1. Introduction

Nowadays fiber lasers have established themselves as an enabling technology that is widely used in many fields of research and industry [1]. For example, fiber-based laser systems are promising candidates for the next generation of gravitational wave detectors [2]. Due to their excellent beam quality, fiber lasers are also used in industry-related applications such as laser materials processing [3,4]. All of these applications pose stringent requirements on the laser operation in order to be able to guarantee the highest quality standards. In this context, one of the key performance parameters of a laser system is its noise characteristic. In this work we discuss the evolution of the amplitude noise, also known as relative intensity noise (RIN), along a fiber amplification chain. This is an important parameter that can also couple into phase noise [5]. Moreover, RIN is suspected to be the trigger of transverse mode instabilities in high-power fiber-laser systems [6]. Therefore, there is a strong interest of the fiber laser community to develop low-RIN systems.

There are numerical [7] and analytical [8] models which can predict the gain and frequency-dependent transfer-function of the RIN (either from the seed or the pump) to the output of a fiber amplifier. These models predict that the RIN transfer-function (in frequency domain) exhibits a high-pass filtering behavior for the seed signal noise and a low-pass filtering behavior for the pump noise. Furthermore, they also predict that the saturation of the amplifier should play a major role for the RIN-transfer dynamics [7,8]. These models, which are very useful tools, only consider the RIN-transfer dynamics through one amplifier and under ideal conditions. However, real fiber laser systems usually comprise several amplification stages and, therefore, it would be interesting to learn how the RIN propagates through the different stages of a fiber amplification chain. Moreover, it would be also very useful to obtain guidelines about the best configuration of the whole system to reach a low amplitude noise output. In this work we have experimentally investigated the gain and frequency dependent RIN-transfer behavior, both for seed and pump power fluctuations, of a fiber amplifier chain that contains two amplification stages. To the best of our knowledge this is the first time that the evolution of the RIN-transfer-function through a complete Yb-doped fiber amplifier chain has been experimentally investigated. Besides, with the help of the experimental findings, we have derived useful guidelines for the optimal configuration of a fiber amplifier chain to obtain a low amplitude-noise output.

The paper is organized as follows: section 2 provides an overview of the experimental setup and of the operating principle. Later on, in section 3, the experimental results are presented and analyzed. Finally, some conclusions are drawn and the guidelines for the best configuration of a fiber laser system are described.

2. Experimental setup and analysis method

The seed signal is generated by a passively mode-locked, Ytterbium-doped fiber oscillator delivering ~40 ps pulses with a repetition rate of approximately 32 MHz at a wavelength of 1032 nm. The architecture of the resonator was adopted from that of a normal net-dispersion mode-locked oscillator [10]. The oscillator has a relative intensity noise below 0.027% r.m.s. in the frequency range of 1 Hz – 100 kHz.

In order to measure the RIN-transfer-function, the seed or the pump power of each stage was sinusoidally modulated with a modulation depth of 1% at different frequencies. To generate the desired amplitude noise on the seed, the signal emitted by the seed laser could be modulated by a fiber-coupled acousto-optical modulator (AOM). An arbitrary function generator connected to the AOM-driver (labelled as seed control in Fig. 1) imprinted the desired signal modulation. The seed power delivered to the amplifier chain was 7 mW. Alternatively, to modulate the pump power, an arbitrary function generator (labelled as pump control in Fig. 1) was directly connected to the driver of the pump diode. The complete setup can be found in Fig. 1.

 

Fig. 1 Schematic diagram of the complete setup comprising the oscillator and two amplification stages with their respective seed and pump power controls. WDM: wavelength division multiplexer, Yb: Ytterbium doped active fiber, TAP: tap coupler, ISO: optical isolator, LPD: laser pump diode, AOM: acousto optical modulator, PD: photodiode, PM: power meter.

