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An optical parametric amplifier that delivers nearly transform limited pulses is presented. The center wavelength of these pulses can be tuned between 993 nm and 1070 nm and, at the same time, the pulse duration is varied between 206 fs and 650 fs. At the shortest pulse duration the pulse energy was increased up to 7.2 µJ at 50 kHz repetition rate. Variation of the wavelength is achieved by applying a tunable cw seed while the pulse duration can be varied via altering the pump pulse duration. This scheme offers superior flexibility and scaling possibilities.
©2010 Optical Society of America
1. Introduction
Laser pulses with femtosecond pulse duration have revolutionized natural sciences in many ways. For example, they enabled the investigation of processes in biology and chemistry on ultrashort timescales and have led to better understanding in these fields [1]. Recently, biological and medical imaging via Coherent Anti-Stokes Raman Scattering (CARS) has attracted a lot of interest due to the possibility of obtaining images without the need for any labelling [2,3]. One of the challenges for CARS microscopy is to obtain tunable sources for the pump and stokes pulses, respectively. A main requirement is to yield transform limited picosecond pulses at high repetition rates that can be tuned in their central frequency.
Several concepts based on either fiber lasers [4] or optical parametric amplifiers (OPA) and oscillators (OPO) [5] have been presented to demonstrate CARS, but still have not shown the full tunability of pulse duration and wavelength.
Another application of ultrashort pulses has been enabled by the amplification of femtosecond pulses to millijoule pulse energy and beyond, namely fundamental studies of light-matter interaction. Such pulses also made possible the generation of coherent XUV radiation via high harmonic generation (HHG) [6,7]. When focusing femtosecond pulses to intensities of the order of 1014 W/cm2 the fundamental wavelength is converted to odd multiples of the laser frequency. This coherent radiation has found a great variety of applications such as lensless imaging [8], the study of molecular motion [9] or the generation of attosecond pulses [10]. One main limitation of these processes is the low conversion efficiency that either requires long integration times or high repetition rate laser systems that are under investigation, but still require improvements [11–13]. Besides this, there is still ongoing discussion how conversion efficiency and cutoff scale with the wavelength of the driver [14,15]. Therefore, ultrashort pulses tunable in their central wavelength are of interest to probe such dependencies.
Here we present a versatile source tunable in center wavelength and pulse duration realized via a cw seeded optical parametric amplifier. A similar scheme was presented before [16,17], but has not been operated with a tunable cw seed and tunable pulse durations. The tunable cw seed is applied to a first OPA that is pumped by the frequency doubled output of a state-of-the-art fiber chirped pulse amplification system. The idler of the first stage which is cw background free is amplified in a second OPA to µJ pulse energies by the remainder of the first stage pump.
2. Nearly transform limited pulses via cw seeding of an optical parametric amplifier
Optical parametric amplification provides a powerful tool for the amplification of ultrashort pulses. Conventionally, a broadband seed is generated via continuum generation in optical fibers [18,19] or in sapphire plates [20] that eventually has to be compressed after amplification. Typically, the generation of a stable broadband seed is challenging and subsequent recompression needs state-of-the-art dispersion management to obtain transform limited pulses with ultrashort durations. Considering possible applications that require tunable sources the management of dispersion becomes even more challenging with conventional OPA or optical parametric chirped pulse amplification schemes that are designed for a certain center wavelength and bandwidth.
An approach without the need for dispersion management relies on the amplification of parametric superfluorescence. It is called travelling-wave optical parametric amplifier and yields tunable pulses when the design of the system is appropriate [21].
In [16,17] it was shown that a cw seed applied to an optical parametric amplifier can yield nearly transform limited pulses. The authors presented an OPA that is seeded with a fixed cw wavelength and tunabiltiy is achieved by rotating the crystal angle. This limits the tuning range of the OPA to wavelengths near the cw seed wavelength. Furthermore, no demonstration of the variation of the pulse duration of the generated signals is presented, but will be carried out in this work. In addition, we show a significant increase in repetition rate, since the work presented in [16,17] has been performed at 1 kHz.
In an optical parametric amplifier energy and momentum conservation govern the nonlinear interaction that requires high intensities in the nonlinear medium, typically a borate crystal such as BBO. This intensities are provided by a pulsed pump beam meaning that the nonlinearity, due to its instantaneous nature, is switched on and off by this pulsed radiation (left side of Fig. 1 ).
