We present a simple and robust pulse shaping device based on coherent pulse stacking. The device is embedded in a polarisation maintaining step index fiber. An input pulse is sent through a fiber optical circulator. Up to four pulse replicas are reflected by fiber Bragg gratings and interfere at the output. Temperature control allows tuning of the relative pulse phases of the sub-pulses. Additionally fine tuning of the sub-pulse amplitudes is demonstrated. We experimentally generated 235 ps and 416 ps long flattop pulses with rising and falling edges shorter than 100 ps. In contrast to other pulse shaping techniques the presented setup is robust, alignment free, provides excellent beam quality and is also suitable for pulse durations up to several nanoseconds.
© 2009 OSA
1. Introduction and Motivation
During the last decade the technique of optical parametric amplification (OPA) has opened up a new path towards generating few-cycle laser pulses due to the enormous gain bandwidth which can be achieved in a non-collinear geometry (NOPA). The shortest pulses, generated with this technique so far, have been as short as 3.9 fs . Additionally, the technique of optical parametric chirped pulse amplification (OPCPA) allowed high energy pump lasers with pulse durations typically in the picosecond to nanosecond range. Today OPCPA laser systems delivering TW peak power few-cycle pulses have been developed [2,3] and will be a powerful tool for the investigation of laser-driven strong-field phenomena .
Besides these Terawatt laser systems there is a huge demand of compact gigawatt peak power laser systems e.g. for tabletop generation of coherent XUV light . A power scalable concept, combining the excellent properties of Yb doped fiber amplifiers and OPCPA, has recently been demonstrated , and is a promising candidate for compact high repetition rate and high average power gigawatt class laser systems.
Especially for high power laser systems, but in addition for all OPCPA based laser systems, the conversion efficiency of the parametric amplifier is a major aspect. Since the parametric gain of the OPCPA sensitively depends on the pump intensity a uniform intensity profile is desirable to achieve high conversion efficiency and to avoid gain narrowing effects. However, in most cases a pump pulse with a Gaussian or sech2 temporal profile is delivered by the pump laser. In this case the pump pulse has to be significantly longer to avoid spectral narrowing of the chirped signal pulses during amplification. In this case a huge fraction of the pump pulse is not involved in the nonlinear process and therefore lowering the overall conversion efficiency of the OPA.
In contrast, a pump pulse with rectangular temporal profile and durations comparable to that of the signal would provide a uniform gain for all spectral components, thereby avoiding spectral narrowing and increasing the pump to signal conversion efficiency. To investigate these effects in detail the coupled wave equations for the optical parametric amplifier are solved numerically for four different pump pulse shapes, shown in Fig. 1(a) . We assumed either a flattop pulse, a Gaussian shaped pulse or two temporally shaped pulses. The temporal shaped pulses consist of two or four Gaussian replicas and their generation will be studied in detail in section 2. Since we want to follow reasonable experimental setups we limit the number of Gaussian replicas to four, but in principle the number of pulse replicas is not limited. We assumed a pump pulse with the following parameters: pulse energy 5 mJ, pulse peak power 20 MW, central wavelength 515 nm. The signal pulses are assumed to have a Gaussian spectrum with a spectral bandwidth of 100 nm (FWHM) at 800 nm central wavelength. These pulses are stretched to a pulse duration of 250 ps (FWHM) by second order dispersion, in order to model a grating-type stretcher.
The OPA itself consists of a 10 mm long BBO crystal (beta barium borate, deff = 2.0 pm/V) which is operated at 10 GW/cm2 pump intensity. Group Velocity mismatch, diffraction and transversal separation has been neglected as we work with relatively long and loose focused pulses. We assumed perfect phase matching which is satisfied for a large spectral range around 800 nm for a noncollinear BBO driven by 515 nm pump pulses . Additionally, we assumed uniform beam profiles for simplicity with a diameter of d = 1.4 mm. The signal pulse energy has been chosen to be 2.3 µJ which results in 100% pump depletion in the peak of pump and signal pulse. Back conversion is avoided as it is known to distort the beam profile in real world OPAs . Figure 1(a) shows the assumed pump pulse profiles and Fig. 1(b) the resulting normalized spectra of the amplified signal. The results, such as amplified signal pulse energies and pump to signal conversion efficiency, are summarized in Table 1 . Additionally, the pulse duration and pulse peak power has been calculated by Fourier transform of the amplified spectra, assuming zero phase for all spectral components thus a perfect compressor.
