1. Introduction

Fiber optical parametric amplifiers (FOPAs) have attracted a lot of interest in the context of telecommunication applications during the last two decades [1, 2]. It offers instantaneous amplification with high gain values [3], large bandwidths [4, 5], low noise figures close to the fundamental limits in phase insensitive configurations [6] or in phase sensitive ones [7]. All these results have been reported in the telecommunication window, in the low dispersion region of optical fibers designed for telecommunication applications. They can operate at any other wavelength provided that a waveguide owning a zero dispersion wavelength (ZDW) in this wavelength span exists. The recent development of air silica photonic crystal fibers (PCF) with a ZDW located around 1 µm allowed to construct FOPAs in this new spectral region [8,9] where many short pulse fiber lasers operate. It then paves the way for new applications for these amplifiers, where their high gain and ultra-large bandwidth properties can be used to amplify ultra-short stretched pulses [10, 11]. In this context of application, they are labelled as Fiber Optical Parametric Chirped Pulse Amplifiers (FOPCPA) [10, 11], and represent very promising candidates to achieve all-fiber short pulse amplifiers since they do not suffer from the detrimental gain narrowing process occurring in rare earth doped fiber amplifiers. In addition, pulsed pumps can be implemented as they can be synchronized with the signals and this avoids the generation of amplified spontaneous emission between the pulses to amplify. This constitutes an important advantage compared to rare earth doped amplifiers. However, FOPCPAs are not ideal setups for achieving all-fiber short pulse amplification. Indeed, their gain curve shape has a bell shape and in order to benefit from the whole gain band of these amplifiers and/or not to distort signals to be amplified, it is necessary to flatten these gain curves. To reach this aim, different configurations have been reported, for instance, by employing a two pump configuration [12], single pump one with a stretched short pump pulse [13], an idler-band distributed fiber loss [14] or multi-section fiber arrangements with non-periodic [2,15,16] or periodic profiles [17]. In this later case, it has been reported that the gain bandwidth can be extended by using a few segments of fibers (compensating + nonlinear). By using a larger number of segments it has been shown theoretically that the gain bandwidth keeps increasing at the expense of the gain ripple. Indeed, multiple discrete peaks appear inside the gain band whose position depends on the periodicity. This is similar to observations in dispersion oscillating fibers (DOFs) [18], where the group velocity dispersion of a unique fiber is periodically modulated. While having wide overall gain bands, their discrete nature makes this configuration completely unnecessary for applications cited above requiring smooth wide bandwidth. In this paper, we propose to benefit from the fact that wide gain bands can be obtained in DOFs and to fill spectral gaps between multiple peaks by tuning the frequency of the modulations along the fiber. We will use a single fiber whose properties have been directly tailored during the drawing process avoiding problems of splicing between different sections. By using an inverse algorithm, we numerically designed the optimized longitudinal dispersion modulations which allow to reach the best fitting of an ideal wide and flat parametric gain profile of 40 dB over 12 THz.

