threshold. PPKTP SPOPO output power dependence on pump power/peak intensity for different signal wavelengths and the corresponding parametric oscillation thresholds (which are minimum pump power/intensity values for which output power is nonzero) are depicted in Fig. 8. Minimum estimated oscillation threshold was roughly 150 mW 777
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Optics Communications 410 (2018) 774–781
(a) (a)
(b)
(b)
Fig. 8. PPKTP SPOPO output power dependence on pump power for various signal wavelengths (a) and corresponding parametric oscillation thresholds at certain signal wavelengths (b).
Fig. 7. Pump and signal wave group velocity mismatch in PPKTP crystal (a) and PPKTP SPOPO net cavity losses dependence on wavelength (b).
(𝐼 = 1.12 GW∕cm2 ) at 𝜆 = 1734 nm which is well below the maximum pump power meaning that operation of our SPOPO is quite stable: any mechanical vibrations, small fluctuations of pump power, etc. should not stop SPOPO operation. Parametric oscillation threshold variations are related to parametric gain (hence, output power) dependence on pump peak intensity/power, therefore, its dependence on signal wavelength is related to the same factors as output power dependence on signal wavelength which were discussed in the paragraph above. Finally, we measured durations of signal pulses. Measurements were performed using commercial multi-shot autocorrelator GECO® . Experiment results (Fig. 9) showed that pulse durations ranged from 91 fs to 280 fs. As pump pulse duration was 155 fs, the signal/pump pulse duration ratio ranges from ≈ 0.6 to 1.8. In addition, we determined timebandwidth product of signal pulses and we can claim that output pulses were slightly chirped. This is not surprising, since, as mentioned in the experimental setup section, pump pulses were also slightly chirped. Generated signal pulse duration oscillations correlate with net cavity GDD oscillations (Fig. 5). However, the correlation in not strong. One reason for this is the fact that, as mentioned before, net cavity GDD estimation given in Fig. 5 is only approximate. Another, more important and complicated factor is related to signal pulse formation in SPOPO. We will briefly discuss it. For parametric oscillation and following amplification of generated pulses to occur, the round-trip parametric gain for the signal pulse needs to be greater than net round trip loss in the cavity. If this is
Fig. 9. PPKTP SPOPO output pulse durations (FWHM) and time-bandwidth product at various signal wavelengths.
achieved, signal pulses will be generated and amplified as long as the aforementioned condition is met. Parametric gain is a function of signal wavelength and, in general, other wavelength-dependent factors, such as group velocity mismatch, between pump and signal waves also influence parametric amplification process, therefore, the number of 778
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cavity round-trips that distinct signal wavelengths make during pulse formation process is different. This means that the amount of GDD that distinct signal wavelengths are affected by during pulse formation might be noticeably different. Despite some wavelength-dependent variation of output radiation characteristics, which, as discussed, are unavoidable due to complex physics of SPOPO operation and pulse formation, PPKTP SPOPO proved to be an efficient device with broad wavelength tuning range and low generation threshold. 3. Numerical simulation model and results In this section we briefly present the numerical simulation algorithm we used and compare numerical simulation results with experimental data. In the periodically poled KTP crystal, the three wave interaction of the signal, idler and pump waves with central wavelengths 𝜆10 , 𝜆20 and 𝜆30 , respectively, is described by the governing equations: ( ) 𝜕𝑆1 2𝜋 = 𝑖𝑘′1 𝑆1 + 𝜎1 𝑃̂1 exp −𝑖 𝑧 , (1a) 𝜕𝑧 𝛬 ( ) 𝜕𝑆2 2𝜋 = 𝑖𝑘′2 𝑆2 + 𝜎2 𝑃̂2 exp −𝑖 𝑧 , (1b) 𝜕𝑧 𝛬 ( ) 𝜕𝑆3 2𝜋 = 𝑖𝑘′3 𝑆3 − 𝜎3 𝑃̂3 exp 𝑖 𝑧 , (1c) 𝜕𝑧 𝛬 where 𝑆1,2,3 (𝛺) is the Fourier transform of the field 𝐸1,2,3 (𝑡). Here, 𝑡 is ̂1 , 𝑃 ̂2 and 𝑃 ̂3 are the Fourier time and 𝑧 is the propagation distance. 𝑃 transforms of the products 𝐸2∗ 𝐸3 , 𝐸1∗ 𝐸3 and 𝐸1 𝐸2 , respectively. 𝜎𝑗 = 𝜔𝑗0 ∕(𝜔30 𝑎30 𝐿𝑛 ) is the nonlinear coupling coefficient that is proportional to the central frequency 𝜔𝑗0 of the wave (𝑗 = 1, 2, 3). 𝐿𝑛 is the nonlinear interaction length, 𝑎30 is the pump amplitude. 𝑘′𝑗 = 𝑘𝑗 −𝛺∕𝑢10 , wavenumbers are calculated from 𝑘𝑗 = 𝑘(𝜆𝑗 ) = 2𝜋𝑛(𝜆𝑗 )∕𝜆𝑗 where 𝑛 is the refractive index given by the Sellmeier equation, 𝑛𝑧 in [19]. 𝜆𝑗 = 2𝜋𝑐∕(𝜔𝑗0 + 𝛺) is the wavelength and 𝑐 is speed of light. 𝑢10 = 1∕(𝑑𝑘∕𝑑𝜔)|𝜔10 is the signal group velocity. 𝛬 is the period of the PPKTP grating and is found from 𝛬 = 2𝜋∕(𝑘30 − 𝑘10 − 𝑘20 ), where 𝑘𝑗0 = 𝑘(𝜆𝑗0 ). The term 𝛺∕𝑢10 is subtracted from the wavenumber 𝑘𝑗 , so Eqs. (1) describe the propagation with respect to the signal wave. At 𝑧 = 𝐿 the fields are modified as follows: √ ( ) 𝑆1 → 𝑅 exp 𝑖𝛿𝐿𝛺∕𝑢10 + 𝑖𝐺0 𝛺2 ∕2 𝑆1 , (2a) 𝑆2 → 0,
(2b)
𝑆3 → 𝑆3 (𝑧 = 0),
(2c)
Fig. 10. Signal wave spectrum at different 𝛿 values (correspondingly, resonator length values). 𝜆10 = 1.55 μm, 𝑁 = 1000, 𝐺0 = 0.
