We report on a significant improvement of the total bandwidth amplified in an optical parametric process. By pumping a parametric amplifier with a broadband pump, we demonstrate amplification of a supercontinuum whose spectrum expands over nearly an octave ranging from less than 600 nm up to 1200 nm. Our amplifier stage is set to provide amplification at degeneracy in the quasi-collinear configuration with a temporally as well as angularly dispersed pump.
© 2009 Optical Society of America
During the past few years, optical parametric amplification has proven to be a remarkable technique to produce intense and ultra short pulses . Thanks to many outstanding properties such as broad amplification bandwidth, high single pass gain, high spatial beam quality and signal to idler phase-conjugation, Optical Parametric Chirp Pulse Amplification (OPCPA) is an attractive solution providing intense radiation with tunable parameters. The absence of energy storage in the medium gives to parametric amplification a large potential for operation at high average power (i.e. high repetition rate). Furthermore, the broad gain bandwidth of optical parametric amplifiers in various configurations allows it to generate intense few-cycle pulses in the UV to the NIR spectral range .
Such systems are now routinely used in particular in photo-chemistry or photo-biology applications where the parametric process is exploited to easily vary the wavelength [3, 4]. Alternatively, many studies are devoted to take advantage of the gain bandwidth properties. In fact, the large gain bandwidth allows the amplification of broad spectra leading to potentially short pulses [4, 5]. The gain bandwidth of the parametric process is determined by the phase matching conditions and depends on the geometry as well as the type of the crystal . Several solutions have been proposed to enhance OPCPA gain bandwidth [4, 6, 7]. In  for instance, the authors have successfully implemented a non-collinear optical parametric amplifier whose gain bandwidth covers several hundreds of nanometers and get output compressed pulses of 4,7 fs. Both collinear and non-collinear geometry can also be improved using broadband pump pulses [5, 6]. Lately, a more versatile geometry has been proposed and consists of spatially dispersing either the pump wave [5, 6]or the signal wave .
In general, the white light seed is generated by focusing a short pulse laser beam into a glass or sapphire plate. However, wide supercontinua are only achieved if intense pulses are used. Here, we propose to implement another solution based on highly non-linear micro-structured photonic crystal fibers (PCF). Due to the very tight confinement of light in the core of the fiber, it is possible to generate huge spectral broadening with only a few nJ of energy, thus creating the supercontinuum. Recently Möhring et al. have succeeded in amplifying a spectrum as large as 100 nm and recompressing the pulses down to 13 fs demonstrating the validity of this alternative.
Using the latter techniques in a previous OPCPA experiment at degeneracy , we exploited a large 10 nm pump-bandwidth to enlarge the total amplified bandwidth around 800 nm. In this configuration (collimated pump beam) the whole theoretical phase-matched region , expanding over 400 nm from 600 nm to 1000 nm (cf. Fig. 1), was amplified. This performance was demonstrated by paying careful attention to the relative temporal dispersion of both the pump and the signal beam. In this paper, we propose to extend the parametric amplification bandwidth to reach 600 nm. The idea implemented here, which has already been studied in the non-collinear regime [6, 11–13], is an extension of our previous experiment based on broadband pumping . Keeping a quasi-collinear geometry, the 10 nm bandwidth of the pump is now spatially dispersed over ∆α=1.5 degrees before interacting with the signal. As illustrated in Fig. 1 the theoretical extreme phase-matching curves (for the 400 nm and the 410 nm pump wavelengths) are moved apart compared to the case where the pump beam is collimated (α=1°). As a consequence, the amplification bandwidth now covers a full octave lying from 600 nm up to 1200 nm.
2. Theoretical background
To predict the parametric amplifier behavior under such conditions, we numerically solve the coupled propagation equations system that characterizes the interaction between three waves in a non-linear media [12, 13].
The system reads:
A Runge-Kutta method is used to numerically integrate this system assuming plane-wave propagating fields and a slowly varying envelope in anisotropic media. More information about the theoretical concepts of OPCPA and about the simulation code used in the present study can be found in . The authors have explored several parameters acting on the parametric amplifier’s gain, thus giving information on critical parameters and optimal settings. The amplified spectrum is determined by discretizing the pump and signal spectra while the idler power is set to zero and solving the above system. The theoretical gain curves are presented as graph (b) of Fig. 2, 4 and 5 and as the blue curve of Fig. 10(b).