2. Simulations

Numerical simulations have firstly been performed to design the fiber dispersion topography in order to reach the targeted parametric gain profile for a pump power fixed at 20 W which is available from our laser system. The goal is to find dispersion properties in a single fiber whose amplitude modulation and periodicity change as a function of length such as the parametric spectral gain is wide and flat. Gain curves have been obtained by using the method described in [17] for uniform fibers but including the Raman contribution as it is reported in [19] with a fraction contribution of the Raman response to nonlinear effects equals to 0.22. In order to calculate the gain in a DOF, the fiber has been sampled into more than 1000 uniform steps. This method is much faster than the usual split step technique resolving the nonlinear Schrödinger equation and it gives the same results provided that the number of sample is large enough (not shown here). We assume losses (7.5 dB/km), the nonlinear coefficient (γ = 7.5 W⁻¹.m⁻¹), the third order (β₃ = 6.5x10⁻⁴¹ s³/m) and fourth order dispersion coefficients (β₄ = −1.0x10⁻⁵⁵ s⁴/m) to be constant along the whole fiber meaning that only β₂ evolves longitudinally as in [18]. An inverse algorithm based on the Hill Climbing method [20] has been implemented to determine the optimized dispersion profile allowing to obtain the targeted gain. Other methods based on genetic algorithm as in [16] are also efficient to find relevant and unique design from large numbers of parameters but our algorithm has been developed for low computation time. The optimized design outcome has been checked by running the algorithm with different input dispersion profiles. The targeted gain is represented in dashed blue line in Fig. 1(c). It has a 47 nm large-flat bandwidth centered at 1090 nm and a gain value of 40 dB. It is located on the Stokes side of the pump in order to benefit from the Raman gain contribution. We remind that in a single DOF, multiple discrete peaks have been generated [18]. Multi-peak gain spectrum can be tailored and sideband relative contribution can be canceled or enhanced by adjusting dispersion properties [21]. From these previous studies, we can intuitively expect that several successive tailored DOFs should generate shaped gain curve. In our simulations, the fiber is chosen with three consecutive DOFs with different period to smooth the gain curve. Based on several preliminary simulations, when the number of segment increases, the gain bandwidth enlarges with a higher modulation depth. Three segments and the targeted gain profile are good compromises between gain bandwidth, spectral gain ripple and computation time. Note that we add a small chirp on these frequencies to optimize the results and the longitudinal evolution of β₂ reads:

 

Fig. 1 (a) Experimental longitudinal evolution of the diameter and the insert shows the input fiber SEM, (b) Optimal (dashed red line) and estimated experimental (green line) longitudinal evolution of the second order dispersion β₂ expressed at the pump wavelength (1050.70nm), (c) Corresponding gain curves for 20 W pump power. The dashed blue line represents the targeted gain profile. Dotted red line and blue line are results from optimal longitudinal dispersion evolution with and without Raman contribution, respectively. Dashed green line is the gain profile calculated with the dispersion extracted from the SEM image.

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Table 1. Parameters for the second order dispersion β₂ evolution for the three segments

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During the drawing process of the optimized fiber profile, the diameter has been intentionally and carefully modulated along the fiber to control the dispersion profile (Fig. 1(a)). The β₂ longitudinal evolution was calculated using the model described in [22] using empirical relations only dependent on the structural parameters. The d (holes diameter) and Λ (pitch of the periodic cladding) values have been extracted from scanning electron microscope (SEM) images (insert in Fig. 1(a)) at the fiber input. The ratio d/Λ ( = 0.36) has been kept constant during the drawing process and thus structural parameters can be deduced from the external diameter modulation (Fig. 1(a)). The two big air-holes in the fiber structure were included to ensure a polarization maintaining (PM) behavior with an extinction ration of about 18 dB. The experimental longitudinal evolution of the second-order dispersion (from SEM) at the pump wavelength (λ_p = 1050.7 nm) is plotted in Fig. 1(b) (green curve) and is very close to the aimed one. We checked that the small discrepancy does not affect significantly the gain shape by calculating the gain curve from the experimental evolution of β₂. This gain shape is represented in Fig. 1(c) in dashed green line and is expected to be closer to the experimental gain curve. The mean gain is also ~40 dB and both spectral bandwidths are ~12 THz. By including the experimental β₂ evolution, the average gain is not affected but it only leads to small increase of the gain ripple in the plateau (7 dB compared to 3.5 dB) beyond 1074 nm. The first ripple at 1072 nm has an 11 dB amplitude and the discrepancy with the gain curve calculated from the optimal longitudinal dispersion (Fig. 1(c)) is mainly due to the dispersion divergence at the end of the fiber (see the last 10 m in Fig. 1(b)).

3. Experiment results

The experimental set-up is displayed in Fig. 2. A continuous wave tunable laser (TL) is injected in an intensity modulator (MOD) to obtain Δt = 2 ns electrical square pulses at f_rep = 1 MHz, then amplified in two ytterbium doped fiber amplifiers (YDFAs). The pump pulsed mode is required to reach high peak power at few tens of watts level and to mitigate stimulated Brillouin light scattering contribution in the PCF. A narrow spectral filter (1 nm @ 3 dB) was used to reduce amplified spontaneous emission (ASE) in excess. All components are PM. The pump pulse was then injected in the DOF and its polarization was aligned along one of the neutral axes of the fiber. Output spectra have been recorded with an optical spectrum analyzer (OSA).