Fig. 11. Signal wave spectrum at different 𝛬 values [μm]: 37.39 (left), 38.06 (center) and 38.42 (right). 𝑁 = 1000, 𝐺0 = 0. Parameter 𝛿 (corresponding to different cavity lengths) was varied for each case as well.
Examples of simulated signal wave spectra at different cavity lengths for 𝜆10 = 1.55 μm is depicted in Fig. 10. Parameter 𝛿 was varied and 𝐺0 was set to zero. Parameter value 𝛿 = −16 × 10−4 (which corresponds to relative cavity length change in experiment) is optimal (curve (2)) because the spectrum amplitude reaches the maximum at this value. The optimal value is nonzero due to the temporal walk-off between the signal and pump waves which is caused by group velocity mismatch between them (zero value corresponds to case when temporal walk-off between pump and signal waves is zero). From Fig. 10 we can also see that for 𝛿 values further away from perfect phase matching value, signal spectral width increases. This is also due to the temporal walk-off effect between pump and signal waves which causes greater amplification of wing components of signal pulse spectrum (at the expense of central spectral components) yielding broader spectrum, but with considerably smaller peak intensity. Changing PPKTP grating period 𝛬 during numerical simulation also yields signal wavelength tuning, as depicted in Fig. 11. Some optimal 𝛿 values exist (curves (2) in Fig. 11) for which both phase matching condition and synchronous pumping condition are best satisfied. The 𝛿 value corresponding to maximum intensity is different for distinct signal wavelengths. It is also clear that spectral widths increase with increasing wavelength which is in very good agreement with experimental data. Further on, we calculated pump to signal conversion efficiency 𝜂 and signal pulse duration 𝜏𝑠 at the output. During numerical simulation
where 𝐿 is the crystal length, 𝑅 is the reflection coefficient. By varying parameter 𝛿 we change the signal phase so that the variation of the cavity length is taken into account. 𝐺0 is the group delay dispersion impact of the cavity mirrors that depends on the central wavelength 𝜆10 , crystal GDD was accounted for in numerical simulations in wavenumber expression. The idler and pump waves leave the resonator after one trip. The signal wave propagates through the crystal 𝑁 times and at each round-trip some part of the signal leaves the resonator. The input fields at 𝑧 = 0 and 𝑁 = 1 are given by 𝐸10 = 𝑎0 𝜉1 (𝑡),
(3a)
𝐸20 = 𝑎0 𝜉2 (𝑡),
(3b)
(
𝐸30 = 𝑎30 exp −2 ln(2)
𝑡2 𝜏𝑝2
) .
(3c)
𝐸1,20 are the delta-correlated random fields of normal distribution with the zero mean and variance equal to |𝑎0 |2 . 𝜏𝑝 is the pump pulse duration at FWHM. We simulated Eqs.(1) by the use of the Fourier split-step method [20]. Parameters were the following: 𝜆30 = 1.033 μm, 𝜏𝑝 = 155 fs, 𝐿 = 30𝛥, 𝐿𝑛 = 𝐿∕2, 𝑎0 ∕𝑎30 = 10−6 , 𝑅 = 0.85. The chosen nonlinear interaction length corresponds to the pump intensity of 3.4 GW/cm2 . Crystal length is approximately 1 mm. 779
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is always greater than pump pulse duration. Moreover, signal pulse duration oscillations correlate with net cavity GDD oscillations (Fig. 5). Considering the abundance of factors influencing SPOPO output radiation characteristics, we can conclude that numerical simulation results are in reasonable agreement with experimental data. 4. Conclusions We have presented a detailed characterization of synchronously pumped optical parametric oscillator (SPOPO) with femtosecond modelocked Yb:KGW laser oscillator as pump source and periodically poled potassium titanyl phosphate crystal (PPKTP) as nonlinear medium. We also presented a numerical simulation model, its results and discussed their correlation with experimental data. The PPKTP SPOPO enabled wavelength tuning in 1470 nm –1970 nm spectral range with maximum output power reaching 375 mW and pump to signal conversion efficiency as high as 37.5%. Wavelength tuning for our SPOPO was easy and was achieved by using different period PPKTP crystal gratings and by adjusting cavity length. Moreover, parametric generation threshold was well below maximum pump power yielding stable operation of the device. Pump pulse durations ranged from 91 fs to roughly 280 fs and such oscillations were related to net cavity GDD oscillations and signal pulse formation processes during parametric oscillation. Numerical simulation results are in good qualitative agreement with experiment. We believe that the complexity of SPOPO operation and many factors influencing output radiation characteristics prevented us from getting better coincidence with experiment results. All things considered, the results of this study show great promise for future development of these devices and prove that SPOPOs pumped by ytterbium lasers are a very promising alternative to Ti:sapphire based SPOPOs as a source of continuously tunable femtosecond laser radiation in the near and mid-IR range.
