Filtered pseudo random modulated fiber amplifier with enhanced coherence and nonlinear suppression

Brian M. Anderson; Angel Flores; Iyad Dajani

doi:10.1364/OE.25.017671

1. Introduction

Power scaling of single-mode, high-power fiber amplifiers are generally limited by thermal and nonlinear effects. For single-frequency and narrow linewidth fiber amplifiers, stimulated Brillouin scattering (SBS) is the primary limiting nonlinear effect. As such, numerous techniques have been developed to suppress SBS, including tension [1], temperature gradients [2], laser gain competition [2,3] and more prominently spectral linewidth broadening via phase modulation [4,5]. In this case, the broadening is achieved through RF frequency modulation and suppression occurs when the phase variation is on a time scale shorter than the phonon lifetime (approximately 17 ns at 1µm). Specifically, white noise source (WNS) and pseudo-random binary sequence (PRBS) [4] phase modulation have been the prevalent linewidth broadening schemes. Moreover, through external phase modulation at the GHz level, kW class Yb-doped fiber amplifiers have been recently demonstrated.

Whereas broader linewidths are generally preferred for optimal nonlinear suppression in high power fiber amplifiers, larger optical bandwidths may hinder efficient beam combining. In coherent beam combining (CBC), larger linewidths reduce the laser coherence length causing strict path length matching tolerances. In spectral beam combining (SBC), broader linewidths may reduce the number of channels that can be combined within the finite Yb gain spectrum and lead to beam quality degradation. Recently, in a direct comparison conducted at the kW level in Yb-doped fiber amplifiers, PRBS phase modulation was shown to provide superior SBS suppression to that provided by WNS [5]. In terms of CBC, however, the effectiveness of PRBS may be reduced due to its linear visibility (coherence) function; which results in a lower coherence length for small path length mismatches. Towards that end, we herein demonstrate a filtered PRBS phase modulation approach for improved coherence length and SBS suppression in high power Yb-doped fiber amplifiers.

The visibility function of filtered and non-filtered kilowatt-class fiber amplifiers are analyzed. We show that low pass filtering of the PRBS modulation source to mitigate the power spectral density (PSD) sidelobes, enhances the coherence length by up to 27% in a kilowatt class fiber amplifier. Simultaneously, the SBS threshold of the filtered PRBS source is increased by ~10% compared to the unfiltered PRBS source. This is due to an apparent reduction of the SBS seeding process caused by the RF filters. Particularly, we have shown that Rayleigh scattering and other sources of back reflected light can substantially alter the SBS threshold in high-power fiber amplifiers [4]. In this work, we present theoretical and experimental analysis further examining the SBS seeding effect in phase modulated fiber amplifiers. Overall, the increased coherence length and SBS threshold is exceptionally beneficial for narrow linewidth, high-power fiber amplifiers.

2. Theoretical background

2.1 SBS

Theoretical analysis of SBS in optical fibers seeded with phase modulated light has been developed based on the transient coupled wave equations [6]. While these equations correctly describe the evolution of the laser field, the Stokes field, and the phonon field, they don’t take into consideration the seeding effects which can occur when the bandwidth of the laser field overlaps with the Stokes shifted field. At a wavelength of 1064 nm, the Stokes frequency shift is approximately 16 GHz. Therefore, it is expected that the spectral overlap and hence SBS seeding would become more significant at the GHz phase modulation frequencies common in kilowatt class all-fiber amplifiers.

To include the seeding effects, we derive the coupled wave equations using the total electric field in the slowly varying envelope approximation as shown in Eq. (1). Here, we include the forward propagating electric field (A_LF), the backwards propagating electric field (A_LB), and the backward propagating Stokes field (A_S). To simplify the phase matching conditions, we have rewritten the backwards propagating laser field such that the optical frequency (k_L, ω_L) is written in terms of the Stokes shifted frequency (k_S, ω_S).

\begin{matrix} \tilde{E} ​ = A_{L F} (z, t) e^{i (k_{L} z - ω_{L} t)} \\ + A_{L B} (z, t) e^{i (- k_{S} z - ω_{S} t)} e^{- i Ω_{B} (z n / c + t)} \\ + A_{S} (z, t) e^{i (- k_{S} z - ω_{S} t)} + ​ c . c . \end{matrix}