 

Fig. 2 Experimental set-up

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Firstly, we fixed the pump peak power to 22 W and we slightly tuned the pump wavelength in order to finely adjust the average β₂ value because, although there is a good agreement between the targeted modulation amplitude and the one calculated from the fabricated fiber, there is a small uncertainty regarding the average values. After the pump injection in the PCF, the parametric fluorescence spectrum was recorded. Then, by adjusting the pump wavelength we looked for the flattest curve on the Stokes side of the pump. As it can be seen in Fig. 3 (blue curve), an optimum has been obtained when the pump is located at 1050.70 nm. We then measured the amplification gain by combining a weak continuous wave CW signal at 1068 nm (Fig. 3(a), red curve) in the DOF with a 90/10 polarization maintaining coupler (PM-C) together with the pump pulse. The signal has been attenuated to sub-µW level to avoid any saturation process in the amplifier. The output spectrum is represented in green curve in Fig. 3(a). Indeed, we observe that the signal has been amplified and an idler has been generated during the propagation. It is important to point out that the output/input difference at the signal wavelength does not give directly the net gain of amplification. It is necessary to account for the signal CW and the pump laser duty cycle to calculate it. It leads to G(dB)~ΔA-10.log(Δt.f_rep) ~ΔA + 27 dB with ΔA(dB) the power difference recorded with the OSA between the two peaks at the signal wavelength with and without amplification. It is estimated at ~60 dB at 1068 nm. Similarly, to estimate the optical signal to noise ratio (OSNR), the laser duty cycle also needs to be considered. From Fig. 3(a), the OSNR has been calculated with a 1 nm wide spectral filter around the signal and it is equal to ~27 dB at 1068 nm, leading to a noise figure of ~8 dB. This value is quite important compared to the 3 dB limit and we expect that the relatively weak OSNR of the pump is responsible for this signal OSNR degradation. However, this value cannot be considered as a good indicator for the quality of amplification of FOPCPAs. We remind that such amplifiers are dedicated for ultra-short pulse amplification. Therefore, it is difficult to compare with usual FOPA properties designed for telecommunications since input conditions and operating modes are very different. For example, operating in slightly saturated regime allows to extract much more pump energy in FOPCPAs without inducing significant impact on the quality of amplification of stretched pulses [23] (compression factor and contrast) while it leads to strong distortions of telecommunication signals in FOPAs. As a consequence, the quality of amplification of FOPCPAs cannot be fairly estimated with tools suitable for continuous or quasi-continuous wave signals. It requires the use of pulsed signals that is out of the scope of this paper, which is devoted to the experimental demonstration of a flat gain band parametric amplifier in the small signal regime. The gain has also been measured between 1065 and 1073 nm in the small gain regime (red circles in Fig. 3(b)). This spectral range has been limited due to the laser tunability range available in the experiment. However, when the FOPA does not saturate, the fluorescence spectrum is a good representation of the spectral shape of the gain curve. In our case, we checked the parametric process occurs in the small regime since the gain value remains constant while the signal input power decreases. This is also confirmed with the good agreement between the gain measurement in the accessible spectral range (Fig. 3(b) red circles) and the experimental fluorescence profile (blue curve in Fig. 3(b)). In this case, the fluorescence spectrum has been scaled to the measured absolute gain value since its shape gives usually a good insight of the parametric gain band. For sake of comparisons, the simulated gain profiles from Fig. 1(c) are displayed in Fig. 3(b) (red and green curves) for the optimal longitudinal dispersion and the dispersion calculated from SEM (red and green curves respectively in Fig. 1(b)). Both simulations and experimental results are in good agreement. The bandwidths and the average gain values are similar but the main discrepancy appears in the gain ripple amplitude with ΔG = 15 dB for the experimental one, 7 dB for the gain curve calculated from the measured β₂ and 3.5 dB for the ideal β₂ evolution provided by the inverse algorithm. These values have been measured in the plateau beyond 1074 nm. We remind the first ripple at 1068 nm (blue curve) and at 1072 nm (green curve) are mainly due to dispersion deviation of the fabricated fiber compared to the targeted one in the last segment (Fig. 1(b)). The higher value of the experimental gain ripple amplitude might be from the fiber dispersion longitudinal fluctuation. This value is relatively important but it should be compared to results obtained in standard FOPA. Indeed, the broad band gain has usually a bell shape with few THz bandwidth over more than 20 dB dynamics [9].