It can be seen that the best results in terms of conversion efficiency and pulse peak power of the recompressed amplified signal pulse can be achieved with a flattop pump pulse. In contrast, a Gaussian pump pulse leads to reduced conversion and additionally narrows the spectral bandwidth. This results in about 40% lower peak power of the recompressed amplified signal pulse. Shaping the pump pulse out of several Gaussian replicas, as explained in section 2, helps to increase the conversion efficiency substantially in comparison to a Gaussian pendant. Obviously, the more uniform the pump pulse (more Gaussian replicas), the higher is the conversion efficiency and the gain bandwidth. Please note that for real beam profiles and especially for Gaussian beams the calculated conversion efficiencies are significantly reduced. However, the qualitative behaviour in the temporal and spectral domain remains the same. Of course spatial shaping of the beam profile is a useful technique to overcome this problem and a record high conversion efficiency of 29% has been reported for an OPA based on spatiotemporal shaped pulses .
2. Picosecond pulse shapers
Having shown the advantage of temporal shaped pump pulses in the previous section, we now focus on how to generate these pulses on a timescale relevant for OPCPA. The pulse duration of typical OPCPA systems is in the range of tens of picoseconds [2,3] up to several hundred picoseconds . These timescales are challenging, even for fast electro-optical modulators.
Today’s femtosecond pulse shapers are usually based on two gratings, placed in the focal plane of a confocal lens or mirror pair and a spatial light modulator located in the Fourier plane . Unfortunately, due to their small spectral bandwidth, picosecond pulses require high grove density gratings and high-quality optics with long focal lengths of several meters. This shaper with long optical path lengths will be extremely sensitive to alignment and laser pointing instabilities and therefore unsuitable for complex laser systems.
Acusto- optical pulse shapers  are limited to a repetition rate of ~30 kHz due to the slow speed of the acustic wave. Furthermore their spectral resolution (~0.5 nm) and temporal delay (~3 ps) is not sufficient for picosecond pulse shaping.
A more straight-forward method is the so called pulse stacking of picosecond pulses. These stackers split an incident laser pulse into several replicas, which are recombined after travelling different optical path lengths . The output pulse is formed by interference of the sub-pulses. Especially pulse stackers based on birefringent crystals provide a simple experimental setup and phase control of the superimposed pulse replicas via tuning of the crystal temperature [14,15]. Flattop pulses with 21.5 ps pulse duration and a rise time of 2 ps have been generated using ten birefringent YVO4 crystals and controlling their rotation angle and temperature. With regards to longer shaped pulses, which are required to scale the pulse energy of OPCPA systems further, this concept has several limitations. For example, for a 300 ps temporal delay the required crystal length is already as large as 400 mm and the required precision of temperature control is of the order of 0.01 K.
During the last decade a lot of effort has been made in pulse shaping by superstructured fiber Bragg gratings (SFGB). Indeed, rectangular pulses with a duration of 20 ps have been generated starting with 2.5 ps soliton pulses by a carefully designed and fabricated SFBG . Besides the complicated design and fabrication of the SFBG this approach is sensitive to input pulse parameters and limited to a time-scale which is given by the length of the SFBG.
On the other hand shaping of periodic pulses with cascaded uniform FBGs has been demonstrated by controlling the phase and amplitude of six spectral harmonics of the pulses using six uniform FBGs . However this approach is limited to a fixed repetition rate and a high duty cycle, which is not desirable for intense laser pulses.
Recently, a picosecond pulse stacker based on fiber couplers has been reported . However, phase control of the interfering sub-pulses was not given during the experiment and is not easily achievable, which leads to strongly modulated pulse shapes.
In this contribution we propose a very simple pulse shaper based on uniform fiber Bragg gratings (FGBs) without the complexity of a superstructure. The FBGs are arranged linearly in a fiber with a certain distance, as shown in Fig. 2 , giving a corresponding temporal delay. Every grating reflects a sub-pulse and these sub-pulses interfere in backwards direction. Splicing this fiber to a fiber optical circulator leads to a simple, compact, monolithic and alignment free pulse shaper. The fabrication of the FBG pulse shaper is described in section 3, while the experimental characterization of the pulse shaper is presented in section 4.