\nabla^{2} \tilde{E} - \frac{n^{2}}{c^{2}} \frac{\partial^{2} \tilde{E}}{\partial t^{2}} = \frac{1}{ε_{0} c^{2}} \frac{\partial^{2} \tilde{P}}{\partial t^{2}}

\tilde{P} = ε_{0} γ_{e} \tilde{ρ} \tilde{E}

The interaction of the electric field and the density wave is given by the wave equation Eq. (2), where n is the index of refraction, c is the speed of light, ε₀ is the vacuum permittivity, and $\tilde{P}$ is the nonlinear polarization given by Eq. (3). In Eq. (3), $γ_{e}$ is the electrostrictive constant, and $\tilde{ρ}$ is the density wave given by $\tilde{ρ} = \exp (i (q z - Ω_{B} t)) + c . c .$ , where q is the phonon propagation constant and $Ω_{B}$ is the Stokes shift. Inserting the electric field Eq. (1) into Maxwell’s equations Eqs. (2) & (3), dropping the fast oscillating terms and the non-phased matched terms gives the following equations:

\frac{c}{n} \frac{\partial A_{L F}}{\partial z} + \frac{\partial A_{L F}}{\partial t} = \frac{ω γ_{e}}{2 n^{2} ρ_{0}} ρ (A_{S} + A_{L B} e^{- i Ω_{B} (z n / c + t)})

- \frac{c}{n} \frac{\partial A_{L B}}{\partial z} + \frac{\partial A_{L B}}{\partial t} = \frac{ω γ_{e}}{2 n^{2} ρ_{0}} ρ^{*} A_{L F} e^{i Ω_{B} (z n / c + t)}

- \frac{c}{n} \frac{\partial A_{S}}{\partial z} + \frac{\partial A_{S}}{\partial t} = \frac{ω γ_{e}}{2 n^{2} ρ_{0}} ρ^{*} A_{L F}

Likewise, the electric field Eq. (1) is inserted into the density equation below Eq. (7) to give the following relation Eq. (8). Here, $Γ_{B}$ is the Brillouin bandwidth, $v_{s}$ is the speed of sound in the medium, and $\tilde{f}$ is the stochastic noise driving the phonon relation [6]. In Eq. (8), the second derivative in the density field is kept. However, in practice this term has been found to add only a small (<3%) correction to the final solution for phase modulation frequencies of less than 10 GHz.

\frac{\partial^{2} \tilde{ρ}}{\partial t^{2}} - \frac{Γ_{B}}{q^{2}} \nabla^{2} \frac{\partial \tilde{ρ}}{\partial t} - ν_{S}^{2} \nabla^{2} \tilde{ρ} = - \frac{1}{2} ε_{0} γ_{e} \nabla^{2} 〈 {\tilde{E}}^{2} 〉 + \tilde{f}

\begin{array}{l} \frac{\partial^{2} ρ}{\partial t^{2}} + (Γ_{B} - 2 i Ω_{B}) \frac{\partial ρ}{\partial t} - i Ω_{B} Γ_{B} ρ \\ = ε_{0} γ_{e} q^{2} A_{L F} (A_{S}^{*} + A_{L B}^{*} e^{i Ω_{B} (z n / c + t)}) - 2 i Ω_{B} f \end{array}

Due to our initial assumptions, the backwards oscillating laser field (A_LB) in Eqs. (4)–(6) and Eq. (8) includes a fast oscillating phase term. For a single frequency source, the amplitude of this fast oscillating term will quickly average to ‘0’ as the fiber length and integration time is significantly longer then the oscillating period. However, for a broadband source, many frequency components will oscillate at the correct frequency to cancel this term and give the correct phase matching conditions. In the case of PRBS, the sidelobes generated from the digital modulation extend well beyond the clock rate. This broad spectrum will therefore have many frequency components which have the correct phase matching conditions to seed the SBS process, and is therefore important to consider when modeling SBS in high power fiber amplifiers. As a result, the time-dependent model was expanded to include the fast phase oscillating term.

