1. Introduction

The few-cycle pulses have found their place in strong field physics and are of paramount importance for applications such as time resolved optical spectroscopy and study of light-matter interactions in atomic dynamic events [1]. Beside the few-cycle laser pulses centered around 800 nm using Ti:sapphire systems, recently sources of few-cycle optical pulses with longer wavelengths have been recognized as a versatile tool for a variety of applications such as spectroscopy in the molecular fingerprint [2, 3], strong field photoionization [4–6], control of electron localization during dissociation [7] and driving the high-order harmonic radiation to higher photon energy [8–10].

Due to the absence of suitable laser media, broadband long wavelength sources rely on OPA methods to down-convert the frequency of short wavelengths Ti:Sapphire lasers. In an OPA system, group velocity mismatch (GVM) directly affects the phase matching bandwidth. Using thicker non-linear crystals will accumulate the introduced GVM into the system, resulting in reduction of the bandwidth. On the other hand the effective interaction length (l_{e f f}) for the parametric interactions is dependant on the pulse splitting time (τ) for both signal and the idler, and it has a reverse relationship with GVM, (l_{e f f} = τ / δ_jp, j=i,s), δ_jp is the GVM between the interacting waves and j=i,s represents idler and signal waves [11].

To remove the GVM and broaden the bandwidth, application of OPA systems operating at the degeneracy has been proposed [12–14]. Brida et al. in a single stage OPA operating at degeneracy and centered at 1600 nm, with 80 μJ pump pulse energy have realized an ultra-broad bandwidth which covers 1200–2100 nm with 2 μJ output pulse energy [12].

Ishii et al. have achieved sub-two-cycle pulses centered at 1600 nm, exploiting the fact that at 1580 nm wavelength, even group delay dispersion (GDD) of the BiB₃O₆ crystals becomes zero and the phase-mismatch which is originated from signal and idler’s GDDs vanishes and becomes third-order-dispersion-limited [15]. Limpert et al. have reported a broadband collinear OPA operating at degeneracy and centered at 800 nm with 400 nm full width at half maximum (FWHM) bandwidth which is capable of providing 5 μJ output energy using a 500 μJ pump field [16]. Subsequently using a two stage collinear OPA, operating at degeneracy and pumped by pulses with 100 μJ energy and centered at 800 nm, Siddiqui et al. managed to achieve 15 μJ output pulse energy with 280 nm gain bandwidth for their system [17].

However, experiments in photochemistry and photobiology often additionally require tunability of the central wavelength [18–21] therefore OPA systems which are capable of providing enough tunability for these applications are favorable.

Moreover in the interest of strong field physics, Takahashi et al. proposed a two-colored non-degenerate synthesis scheme by combining a 1300 nm 40 fs field with an 800 nm, 30 fs driver field which successfully obtained the highest reported pulse power (of the order of 2.6 GW) for 500 as pulses [22]. It has been predicted that isolated attosecond pulse durations can be further reduced to 100 as region by optimizing 15 fs 800–1300 nm two color synthesis [23, 24]. These pioneering experimental results and theoretical predictions stimulate the quest for few-cycle IR source at non-degenerate wavelengths. On that account in order to achieve broad bandwidths and tunability, application of non-collinear OPA (NOPA) schemes were suggested [25–27], introducing the non-collinear angle to the parametric interaction will help overcoming GVM but the idler of NOPA scheme will suffer from angular dispersion. Since the passively CEP stable idler pulses play a pivotal role in the applications of the few-cycle pulse systems, using non-collinear schemes requires additional considerations to compensate this angular dispersion in advance accordingly [28, 29].