3. FBG shaper design and fabrication
As the pulses propagate through the fiber they are partly reflected by the FBGs (Fig. 2). In the following, for illustration purposes, only two FBGs and a Gaussian input pulse will be assumed. The temporal delay τ of two sub-pulses is given by
The intensity profile of the interfering pulses, which can be obtained at the shaper output, is determined by the amplitude ratio (Aa/Ab), the delay τ and the relative phase Δϕ. Figure 3 shows the calculated pulse profiles for different delays between both sub- pulses (τ~100 ps Aa = Ab = 1). As our fiber laser source delivers 100 ps long nearly Gaussian pulses, we assumed 100 ps (FHWM) long Gaussian pulses for the calculation. It can be seen that a flattop like pulse shape can be achieved for a phase difference of Δϕ = 0.6π.
The fabrication technique of the FBGs, which is based on a modified Talbot interferometer in combination with an excimer KrF laser at 248 nm, is described in detail in . The polarization maintaining (PM) fiber (Nufern PS-PM980), used for fabrication of the FBGs, was hydrogen loaded to increase its UV photosensitivity. The reflection and transmission spectra of the gratings were monitored during the FBG writing process. The distance of the FBGs was chosen to be 10 mm, which corresponds to 100 ps time delay between two reflected sub-pulses and the grating length was 5 mm. The amount of pulse energy which is reflected back to the output by each grating has been chosen to be 10% (5%) for the two (four) FBG elements.
In contrast to other publications , in our case multiple reflections at the FBGs cannot be neglected. Thus, the second, third and fourth grating need to have a larger reflectivity, to compensate for reflection at the previous gratings. To calculate the required reflectivity for each grating we assume an incident Intensity I0 and a target effective reflectivity R. Therefore, the required reflectivity of the first grating is R1 = R and, if losses are neglected, the transmitted intensity is given by IT1 = I0T1 = I0(1-R). The light which is reflected by the second grating is then given by IR2 = IT1R2 = I0(1-R)R2. As this light is again partially reflected at the first grating, the intensity at the shaper output, coming from the second grating is calculated to IR2eff = T1IR2 = I0(1-R)2R2. The required reflectivity of the second, third and fourth grating is now calculated to R2 = R/(1-R)2, R3 = R/[(1-R)2(1-R2)2] and R4 = R/[(1-R)2(1-R2)2(1-R3)2]. The calculated reflectivity for each grating is shown in Table 2 .
Please note that in principle the reflectivity of the FBGs can be further increased and up to 99% reflectivity have already been achieved with the same fiber and writing technique. However, as the first gratings have to have a lower reflectivity than the following ones, the effective reflectivity is limited to 0.38 (0.16) for a two (four) grating shaper, as shown in the last two rows of Table 2. Here a maximum grating reflectivity of 99% is assumed and the corresponding efficiency of the pulse shaper is therefore limited to 72% (64%).
As a result of multiple reflections at the gratings two FBGs form a Fabry-Perot cavity . Assuming weakly reflecting gratings, the free spectral range Δλ (FSR) is given by
For high grating reflectivities the effective grating length has to be considered, leading to a reduced effective distance of the FBGs and therefore larger free spectral range . For our experiments a FSR of 37 pm is calculated for 10 mm grating distance. As the spectral bandwidth of the pulses in our experiments is smaller than 20 pm and the finesse of the Fabry-Perot cavity is low, the expected influence on the spectrum and temporal shape of the generated pulses is very low. Additionally, interference only takes place at the overlap region of two pulses. In our case, caused by the design of the pulse stacker, this region is small, leading to reduced influence and visibility of the interference.
Of course for very high grating reflectivities the Fabry-Perot effects have to be considered, and multiple roundtrips of the pulses will lead to unwanted post pulses.
4. Pulse shaping - Experimental results
The fabricated FBG pulse stackers were glued to a solid aluminum block which is temperature controlled. To characterize the spectral behavior, the FBGs were spliced to a commercially available PM fiber optical circulator. A broadband seed, linearly polarized in the slow axis, is delivered by an Yb doped PM fiber ASE source. The spectrum of the reflected light is measured at the circulator output and shown in Fig. 4 . At a temperature of 80.0°C, the reflection peak is located at 1029.87 nm, matching with the available pulsed laser source. The spectral bandwidth of the FGBs is measured to be 100 pm and a Fabry Perot modulation with a period of 38 pm is visible, which confirms the calculation at section 3.