The coupled differential equations shown in Eqs. (4)-(8) are solved using the method of characteristics as described in [6]. In order to investigate the effect of the SBS seeding process, we added the boundary condition shown below

A_{L B} (z = L, t) = \sqrt{R} A_{L F} (z = L, t)

The slowly varying component of the backwards traveling laser field is fixed at the end of the fiber by the reflected component of the forward traveling laser field. The reflectivity, R, has been estimated to be 1*10⁻⁵ based on experimental work. In practice, this reflectivity is affected by a variety of properties including: end cap length, output fiber cleave angle, AR coating on the end cap, and any partial reflections from free space elements. Particularly, the enhanced boundary conditions allow us to theoretically analyze the SBS seeding process when driven with phase modulated light. This is a critical component when designing high power Yb-doped fiber amplifiers with linewidths that are on the order of the Brillouin shift frequency (~16 GHz at 1064 nm).

2.2 Coherence

Although SBS mitigation is required to scale the power of individual fiber lasers, beam combination of multiple fiber lasers is needed to ascend to even higher powers of interest. With respect to coherent combining, the coherence length and visibility function are vital metrics. For a narrow linewidth laser source the visibility function is defined by the Wiener-Khinchin theorem, involving a Fourier transform relationship between the power spectral density and visibility (V):

| V (τ) | = | \int_{- \infty}^{+ \infty} P S D (ω) e^{- i ω τ} d ω | = \frac{I_{m a x} - I_{m i n}}{I_{m a x} + I_{m i n}}

P S D (ν) = {| \int_{- \infty}^{+ \infty} A_{L F} (z = 0, t) e^{i ω t} d t |}^{2}

As shown previously [7], it is evident that suppressing the high frequency components of the phase modulated signal will increase the coherence length.

Experimentally, to measure the visibility function of our phase modulated system, a Mach-Zehnder interferometer was used. The interferometer, shown in Fig. 1, consists of a phase modulated seed which was sampled by a 50/50 fiber coupled splitter. The lower arm then contains a variable delay line (VDL) for optical path length sweeping and an electro-optic phase modulator for active phase stabilization via the LOCSET phase locking technique [8]. The LOCSET phase modulator output is then sent to the input leg of a 2x2 fused fiber splitter. The top arm of the interferometer is amplified to kilowatt class power levels by a commercial Yb-doped fiber amplifier. After the amplifier, an AR coated wedge is used to pick off a small portion of the beam and was coupled into a fiber collimator. The sampled output signal was then sent to the other input leg of the 50/50 splitter. The power levels of the signals were approximately balanced to maximize combining efficiency.

Fig. 1 Experimental diagram for measuring the visibility of the phase modulated amplifier. The 1064 nm seed is linewidth broadened using a phase modulator before being split into two paths using a 3dB coupler. One portion of the beam is amplified to high power and an AR coated wedge is used to sample the beam. The other portion of the beam is RF tagged using a phase modulator controlled by LOCSET and path length matched to the high power beam. The two beams are interfered, and the bright and dark fringes are measured using a slow photodiode.

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The subsequent interference between the low power seed signal (lower arm) and sampled output signal (top arm) is captured by two detectors acting as bright and dark ports. After LOCSET phase locking and coherent combining, the delay line was set to sweep the optical path difference (OPD) between the two channels and generate the visibility curve. In high power CBC applications, the overall combining efficiency is constrained by the cumulative effect of various aberrations and mismatches between fiber amplifiers [9]. As a result, only minor drops in visibility are tolerable. In this work, we report the coherence length as the OPD where the visibility drops to 90% of its maximum; which corresponds to a combining efficiency of 95% in a two-channel beam combination system (Efficiency = $(1 + V) / 2$ ). For an N-channel CBC array, the combining efficiency is equal to $V + (1 - V) / N$ , indicating that the combining efficiency approaches the visibility function for a large number of channels.