Using non-collinear scheme and employing a BBO crystal while benefitting from pulse-front-matching in their design, Shirakawa et al. have achieved 5 μJ output pulses covering 500-800 nm wavelengths [31], In a later research presented by Isaienko et al. using a pump laser centered at 800 nm with 135 μJ pulse energy and utilizing a KTP crystal while benefitting from pulse-front-matching, 4.5 μJ output pulse energy for a bandwidth covering 1100–1300 nm have been reported [30]. Also Manzoni et al. using 200 μJ pump pulse energy, have reported NIR signal pulses tunable from 900–1600 nm wavelengths with 1 μJ pulse energy and a bandwidth that covers 200 nm in a two-color scheme [32].

Schmidt et al. have obtained 10 μJ output pulse energy on a 320 nm FWHM bandwidth using 150 μJ pump pulses in a type II phase matching NOPA centered at 1300 nm [33]. Higher efficiencies using non-collinear design have been obtained by Harth et al. in a two-color pump scheme which with 7 μJ pump pulse energy, delivers an ultra-broadband bandwidth covering 430–1300 nm and 1 μJ signal energy [34].

In contrast collinear schemes provides passively CEP stable idler pulses which do not suffer from angular dispersion but with the drawback of narrower bandwidth for each amplification stage at non-degenerate wavelengths [35]. To solve the trade-off problem between power and bandwidth, various GVM compensation methods have been suggested [36]. Using temperature regulation on periodically poled LiNbO3 has been suggested by Zhong et al. [37] which theoretically can remove GVM to near perfect levels. However this method is not applicable for systems using bulk non-linear crystals such as BBO and it requires thermal considerations which are challenging on their own. Furthermore frequency domain OPA has been suggested that overcomes the limitations of the conventional OPA systems in general [38].

Applying broadband pump pulses in an OPA system will fundamentally increase the bandwidth of the amplified signal even at the presence of the GVM. Shorter pump pulses are correspondent to smaller splitting time hence shorter effective length [11], this decrease in effective length accompanied by the temporal walk-off caused by GVM (v_p < v_s < v_i) will lower the gain and limit the bandwidth of such OPA systems drastically.

In order to increase the gain and bandwidth for pump fields with shorter than 50 fs pulse durations, control over the splitting time and optimization of the temporal overlap becomes of paramount importance. Using a medium with a net positive group delay (v_p > v_s > v_i) can well compensate the temporal walk-off.

In this article we propose a scheme through which, we firstly experimentally prove the positive impact of our designed group delay compensation plate on DOPA as have been predicted in the previous simulations. Furthermore we introduce a practical approach to obtain few-cycle pulses using this concept. The proposed scheme demonstrates the applicability of the GD compensation method in order to achieve optimized collinear OPA systems operating in non-degenerate wavelengths that are capable of providing few cycle pulses in a simple and straightforward structure.

This goal has been achieved using a dual-crystal OPA structure which by means of a simple group delay compensation plate (BaF₂) will benefit from better temporal overlap. This scheme also exploits the short pulse duration of the pump laser and can preserve the bandwidth of the OPA whilst it provides high conversion efficiency (30%). Figure. 1 illustrates this principle.

 

Fig. 1 Key principle of the group delay compensation and the effect of the group delay compensation plate on the three wave system

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Applying this scheme to an unchirped pump field we managed to reach 20 fs temporal limits (theoretically this value can be compressed to 12 fs using a prism pair, which corresponds to sub-four-cycles for 1300 nm wavelength) on a bandwidth which covers 1150–1500 nm (210 nm FWHM). Using GD compensation we have broadened the FWHM bandwidth around 75 nm (almost four times the estimated value by the simulation results). Our scheme also has the potential to operate as a multiple stage OPA system to further improve the output power whilst preserving the bandwidth.

2. Experimental setup

Figure. 2 illustrates the schematic of the experimental setup for performing group delay compensation. The pump source in our setup is a commercially available 800 nm Ti:Sapphire laser (Legend Elite Duo - COHERENT.inc) with 1 KHz repetition rate and 30 fs pulse duration.