Fig. 12. Pump to signal conversion efficiency and signal pulse duration (for 𝜆𝑠 = 1.55 μm) dependence on the number of cavity round-trips. 𝛿 = −16 × 10−4 , 𝐺0 = 0.
Acknowledgment This study was partially supported by the Lithuanian Agency for Science, Innovation and Technology (Grant No. 31V-35, project MEGAOPO).
Fig. 13. Pump to signal conversion efficiency (1, 2) and signal pulse duration (3, 4) dependence on signal wavelength. 𝑁 = 1000, optimal 𝛿 values. 𝐺0 ≠ 0 in (1, 3) and 𝐺0 = 0 in (2, 4).
References we observed evolution of various SPOPO characteristics until a certain number of cavity round-trips was reached. Pump to signal conversion efficiency 𝜂 and signal pulse duration 𝜏𝑠 dependencies on the number of cavity round-trips (for 𝜆𝑠 = 1.55 μm) and on signal wavelength are depicted in Figs. 12 and 13, respectively. Here, 𝛿 values were set to be optimal. The dependence on round-trip number shows that for 𝜆𝑠 = 1.55 μm both conversion efficiency and signal pulse duration approach stable state after roughly 100 cavity rounds-trips which corresponds to approximately 1.3 μs after the initial signal pulse generation. This marks the beginning point of stationary operation when parametric amplification is equal to net losses of the cavity. In Fig. 13, two pairs of curves corresponding to 𝐺0 = 0 and 𝐺0 ≠ 0 are depicted. 𝐺0 values were taken from Fig. 5. As we can see, pump to signal conversion efficiency decreases when the signal wavelength increases due to the decrease of the nonlinear coupling coefficient 𝜎1 ∝ 𝜔10 , curves (1, 2). The pump to signal conversion efficiency is greater when cavity GDD impact is included, (curves (1) and (2)). Either way, the theoretical conversion efficiency is somewhat greater than measured experimentally. This is mainly due to the fact that only output coupler losses (and not the net cavity losses) were taken into account during numerical simulations. Signal pulse duration when cavity GDD is not taken into account (curve (4)) is shorter than pump pulse duration, whereas when cavity GDD is accounted for, it
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Characteristics of optical parametric oscillator synchronously pumped by Yb:KGW laser and based on periodically poled potassium titanyl phosphate crystal Julius Vengelis a, *, Adomas Tumas a , Ieva Pipinyte˙ a , Migle˙ Kuliešaite˙ a , Viktorija Tamuliene˙ a , Vygandas Jarutis a , Rimantas Grigonis a,b , Valdas Sirutkaitis a a b
Laser Research Center, Vilnius University, Sauletekio ave. 10, Vilnius LT-10223, Lithuania Light Conversion Ltd., Keramiku st. 2, LT-10223 Vilnius, Lithuania
a r t i c l e
i n f o
Keywords: Nonlinear optics Optical parametric oscillator Synchronous pumping Periodically poled potassium titanyl phosphate crystal Yb:KGW laser
a b s t r a c t We present experimental data and numerical simulation results obtained during investigation of synchronously pumped optical parametric oscillator (SPOPO) pumped by femtosecond Yb:KGW laser (central wavelength at 1033 nm). The nonlinear medium for parametric generation was periodically poled potassium titanyl phosphate crystal (PPKTP). Maximum parametric light conversion efficiency from pump power to signal power was more than 37.5% at 𝜆𝑠 =1530 nm wavelength, whereas the achieved signal wave continuous tuning range was from 1470 nm to 1970 nm with signal pulse durations ranging from 91 fs to roughly 280 fs. We demonstrated wavelength tuning by changing cavity length and PPKTP crystal grating period and also discussed net cavity group delay dispersion (GDD) influence on SPOPO output radiation characteristics. The achieved high pump to signal conversion efficiency and easy wavelength tuning make this device a very promising alternative to Ti:sapphire based SPOPOs as a source of continuously tunable femtosecond laser radiation in the near and mid-IR range. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Optical parametric oscillators (OPO) have long been used as an efficient way to get tunable laser radiation in a broad spectral range. Near-IR and mid-IR radiation of such light sources can be used in various applications: as a source for further spectrum conversion [1,2], in nonlinear microscopy [3–5], spectroscopy [6,7], gas sensing [8], etc. Some applications require ultrafast tunable laser source working at high repetition rate. In order to fulfill these requirements, synchronously pumped optical parametric oscillators (SPOPO) are used. Synchronous pumping means that pump pulse repetition rate matches repetition rate of generated pulse so that the generated pulse meets with pump pulse in the nonlinear medium after each round trip [9]. Currently, quasi– phase-matched materials dominate in such near and mid-IR SPOPO systems due to the fact that in such crystals the highest possible nonlinear coefficient can be used. Due to high nonlinear coefficient 𝑑𝑒𝑓 𝑓 = 16 pm/V [10], periodically poled lithium niobate crystals (PPLN) or magnesium doped PPLN (MgO-PPLN) [9–16] remain the most popular nonlinear materials for infrared SPOPO. However, low
laser-induced damage threshold (LIDT) of these crystals limits the maximum usable power of the pump source, hence the SPOPO output power [9]. Good alternative could be periodically poled potassium titanyl phosphate crystal (PPKTP). Although it has smaller nonlinear coefficient 𝑑𝑒𝑓 𝑓 = 13.7 pm/V [17] compared to lithium niobate, it has higher LIDT so higher pump intensities can be used. Another advantage is no photorefractive effect and, hence, no need for crystal heating, which is important in case of PPLN [12]. First femtosecond SPOPO with PPKTP crystal was reported in 1998 [18]. The 22 % signal power conversion efficiency and 150 mW OPO generation threshold were observed in the 1000 nm–1235 nm spectral range using the Ti:sapphire laser (𝑓 = 76 MHz, 𝜆 = 758 nm, 𝜏 = 215 fs) as pump for this SPOPO. Up to now, demonstrated SPOPO experiments and commercial SPOPO systems based on PPKTP are pumped by Ti:sapphire lasers operating at 0.8 μm. Alternative for such pumping systems are ytterbium lasers operating around 1 μm. This pumping source can give some advantages because the absorption maximum of ytterbium ions is at 980 nm, therefore they are suitable
* Corresponding author.