3. Beam combining and power scaling of filtered PRBS amplifiers

A single frequency non-planar ring oscillator (NPRO) operating at 1064 nm was phase modulated and subsequently amplified using a commercial kilowatt class fiber amplifier [10]. The fiber amplifier has a 1m delivery fiber with a non-polarization maintaining (PM) 25 μm diameter core and a 400 µm diameter cladding. The delivery fiber has an AR coated flat cleave output. Although the amplifier is non-PM, a closed loop polarization controller is used to stabilize the polarization. A tap inside the amplifier was used to measure the backward reflected Stokes signal in order to characterize the SBS threshold for the different phase modulation schemes. Here a backwards reflectivity between 0.01% and 0.015% was used as the threshold. At this level there is a clear deviation from the normal linear rise in reflectivity. Additionally, with respect to backward spectral density at these reflectivities the Stokes signal surpasses the Rayleigh signal by approximately 10 dB, another indication of operation near the SBS threshold.

A 2.88 GHz, 2⁹-1 PRBS pattern was low pass filtered and applied to an electro-optic phase modulator. The resulting optical signal was then measured using a heterodyne technique, which was based on the interference between the phase modulated seed input and a second unmodulated, frequency detuned seed. The forward heterodyne signals for various PRBS and WNS cases are presented in Fig. 2. Through standard PRBS modulation with no RF filter (blue curve), the sidelobes generated by the 2.88 GHz PRBS pattern extend well beyond 13 GHz, meaning only ~93% of the optical power resides within the central peak. With a corresponding linear visibility function, such a spectrum reduces the coherence length. Next, we tested various RF low pass filters to determine an optimal filter cutoff frequency. As the cutoff frequency of the low pass filter is reduced, the resulting sidelobes generated by the PRBS are suppressed. Using a filter equal to approximately half the modulation frequency (red curve) completely suppresses all of the generated sidelobes, generating an approximate Gaussian spectral distribution. For comparison, the forward spectrum of a Gaussian broadened WNS with 3.06 GHz full width at half maximum (FWHM) linewidth was also measured (black curve). We note that the Gaussian PSD generates a more advantageous Gaussian visibility function, where the gradual degradation in visibility leads to longer coherence lengths and greater tolerance to small path length deviations.

Fig. 2 Heterodyne measurement of the optical spectrum for a variety of phase modulations schemes: 1) 2.88 GHz 2⁹-1 PRBS with no RF filter, 2) PRBS with 3.08 GHz filter, 3) PRBS with a 1.3 GHz filter, 4) A WNS with 3.06 GHz FWHM.

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Accordingly, the visibility functions of the standard (unfiltered) and filtered PRBS modulation schemes were measured and compared to the corresponding WNS modulation technique. Based on the experimental setup depicted in Fig. 1, the measured visibility versus optical path length differences are plotted in Fig. 3. As expected, given the relations described by Eqs. (10) and (11), the reduction in the sidelobe spectral distribution results in a longer coherence length. Based on the desired beam combining coherence length metric (90% visibility), the WNS modulated amplifier (black curve) has a coherence length of 17.8 mm, with a Gaussian visibility curve. However, the unfiltered PRBS (blue curve) has a coherence length of 13.4 mm with a linear drop in visibility. Filtering the RF signal with a 3.08 GHz LPF increases the coherence length to 16.7mm (green curve), and further filtering using a 1.30 GHz LPF increases the coherence length to 18.6 mm (red curve). After investigating several different types of filters, it was determined that filters with cutoff frequencies at approximately half the modulation frequency provide the best coherence length improvement. This is due to the complete sidelobe suppression at these cutoff frequencies, as shown in Fig. 2. Significantly, by filtering the higher frequency components of the RF signal, the coherence length can be enhanced by 38.8% over standard unfiltered PRBS. The enhanced coherence length is even greater than the coherence length attained with a 3.06 GHz WNS (Filtered PRBS: 18.6 mm versus WNS: 17.8 mm).

Fig. 3 Measurements of the visibility comparing the unfiltered PRBS (blue), to the filtered PRBS (green, red) and the reference WNS (black).