 

Fig. 2 Schematic of the experimental setup. M (mirror), DM (dichromatic mirror), L (lens), BS (beam splitter), VDF (variable density filter), WP (waveplate), SP (sapphire plate), PL (polarizer), LPF (long pass filter), GDC (group delay compensation plate).

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It should be noted that since in our scheme we are using short pump pulses and benefiting from shorter durations and their characteristics, applying chirp to the pump will lower the peak intensity and also causes duration mismatch between signal and pump pulses which results in a lower gain therefore, we had used the plain unchirped pump field as our system’s initial pump which acts as the pump source for both OPA stages and the white light generation system.

As the first step we reduce the initial beam diameter from 10 mm to 5 mm using a convex/concave lens pair (L1–L2). 10% of the pump energy is picked up by a beam splitter (BS1)to be used for the seed generation. After the variable density filter (VDF), 4 mW of this power will be focused into a sapphire plate (10 × 10 ×1 mm) using a convex lens (L3, f=150 mm) in order to generate white light. The continuum’s spectra generated by this method expands from visible (420nm) to IR region (1500 nm) with the energy in order of pJ per nm of bandwidth [39].

The 90% transmitted portion from BS1 will enter the second beam splitter (BS2). Another 10% of the beam is picked to act as the first stage pump (140 mW), which will be sent to a delay-line (M2–M3) that is used to achieve temporal overlap for the first amplification stage. Pump and seed beams will be combined in a dichroic mirror (DM1) and using L7 and L4 convex lenses, they will enter the first BBO (BBO1) in a slightly focused manner. We have introduced a small external non-collinear angle (<1°) to separate the signal and idler spatially, after the first stage.

It is noteworthy that the position of BBO crystal’s surface compared to the focal point is chosen based on the suitable trade off between conversion efficiency and the bandwidth while avoiding the super continuum generation, and through diligent measurements, no continuum generation had been observed after BBO1. After the first amplification stage the amplified signal will be re-collimated using another lens (L8) and the residual of the first pump centered at 800 nm will be removed using a long pass filter (LPF1).

The other 90% of the laser pump transmitted through BS2 will be used as the second stage pump. Its beam diameter will be reduced to 2.5 mm for the second stage using another lens pair (L5–L6). At this stage the control over second stage pump power will create the possibility to examine system’s power scalability, therefore using a waveplate and a polarizer (WP2–PL) we can adjust the second stage pump power.

The second pump and the amplified signal from the first stage will be combined in the second dichroic mirror (DM2). The temporal overlap in the first BBO crystal of the DOPA structure (BBO2) is achieved through another mechanical delay-line (M6–M7). The three beams combination will enter the group delay compensation plate which is fixed on a rotatable stage and will impose the improved temporal overlap before the last BBO (BBO3). The remainder of the second pump after BBO3 will be removed by another long pass filter (LPF2) and the beam will be sent to a spectrometer and an auto-correlation system for its spectral and temporal characteristics to be investigated.

3. Experimental results

In the following section we will present the obtained results from our group delay compensated DOPA for two different sets of experiments. In the first experiment we will set the experimental conditions identical to those of the previously published simulations. These simulations have predicted 20 nm improvement on the bandwidth of the DOPA using our designed group delay compensation plate [40], after collecting the obtained data we can evaluate the positive effect of the GD plate. This can be considered as a proof of principle for the proposed scheme.

In the second experiment we recalibrate the system in order to achieve the highest possible output power and widest bandwidth. This will provide a practical method which just benefitting from the concept of group delay compensated DOPA is capable of achieving few cycle pulses.

3.1. Confirmation of the positive effect of the GD compensation plate

Using the scheme described in section 2 we conduct our first experiment. In a type-I (10 × 10 × 2 mm, cut at θ=20°) BBO crystal we managed to achieve 15 mW total amplification (signal + idler) for the first stage, which represents a total 10% conversion efficiency centered at 1300 nm and 2100 nm respectively. The yellow trend (dashed line) in Fig. 4(a) shows the spectrum of the first amplification stage. After removing the first pump and idler, we re-collimated and guided the beam to be combined with the second pump which can have variable powers from 150 mW to 400 mW. Since in our simulations we had set the pump power for the second stage to 150 mW we will keep the same value in the experiment too. Second stage of the DOPA includes two thin BBO crystals (10 × 10 × 1 mm, cut at θ=20°) which had been placed as closely as possible to each other.