Depending on the pump spectral density, the gain curve can exhibit very strong variations. In the following study, we present three gain curves obtained using Gaussian, flat and ramped pump spectral densities. For a classical Gaussian shaped pump, the gain curve (cf. Fig. 2) is strongly modulated and a low gain is observed in the center of the phase-matched spectral region. A gain variation going from 3200 to 70 000 is predicted.
This strong modulation over the amplified bandwidth is due to the shape of the pump spectral density. Each component of the pump is phase-matched with a different wavelength region of the supercontinuum. But, since the pump spectral density is shaped, each pump wavelength has a different optimal interaction distance zNL as shown on Fig. 3 and Fig. 10(b) at which a maximum energy transfer from pump to signal occurs. This distance is minimal for the wavelengths phase-matched by the most intense 405 nm component, i.e. 650 and 1050 nm. It is maximal (1.6 times longer) around 800 nm which is phase-matched by the less intense 410 nm component. The strong modulation of the gain directly depends on the difference between the effective interaction distance fixed by the spatial overlap of the two beams (the experimental interaction length Zexpis calculated using the geometry of the system and is found to be as large as 3 mm) and the wavelength dependent zNL. The experimental interaction distance is drawn on Fig. 3 as a black vertical line. The output signal gain is maximal when zNL is close to zexp and minimal when it is far. The role of zNL in our context is better understood if we plot the evolution of the signal as it gets amplified during propagation in the crystal. Figure 3 shows both evolutions of a signal component at 1000 nm (Signal 1) pumped by the strong pump at 406 nm (Pump 1) and of another signal component at 800 nm (Signal 2) amplified by the weak pump at 410 nm (Pump 2). Due to a stronger pump power at 406 nm (Pump 1) than at 410 nm (Pump 2), zNL 1 is shorter than zNL 2. Considering now an effective interaction length zexp of 3 mm, better energy transfer and thus amplification is obtained for Signal 2 than for signal 1. Indeed, maximum gain for Signal 1 is reached before zexp leading to energy back conversion between zNL 1 and zexp and resulting in a poor signal power at zexp. On the contrary, zNL 2 is greater than zexp. In that case Signal 2 hasn’t got time to be fully amplified but is already more powerful than Signal 1 at zexp. This different amplification factor over the signal spectrum results in strong modulation of the gain curve.
To avoid this strong modulation of the gain over the octave, zNL must be kept close to zexp as much as possible for each single wavelength thus ensuring maximum energy transfer. If a spectrally uniform intensity distribution is given to the pump, as shown in Fig. 4(a), the flatness of the parametric gain is already much better as illustrated in Fig. 4(b). In that case, the strong modulation has disappeared and the gain varies by a maximum factor 2 although smaller on average.
In order to flatten the gain curve even more over the octave, the pump beam spectrum can be shaped. By properly ramping the pump spectral distribution (cf. Fig. 5(a)), the shape of the parametric gain can be tailored as shown in Fig. 5(b).
In this configuration, a constant gain around 1750 is observed for all signal phase-matched wavelengths. This last result is very interesting. Indeed, the pump spectrum can be easily shaped in order to obtain such a monotonically decreasing spectral density, thus making this method perfectly suitable for very short pulse amplification and recompression.
All previous simulations have been performed using a flat density distribution for the signal beam. We have chosen to present those simple simulations to highlight the strong impact of pump spectral density on gain behaviour. We then have carried out a more complete theoretical study which better fit experimental parameters by taking into account both the pump and the supercontinuum spectral density. The graphs presented in Fig. 6 are the theoretical gain curves calculated for three different crystal lengths. As one can see, gain is strongly influenced by the effective interaction length. If it is too short (1mm) the low signal wavelength are not yet amplified at the output of the crystal. On the contrary, if it is too long, back conversion of the energy occurs leading to a poor amplification of the signal. This phenomenon can be observed on the gain curve for the 3 mm long nonlinear crystal where the spectral region around 850 nm is weakly amplified due to a mismatch between zNL and zexp as already explained above.
Those simulations have been carried out to evaluate the key factors influencing the efficiency of extremely large parametric amplification processes. Consistent with our first experiment designed to amplify a 400 nm spectral bandwidth,  we have built a system able to enhance the phase-matched region to nearly an octave centered at 900 nm. As will be shown, experimental data are in good agreement with the theoretical simulations described here.