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In addition to the coherence length and beam combining properties, SBS suppression is equally critical for power scaling of kilowatt class Yb-doped all-fiber amplifiers. Consequently, we analyzed SBS threshold enhancements in filtered PRBS modulated fiber amplifiers. We note that the optimal PRBS modulation amplitude changes between unfiltered and filtered PRBS. Nevertheless, similar to the unfiltered PRBS scheme, the voltage of the filtered PRBS RF signal was tuned such that backwards reflected SBS signal was minimized. In Fig. 4, the backward reflectivity versus output power was measured for the corresponding modulation schemes presented in Figs. 2 and 3. For example, although WNS had the second longest coherence length, it has the lowest SBS threshold at 360 W (black curve). The unfiltered 2.88 GHz PRBS has a larger SBS threshold of 426 W (blue curve). Alternatively, using a 3.08 GHz filter increases the SBS threshold to 454 W, and a 1.30 GHz filter increases the SBS threshold to 479 W (red curve) for a maximum improvement of 12.4% over standard unfiltered PRBS (and 33% SBS threshold improvement over WNS). The apparent power scaling improvement of filtered PRBS modulation is due to suppression of the SBS seeding phenomena observed in phase modulated narrow linewidth amplifiers. This will be analyzed in a later section. Nevertheless, both improved coherence length and SBS suppression were concurrently observed via filtered PRBS modulation.

Fig. 4 SBS threshold measured for the 2.88 GHz PRBS (blue) and compared to the filtered PRBS (green, red) and WNS (black). Filtering the PRBS increases the SBS threshold due to the suppressed sidelobes.

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To quantify the scalability of the different phase modulation configurations, a figure of merit is created by multiplying the coherence length with the SBS power threshold. This figure of merit is shown in Table 1 for a modulation frequency of 2.88 GHz. Here we see that despite the larger SBS threshold of the conventional unfiltered PRBS over the WNS, the larger coherence length of the latter gives WNS a 12.3% improvement over the unfiltered PRBS. In contrast, filtering the higher frequencies of the PRBS gives a significant improvement on both the coherence length and SBS threshold, giving a maximum 55.9% figure of merit improvement over unfiltered PRBS.

Table 1. Summary of 2.88 GHz PRBS measurements.

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In order to scale to kilowatt class power levels we also investigated filtered PRBS phase modulation at higher modulation frequencies. Specifically, the power scaling and visibility experiments were repeated at modulation frequencies of 5 GHz and 7.5 GHz as summarized in Tables 2 and 3, respectively. Once again, an optimal PRBS pattern of 2⁹-1 was applied to all cases. In terms of both the coherence length and SBS threshold, the 5 GHz PRBS could be enhanced by 33.4% using an 2.575 GHz RF filter (Table 2) while the 7.5 GHz PRBS could be enhanced by up to 39.2% using a 3.95 GHz filter (Table 3). Some reduction in the enhancement of the coherence length at higher clock frequencies is observed due to filtering effects already present in the system, such as: the limited frequency response of the phase modulator and the pattern generator. In addition, while filtered PRBS has been shown to mitigate nonlinear seeding effects, it does not completely eliminate it. Thus, at higher frequencies approaching the Brillouin frequency we expect more overlap with the Stokes wave, and reduced power scaling improvements. We note that the filtered 7.5 GHz PRBS has a coherence length of 7.83 mm, nearly equivalent to the unfiltered 5 GHz PRBS (7.97 mm). Therefore, in practice, a fiber amplifier modulated at 7.5 GHz with a filtered PRBS signal can have identical coherence length of the 5 GHz PRBS while providing a 29.6% improvement in SBS threshold (954 W). Notably, this alleviates the common tradeoff between improved SBS suppression attained with larger optical bandwidths at the expense of reduced coherence lengths. Filtered PRBS allows us to utilize larger bandwidths for improved SBS threshold while still maintaining the superior coherence lengths observed at narrow bandwidths. Unfortunately, for frequencies beyond 7.5 GHz our commercial fiber amplifier was pump limited, but similar improvements should be observed at higher power levels.

Table 2. Summary of 5 GHz PRBS measurements.

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Table 3. Summary of 7.5 GHz PRBS measurements.

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4. Suppression of SBS seeding

4.1 Simulations

Previously, we have shown that phase modulated signals at linewidths approaching the Brillouin frequency shift (~16 GHz) can result in seeding of the SBS process. Seeding effects due to the spectral overlap of the Stokes and Rayleigh signals were shown to reduce the SBS threshold by up to 25-30% [4]. Thus, due to the suppression of these sidelobes via RF filtering, we can assume that the increased SBS threshold of filtered PRBS is due to a seeding reduction. As discussed in Section 2, we have expanded our time dependent model to account for backward reflectivity and the SBS seeding phenomena. Consequently, we simulated the seeding effects with unfiltered and filtered PRBS phase modulated light.