E-mail address: [email protected] (J. Vengelis). https://doi.org/10.1016/j.optcom.2017.11.057 Received 9 October 2017; Received in revised form 15 November 2017; Accepted 20 November 2017 0030-4018/© 2017 Elsevier B.V. All rights reserved.
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for direct pumping by InGaAs diodes. More than that, the difference between pump and emitted radiation wavelengths is very small for ytterbium lasers compared to Ti:sapphire lasers – this allows creating more compact, efficient and less expensive laser systems. However, up to now, no studies of femtosecond SPOPO based on PPKTP and pumped by ultrafast ytterbium lasers were reported. In this paper we present, for the first time to the best of our knowledge, a detailed experimental investigation of femtosecond SPOPO based on PPKTP and pumped by Yb:KGW laser oscillator emitting 1033 nm radiation. We achieved more than 26 % conversion efficiency in the 1470 nm–1970 nm spectral range with maximum conversion efficiency of 37.5% at 𝜆𝑠 = 1530 nm wavelength, which is a promising result of such device for its further development and application. A numerical model is also presented and its results are compared with the experimental data. 2. Experiment results and discussion 2.1. Experimental setup Fig. 1. Principal experimental setup of femtosecond PPKTP SPOPO: M – highly reflective (at 1000 nm–1060 nm range) mirror, L1, L2 – lenses (𝑓 = 125 mm and 𝑓 = 25 mm respectively) for beam expansion, L3 – focusing lens (𝑓 = 100 mm) for SPOPO, 𝜆∕2 – 𝜆∕2 phase plate, BrPol – Brewster type polarizer, BD – beam dump, MN – curved mirror (𝑅 = −100 mm), BM – broadband mirror, OC – output coupler (𝑇 = 15%).
The experimental setup of SPOPO based on PPKTP crystal is shown in Fig. 1. The pump source for the SPOPO was a mode-locked Yb:KGW laser oscillator providing pulses at 76 MHz repetition with average power of 5.5 W at central wavelength of 𝜆 = 1033 nm. Measured (before SPOPO cavity) pump pulse duration was 155 fs. It is important to note that laser pulses reaching the SPOPO cavity were slightly chirped during propagation through some optical components before SPOPO cavity. The 𝜆∕2 phase plate and Brewster-type polarizer were used as attenuator to control pump power. Pump power for SPOPO under our focusing conditions (the diameter of the focused pump beam in the crystal was 38 μm at 1∕𝑒2 level) was limited to 1 W due to highly probable laser induced damage at greater pump powers. Since we had only one PPKTP crystal, we could not perform laser induced damage threshold (LIDT) measurements and specify and exact LIDT value for PPKTP crystal. However, we did measure LIDT for periodically poled lithium niobate (PPLN) crystal under the same experimental conditions: the measured LIDT corresponds to 3 W pump power. Since PPLN has higher 𝑑𝑒𝑓 𝑓 , we believe that LIDT for PPKTP should be somewhat higher than for PPLN. As there is a general recommendation that for any optical element maximum used laser intensity should be several (5–10) times less than LIDT of that element, so choosing 1 W maximum pump power for our SPOPO is a fairly accurate and safe limit. The SPOPO cavity was folded and consisted of two curved mirrors (MN) with 100 mm radius of curvature, three plane broadband mirrors (BM) and 15% transmittance (in 1500 nm–2000 nm spectral range) output coupler (OC). The resonator length was adjusted by moving the output coupler mirror which was mounted on high precision (1.25 μm step) translation stage. Nonlinear medium for parametric generation was 1 mm thick periodically poled KTP crystal (from ‘‘Eksma Optics’’) with eight gratings of periods ranging from 32 μm to 38.8 μm with 1 μm step (Fig. 2a). It was also AR-coated (𝑅 < 2%) for 1350 nm–1750 nm spectral range. PPKTP crystal was mounted on a translation stage for adjusting the grating period used for parametric generation. Wavelength tuning was achieved by changing the grating period and by adjustment of cavity length. Calculated theoretical quasi-phase matching curve for PPKTP crystal pumped with 1033 nm radiation is depicted in Fig. 2(b). Wavelength tuning by adjusting resonator length will be discussed in detail in the results section. In order to achieve the best stability, we constructed singly resonant optical parametric oscillator. Therefore, all cavity mirrors were coated with high reflection (HR) broadband coatings for 1500 nm–2000 nm spectral range which roughly matches the entire signal wave tuning range. In this way we ensured that only signal wave oscillates in the cavity. The idler wave in such case does not oscillate in the cavity since
(a)
(b)
Fig. 2. Principal view of PPKTP crystal geometry (a), calculated theoretical quasi-phase matching curve for PPKTP crystal pumped with 1033 nm wavelength (b). Sellmeier coefficients for calculation were taken from [19].