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The whole setup is fiber-integrated and polarization-maintaining. Each amplification stage consists of a semiconductor pump diode (LPD) emitting at 976 nm, a wavelength division multiplexer (WDM), the active fiber (i.e a Liekki Yb1200-6/125DC-PM Yb-doped fiber of approximately 30 cm length for the first stage and a Nufern PM-YSF-HI Yb-doped fiber of ~90 cm length for the second stage) and an optical isolator (ISO) at the amplifier output (please note, that the difference in fiber type and length has a negligible impact on the revealed characteristics of the amplitude noise transfer function of the amplifier chain). Both amplification stages were core-pumped in the co-propagating direction. Finally, in order to detect the evolution of the imprinted modulation depth on the laser output power and, thus, the amplitude noise along the amplifier chain, several measurement points were distributed in the system. These comprised tap-couplers (TAP) and InGaAs photo-diodes (PD) with neutral density filters that were used to prevent the optical saturation of the PD. Additionally, since high-frequency components (e.g. those close to the repetition rate of the oscillator) are not of particularly interest for this work (since most of the noise concentrates in a frequency range <100 kHz), low-pass electric filters (240 kHz) were applied.

2.1. Detection scheme

In this section, the analysis technique used to measure the RIN-transfer-function of the seed and pump power through the amplifier chain is described. In order to determine the evolution of the RIN, the time dependent signals are detected using the photodiodes at each of the measuring points (see Fig. 1), which is then recorded by an oscilloscope (12 bit-oscilloscope by LeCroy). In the next step, the time-dependent input signals are converted to the frequency domain via Fourier-transformation, which unveils the power spectral density (PSD). In the third step of the analysis, the PSD is integrated over a selected frequency interval to obtain an integrated value of the amplitude noise. More precisely, the root mean square of the cumulative sum of the PSD was calculated. In our case, the PSD was integrated starting from 100 kHz but in progressively broader spectral windows (expanding towards lower frequencies). Using this integrated plot of the amplitude noise, it is possible to isolate and track noise changes caused by particular noise frequency components (e.g. those artificially introduced by the modulators). The RIN evaluation procedure will be illustrated in the following using a measurement example in the frequency interval from 1 Hz to 100 kHz. For this, the seed power (7 mW input signal) was modulated with a sinusoidal function of 1 kHz frequency and a modulation depth of 1%. This modulated seed was then amplified with the first amplifier stage delivering an output signal of 50 mW. The pump power was not modulated in this case. The selected measurement parameters can be found in Table 1 and the results of the PSD (top) and the integrated PSD (bottom) are shown in Fig. 2.

Table 1. Measurement parameters

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Fig. 2 Measurement results for the power spectral density (top) and the integrated power spectral density (bottom) of the modulated seed signal (input signal, green line) together with the corresponding output signal after amplification through one amplifier stage (blue line). The black line depicts the dark current of the photodiode.

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Note that the PSD was normalized to its DC carrier power and that the integrated PSD (cumulative sum) was integrated in the stated frequency interval. The PSD will not be further considered in this analysis, since it is only used to calculate the integrated PSD. The black curve represents the dark current of the photodiode and can be seen as the lower limit of the measurement. The green curve corresponds to the modulated input seed signal and the blue curve is the one corresponding to the amplified output signal after one amplifier stage. As can be seen in the lower plot of Fig. 2, the strongest contribution to the noise (i.e. strongest jump in the plot) occurs at 1 kHz, i.e. at the frequency of the modulation imprinted on the seed signal. In fact, the amplitude of this jump in the green curve (i.e. that corresponding to the seed signal) is approximately 1%, which corresponds to modulation depth applied to the signal. However, the amplitude of the jump in the blue curve (i.e. that corresponding to the output signal) is just ~0.6% at the modulation frequency. This means that the RIN at 1 kHz has been attenuated by the amplifier. By dividing the amplitude of the modulation at the output of the amplifier by that applied to the input signal/pump, it is possible to determine the RIN-transfer-function (ΔRIN) at the frequency of the modulation. Thus, the complete RIN-transfer-function in the desired frequency window can be obtained by sweeping the frequency of the modulation.