Fig. 1 Working principle of cw seeded optical parametric amplifier. The left hand side shows how the pump pulse switches the nonlinearity on and off. On the right hand side the temporal behaviour of pump, signal and idler pulses are shown, respectively. Typically, the signal pulses possess a strong cw background while the idler is only generated in a time frame that is governed by the pump pulse duration. Note that the duration of the idler beam is typically much shorter than the pump pulse due to the nonlinear interaction.
When a cw seed is applied to the nonlinear medium together with the pump beam, the signal, given that phasematching conditions are chosen appropriate, will be amplified.
However, due to the pulsed pump the cw signal will only be amplified in short time periods corresponding to the pump pulse duration and repetition rate (right side of Fig. 1). Therefore, it will possess a strong background and most of its energy will still be located in continuous wave radiation, omitting applications such as CARS or high harmonic generation.
The temporal modulation of the cw signal creates new wavelength components corresponding to the duration of the nonlinear interaction. The idler carrying the remainder of the pump photon energy is only generated within the pump pulse duration. Consequently, the idler will not have a cw background leading to superior temporal contrast. The temporal shape of the idler will be determined by the pump pulse, but is not necessarily equal to it. A first approximation can be found when considering a high gain optical parametric amplifier with no pump depletion, where the temporal behaviour of the idler can be described as [23]
where L is the crystal length, deff is the effective nonlinearity, Ip(t) is the temporal pump intensity profile, ni, ns and np are the refractive indices of the idler, signal and pump, λi and λs are the wavelength of idler and signal, ε0 is the vacuum permittivity and c0 is the vacuum speed of light. Note that both equations do not account for group velocity dispersion or walk-effects. Equations (1) and (2) imply that the idler is not Gaussian or Sech2 shaped even if the pump pulse has this kind of pulse shape. To get a deeper understanding of the dependence of the idler pulse duration we performed a simulation which numerically solves the coupled differential equations for optical parametric amplification in plane wave approximation also neglecting dispersion and group velocity effects [23]. The calculations were carried out for the case of degeneracy meaning that λs = λi = 1030 nm for a pump wavelength of 515 nm. The crystal was chosen to be a 4 mm BBO and perfect phase matching was assumed.Figure 2(a) and (b) show the results of the simulation for Gaussian (black curve) and Sech2 pulses (red curve). It shows that the idler pulse duration decreases with increasing peak intensity owing to higher gain values. However, at about 30 GW/cm2 depletion of the central region of the pump sets in leading to saturation, and therefore, longer pulses. When the pump intensity is set to a certain value (22 GW/cm2) the idler pulse duration will be proportional to the pump pulse duration, as can be seen in Fig. 2(b). Consequently, the idler pulse duration can be altered by the gain or the pump pulse duration. However, there are limitations on the pulse duration variation. For high peak intensities (>30 GW/cm2) the pulse duration lengthens due to saturation and at some point will exceed the damage threshold of the nonlinear crystal. Therefore, the variation of the idler pulse duration can be performed via altering of the pump pulse duration as will be shown experimentally. The center wavelength of the idler will be determined by the wavelength of the applied cw seed, since energy conservation needs to be fulfilled. Altogether, this offers a device with great flexibility in terms of pulse duration and center wavelength that can be tuned by the applied cw seed wavelength and the pump pulse duration, respectively.
Fig. 2 (a) Duration (FWHM) of the idler pulses generated by a 650 fs (FWHM) Gaussian (black) or Sech2 (red) shaped pump pulse with respect to the pump intensity (peak intensity of the pump). (b) Idler pulse duration with respect to the pump pulse duration (Gaussian-black, Sech2-red) for a fixed peak intensity of 22 GW/cm2. Both simulations have been carried out for a 4 mm BBO crystal, λp = 515 nm, λs = 1030 nm and λi = 1030 nm.
3. Two stage optical parametric amplifier
In section 2 the basic principles of a cw seeded optical parametric amplifier were explained. For the operation of the OPA a high energy pump beam is required. For the pump pulse generation we used a state-of-the-art fiber chirped pulse amplification system that has been presented in [22]. The system was operated at 50 kHz with a pulse energy of 300 µJ and a pulse duration of 760 fs (Fig. 3(a) ).
Fig. 3 Autocorrelation traces of the fundamental (a) and the second harmonic signal (b). The pulse energy of the infrared pulse is 300 µJ with an autocorrelation width of 1.17 ps corresponding to a pulse duration of 760 fs. The second harmonic signal has a pulse energy of 160 µJ with an autocorrelation width of 1.00 ps corresponding to 650 fs
For pumping the optical parametric amplifier the pulses are frequency doubled in a critically phase matched 1mm BBO with a conversion efficiency of 53% yielding 160 µJ, 650 fs pulses at 515 nm (Fig. 3(b)).