it is not reflected by cavity mirrors. Therefore, it leaves the cavity and is directed to the beam dump element (as depicted in Fig. 1). We can note that in order to achieve tunable femtosecond radiation in the idler spectral region, one would need to use different cavity mirrors which would reflect idler wavelengths (roughly 2000 nm–3500 nm). From Fig. 2(b) one can see that signal wave tuning range is slightly broader 775
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Fig. 3. Normalized PPKTP SPOPO output signal spectra across the tuning range. Spectral widths at FWHM are (from left): 30 nm, 53 nm, 62 nm, 39 nm, 157 nm and 52 nm.
than HR mirror bandwidth. We could not choose broader bandwidth cavity mirrors due to the fact that the manufacturer of highly reflective mirrors could not achieve broader bandwidth without avoiding large group delay dispersion (GDD) oscillations in the required spectral range. Using broadband mirrors with high GDD oscillations complicates signal wavelength tuning for SPOPO, therefore we decided to use HR mirror with bandwidth limits in the aforementioned spectral range. Pre-alignment of femtosecond SPOPO was complicated due to very small tolerance to cavity misalignment and synchronous pump condition – the period of signal wave round-trip in the cavity must match the period of pump wave round-trip in laser cavity which in reality means that laser and SPOPO cavity lengths must be practically equal with up to a few micrometer accuracy (which corresponds to the pump pulse temporal length). For precise cavity pre-alignment we used a semiconductor laser operating at 1550 nm (which matches one of the signal wavelengths) and after correct alignment we adjusted the resonator length to meet the synchronous pumping condition and achieved parametric oscillation. Final alignment was conducted by measuring the output power and observing the spatial mode of the signal beam. The highest output power and lowest order transverse mode (TEM00 ) corresponded to the best SPOPO cavity alignment. 2.2. Results and discussion In this section we present experimental data and discuss SPOPO operation features when using periodically poled crystal as nonlinear medium. We achieved signal wave tuning in a broad wavelength range: from 1470 nm to roughly 1970 nm. Examples of PPKTP SPOPO signal wave spectra are shown in Fig. 3. As seen from the results, spectral bandwidths (at FWHM) ranged from 30 nm to 157 nm. Such variations of signal wave spectral bandwidth are related to the fact that parametric amplification bandwidth increases as signal wavelength approaches point of degeneracy (𝜆𝑠 = 𝜆𝑖 ). Wavelength tuning was realized by changing the PPKTP crystal grating period (Fig. 2b) and by adjusting cavity length. It is important to note that cavity length adjustment allowed wavelength tuning in a very broad spectral range. Fig. 4 depicts cavity wavelength tuning characteristics at various fixed PPKTP crystal grating periods. We can see that minimum wavelength tuning ranges exceed 100 nm and can be more than 300 nm. Moreover, cavity length tuning limits are also different at different grating periods. These peculiar features can be explained considering the specifics of SPOPO operation. Tuning any optical parametric generator or oscillator by changing the periodically poled nonlinear crystal grating period
Fig. 4. Examples of PPKTP SPOPO wavelength tuning characteristics at various fixed periodically poled crystal grating periods as a function of relative resonator length change. Note that point of zero cavity length change is a relative notation with respect to maximum signal spectrum intensity which is different for each grating period.
means changing the signal and idler wavelengths for which the phase matching is perfect (𝛥𝑘 = 0). In case of synchronously pumped optical parametric oscillator (which is our case), there is another condition that has to be satisfied for this device to operate – synchronous pumping condition. Therefore, it is possible for SPOPO to operate at signal/idler wavelengths that have small phase mismatch, but perfectly satisfy synchronous pumping condition as long as parametric gain outweighs losses – this enables signal/idler wavelength tuning in SPOPO by adjusting cavity length. Adjusting resonator length means changing the 776
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(a) Fig. 5. PPKTP resonator net GDD dependence on wavelength.