We made sure that the coinciding beams would enter both crystals at the same angle in order to evaluate the effect of the GD plate in the system as an isolated factor. In this fashion, all the factors that can affect the experiment will be kept fixed except for the one, which is the presence or the absence of the group delay compensation plate in the experiment.

Our designed group delay compensation plate is made of BaF₂ crystal with 1 mm total thickness. Since the compensation plate affects all three interacting waves, our scheme is capable of compensating the delay for the three beam interaction simultaneously. The plate has been added to the system using a rotatable stage that through which we can change the effective thickness of the plate coinciding with the three beam combination, it should be noted that upon entering the GD plate the phase linkage between the three interacting waves will be broken and we need to consider this effect in order to guarantee the energy flow in the desired direction. Since in our scheme, idler beam will also be present in the last BBO crystal and amplification step, a proper phase relationship should be insured by the GD plate to prevent the up-conversion from happening. This up-conversion can cause a decrease in the performance of the scheme [41]. The phase of the pulses will rapidly modulates in the BaF2 plate and right before entering the last BBO, it is dependent on the GD plate’s thickness. In our experiment we have achieved the best phase relationship, which results in the widest bandwidth and highest output power, when the plate has a 25 degrees angle with the beams. This incidence angle is correspondent to an effective thickness of 1.1 mm for the GD plate. This effective thickness also adjusts the group delays accordingly.

In the simulation for the group delay compensated DOPA with the mentioned pump power and identical BBO angles we have estimated 20 nm bandwidth improvement for the amplified signal pulses bandwidth centered at 1300 nm which is shown in Fig. 3(a). As we can see in Fig. 3(b) for the experimental results we have 107 nm bandwidth for a DOPA without the compensation plate, and adding the plate with the correct angle (25°) widens this bandwidth to 126 nm keeping the conversion efficiency constant (35 mW output power), which is a perfect match with the simulated results (19 nm improvement has been observed), depicted in Fig. 3(b) as the solid red line.

 

Fig. 3 (a) Simulated bandwidth for DOPA. (b) Experimentally observed bandwidth for DOPA. Blue dashed lines represent bandwidth without group delay compensation and solid red lines denote results for group delay compensated scheme.

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3.2. Optimized group delay compensated DOPA scheme

After confirming the positive effect of the GD plate in a dual-crystal scheme in the last section, in this section we propose an optimized GD compensated DOPA scheme which can provide bandwidths as wide as 210 nm, and we will make a full comparison between a SOPA and our scheme in order to have a helpful reference to evaluate the benefits of our new design over the conventional OPA systems.

The key difference in the second experiment is a change in the dual-crystal scheme’s BBO angles. We have changed the two identical angles to two slightly different angles which will cover more phase matching bandwidth, we also have increased the pump power to 300 mW in order to achieve an intense output signal.

We have managed to obtain total 90 mW output beam (signal+idler) corresponding to more than 30% conversion efficiency for all the cases from now on, since the conversion efficiency is intended to be constant and above 30%. Using the two different BBO angles we have managed to achieve 133 nm FWHM bandwidth for the DOPA scheme without the group delay compensation plate, the spectrum of this case is depicted in Fig. 4(a) as the dot-and-dash blue line.

 

Fig. 4 (a) Bandwidth comparison between SOPA and DOPA with and without group delay compensation. (b) Variation of total output power with the beams incidence angle on the GD plate.