The seed of the first OPA stage is provided by an external cavity diode laser in littrow design (Toptica Photonics) that has a variable central wavelength from 1020 nm to 1070 nm with an average output power of about 20 mW and typical linewidths of less than 4 MHz.
The optical parametric amplifier setup is shown in Fig. 4 . After the second harmonic generation the pump pulses are applied to a first OPA stage that uses a 4 mm BBO with type 1 phase matching. The pump pulses are focused to an intensity of about 22 GW/cm2 to achieve a high gain factor of about 70 dB. Due to the applied continuous wave seed the temporal overlap of pump and signal is inherently given requiring only spatial overlap of the two beams inside the crystal.
Fig. 4 Experimental setup of the cw seeded optical parametric amplifier. The second harmonic (SHG) of a fiber chirped pulse amplification system (FCPA) is used to pump the first OPA stage that utilizes a 4 mm BBO crystal. The second OPA stage pumped by the remainder of the pump is then seeded with the idler from the first stage.
As already mentioned, the amplified signal possesses a strong background making its temporal and spectral quality poor. Therefore, the amplified signal is blocked (see Fig. 4) and only the idler is used. The center wavelength of the idler can be tuned by the applied wavelength of the cw seed from 993 nm to 1040 nm (Fig. 5 ) with output powers ranging from 6 mW at 1070 nm to 27 mW at 1030 nm. The parametric superfluorescence that is emitted from the first stage is measured to range from 60 µW to 450 µW (depending on the specific experimental conditions) which is less than 3% of the amplified signal. Note that we expect the superfluorescence to be reduced when the seed is present [24] giving an even better temporal contrast.
Fig. 5 Idler wavelength after the first OPA stage with respect to the applied cw signal wavelength showing the wide tunability of the parametric amplifier. The red curve shows energy conservation with a pump wavelength of 515 nm while the black dots mark the central wavelength of the idler that has been measured after the first stage.
The transform limit of the generated pulses is extracted from the Fourier transform of the corresponding spectrum. The measured idler pulse duration is not exactly transform limited due to dispersion effects and temporal walk off between pump and idler. Its duration has been extracted from the Fourier transform of the corresponding spectrum by adding second order dispersion to match the autocorrelation width that has been measured. This is necessary since no Gaussian or Sech2 shaped pulses are expected due to the nonlinear amplification (section 2). For the idler pulses after the first stage we measured a pulse duration that is about 1.1-1.2 times the Fourier limit of the corresponding spectra. The measured autocorrelation traces are temporally clean with no observable pre- or post pulses and a low level of superfluorescence indicating a good temporal contrast. The Fourier limited pulse duration of the idler after the first stage is between 201 fs and 228 fs and agrees well with the simulations carried out in Fig. 2 for a pump intensity of 22 GW/cm2.
However, after the first OPA stage the pulse energy of these pulses is still low (~400 nJ). To increase the energy we sent the idler pulses into another OPA stage (Fig. 4.) that utilizes a 1 mm BBO crystal. The idler pulses of the first stage are now the seed pulses of the second stage and are amplified by the remainder of the pump radiation of the first stage. The pump pulses are focused to the second stage with an intensity of about 40 GW/cm2. Due to energy conservation the center wavelength of the idler pulses of the second stage will be located at the cw wavelength applied to the first stage giving the full tuning range.
To obtain parametric amplification the pump pulses and the signal pulses need to be matched temporally by means of a translation stage that allows for fine tuning of the temporal delay (Fig. 4). The signal beam diameter is matched to the pump beam diameter by a Keppler telescope. Amplification is obtained for the whole tuning range of the cw laser diode and corresponding signal and idler data have been recorded (see Table 1 .).
Table 1. Output characteristics of the second OPA stage. The subscripts sig and idl denote the signal and idler of the second stage, respectively.
As can bee seen in Table 1 the output power of the second stage signal is ranging from 270 mW at 1025 nm to 360 mW at 1030 nm corresponding to a pulse energy of 5.4 µJ and 7.2 µJ, respectively. The central wavelength of the signal can be tuned within a 50 nm bandwidth starting at 993 nm and ending at 1040 nm without significant change in the pulse characteristics (Fig. 6(a) ).
Fig. 6 Spectra recorded for the signal (a) and idler (b) of the second stage by tuning the applied cw wavelength.