To test the pulse shaping capability of the fabricated FBG pulse stackers, we spliced a fiber based short pulse laser source delivering nearly Gaussian pulses with a duration of 100 ps at a central wavelength of 1029.87 nm to the fiber circulator input. The spectral bandwidth of the pulses is measured to be smaller than 20 pm which is the resolution limit of our spectrometer. We measure the temporal profile of the shaped pulses with a fast photodiode (tR = 18.5 ps) and a 50 GHz sampling oscilloscope. Figure 5(a) shows the temporal pulse profiles for different temperatures. Additionally the corresponding temporal profiles are shown in Figs. 5(b) to (f) for illustration purposes.
When the temperature of both gratings and the fiber in between is changed, mainly two things happen simultaneously. First the central wavelength shifts about 6 pm per Kelvin towards longer wavelengths and second the phase difference of the pulse replica reflected at the first and the second grating is changed due to linear expansion and refractive index change.
Since the central wavelength of both gratings is slightly different, due to different mechanical conditions during manufacturing and in the experiment, the relative amplitude of both pulse replicas can be changed additionally by temperature tuning. Obviously, the required flattop pulse shape is achieved at a temperature of 79.8 °C. The power throughput of the shaper was measured to be −13.5 dB (5%), where a loss of −5.5 dB is caused by the circulator and FC-APC connectors used for input and output. The reflectivity of the two FBGs in this configuration is slightly lower than measured during fabrication (−8.0 dB), indicating that both gratings are operated slightly off peak. As expected, since their spectral bandwidth is smaller than 20 pm, no influence on the spectrum of the input pulses was observed and the generated pulse shapes correspond well to the theory. To compensate altering of the pulses during amplification, which is a well known phenomenon for saturated laser amplifiers , the relative amplitudes of both pulse replicas can be fine tuned. Figure 6(a) shows three different pulse shapes for slightly different temperatures. The black curve shows slightly lowered leading edge of the shaped pulse, which is preferred during amplification in saturated laser media .
In another configuration a group of four FBGs is spliced to the circulator and glued to the aluminum block. In this case three amplitudes and 3 phase differences have to be varied, so additional control of the temperatures of the two additional FBGs and the fiber pieces between second and third and third and fourth FBG is required, giving need for a more complex experimental setup. Nevertheless, we record the pulse shape at the shaper output, while varying the temperature of the whole group of four FBGs. Luckily, we observed a nearly flattop pulse shape, consisting of all four pulse replica, with correct relative amplitudes and phases at a temperature of 42.9 °C (Fig. 6(b)). In this case the throughput was measured to be 3.8%.
It’s worth mentioning that the pulse shapers provided very stable operation for hours. This is achieved by good thermal and mechanical contact to our temperature controlled aluminum block. Additionally the use of polarization maintaining fiber avoids fluctuations of the polarization state.
5. Summary and Outlook
In this contribution we have motivated and demonstrated the generation of flattop like picosecond pulse for OPCPA pumping. The pulses were shaped temporally in a pulse stacker based on FBGs. These gratings have been written into a standard polarization maintaining step index fiber via UV laser and Talbot interferometer. Controlling the temperature of the shaping element enabled to control the relative phase of two pulse replica. Additionally fine tuning of the relative amplitudes has been demonstrated. Pulses with a duration of 235 ps and rising and falling edges shorter than 100 ps have been achieved. In contrast to other pulse shaping techniques our setup is robust, alignment free and can be spliced easily to fiber based lasers and amplifiers.
Additionally, we demonstrated a pulse stacker based on four FBGs resulting in a 416 ps long flattop pulse. To fully control the relative amplitudes and phases here, at least three temperatures have to be controlled in future. For simplicity we propose another approach, using two shapers based on two FBGs each, which is shown in Fig. 7 . Here the pulses pass the first shaper to generate a ~200 ps pulse as shown in Fig. 6(a). If a four port fiber circulator is used, afterwards the pulses pass a second pair of FBGs with doubled separation resulting in ~200 ps temporal delay and ~400 ps pulse duration. With this approach only two temperatures of the two grating pairs have to be controlled similar to a two crystal birefringent pulse shaper . By increasing the FBG reflectivity such a device will have low transmission losses which are mainly determined by the circulator. Of course this pulse shaper is not capable of generating arbitrary pulse shapes but sufficient to generate the flattop pulses, which are required as pump pulses for OPCPA. We are convinced that such a simple and robust device will find many applications. The implementation of the pulse stackers in a fiber laser driven OPCPA system is currently in progress.
This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) with project 03ZIK455 ’onCOOPtics’. S.H. acknowledges the financial support of the Carl Zeiss Stiftung, Germany.
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