1. Introduction

In many fields of application there is a growing need for stable, low noise, high power, single frequency sources. These applications include optical parametric oscillators for spectroscopic purposes, intersatellite communication and ultrahigh-precision interferometry like gravitational-wave detection. For these purposes fiber amplifiers offer a variety of advantages like high efficiency, simple setup, insensitivity to thermal effects, and excellent beam quality [1, 2, 3].

For the characterization and direct comparison of amplifiers with respect to their noise properties it is convenient to have a simple criterion. Respectively, noise figure (NF) measurements have been established for the characterization of the commonly used erbium doped fiber amplifiers in the telecommunication business [4, 5]. Actually, there are several different electrical and optical methods of measuring the NF which should, from the theoretical point of view, all give the same results [6].

The NF is defined as the degradation of the signal-to-noise ratio (SNR) caused by any attenuation or amplification of the signal, expressed in dB:

where G is the optical gain/attenuation and 〈Δ² P _in〉 and 〈Δ² P _out〉 are the power variances of the optical input and output signals, respectively. Hence the NF can simply be determined by measuring the power variances before and after the amplifier. As this measurement depends on the relative intensity noise of the input signal 〈Δ² P _in〉/〈P _in〉² [7] there is a common agreement that the pre-amplified signal has to be shot-noise limited.

According to the quantum theory for ideal quantum limited attenuation or amplification of an optical signal the input variance of the optical signal is changed to [8]

where 〈Δ² P _out〉_shot is the shot noise associated with the optical signal. Assuming a shot noise limited input signal the NF for quantum limited amplification or attenuation results in

On the one hand in the attenuation process this degradation in SNR arises from vacuum fluctuations that are mixed into the signal. On the other hand in the amplification process the vacuum fluctuations are amplified along with the signal causing a degradation in SNR as well. For high gains an asymptotical NF of 3 dB is expected from this prediction.

The different measurement methods for the determination of the NF can be divided into electrical and optical measurements. The optical methods on the one hand are based on an evaluation of the optical spectrum of the amplified signal. The electrical methods on the other hand are based on direct detection of the optical signal with a photodetector and analysis of the intensity noise with a RF-spectrum analyzer.

From the measured current variances 〈Δ² I _ph〉 the NF can be calculated as

Here 〈I _Ph〉 is the mean detected photocurrent and ${〈{\Delta }^2{I}_{\mathrm{ph}}〉}_{\mathrm{shot}}$ is the corresponding shot noise. In the electrical measurement all noise terms like signal-spontaneous emission beat noise or multipath interference noise [6] are automatically taken into account. Concerning the measured current variance one has to ensure that the non-unity photodetector efficiency and the detection system noise floor are adequately taken into account.

The main drawback of the electrical method is the limitation to the detection of relatively small signal powers. High power signals (≫ 100 mW) require precedent attenuation of the signal and the accuracy of the measurement will be substantially reduced as vacuum fluctuations are mixed into the signal according to Eq. (2).

Optical noise figure (ONF) measurements are based on a calculation of the signal-spontaneous emission beat noise. For this purpose the absolute power density ρ _ASE of amplified spontaneous emission (ASE) in the same polarization state as the signal has to be measured at the signal wavelength. Assuming again a shot noise limited input signal the ONF results as

 

Fig. 1. Setup of the fiber amplifier for the noise figure measurements.

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With this method NF measurements of high power signals are possible as long as the proper ASE-level can be determined in spite of the necessary attenuation. Nevertheless, the optical method assumes linear amplification since saturation of the amplifier can change the photon statistics. However, there is no common agreement yet about the validity and the limits of the optical method in the saturated regime [9, 10].