In fact, also the pulse duration does not change significantly. The shortest pulses of 206 fs have been obtained at 1025 nm while the longest pulses of 258 fs were recorded at 1035 nm. Typically, the pulse durations are within 1.1-1.5 times the Fourier limit of the corresponding spectra while for some wavelengths even better results have been obtained (Fig. 7(a) ). Note that additional dispersion and walk off effects lead to slightly higher pulse durations compared to the first stage. In addition, also saturation effects will play a role, since we almost achieve a conversion of 10% (pump to signal and idler). Actually, we were able to obtain more output power, but we could see a lengthening of the pulse duration and back conversion in the spectrum. We adjusted our OPA to give the highest possible output power (energy) without observation of longer pulses or back conversion. This observation is supported by numerical simulations based on the coupled differential equations for the OPA process [23]. When performing a calculation of a two stage OPA with the experimental parameters we see the onset of depletion in the center of the temporal profile of the pump and a saturation effect for the idler and signal pulses leading to slightly longer pulses.
Fig. 7 Autocorrelation traces of the signal (a) and idler (b) pulses (black lines) together with the transform limited pulses (red area) that have been obtained by Fourier transform of the corresponding spectrum. The graph shows near transform limited pulses are obtained for signal and idler, respectively. The beam profile of the signal after the second stage is shown in (a).
Similar pulse parameters have been obtained for the idler which are near the transform limit (Fig. 7(b)) and can be tuned within the cw tuning range of 1020 nm to 1070 nm (Fig. 6(b)). The typical pulse energy of the idler is 6 µJ for most of the tuning range while the pulse duration is between 214 and 276 fs. Note that no spatial chirp of the idler has been observed in this amplification scheme. However, for shorter pump pulses, and hence, broader seed spectra at the second stage the effect of spatial chirp of the idler will decrease its quality. Additionally, the spatial profiles of the amplified beams are clean as indicated by the inset in Fig. 7(a). The level of parasitic background, i.e. parametric superfluorescence, in the second stage is less than 5 mW if only the pump is present. As already mentioned the presence of the seed will reduce the level of background and lead to a better temporal contrast [24]. In the second stage the effect is expected to be less important compared to the first stage, since the seed pulse energies are higher.
To obtain full tunability we have also varied the pump pulse duration and measured the pulse duration of the idler in the first stage. By detuning the compressor of our fiber chirped pulse amplification system the duration of the second harmonic signal was tuned from 650 fs to 1.23 ps. Due to the high gain factor that is required for obtaining the idler we also had to increase the pump pulse energy up to 188 µJ.
Figure 8 shows the dependency of the idler pulse duration with varying pump pulse duration. By variation of the pump pulse duration from 650 fs to 1.23 ps the idler pulse duration was increased from about 200 fs to 650 fs which also agrees with our simulations carried out in section 2.
Fig. 8 Autocorrelation width of the idler pulse after the first OPA stage with respect to the pump pulse duration (autocorrelation width of the second harmonic signal). The estimated pump intensities are stated as well.
Summary and outlook
A versatile source of almost transform limited pulses tunable in wavelength and pulse duration has been presented by applying a cw seed to a two stage optical parametric amplifier. At 50 kHz pulses with up to 7.2 µJ and as short as 206 fs have been obtained with a tunable central wavelength between 993 nm and 1070 nm, therefore, covering a range of almost 80 nm. Generally, the tuning bandwidth is limited by the tuning range of the laser diode and the phasematching condition of the nonlinear crystal. Since BBO can be phasematched for signal wavelengths ranging from 700 nm to 1500 nm [25] and greater tuning ranges of laser diodes are available, this scheme offers great potential for larger tuning ranges. Furthermore, we demonstrated a scaling possibility by tuning the pulse duration between 200 fs and 650 fs by variation of the pump pulse duration. The generation of ultrashort pulses (< 100 fs) requires short crystals (≤ 1 mm) to obtain nearly transform limited pulses.
Scaling of our pump source to higher energies (~1 mJ) and repetition rates will make available higher output energy and eventually will make the output pulses applicable to processes such as high harmonic generation at high repetition rates. The average power scalability of femtosecond fiber chirped pulse amplification schemes has been presented very recently [26].
With pump pulse energy and duration scaling in reach such an OPA offers great potential for studying the dynamics of high harmonic generation with respect to the driver wavelength.
Acknowledgements
This work has been partly supported by the German Federal Ministry of Education and Research (BMBF) with project 03ZIK455 ’onCOOPtics’ and the Helmholtz Institute Jena. S.H. acknowledges financial support of the Carl Zeiss Stiftung Germany.
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