 

Fig. 3 (a) Experimental fluorescence (P = 22 W, λ_p = 1050.70 nm in blue curve). Output spectra corresponding to pump on (green curve), and off (red curve) when the FOPA amplifier is seeded by a monochromatic signal at 1068 nm. (b) Comparison between the scaled experimental fluorescence spectrum (blue curve) with gain measurements (red circle). Simulated gain profiles (dotted red line and dashed green line) are also displayed for the optimal longitudinal dispersion evolution and the dispersion calculated from SEM.

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In order to investigate the sensitivity to power variation and pump wavelength, we measured the unsaturated gain curves for two pump power values (17 W, 30 W) (Fig. 4(a) and 4(b)) at 1050.70 nm and for two detuned wavelengths (1049 nm and 1052 nm) at 22 W (Fig. 4(c) and 4(d)). When the pump peak power is changed (Fig. 4(a) and 4(b)), gain shapes remain relatively flat with similar bandwidth (~12 THz) and spectral ripple amplitudes equal to 10 dB and 7 dB respectively. As expected, the gain also grows with pump peak power. For example with 17 W pump power, 30 dB average gain are obtained while when the power is around 30 W, an average gain value higher than 63 dB is reached with a smooth flat bandwidth. In standard FOPA, the broad gain bandwidth is usually obtained in the anomalous dispersion but its central frequency shifts with pump power for a constant β₂ value. In our case, the second order dispersion evolves longitudinally with an average β₂ in the normal regime and we did not observe significant spectral gain window shift with pump power. Simulations with optimal and experimental dispersion longitudinal evolutions are also displayed (dotted red and dashed green curves in Fig. 4 respectively) and are in good agreement with experimental results (blue curve, Fig. 4) for each case. When the pump wavelength is detuned from the optimal one at fixed pump peak power, the gain bandwidth decreases preferentially at the low wavelength edge (solid red line in Fig. 4(c) and Fig. 4(d)). For comparison, the optimal experimental gain shape recorded with λ_p = 1050.70 nm is also plotted in blue line. In fact, when the pump wavelength is shifted, the β₂ average value is modified from the targeted dispersion profile (Fig. 1(b)) inducing a variation of the gain shape. Simulations including the experimental dispersion longitudinal evolutions are also displayed and reasonable agreements are obtained with the experimental results.

 

Fig. 4 (a)-(b) Experimental gain profile (red curve) for two pump power values (17 W, 30 W). The pump wavelength is 1050.70 nm Simulated gain profiles for the optimal longitudinal evolution and the dispersion calculated from SEM are represented in dotted red and dashed green lines respectively. (c)-(d) Experimental gain profile (solid red line) with pump wavelength at 1049 nm and 1052 nm for P = 22W. Corresponding simulated gain profile with the dispersion calculated from SEM (dashed green line). Blue lines (c and d) represent the gain profile for λ_p = 1050.70 nm at 22 W.

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7. Conclusion

A robust FOPA with a flat and large gain bandwidth has been demonstrated around 1 µm by employing a unique fiber with several consecutive quasi-periodic dispersion modulation. The parametric amplifier has been designed by realistic numerical simulations and then experimentally implemented with an axially-varying fiber specifically drawn for broad band amplification. We obtained a 12 THz flat parametric gain with a gain ripple as low as ~7dB and a maximum average gain value of more than ~60 dB. In addition, the gain profiles are not significantly pump power dependent. Such high gain-broad band amplifier could provide numerous interests for applications. For example in the context of short pulse amplification, sub-40 fs pulses can be expected with reduced gain narrowing which is not possible with standard rare earth doped amplifiers.