The SBS Eqs. (4)-(9) were initially solved assuming no backward reflectivity (R = 0). Similar to Ref [6], a core diameter of 10 µm and fiber length of 9 m was simulated. We have shown that the SBS enhancement factors between 10 µm and large mode area fibers (20-25 µm) do not vary when normalized to their corresponding single-frequency SBS thresholds [4]. Similarly, the SBS enhancement factor is normalized to the un-modulated (i.e. single-frequency) SBS threshold for the same amplifier configuration. Therefore, although we do not know the exact core dimensions of the commercial fiber amplifier, the SBS enhancement factors modelled should be applicable.

The results are plotted in Figs. 5(a) and 5(b) for the unfiltered and filtered PRBS cases, respectively. In Fig. 5(a), the unfiltered PRBS results in the standard SBS threshold dependence on the modulation frequency and pattern length. In Fig. 5(b), the PRBS is filtered using a 5th order Butterworth filter with a cutoff frequency set to half the modulation frequency. For the smaller patterns with lower number of sidebands (i.e., 2⁵-1 and below), the filtering can reduce the SBS threshold due to reductions in the main sinc² central lobe. Alternatively, for higher PRBS patterns with larger number of sidebands, filtering has less effect on the overall SBS threshold. For the 2⁹-1 pattern, which has higher SBS threshold enhancement and is more applicable for high power fiber amplifiers, there is little enhancement difference between the filtered and unfiltered PRBS cases. Here a small 10% increase is seen for modulation frequencies less than 8 GHz for the case without seeding. Beyond these frequencies the threshold is reduced by 5%.

Fig. 5 Theoretical modeling of the SBS enhancement factor without seeding. (a) No RF filter is used showing the expected dependence on PRBS modulation frequency. (b) A 5th order Butterworth filter is used to filter the PRBS reducing the SBS enhancement factor for low PRBS patterns.

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In practice, fiber amplifiers with some level of backward reflectivity represent a more realistic scenario. Among other things, this is due to minor reflections from end caps, splices, or free-space optics. Accordingly, the seeding effect is introduced by adding a reflectivity term, R to Eq. (9). The SBS threshold enhancement versus modulation frequency for R = 10⁻⁵ are shown in Fig. 6. In Fig. 6(a), the unfiltered PRBS is used, showing an approximately 20% reduction in the SBS threshold for all patterns caused by the backward reflectivity or seeding. We note similar reductions in SBS threshold were previously reported experimentally in unfiltered PRBS modulated fiber amplifiers [4]. Comparing Fig. 5(a) to Fig. 6(a), we observe similar enhancement factors at lower frequencies. However, as frequencies increase beyond 3-4 GHz, more pronounced reductions in SBS enhancement is seen. This is expected, since seeding becomes more prominent at higher frequencies that start to approach the Brillouin frequency shift. Additionally, the reduction is most prominent for the 2⁹-1 pattern, where the small sideband separation leads to more spectral overlap between the Rayleigh and Stokes broadened signals.

Fig. 6 Theoretical modeling of the SBS enhancement factor with seeding. (a) No RF filter is used, the SBS threshold is reduced due to spectral overlap. Fluctuations seen are due to the change in the overlaps of the Stokes and reflected spectrums. (b) An RF filter is used with the PRBS modulation, increasing the SBS enhancement factor to levels approaching the enhancement factor without seeding.