2.2 Transfer function of seed and pump power fluctuations through a single amplifier

A major contribution to noise in fiber amplifiers are seed and pump power fluctuations. In this context, assuming noise-free fiber amplifiers (i.e. amplifiers that do not contribute to noise), the propagation of the noise along an amplifier chain can be predicted using transfer functions. They describe how the amplitude noise of the seed or the pump laser is transferred, via the laser dynamics, to the output power of the fiber amplifier. In the case of an inverse three-level system, such as Yb-doped fibers pumped at 976 nm and emitting at 1030 nm, numerical [7] and analytical [8,11] models allow calculating the expected RIN transfer functions. Based on these simulations, a quantitative expectation on the behavior of the RIN-transfer-function can be obtained. The above mentioned models propose also the introduction of the corner frequency. This frequency is related to the inverse value of the effective ion life-time of the excited state and represents a cut-off frequency for the RIN-transfer function. For example, the above stated models show a high-pass filtering behavior (in frequency) of the RIN-transfer function for the seed noise. This means that high frequencies (>10 kHz) of the seed RIN will be transferred without attenuation to the output. However, in a frequency window below a certain corner frequency (which is typically of a few kHz), the RIN at the output of the amplifier is lower than the seed RIN (i.e. the RIN introduced by the seed has been attenuated). Depending on the saturation level of the amplifier, this attenuation of the RIN introduced by the seed can be very significant (i.e. >10 dB for strongly saturated amplifiers). On the other hand, the RIN transfer function corresponding to the pump noise shows the inverse behavior and acts like a low-pass filter (in frequency domain). This means that low frequencies components (i.e. those below the corner frequency) of the pump RIN will be transferred almost undamped to the amplifier output whereas, depending on the amount of saturation in the amplifier, high frequencies can be strongly suppressed. Our measurements (see Fig. 3) regarding the RIN-transfer function (both of seed and pump power modulations) of a single fiber amplifier, are in good agreement with the behavior expected from theory and other publications [7,9,12].

 

Fig. 3 Measured RIN-transfer-function for seed (left) and pump power modulations (right), after propagation through one amplification stage. Dots represent the measured data and solid lines are fit functions used to guide the eye (i.e. they have no physical meaning in themselves). The black graph shows the case in which the amplifier is transparent and the red graph shows the case for the highest possible gain in our systems.

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In Fig. 3, the black line and dots correspond to the case with low pump power (~70 mW) in which the amplifier has just reached transparency, i.e. the input and output powers are the same (7 mW). The red line and dots depict the case with high-pump power (~285 mW), which results in an output power of 50 mW. Increasing the pump power leads to a stronger saturation of the amplifier and, therefore, to a stronger attenuation of the RIN induced by the seed power at lower frequencies (<1 kHz, see Fig. 3 left diagram). In the case of the pump RIN-transfer function (see Fig. 3 right diagram) the stronger saturation of the amplifier means that the whole transfer function (and also the corner frequency) is shifted slightly to higher frequencies. This is to be expected, because the corner frequency depends among fiber specific parameters, on the average pump power and increases successively with higher output powers [12].

3. Experimental results and discussion

In order to gain a deeper understanding of the RIN-transfer function both for the seed and the pump in a fiber amplification chain, several scenarios have been measured and will be presented and discussed in this chapter. To the best of our knowledge, the characterization of the evolution of the RIN-transfer function through an entire Yb-doped fiber amplifier chain (as opposed to a single fiber amplifier) is carried out here for the first time.

Our experiments address two general operating configuration for the amplifier chain in which its output is kept at a constant power of 100 mW, but the gain is distributed differently between the amplification stages. In the first scenario the pre-amplifier was operating in transparency (i.e. gain~1), and the gain of the main-amplifier was set to achieve the output power of 100 mW. In the second configuration, the pre-amplifier was adjusted to deliver 50 mW of output power and the main-amplifier was adjusted accordingly to obtain 100 mW of output power at the end of the amplification chain. These settings were not chosen randomly, but they represent the lowest and highest amplification limits of the experimental setup. Furthermore, the first setting can be understood as a system consisting of one amplifier (due to the transparency of the pre-amplifier) and the second settings as a setup with two amplifiers, which achieves a higher system saturation. There have also been measurements carried out with configurations that fall between these limits, and they show the expected smooth transition between the extreme behaviors that will be illustrated in the following. The RIN-transfer functions for both the pump and the seed signal have been measured for each of the system configurations discussed above. Before presenting the results, we will discuss the overall noise performance of the system without artificially applied modulations. The two scenarios described above were realized (Fig. 4(a) transparent pre-amplifier and 4(b) two amplifier case) and the optical signals at the output of the oscillator (after the AOM with P_out = const.), pre-amplifier and the main-amplifier were recorded. To obtain satisfying results, we have measured several traces over two hours and calculated the temporal average of the resulting integrated power spectral densities. The black graph depicts the data obtained at the output of the oscillator, the red graph that at the output of the pre-amplifier and the blue graph that at the output of the main-amplifier. The graphs show an almost homogeneous curve progression of the RIN along the entire frequency bandwidth.

