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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 7 — Mar. 26, 2012
  • pp: 7422–7435
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Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control

Stephen Palese, Eric Cheung, Gregory Goodno, Chun-Ching Shih, Fabio Di Teodoro, Timothy McComb, and Mark Weber  »View Author Affiliations


Optics Express, Vol. 20, Issue 7, pp. 7422-7435 (2012)
http://dx.doi.org/10.1364/OE.20.007422


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Abstract

Two high pulse contrast (> 95 dB) polarization maintaining all-fiber amplifier chains were coherently combined to generate 0.42 mJ, 1 ns 25 kHz pulses with 79% efficiency despite 38 radians of intra-pulse phase distortion. A recursive intra-pulse phase compensation method was utilized to correct for the large nonlinear chirp providing a path for improved coherent waveform control of nanosecond pulse trains.

© 2012 OSA

1. Introduction

Remote sensing applications, such as three dimensional laser detection and ranging (LADAR) typically require laser sources with a combination of single nanosecond pulse durations, megawatt peak powers, multi-kilohertz pulse repetition frequency (PRF), diffraction-limited beam quality, and near transform-limited time-bandwidth products. Interest in deploying these sources on unmanned aerial vehicles is prompting the investigation of high efficiency, robust fiber based solutions as an alternative to traditional bulk solid state lasers.

Scaling fiber peak powers to megawatt levels is challenging owing to nonlinearities that lead to spectral broadening, temporal pulse distortions and ultimately damage [1

1. F. Di Teodoro, High-Power Laser Handbook (McGraw-Hill, 2011), pp. 463–498.

]. The Kerr nonlinearity can be conveniently parameterized by the nonlinear phase, or the B-integral, accumulated by a pulse upon amplification. While the B-integral can be reduced by increasing the fiber mode field area, this approach is limited by the concurrent challenge of maintaining single-transverse-mode propagation.

A complementary approach is to explore parallel scaling via actively stabilized coherent beam combination (CBC) of multiple amplifier chains [2

2. L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011). [CrossRef] [PubMed]

6

6. E. C. Cheung, M. Weber, and R. R. Rice, “Phase locking of a pulsed fiber amplifier,” in Advanced Solid-State Photonics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper WA2.

]. Seise et al. [5

5. E. Seise, A. Klenke, S. Breitkopf, M. Plötner, J. Limpert, and A. Tünnermann, “Coherently combined fiber laser system delivering 120 μJ femtosecond pulses,” Opt. Lett. 36(4), 439–441 (2011). [CrossRef] [PubMed]

] recently demonstrated CBC of two large-mode area, chirped-pulsed, rod-type photonic crystal fiber rod (PCFR) amplifiers in the ultrafast domain. While the extreme 100 μm core diameter enabled a low B = 1.1 rad. phase chirp despite the ~200 kW peak power in fiber, the rod-type PCF approach is currently of limited utility outside lab environments due to its sensitivity to alignment conditions and significant reliance on free-space optics.

This effort focused on the development of relatively low duty factor (25 kHz), high pulse contrast (> 95 dB) pulse sequences appropriate for long range active sensing applications. These constraints required modifications to coherent phase control techniques previously developed for pulsed and continuous wave (CW) applications. In this work, we explore the feasibility of pulsed fiber CBC in the high nonlinearity regime with by combining two pulsed polarization maintaining Yb doped fiber amplifier (PM-YDFA) chains that have smaller cores but more robustly single-mode and are amenable to all-fiber based architectures. Matching of the linear and nonlinear responses of the two amplifiers enabled 79% combining efficiency and 424 μJ output pulse energy at B = 38 rad. at 25 kHz repetition rate via active piston phase control. A method for adaptive intra-pulse phase control on the ensemble was also demonstrated to substantially reduce/modify the intra-pulse phase profiles. Our work extends the results of Xu et al. on self phase modulation (SPM) compensation [7

7. C. Xu, L. Mollenauer, and X. Liu, “Compensation of nonlinear self-phase modulation with phase modulators,” Electron. Lett. 38(24), 1578–1579 (2002). [CrossRef]

9

9. G. Zhu, J. Edinberg, and C. Xu, “Nonlinear distortion free fiber-based chirped pulse amplification with self-phase modulation up to 2pi,” Opt. Express 15(5), 2530–2534 (2007). [CrossRef] [PubMed]

] to higher nonlinear chirp levels in fiber based architectures. A part of this development involved real time measurement and phase reconstruction of the intra-pulse chirp through coherent homodyne phase-locked mixing of the signal pulse with a (CW) reference thereby providing an initial step towards dynamically chirp controllable fiber based arrays.