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Now by keeping all the experimental conditions constant we have added the GD plate to the dual-crystal scheme and using the rotatable stage after achieving correct angle (correspondent to the BaF2 thickness of 1.1 mm), we have observed a sudden widening effect on the bandwidth. Since the addition of the GD plate to the system is the only change made in the system, once again the positive effect of a better simultaneous temporal overlap for all three interacting waves in the last BBO crystal is confirmed to be caused by the GD plate. The spectrum of the GD compensated DOPA with two different BBO angles is presented in Fig. 4(a) as the thick solid red line. The improvement applied to the bandwidth is 75 nm which makes the total FWHM bandwidth 210 nm that is correspondent to 12 fs transform limited pulses. The variation of the total output power with different incidence angle on the GD plate is depicted in Fig. 4(b).

In the optimized condition where the GD plate would enforce sufficient delay to the beams before they enter the last BBO we will observe an obvious bandwidth broadening, through our experiments we have found that the limits of this broadening is dependent on two major factors: the pump power and the angle that the beams coincide with the two thinner BBO crystals.

Using two slightly different BBO angles can actually amplify two different, but very close to each other, center wavelengths, which broadens the bandwidth boundaries, exploiting the short pulse durations of the pump laser. The best angles have been obtained experimentally before adding the GD plate to the system by observing the widest bandwidth on the spectrometer and highest output power.

At the same time increasing the pump power whilst avoiding the super-fluorescence generation threshold, can lead to a more efficient amplification [42]. The improved bandwidth can expand as large as 210 nm with 90 mW output power, the slight decrease in the power is caused by the fact that none of the surfaces (BBO crystals and the compensation plate) have any anti-reflection coatings and loss of power is expected to these degrees.

It should be noted that even though the two slightly different BBO angles will slightly broaden the bandwidth in general, but this improvement becomes appreciable only and only when group delay compensation plate is used and higher gains are achieved, using this method we have managed to increase the bandwidth improvement to 75 nm which is almost 4 times more than the identical BBO angles’ case and simulations. Without the plate this slight improvement will be gained at the cost of lower conversion efficiency which in general is considered a disadvantage.

Changing the dual-crystal formation to a single crystal in the last stage will change our construct to a conventional SOPA. Obtaining amplification results of a SOPA will be a good reference to evaluate the viability of our scheme for substituting conventional systems. We have replaced the two thin BBO crystals with a thicker BBO (10 × 10 × 2 mm, cut at θ=20°) which has a similar total thickness of 2 mm with the dual-crystal scheme. We conducted the experiment keeping the pump power constant at 300 mW and have observed that for the optimal BBO angle and 90 mW amplification output power we will have a FWHM bandwidth of 138 nm which is quite similar to the DOPA without the GD plate.

The spectrum of the SOPA is depicted in Fig. 4(a) as the thin green solid line. As we can see boundaries of the group delay compensated scheme goes 30 nm beyond the first stage OPA. It means 76 nm improvement on the bandwidth of the amplified signal compared to the scheme without the compensation plate and also this bandwidth is 72 nm larger than the SOPA scheme. This shows that through group delay compensation and applying diligent optimizations, DOPA can achieve broader bandwidths than SOPA and this can be the basis for the design of multi-crystals OPA systems. It is important to notice that, compared to DOPA with identical BBO angles from the last section, two different BBO angles DOPA with higher pump power and without the GD plate, provides a wider bandwidth as expected. However this bandwidth is almost identical to the SOPA scheme. Without the GD plate the effect of temporal walk-off between the three interacting waves accompanied by the inefficient pump presence on the second BBO (caused by reflection from the surfaces) will impact the obtainable bandwidth. It is through diligent GD compensation that the signal can be kept under the most intense part of the pump beam to achieve an efficient amplification which results in a broad bandwidth.