3. Experimental setup
Our setup (see Fig. 9) implements a collinear parametric amplifier pumped by a large bandwidth angularly dispersed beam . The primary source of the setup consists in a Ti: Sapphire femtosecond laser chain operating at 1 kHz and set to deliver around 600 mW after the compressor. The beam is split in two parts by a pair of 4 % reflection mirrors. The low energy arm is used to produce the ultra-broadband signal in a photonic crystal fiber, while the high energy arm is frequency doubled to create the broadband pump. The second harmonic generation (SHG) stage consists of a 300 μm thick type I BBO crystal. With an efficiency of 20 % we obtain more than 100 mW of blue pulses with a spectrum extending from 400 to 410 nm (FWHM) (cf. Fig. 7).
The ultra-broad spectrum signal is generated in a photonic crystal fiber with a zero dispersion wavelength at 810 nm. A detailed description of the generation of a supercontinuum in PCF is given in . When injecting a fiber close to the zero dispersion wavelength in the anomalous dispersion side, the pulse excites a soliton of order N, which can be described as a superposition of N fundamental solitons having different peak powers and durations. The perturbations by higher order dispersion terms and Raman scattering lead to a fission of the initial Nth order soliton into N fundamental solitons with different center wavelengths. Due to intra-pulse Raman scattering fundamental solitons are red-shifted. As they have different duration and peak power every fundamental soliton experiences a different spectral shift. The creation of visible components of the continuum is explained by the emission of phase-matched radiation in the normal dispersion regime called resonant or linear waves. Every fundamental soliton gives rise to a single linear wave. Finally, the overlap of several fundamental solitons and the created linear waves by soliton fission composes the spectrum which is known as supercontinuum (SC).
As can be seen in Fig. 8, the chirp of the SC is quadratic. As a consequence, to obtain a perfect temporal overlap of every phase-matched wavelength, the pump must be linearly chirped. This is schematically represented in Fig. 8 with the three vertical red lines which represent the different spectral components of the pump. As can be seen, the 410 nm wavelength must arrive before the 405 and the 400 nm components. Therefore, we use a fused silica prism sequence compressor to fine tune the temporal overlap between each component of the pump and the signal.
As shown in Fig. 1, phase-matched wavelengths extend from 650 nm to 1040 nm for a collimated pump beam. However, by spatially dispersing the wave vectors of the pump it is possible to significantly enhance the phase-matched range. Indeed, if the pump beam wavelengths arrive in the crystal with angles varying continuously from 0,5° (for the 400 nm component) to 2° (for the 410 nm) (cf. Fig. 9), phase matching is achieved over an octave ranging from 600 nm to slightly more than 1200 nm. The wave vector dispersion is set by adjusting the right distance (3m) between a dispersing LaKL 21 prism and the focusing lens located before the parametric amplification crystal.
The supercontinuum is launched in the crystal with an angle of 27,3° with respect to the optical axis (O.A.) and at 0,5° from the 400 nm component of the pump. Under these conditions, the 410 nm component of the pump amplifies the 800 nm region of the signal while the 400 nm of the pump transfers its energy to both the signal components at 600 nm and 1200 nm. Accordingly, the remaining components located between 400 and 410 nm will fulfill phase matching for signal wavelengths between 600 and 1200 nm.
Figure 10 (a) shows the measured spectra. The bottom curve is the signal continuum without amplification. The upper curve is the spectrum obtained with amplification. As expected, the spectrum extends from below 600 nm up to 1200 nm, showing important gain variation. The intermediate curves are obtained by pumping the amplifier with a spectral fraction of the pump beam. Since the pump beam is spatially dispersed it is easy to clip the beam with a blocker before the focusing lens and thus select part of the spectrum. For instance, the lowest inner curve in Fig. 10 (a) (violet curve) results in amplification with a pump beam limited to wavelengths below 400 nm. The two amplified peaks at 600 nm and 1200 nm are consistent with the phase matching curves of Fig. 1. As we moved the blocker out of the pump beam more and more wavelengths are participating to the amplification process resulting in more signal wavelength being amplified (upper 2 inner curves on Fig. 10 (a): blue and green curves).