2. Experimental setup

In our setup (see Fig. 1) the radiation of a 1064 nm-Nd:YAG single-frequency nonplanar ring oscillator (NPRO) was passed through a Faraday isolator in order to protect it against backreflections. It was then focused into the active core of a single-mode Nd (ø_core=6 µm) or Yb (øcore=4:2 µm) doped double-clad fiber, respectively. The amplifier was pumped counterdirectional by a fiber-coupled diode laser at 808 nm for Nd and 975 nm for Yb. The 15 m long Nd fiber was doped with 1300 mol ppm Nd₂O₃. Additionally, a 10 m long Yb doped fiber with 6500 mol ppm Yb2O3 was used. On the pump side of the fiber the amplified signal was imaged on an iris aperture to cut off radiation from the pump core. In order to avoid backreflections and lasing oscillation of the amplifier both fiber ends were polished at an angle of about 8°. For the optical measurements a quarter waveplate, a half waveplate and a polarizing beam splitter were inserted in the output beam to select the polarization of the analyzed signal.

The electrical measurements were carried out at Fourier-frequencies above 10 MHz as the NPRO is shot noise limited at high frequencies well above its resonant relaxation oscillations around 500 kHz [11, 12]. We used two different InGaAs-photodetectors, optimized for the detection of optical powers up to approximately 2 mW and up to 100 mW, respectively. The bandwidth of the measurements was only limited by the bandwidth of the photodetectors of about 40 MHz in both cases. Both photodetectors and the RF-spectrum analyzer were thoroughly calibrated independently with white light measurements. By this method the frequency dependent gain of the setup was determined. In all measurements the noise floor of the detection system was subtracted and the response curve of the equipment was accounted for. In order to determine the true noise level of the optical signal the actual detection efficiency of the photodetectors was determined and the actual variances were calculated from the measured variances by means of Eq. (2). Finally the NF was calculated by means of Eq. (4).

In the optical measurements amplified source-ASE can bias the determination of the absolute power density ρ _ASE caused by the amplification process. The NPROs ASE spectral density was measured to be below 8·10^-7 mW/nm. It was verified that even the amplified NPRO-ASE was well below all measured power densities in the optical measurements and could therefore be neglected.

 

Fig. 2. Spectral hole burning and polarization dependent gain in Nd. The ASE spectral density is higher in the polarization state perpendicular to the main signal due to polarization dependent gain (main figure). The actual ASE-level at the signal level was determined by extrapolation of the ASE-bands on both sides of the main signal (inset).

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Due to the presence of polarization dependent gain both in the Yb and the Nd doped amplifier [13] (see Fig. 2) the polarization extinction technique [6] for the determination of ρ _ASE was not applicable. Hence we performed a direct measurement of the ASE-component in the same polarization state as the main signal by adjusting the waveplate combination behind the amplifier for maximum transmission of the optical signal. Thus the spontaneous emission in the orthogonal polarization was suppressed. Owing to spectral hole burning especially in the Nd doped amplifier (see Fig. 2) the proper determination of ρ _ASE was difficult to perform. Therefore we extrapolated the ASE-bands at both sides of the carrier in order to interpolate the ASE-level at the signal-wavelength. It must be kept in mind that this method assumes a straight continuation of the ASE bands towards the carrier. Hence the actual ASE-level and therefore also the ONF might be slightly different than presented here. The upper extreme would be given by a horizontal ASE interpolation which would result in values that are up to 1 dB higher.

For the accurate determination of the ONF the effective resolution bandwidth (RBW) of the optical spectrum analyzer (OSA) must be known. We determined the effective RBW by taking a sample spectrum of the unamplified NPRO. As the NPRO-linewidth is much smaller than the nominal RBW of the OSA of about 0.5 nm, this measurement reflects the instrument function of the OSA. The effective RBW for the ASE spectral density measurements was then determined by the area under the normalized instrument function to be 0.56 nm.

3. Results and discussion

In the NF measurements on the Nd doped amplifier we observed the behaviour of a quantum limited amplifier. The measurements carried out with the electrical method (Fig. 3(a)) closely follow the theoretical prediction of Eq. (3) within the estimated measurement accuracy of about ±0.2 dB. At unity-gain the pump power is switched off. Due to its 4-level structure there is no reabsorption of the seed signal in the fiber and hence no gain values below unity occur.