signal/idler wavelength for which synchronous pumping condition is satisfied. In Fig. 4 the highest intensity points correspond to wavelengths that both have smallest phase mismatch and perfectly satisfy synchronous pumping condition. The signal wavelength tuning limits increase with increasing grating period can be explained in the following way. From Fig. 2(b) it follows that signal wavelengths increase with increasing grating period. Since parametric amplification bandwidth increases as signal wavelength approaches point of degeneracy, cavity length tuning limits for bigger PPKTP grating periods also become broader. From Fig. 4 one can also notice that wavelength tuning characteristics have somewhat different and dependencies. This is due to group delay dispersion (GDD) oscillations of cavity ultrabroadband dielectric coatings. Fig. 5 shows net cavity GDD dependence on wavelength determined by summing single cavity mirror reflection GDD according to the number of reflections from certain mirror and adding calculated PPKTP crystal GDD. We need to note that the depicted GDD estimation is not strictly accurate because signal beam angle of incidence at certain cavity ultrabroadband mirrors is slightly more than zero degrees, therefore the GDD for these mirrors is somewhat different from the value at 0 degrees of incidence – the angle at which ultrabroadband mirror GDD was measured and used in net GDD calculations. Since net cavity GDD determines the temporal delay of signal pulses when they propagate in SPOPO cavity, its oscillations mean that wavelength tuning by cavity length adjustment step (𝛥𝜆𝑠 per 𝛥𝐿) will be different for different wavelengths. As a result, at different PPKTP crystal grating periods wavelength tuning colormaps are different. The difference depends on the amplitude of GDD oscillations which in our case is relatively small at the region of signal wavelength tuning. The ideal case would be to have ultrabroadband mirrors with no oscillation, however, this is impossible due to technological limitations related to ultrabroadband dielectric coatings. PPKTP SPOPO output power (at maximum pump power) dependence at various signal wavelengths, when cavity length tuning is applied, and maximum pump to signal conversion efficiencies for different crystal grating periods are depicted in Fig. 6. It is important to point out that due to high nonlinearity of PPKTP crystal multiple cascaded nonlinear processes (such as second harmonic generation of pump and signal wavelengths, sum-frequency of pump and signal generation, etc.) also occur in the crystal. Although SPOPO cavity mirrors are highly reflective for only 1500 nm–2000 nm radiation, some light from these cascaded processes may still come through the output coupler. Therefore, in order to make sure that only signal wave power is measured we additionally used filters which allow only signal wavelength to pass. As seen from Fig. 6, maximum SPOPO output power exceeds 225 mW for any PPKTP crystal grating period and may be as high as 375 mW.
(b)
Fig. 6. PPKTP SPOPO output power dependence on wavelength (a) and maximum pump to signal conversion efficiency for different PPKTP grating periods (b).
This corresponds to maximum pump-signal conversion efficiency of 37.5%. Maximum output power/conversion efficiency dependence on wavelength can be explained considering signal/pump photon energy ratio, pump and signal wave group velocity mismatch in PPKTP crystal (Fig. 7a), crystal’s nonlinearity coefficient dependence on wavelength and net cavity losses dependence on wavelength (Fig. 7b). At shortest signal wavelengths (34 μm grating period) pump and signal energy ratio and GVM are smallest, but there are two sharp peaks (at 1440 nm and 1507 nm) in cavity losses in this spectral region which limit maximum output power/conversion efficiency. Therefore, maximum pump to signal conversion efficiency is achieved for longer wavelengths (35 μm grating period) after spectral region of sharp peaks in cavity losses. For even longer signal wavelengths, output power/conversion efficiency decreases due to lower signal/pump photon energy ratio, increasing pump-signal GVM, decreasing nonlinearity coefficient of PPKTP crystal and increasing cavity losses (for longest signal wavelengths). Within single PPKTP crystal grating output power dependence on wavelength is additionally related to the phase matching conditions – for a single grating period perfect phase matching can be achieved at certain signal/idler wavelength, so output power dependence has to have a peak at wavelength which experiences perfect phase matching. Another important energy characteristic of any SPOPO is parametric oscillation threshold. PPKTP SPOPO output power dependence on pump power/peak intensity for different signal wavelengths and the corresponding parametric oscillation thresholds (which are minimum pump power/intensity values for which output power is nonzero) are depicted in Fig. 8. Minimum estimated oscillation threshold was roughly 150 mW 777
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(a) (a)
(b)
(b)
Fig. 8. PPKTP SPOPO output power dependence on pump power for various signal wavelengths (a) and corresponding parametric oscillation thresholds at certain signal wavelengths (b).
Fig. 7. Pump and signal wave group velocity mismatch in PPKTP crystal (a) and PPKTP SPOPO net cavity losses dependence on wavelength (b).
(𝐼 = 1.12 GW∕cm2 ) at 𝜆 = 1734 nm which is well below the maximum pump power meaning that operation of our SPOPO is quite stable: any mechanical vibrations, small fluctuations of pump power, etc. should not stop SPOPO operation. Parametric oscillation threshold variations are related to parametric gain (hence, output power) dependence on pump peak intensity/power, therefore, its dependence on signal wavelength is related to the same factors as output power dependence on signal wavelength which were discussed in the paragraph above. Finally, we measured durations of signal pulses. Measurements were performed using commercial multi-shot autocorrelator GECO® . Experiment results (Fig. 9) showed that pulse durations ranged from 91 fs to 280 fs. As pump pulse duration was 155 fs, the signal/pump pulse duration ratio ranges from ≈ 0.6 to 1.8. In addition, we determined timebandwidth product of signal pulses and we can claim that output pulses were slightly chirped. This is not surprising, since, as mentioned in the experimental setup section, pump pulses were also slightly chirped. Generated signal pulse duration oscillations correlate with net cavity GDD oscillations (Fig. 5). However, the correlation in not strong. One reason for this is the fact that, as mentioned before, net cavity GDD estimation given in Fig. 5 is only approximate. Another, more important and complicated factor is related to signal pulse formation in SPOPO. We will briefly discuss it. For parametric oscillation and following amplification of generated pulses to occur, the round-trip parametric gain for the signal pulse needs to be greater than net round trip loss in the cavity. If this is
Fig. 9. PPKTP SPOPO output pulse durations (FWHM) and time-bandwidth product at various signal wavelengths.