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Alternatively, filtering the PRBS signal does not cause a drastic reduction in SBS enhancement factors as observed by Figs. 5(b) and 6(b). The SBS response for all patterns using filtered PRBS is nearly equal with (Fig. 5(b)) or without (Fig. 6(b)) backward reflectivity included in the model. This partly indicates that the filtered PRBS can mitigate the SBS seeding caused by the backward reflectivity. When compared to the unfiltered PRBS modulation with seeding (Fig. 6(a)) for the optimal 2⁹-1 pattern, we note that the filtered PRBS provides a 15-20% improvement in SBS enhancement factor. For the smaller patterns, the SBS enhancement factors of the filtered PRBS are almost equal or slightly less than the unfiltered case. Once again, this can be partly attributed to the reduced number of sidebands within the central lobe that are being suppressed by the low pass filter. As the pattern number and hence number of sidebands increase, the filtering has less effect on the central lobe reduction. Significantly, by including the SBS seeding effect in the model we have shown that filtered PRBS can improve the SBS threshold of high power fiber amplifiers for optimal patterns (e.g. 2⁹-1) over conventional unfiltered PRBS.

4.2 Experiment

To further substantiate our SBS seeding simulations, we experimentally investigated this effect via a backward heterodyne measurement, as shown in Fig. 7. Here a 40 dB tap was used before the final amplification stage to pick off a portion of the backwards reflected signal. This reflected signal was then interfered with a portion of the single-frequency master oscillator. The interference pattern was detected using a 25 GHz high-speed photodetector and analyzed with a radio-frequency spectrum analyzer (RFSA).

Fig. 7 Heterodyne setup for measuring the spectrum of the Stokes signal.

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The heterodyne measurements, shown in Fig. 8(a) reveal the spectral overlap between the Stokes and Rayleigh signals for the unfiltered 7.5 GHz modulated PRBS amplifier near the 16 GHz Brillouin frequency shift. A PRBS pattern of 2⁶-1 was applied to allow for sufficient sideband separation to fully resolve the Brillouin gain spectral sidelobes. Particularly, by tuning the modulation frequency to 7.506 GHz, the discrete spectral lines of the PRBS are tuned to maximally overlap with the broadened Stokes shifted signal. In contrast, tuning the frequency to 7.480 GHz minimizes the overlap between the two signals. The SBS threshold for both cases was also analyzed and a plot of the reflectivity versus output power is shown in Fig. 8(b). As expected, the maximal overlap case had a lower SBS threshold of 614 W than the minimally overlapped case, where an SBS threshold of 659 W was recorded. Overall, the lower SBS threshold of both cases was due to the smaller PRBS pattern applied.

Fig. 8 (a) Heterodyne measurement of the backwards reflected signal with the unfiltered PRBS. (Red) PRBS frequency has been tuned to 7.506 GHz to maximize the spectral overlap between the Stokes and Rayleigh signal. (Black) PRBS frequency has been tuned to 7.480 to minimized the spectral overlap. (b) Backwards reflectivity vs. output power.

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Accordingly, the backward heterodyne measurements were also performed for the filtered PRBS case, as presented in Fig. 9(a). A 3.95 GHz low pass filter was applied, which substantially suppresses the amplitude of the spectral lines overlapping with the Stokes spectrum by more than 10 dB. The backward reflectivity and SBS threshold were also studied as shown in Fig. 9(b). We note that for filtered PRBS the SBS threshold remains nearly identical regardless of whether the Rayleigh and Stokes signals are maximally or minimally overlapped. The SBS threshold power is also nearly equal to the optimally tuned unfiltered PRBS case (Fig. 8(b)). Therefore, in agreement with the simulation results we can surmise that a reduction in SBS seeding effect leads to the improved SBS suppression with filtered PRBS modulation. More importantly, the simultaneous SBS suppression and coherent beam combining benefits of the filtered PRBS approach can have a significant impact for high power, beam combinable all-fiber amplifiers.

Fig. 9 (a) Heterodyne measurement of the backwards reflected signal with the filtered PRBS. (Red) The PRBS has been tuned to maximize the seeding effect. (Black) The PRBS has been tuned to minimize the seeding effect. Note that the amplitude of the Rayleigh signal has been reduced by more than 10dB. (b) Backwards reflectivity vs. output power.