 

Fig. 4 Average values of the integrated power spectral density of the amplifier chain without artificial amplitude modulations (of the seed or pump power). The top diagram depicts the case in which the pre-amplifier is transparent and the bottom diagram shows the case in which both amplifiers provide gain. Black lines represent the data obtained at the oscillator output, red lines at the pre-amplifier output and blue lines at the main-amplifier output.

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For the transparent pre-amplifier case (Fig. 4, top diagram), the RIN decreases progressively along the propagation through the amplifier chain, which results in the lowest RIN values being reached at the end of the amplifier chain. The little jumps that can be seen at 50 Hz and 150 Hz are related to the electrical power grid and can be neglected. For the two-amplifier case (Fig. 4, bottom diagram), both the pre- and main-amplifier add more noise. This is probably related to pump noise, as we will explain later.

3.1 RIN-Transfer function for seed-power modulations through the complete amplifier chain

In this case the AOM modulated the amplitude of the oscillator output whereas the pump of the pre- and main-amplifier remained unmodulated (see Fig. 5(a)-5(c)). As it can be seen from the black line and dots, there is almost no attenuation of the input RIN when the pre-amplifier is operated in transparency, as could be expected. This means that the amplitude noise of the seed power can propagate almost unperturbed through the transparent pre-amplifier. However, when the signal reaches the main-amplifier, as shown by the red line and dots (which represent the RIN-transfer function of the main-amplifier) the RIN is attenuated in the low frequency (<1 kHz) region. Furthermore, the measured curve exhibits the high-pass behavior expected from theory, where there is no attenuation of the RIN at higher frequencies (>10 kHz). The sum of the measured data points for the pre- and main-amplifier (black and red dots) at each frequency results in the values of the blue dots, which represent the RIN-transfer-function of the complete amplification chain. It is interesting to compare the results now with those obtained for the second configuration of the system (i.e. when the pre-amplifier is operating with its highest gain). Here a strong suppression of the RIN at low frequencies can be observed in both the pre- and the main-amplifier (see Fig. 5(c)). However, it is important to note that the RIN-transfer function of the main-amplifier (red dots) has not changed significantly with respect to the one measured for the previous configuration.

 

Fig. 5 Schematic setup of the amplifier chain for seed power modulations (PD: photodiode, AOM: acousto-optical modulator) (a). Results for transparent pre-amplifier (b) and pre- amplifier operated at highest gain (c). The dots represent the measured data and the solid lines are fit functions to guide the eye. The black graphs represent the RIN-transfer function through the pre-amplifier (PD1 to PD2), the red graph represent the RIN-transfer function through the main-amplifier (PD2 to PD3) and the blue graph represents the RIN-transfer function through the complete amplifier chain (PD1 to PD3).

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This is a remarkable result that demonstrates, for the first time to the best of our knowledge, that the configuration of the system (i.e. the gain distribution along the amplification chain) can significantly affect its noise characteristics.

3.2 RIN-Transfer-function for pump power modulations of the pre- and main-amplifier

The results for the RIN-transfer function of the pump (i.e. transfer function of the amplitude noise from the pump to the output signal) for the different amplifier stages are presented in Figs. 6(b)-6(e). As mentioned above, dots represent the measured data and solid lines are fit functions to guide the eye. The RIN-transfer function for the pump of the pre-amplifier is depicted in Figs. 6(b) and 6(c) and for the pump of the main-amplifier in Figs. 6(d) and 6(e) (note that the configuration in which the pre-amplifier is operating in transparency is shown in Figs. 6(b) and 6(d) and the configuration in which both the pre- and the main-amplifier exhibit gain is shown in Figs. 6(c) and 6(e)). For these experiments the seed signal coming from the oscillator was left unmodulated. As done for the modulation of the seed power, a sinusoidal electrical signal with a certain modulation depth (~1%) and frequency was applied to the driving current of the pump diodes. Using the photo-diodes PD4 and PD5 (see Fig. 6(a)), the imprinted amplitude modulation could be monitored. Note that the pump sources for the pre- and the main-amplifier were not simultaneously modulated, but the modulation was applied to either one or the other. The green line and dots in Fig. 6(b) and Fig. 6(c) represent the RIN-transfer function between the pump (PD5) and the output of the pre-amplifier (PD2). On the other hand, the red line and dots represent the RIN-transfer function between the pre-amplifier output (PD2) and the output of the main-amplifier (PD3). Hereby the inverse behavior compared to the green measured data can be observed, where higher noise frequencies are transferred unperturbed to the output. The most remarkable result, however, is depicted by the orange graph, which is a combination of the other two and represents the RIN-transfer function between the pump of the pre-amplifier (PD5) and the main-amplifier output (PD3). It can be clearly seen that all frequencies are damped across the complete measuring bandwidth. However, this attenuation is particularly strong in the case in which the pre-amplifier works in transparency (Fig. 6(b)), which is due to the behavior of the pump RIN-transfer function, as known from theoretical models [7] (i.e. the impact of pump power noise of an amplifier is weaker for lower signal powers, which is the case for the transparent pre-amplifier, compared to the case in which both amplifiers distribute gain in our system). Increasing the signal power and seeding the main amplifier leads to a weaker attenuation of the pump RIN-transfer function, as can be seen on the green and orange curves in Fig. 6(c). Nevertheless, it can be stated that the pump RIN of the pre-amplifier is converted into seed RIN at the input of the main-amplifier, which, in turn, is strongly attenuated at its output. In other words, the pump RIN of previous amplification stages has typically only a weak impact on the RIN of the signal at the output of the main-amplifier.