achieved, signal pulses will be generated and amplified as long as the aforementioned condition is met. Parametric gain is a function of signal wavelength and, in general, other wavelength-dependent factors, such as group velocity mismatch, between pump and signal waves also influence parametric amplification process, therefore, the number of 778
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cavity round-trips that distinct signal wavelengths make during pulse formation process is different. This means that the amount of GDD that distinct signal wavelengths are affected by during pulse formation might be noticeably different. Despite some wavelength-dependent variation of output radiation characteristics, which, as discussed, are unavoidable due to complex physics of SPOPO operation and pulse formation, PPKTP SPOPO proved to be an efficient device with broad wavelength tuning range and low generation threshold. 3. Numerical simulation model and results In this section we briefly present the numerical simulation algorithm we used and compare numerical simulation results with experimental data. In the periodically poled KTP crystal, the three wave interaction of the signal, idler and pump waves with central wavelengths 𝜆10 , 𝜆20 and 𝜆30 , respectively, is described by the governing equations: ( ) 𝜕𝑆1 2𝜋 = 𝑖𝑘′1 𝑆1 + 𝜎1 𝑃̂1 exp −𝑖 𝑧 , (1a) 𝜕𝑧 𝛬 ( ) 𝜕𝑆2 2𝜋 = 𝑖𝑘′2 𝑆2 + 𝜎2 𝑃̂2 exp −𝑖 𝑧 , (1b) 𝜕𝑧 𝛬 ( ) 𝜕𝑆3 2𝜋 = 𝑖𝑘′3 𝑆3 − 𝜎3 𝑃̂3 exp 𝑖 𝑧 , (1c) 𝜕𝑧 𝛬 where 𝑆1,2,3 (𝛺) is the Fourier transform of the field 𝐸1,2,3 (𝑡). Here, 𝑡 is ̂1 , 𝑃 ̂2 and 𝑃 ̂3 are the Fourier time and 𝑧 is the propagation distance. 𝑃 transforms of the products 𝐸2∗ 𝐸3 , 𝐸1∗ 𝐸3 and 𝐸1 𝐸2 , respectively. 𝜎𝑗 = 𝜔𝑗0 ∕(𝜔30 𝑎30 𝐿𝑛 ) is the nonlinear coupling coefficient that is proportional to the central frequency 𝜔𝑗0 of the wave (𝑗 = 1, 2, 3). 𝐿𝑛 is the nonlinear interaction length, 𝑎30 is the pump amplitude. 𝑘′𝑗 = 𝑘𝑗 −𝛺∕𝑢10 , wavenumbers are calculated from 𝑘𝑗 = 𝑘(𝜆𝑗 ) = 2𝜋𝑛(𝜆𝑗 )∕𝜆𝑗 where 𝑛 is the refractive index given by the Sellmeier equation, 𝑛𝑧 in [19]. 𝜆𝑗 = 2𝜋𝑐∕(𝜔𝑗0 + 𝛺) is the wavelength and 𝑐 is speed of light. 𝑢10 = 1∕(𝑑𝑘∕𝑑𝜔)|𝜔10 is the signal group velocity. 𝛬 is the period of the PPKTP grating and is found from 𝛬 = 2𝜋∕(𝑘30 − 𝑘10 − 𝑘20 ), where 𝑘𝑗0 = 𝑘(𝜆𝑗0 ). The term 𝛺∕𝑢10 is subtracted from the wavenumber 𝑘𝑗 , so Eqs. (1) describe the propagation with respect to the signal wave. At 𝑧 = 𝐿 the fields are modified as follows: √ ( ) 𝑆1 → 𝑅 exp 𝑖𝛿𝐿𝛺∕𝑢10 + 𝑖𝐺0 𝛺2 ∕2 𝑆1 , (2a) 𝑆2 → 0,
(2b)
𝑆3 → 𝑆3 (𝑧 = 0),
(2c)
Fig. 10. Signal wave spectrum at different 𝛿 values (correspondingly, resonator length values). 𝜆10 = 1.55 μm, 𝑁 = 1000, 𝐺0 = 0.
Fig. 11. Signal wave spectrum at different 𝛬 values [μm]: 37.39 (left), 38.06 (center) and 38.42 (right). 𝑁 = 1000, 𝐺0 = 0. Parameter 𝛿 (corresponding to different cavity lengths) was varied for each case as well.
Examples of simulated signal wave spectra at different cavity lengths for 𝜆10 = 1.55 μm is depicted in Fig. 10. Parameter 𝛿 was varied and 𝐺0 was set to zero. Parameter value 𝛿 = −16 × 10−4 (which corresponds to relative cavity length change in experiment) is optimal (curve (2)) because the spectrum amplitude reaches the maximum at this value. The optimal value is nonzero due to the temporal walk-off between the signal and pump waves which is caused by group velocity mismatch between them (zero value corresponds to case when temporal walk-off between pump and signal waves is zero). From Fig. 10 we can also see that for 𝛿 values further away from perfect phase matching value, signal spectral width increases. This is also due to the temporal walk-off effect between pump and signal waves which causes greater amplification of wing components of signal pulse spectrum (at the expense of central spectral components) yielding broader spectrum, but with considerably smaller peak intensity. Changing PPKTP grating period 𝛬 during numerical simulation also yields signal wavelength tuning, as depicted in Fig. 11. Some optimal 𝛿 values exist (curves (2) in Fig. 11) for which both phase matching condition and synchronous pumping condition are best satisfied. The 𝛿 value corresponding to maximum intensity is different for distinct signal wavelengths. It is also clear that spectral widths increase with increasing wavelength which is in very good agreement with experimental data. Further on, we calculated pump to signal conversion efficiency 𝜂 and signal pulse duration 𝜏𝑠 at the output. During numerical simulation
where 𝐿 is the crystal length, 𝑅 is the reflection coefficient. By varying parameter 𝛿 we change the signal phase so that the variation of the cavity length is taken into account. 𝐺0 is the group delay dispersion impact of the cavity mirrors that depends on the central wavelength 𝜆10 , crystal GDD was accounted for in numerical simulations in wavenumber expression. The idler and pump waves leave the resonator after one trip. The signal wave propagates through the crystal 𝑁 times and at each round-trip some part of the signal leaves the resonator. The input fields at 𝑧 = 0 and 𝑁 = 1 are given by 𝐸10 = 𝑎0 𝜉1 (𝑡),
(3a)
𝐸20 = 𝑎0 𝜉2 (𝑡),
(3b)
(
𝐸30 = 𝑎30 exp −2 ln(2)
𝑡2 𝜏𝑝2
) .