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5. Conclusion

In conclusion, we have demonstrated a novel enhanced pseudo random phase modulation for high-power fiber amplifiers that simultaneously improves both the coherence length and SBS threshold over previously reported PRBS modulation schemes. The corresponding filtered PRBS technique was applied to a commercial fiber amplifier and with a modulation frequency of 7.5 GHz and 2⁹-1 PRBS pattern, an SBS limited output power of 954 W was achieved. This represented a ~10% increase in SBS threshold over the unfiltered 7.5 GHz case. In addition, beam combining visibility and coherence length measurements were performed. Notably, at the 90% visibility metric, a 27% improvement in coherence length was concurrently attained. The improvement in coherence length is attributed to the power spectral density change caused by the filtering. With the sidelobes filtered, an approximate Gaussian visibility function is generated with longer coherence length, similar to that of the WNS approach.

Similarly, through SBS modelling and experimental validation we have shown that the improved SBS threshold is caused by the reduction of the SBS seeding process induced by the spectral overlap of the Brillouin shifted Stokes and Rayleigh signals. Using our newly developed transient SBS model, we demonstrate that filtered PRBS can suppress these seeding effects. Likewise, experimental analysis of the SBS seeding phenomena via a backward heterodyne technique confirmed the threshold enhancement of the filtered PRBS technique. Overall, the simultaneous SBS suppression and coherence length improvements of the filtered PRBS approach can offer significant advantages for power scaling and coherent combining of many lasers.

Funding

Air Force Office of Scientific Research; Air Force Research Laboratory.

Acknowledgments

This research was performed while Dr. Brian Anderson held an NRC Research Associateship award at the Air Force Research Laboratory. We would also like to thank Dr. John Luginsland of the Air Force Office of Scientific Research (AFOSR) for partially funding this effort.

References and links

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10. Nufern Product Brief. NukW: Kilowatt laser amplifier platform.

Signal type	SBS Threshold	Coherence Length	Figure of Merit	Enhancement
WNS	360 W	17.8 mm	6414 W*mm	12.3%
PRBS, No filter	426 W	13.4 mm	5710 W*mm	0%
PRBS, 3.08 GHz LPF	454 W	16.7 mm	7570 W*mm	32.6%
PRBS, 2.13 GHz LPF	498 W	16.1 mm	8020 W*mm	40.3%
PRBS, 1.30 GHz LPF	479 W	18.6 mm	8910 W*mm	55.9%

Filter type	SBS Threshold	Coherence length	Figure of Merit	Enhancement
None	736 W	7.97 mm	5870 W*mm	0%
4.85 GHz	749 W	9.48 mm	7110 W*mm	21.0%
3.95 GHz	771 W	9.50 mm	7330 W*mm	24.8%
2.575 GHz	787 W	9.95 mm	7830 W*mm	33.4%

Filter type	SBS Threshold	Coherence length	Figure of Merit	Enhancement
None	868 W	6.18 mm	5368 W*mm	0%
7.2 GHz	891 W	6.93 mm	6180 W*mm	15.1%
5.58 GHz	941 W	7.23 mm	6800 W*mm	26.7%
3.95 GHz	954 W	7.83 mm	7470 W*mm	39.2%

Signal type	SBS Threshold	Coherence Length	Figure of Merit	Enhancement
WNS	360 W	17.8 mm	6414 W*mm	12.3%
PRBS, No filter	426 W	13.4 mm	5710 W*mm	0%
PRBS, 3.08 GHz LPF	454 W	16.7 mm	7570 W*mm	32.6%
PRBS, 2.13 GHz LPF	498 W	16.1 mm	8020 W*mm	40.3%
PRBS, 1.30 GHz LPF	479 W	18.6 mm	8910 W*mm	55.9%

Filter type	SBS Threshold	Coherence length	Figure of Merit	Enhancement
None	736 W	7.97 mm	5870 W*mm	0%
4.85 GHz	749 W	9.48 mm	7110 W*mm	21.0%
3.95 GHz	771 W	9.50 mm	7330 W*mm	24.8%
2.575 GHz	787 W	9.95 mm	7830 W*mm	33.4%

Filtered pseudo random modulated fiber amplifier with enhanced coherence and nonlinear suppression

Abstract

1. Introduction

2. Theoretical background

2.1 SBS

2.2 Coherence

3. Beam combining and power scaling of filtered PRBS amplifiers

4. Suppression of SBS seeding

4.1 Simulations

4.2 Experiment

5. Conclusion

Funding

Acknowledgments

References and links

Cited By

Figures (9)

Tables (3)

Equations (11)

Optics Express