 

Fig. 6 Schematic setup of the amplifier chain used to study the pump RIN-transfer function of the different amplification stages (PD: photodiode, AOM: acousto-optical modulator) (a). The diagrams show the results for the RIN-transfer function of the pre-amplifier pump (b-c) and of the main-amplifier pump (d-e). The left hand diagrams represent the outcomes when the system is configured in such a way that the pre-amplifier works in transparency and the right hand ones show the results when both the pre- and the man amplifier have gain.

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The RIN-transfer function between the pump of the main amplifier and its output can be seen in Figs. 6(d) and 6(e). Hereby the grey plots show the transfer function of the pump noise of the main amplifier (PD4) to the output power of the amplifier chain (PD3). This is the RIN-transfer of the pump power through one single amplifier and, therefore, as it has been shown previously, it exhibits the expected low-pass filter behavior.

These plots show the impact of a noisy pump in the final amplifier of an amplification chain. In this situation, no significant difference between the different configurations of the system (i.e. pre-amplifier operating in transparency Fig. 6(d) or with gain Fig. 6(e)) could be observed. This underlines the fact that the RIN of the whole amplifier chain can be dominated by the amplitude noise of the pump of the last amplification stage. The experimental results can be used to derive some useful guidelines for the operation of an Yb-doped fiber amplifier chain, especially the distribution of gain between the different amplification stages (while maintaining a constant output power), to achieve a low output-RIN. It has been shown that saturation mitigates the seed power-RIN for frequencies below 10 kHz. This means that higher seed powers will lead to a stronger attenuation of the RIN in this frequency band. Unfortunately, the pump power-RIN of a single amplification stage is not attenuated in this frequency range but it will be transformed into seed signal-RIN at the output of the amplifier. However, it has been shown that, this pump-induced signal RIN will be usually attenuated in the next amplification stage. Consequently, the pump-RIN of the pre-amplification stages have only a weak impact on the overall RIN of the system. On the contrary, the pump power noise of the last amplification stage is critical, because it will be directly transferred to the output of the amplifier (for frequencies <10 kHz).

4. Conclusion

The goal of this paper was the experimental characterization of an Yb-doped fiber amplification chain comprising two amplifier stages in terms of the propagation of amplitude noise (both from the seed and from the pump) to the output. Overall a very good agreement of the transfer function of the amplitude noise with that predicted by various theoretical models was found. In the first configuration of the system, when the pre-amplifier is operated in transparency, it was found out that the amplitude modulation of the seed power propagates almost undamped through the first amplification stage, only to be strongly attenuated in the following amplification stage. On the contrary, the RIN of the seed was equally attenuated in both amplification stages in the second configuration of the system, where the pre-amplifier is fully pumped, thus resulting in a significantly stronger overall suppression of the seed noise. The analysis of the pump power noise showed that it will be transformed into seed signal-RIN at its output, only to be strongly attenuated at the next amplification stage. Therefore, it can be concluded that the pump power noise of the pre-amplifier stages does not have a major influence on the output power-RIN characteristics of the complete amplifier chain. In contrast to this, it is critical to minimize the pump power noise of the last amplifier stage to get low-noise fiber laser systems.