(3c)
𝐸1,20 are the delta-correlated random fields of normal distribution with the zero mean and variance equal to |𝑎0 |2 . 𝜏𝑝 is the pump pulse duration at FWHM. We simulated Eqs.(1) by the use of the Fourier split-step method [20]. Parameters were the following: 𝜆30 = 1.033 μm, 𝜏𝑝 = 155 fs, 𝐿 = 30𝛥, 𝐿𝑛 = 𝐿∕2, 𝑎0 ∕𝑎30 = 10−6 , 𝑅 = 0.85. The chosen nonlinear interaction length corresponds to the pump intensity of 3.4 GW/cm2 . Crystal length is approximately 1 mm. 779
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is always greater than pump pulse duration. Moreover, signal pulse duration oscillations correlate with net cavity GDD oscillations (Fig. 5). Considering the abundance of factors influencing SPOPO output radiation characteristics, we can conclude that numerical simulation results are in reasonable agreement with experimental data. 4. Conclusions We have presented a detailed characterization of synchronously pumped optical parametric oscillator (SPOPO) with femtosecond modelocked Yb:KGW laser oscillator as pump source and periodically poled potassium titanyl phosphate crystal (PPKTP) as nonlinear medium. We also presented a numerical simulation model, its results and discussed their correlation with experimental data. The PPKTP SPOPO enabled wavelength tuning in 1470 nm –1970 nm spectral range with maximum output power reaching 375 mW and pump to signal conversion efficiency as high as 37.5%. Wavelength tuning for our SPOPO was easy and was achieved by using different period PPKTP crystal gratings and by adjusting cavity length. Moreover, parametric generation threshold was well below maximum pump power yielding stable operation of the device. Pump pulse durations ranged from 91 fs to roughly 280 fs and such oscillations were related to net cavity GDD oscillations and signal pulse formation processes during parametric oscillation. Numerical simulation results are in good qualitative agreement with experiment. We believe that the complexity of SPOPO operation and many factors influencing output radiation characteristics prevented us from getting better coincidence with experiment results. All things considered, the results of this study show great promise for future development of these devices and prove that SPOPOs pumped by ytterbium lasers are a very promising alternative to Ti:sapphire based SPOPOs as a source of continuously tunable femtosecond laser radiation in the near and mid-IR range.
Fig. 12. Pump to signal conversion efficiency and signal pulse duration (for 𝜆𝑠 = 1.55 μm) dependence on the number of cavity round-trips. 𝛿 = −16 × 10−4 , 𝐺0 = 0.
Acknowledgment This study was partially supported by the Lithuanian Agency for Science, Innovation and Technology (Grant No. 31V-35, project MEGAOPO).
Fig. 13. Pump to signal conversion efficiency (1, 2) and signal pulse duration (3, 4) dependence on signal wavelength. 𝑁 = 1000, optimal 𝛿 values. 𝐺0 ≠ 0 in (1, 3) and 𝐺0 = 0 in (2, 4).
References we observed evolution of various SPOPO characteristics until a certain number of cavity round-trips was reached. Pump to signal conversion efficiency 𝜂 and signal pulse duration 𝜏𝑠 dependencies on the number of cavity round-trips (for 𝜆𝑠 = 1.55 μm) and on signal wavelength are depicted in Figs. 12 and 13, respectively. Here, 𝛿 values were set to be optimal. The dependence on round-trip number shows that for 𝜆𝑠 = 1.55 μm both conversion efficiency and signal pulse duration approach stable state after roughly 100 cavity rounds-trips which corresponds to approximately 1.3 μs after the initial signal pulse generation. This marks the beginning point of stationary operation when parametric amplification is equal to net losses of the cavity. In Fig. 13, two pairs of curves corresponding to 𝐺0 = 0 and 𝐺0 ≠ 0 are depicted. 𝐺0 values were taken from Fig. 5. As we can see, pump to signal conversion efficiency decreases when the signal wavelength increases due to the decrease of the nonlinear coupling coefficient 𝜎1 ∝ 𝜔10 , curves (1, 2). The pump to signal conversion efficiency is greater when cavity GDD impact is included, (curves (1) and (2)). Either way, the theoretical conversion efficiency is somewhat greater than measured experimentally. This is mainly due to the fact that only output coupler losses (and not the net cavity losses) were taken into account during numerical simulations. Signal pulse duration when cavity GDD is not taken into account (curve (4)) is shorter than pump pulse duration, whereas when cavity GDD is accounted for, it
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