The agreement between the amplified parts of the continuum and the theoretically phase-matched spectral regions allows to check and to optimize the geometry of the setup. As can be seen in Fig. 10(b) (red curve), the gain varies over two orders of magnitude. It is minimal for the 700 nm to 800 nm region and maximal around 650 nm. The low gain around 750 nm can be explained by two effects. First of all, an angle smaller than 2° for the 410 nm pump component will result in a total lack of amplification around 750 nm. Indeed, to get the broadest amplified spectrum, alignment is done by adjusting the crystal angle with respect to the 400 nm component to ensure that both edges of the spectrum are amplified. As a consequence, the 410 nm component of the pump might be injected with an angle slightly smaller than 2°. For instance, with an angle of 1,85° only the whole region ranging from 700 to 800 nm looses phase-matching and parametric amplification vanishes. This variation of 0,15° represents an error of only 0,6% on the distance between the prism and the focusing lens on the pump arm. At contrast, the gain reaches respectively 500 (~27dB) and 100 (~20dB) for the extreme regions of the octave at 600 and 1150 nm.
Second, the weak amplification around 750 nm is also due to the pump intensity distribution as discussed theoretically. Figure 10 (b) shows both theoretical (blue curve) and experimental (red curve) normalized gains. Also shown is the optimal interaction length zNL for each signal component. We clearly see that as soon as zNL gets longer than actual experimental interaction length zexp, the gain decreases. A difference between the two curves lies in the average gain which is much higher in the theory.
This variation is due to the approximation of perfect phasematching conditions used in the calculations for both the spatial and the temporal overlap. In practice several effects can lead to a decrease of the gain over the whole phasematched region. In our experiment, the signal focal point contained geometrical aberrations due to the 90° off-axis aspheric mirror used to collimate the photonic crystal fibre’s output beam. This decreases the spatial overlap quality and thus the overall gain-bandwidth. Nevertheless we can observe the overall shape-similarity between the two curves, in particular the location of the maxima and minima whose origin was explained earlier. However, this limitation of the efficiency of OPCPA can be overcome thanks to a tailored pump spectral density as discussed in the theoretical section. By optimizing the gain profile along phasematched wavelengths, one could open a new route toward efficient ultra-large band OPCPA. The experiment presented here highlights the necessary tools and physical choices to obtain good parametric amplification over extremely large spectra. A few modifications and improvements can be considered. On the one hand, theoretical studies of octave parametric amplification show solutions exist to compensate pump spectral density effects. To obtain a flat gain over the octave the pump beam must be spectrally shaped. This could be feasible by adding a spectral shaping stage on the pump beam before the prisms stretching stage. On the other hand, amplified signal pulses can be recompressed to lead to few cycle pulses. As show by supercontinuum studies, output pulses from a PCF are hardly recompressible when spectral expansion is initiated by pulses longer than 50 fs . But under certain conditions: short PCF fiber and short pulses, coherence of supercontinuum is increased thus allowing temporal recompression. This property has already been demonstrated in an OPCPA experiment. By implementing a spatial light modulation stage for SC before amplification, they have obtained recompressed pulses as short as 13 fs .
We have presented an experimental as well as theoretical study of parametric amplification of extreme bandwidth. We have demonstrated parametric amplification over a bandwidth covering nearly an octave in the visible-IR domain. We have identified and discussed the main problems limiting the performances of the setup. The theoretical investigations have shown that the intensity distribution of the pump is a key point strongly influencing large modulations in the parametric gain curve. This experiment is based on the control of the dispersion of both the signal (temporal) and the pump (temporal and angular). The control of the pump temporal and spatial dispersion appears to be very sensitive but, if carefully adjusted, turns out to be efficient. The homogeneous amplification of a spectrum ranging over one octave from visible to IR represents a very challenging goal and we have shown that parametric amplification at degeneracy using a broadband pump is an interesting solution. This method can offer an alternative to conventional spectral expansion approaches based on filamentation for all laser source systems that do not deliver high energy pulses. Also, supercontinuum generation in photonic crystal fibers in the present context offers a possibility to obtain very stable signal seed for the OPCPA with a very small fraction of the energy from the initial laser source. Finally, by a proper control of the phase and amplitude of the signal, this technique provides the opportunity of generating potentially extremely short pulses (very few cycles) whose energy can be scaled with the available pump power.
References and links
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