The optical measurements (Fig. 3(b)) are slightly above the theoretical values and the electrical measurements. There was no direct dependence of the deviation on the seed power observed within the estimated measurement accuracy of about ±0.5 dB. The NF-performance of the Nd doped amplifier is independent of the seed power due to the quantum limited amplification. In both measurements the NF approaches the 3 dB-limit at high gain.

In contrast, the Yb doped amplifier shows some reabsorption at 1064 nm due to its quasi-3-level structure. Hence, gain values below unity occur at low pump power levels, compare Fig. 4. In this operational regime the degradation of the SNR is mainly caused by the attenuation of the signal. Additionally, the absorbed signal serves as a pump source of the amplifier and causes spontaneous emission. At unity-gain reabsorption and amplification are balanced over the fiber length. Actually, the signal is first attenuated and then amplified as the amplifier is pumped from the opposite side to the seed signal. At higher gains the reabsorption at the seed side of the fiber decreases due to the higher level of remaining pump light. In addition, the average ratio of the inversion to upper state population increases with increasing gain and the ground state is depleted. Thus, the overall performance gets closer to the characteristics of a 4-level system resulting in a decreased NF.

 

Fig. 3. Noise figure measurements on the Nd doped amplifier with the electrical (a) and the optical method (b).

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With higher seed power a stronger pumping is necessary to maintain the gain values due to the increasing saturation of the amplifier. Similar to the case of increased gain the amount of residual pump light at the seed side of the fiber increases and the seed-signal absorption decreases. Therefore for increasing seed powers the amplifier exhibits decreasing NF-values.

Comparing the electrical (Fig. 4(a)) and optical (Fig. 4(b)) measurements of the Yb doped amplifier, the shapes of the measured traces both resemble each other. At low seed power the optical measurement is only slightly above the electrical measurement. At higher seed powers there is a greater discrepancy between the measurement methods. This may be explained by nonlinear photon statistics due to the increasing saturation of the amplifier [4, 9]. Admittedly,there is no indication of this effect in the Nd measurements. However, probably the effect appeared in the Yb measurement because the measured NF in Yb is much higher than in the Nd measurements.

 

Fig. 4. Noise figure measurements on the Yd doped amplifier with the electrical (a) and the optical method (b).

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In principle, the performance of the Yb doped amplifier can be improved by the use of shorter fibers. In order to keep the overall gain constant the absolute amount of injected pump light has to be increased as a smaller fraction of the pump light would be absorbed in the fiber. Hence, the reabsorption would decrease and this would lead to an improvement of the NF on the cost of higher pump power levels. Respectively, one has to adjust a balance between available pump light, needed gain and acceptable NF.

4. Conclusion

The Nd doped amplifier exhibited a quantum limited amplification behaviour with a 3 dB noise figure for high gains. In contrast, the Yb doped amplifier exhibited a higher NF, comparable to values reported for Er doped fiber amplifiers [9, 10]. As the NF decreases with increasing seed power it is expected that towards the multi-watt regime the Yb doped amplifier will perform even better than demonstrated in this work.

If noise performance is absolutely crucial and the entire amplified optical signal will be detected without any considerable attenuation, a Nd doped amplifier will be the right choice due to its quantum limited behaviour. In the high power regime, i.e. if only a part of the amplified signal will be detected, the Yb doped amplifier will effectively provide a comparable noise performance as the Nd doped amplifier. Therefore, in this regime the dopant can be chosen e.g. according to admissible quantum defect, availability of the pump diodes or limitations due to feasible dopant concentrations and hence resulting fiber lengths.

In direct comparison, the electrical method has proven to be more accurate than the optical method but is limited to relatively low powers. On the contrary, the optical method is suitable for qualitative measurements even in the high power regime, but the actually measured values provided are too high.