Using a convex lens (f=500 mm) the amplified signal of our GD compensated scheme has been slightly focused into a 430×430 pixels CCD camera where the beam quality has been examined before the focal point and the high spatial quality of the amplified signal is provided in inset of Fig. 5(a), also using a home built auto-correlator we have obtained the temporal profile of the signal beam and compared it with the transform limited (TL) profile, the results are shown in Fig. 5(a). The 210 nm FWHM bandwidth of the amplified signal is theoretically correspondent to 12 fs transform limited pulses which is sub-four-cycle for 1300 nm center wavelength. The deviation of the measured value by the auto-correlation system (20 fs) from the TL duration, is due to the temporal stretch caused by dispersive optical components and the non-linear crystals used in the system and needs to be re-compressed. The measured pulse duration is still well-matched with the expectations and using a pair of prisms, pulse can be compressed to near TL value.

 

Fig. 5 (a) Temporal profile: transform limited pulse (red line), measured pulse duration by intensity auto-correlation (pink filled curve), Gaussian fitted trace (Blue line). Inset: focused profile of the signal, pink curves indicate the intensity profiles at the center of the spot. (b) Energy scalability of the scheme, amplified signal’s power as the function of pump power.

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Increasing the pump power in our scheme will further increase the output power of the system thus making this scheme power scalable. Characterization of the gain of our OPA scheme as a function of pump power is provided in Fig. 5(b). Pump power has been increased from 150 mW to 420 mW and total output power (signal+idler) ranging from 38 mW to 135 mW has been obtained, conversion efficiency will continuously stay above 25% for all pump power values in the measurement range. As we previously mentioned one of the key advantages of the non-degenerate systems is their tunability over a range of wavelengths. Our design also considers the tunability factor and we have checked the operable wavelengths with at least 25% conversion efficiencies, as the result we can consider our design to be well functional for wavelengths starting from 1150 nm to 1400 nm.

At the same time we have investigated the effect of the group delay compensation plate on these operable wavelengths and we observed that for the mentioned range the principle is still applicable and we can obtain an improved bandwidth for the amplified signal.

Theoretically this improvement will be larger for 1200 nm components and decreases toward 1400 nm wavelength due to the fact that group delay is bigger for shorter wavelengths and group delay compensation will have a bigger impact for OPAs operating at these wavelengths. Since the thickness and the material of the plate has been chosen in order to optimally compensate 1300 nm components group delay, this wavelength shows the highest improvement in our experiment. Using the plate with a different angle will help to increase the improvement for longer wavelengths, we managed to achieve 55 nm improvement for 1200 nm (an increase from 100 nm FWHM to 155 nm) and 49 nm for 1400 nm components (an increase from 140 nm FWHM to 189 nm) and the results for group delay compensated spectra are shown in Fig. 6.

 

Fig. 6 Group delay compensated spectra for different wavelengths.

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4. Conclusion

In conclusion, applying group delay compensation in a dual-crystal OPA scheme, we have presented a broadband 20 fs intense IR driver source. The fact that our system provides a broad bandwidth (210 nm) which is broader than a SOPA, suggests the possibility of adding new stages and achieving higher powers for our collinear scheme compared to the previously reported systems. The improvements made on the bandwidth implies that shorter pulse durations for an OPA system can be achieved using simple group delay compensation technique.

Theoretically by applying optimized conditions such as increasing the beam diameter from 1.5 mm at the second stage to 20 mm, and increasing the BBO aperture size to the commercially available (20 × 20 × 1 mm), our system is capable of providing output power of order of 10 W for the 1300 nm center wavelength.

The designated operable wavelengths of the system provides adequate tunability as a feature for different applications. The proposed scheme can be used as the driver field for high harmonic generation directly or can be a strong pump field for generating few-cycle and attosecond pulses used in a hollow core fiber system. As many trials previously had shown, using OPA systems in combination with a gas filled hollow fiber, using a pump field of 1200 – 1500 nm wavelength with initially broader bandwidth and shorter pulse durations is a promising method to achieve single-cycle pulse durations, our group delay compensated system is a perfect candidate for such applications and provides a broadband IR field and is able to provide a valuable source for attosecond pulse generation.