2. Principle of operation

The architecture for the intra-pulse phase controlled CBC (IPC-CBC) system, shown in Fig. 1
Fig. 1 Block diagram for the pulsed fiber IPC-CBC architecture. Blue lines: In-fiber, Black lines: Electrical connections.
, consists of an array of matched fiber amplifiers with individual electro-optic (EO) piston adjustments along with a shared intra-pulse EO phase modulator (FM) married with high speed sensing and feedback control electronics. The piston control loop compensates for the low frequency time dependent path length variations between the non-common optical paths while the intra-pulse control is utilized to tailor the phase profile of the pulse itself.

Individual intra-pulse amplitude and phase controls can be incorporated into the architecture but it was found that the response time required by these loops exceeded the 12 GS bandwidth of the arbitrary waveform generator (AWG) available in these studies. Instead the approach was taken to balance the optical gains, active and passive fiber lengths and pump induced noise sources of the non-common path amplifiers as closely as possible in order to push into the high B-integral regime.

3. Experimental demonstrations

3.1 Experimental set-up

The detailed schematic for the IPC-CBC architecture is shown in Fig. 2
Fig. 2 Schematic view of the pulsed fiber amplifier system and combining opto-electronic components. MO: Master Oscillator; PM: Polarization Maintaining ; YDFA: Ytterbium Doped Fiber Amplifier; MFA: Mode Field Adaptor; EO: Electro-Optic; AO: Acousto-Optic; AM: Amplitude Modulator; FM: Phase Modulator; PD: Photodiode; AWG: Arbitrary Waveform Generator; Blue lines: paths of optical signal propagating in fiber; Red lines: paths of free space optical beams; Yellow lines: paths of in-fiber, diode-produced pump beams. Black lines: Electrical connections.
. The master oscillator (MO) is comprised of a low noise, CW single-frequency distributed-feedback (DFB) fiber laser amplified to 1 W by a PM-YDFA. A small portion of the MO output is tapped off to serve as the CW reference beam, while the rest is transmitted through a cascaded acousto-optic (AO) and EO amplitude modulators (AMs) [14

14. L. Lago, D. Bigourd, A. Mussot, M. Douay, and E. Hugonnot, “High-energy temporally shaped nanosecond-pulse master-oscillator power amplifier based on ytterbium-doped single-mode microstructured flexible fiber,” Opt. Lett. 36(5), 734–736 (2011). [CrossRef] [PubMed]

]. The AO-AM first temporally slices an 8 ns long full width at half maximum (FWHM) pulse from the MO CW beam with 65 dB contrast. Each pulse is then sliced again by an EO-AM which further increases the contrast by over 35 dB and results in 1.2 ns FWHM, ~100 pJ seed pulse energy of arbitrary shape and PRF. For the work presented here, a Gaussian pulseshape was utilized and the PRF was set to 25 kHz. The high overall pulse contrast of > 95 dB is desired since many active sensing systems utilize Geiger mode avalanche detector arrays which can saturate due to scattering of the inter-pulse energy from the transmitter to the receiver optical paths.

The sliced pulse train exiting the EO-AM was pre-amplified in a 10 μm core single-mode (SM) PM-YDFA, transmitted through a common-path EO-FM utilized for chirp control, and split by a 3 dB fiber coupler to seed the two parallel PM-YDFA chains. Each chain included a second EO-FM for piston phase control, another 10 μm core SM PM-YDFA, a 10→25 μm core mode-field adaptor, and a final large mode area (LMA) PM-YDFA. Throughout the architecture (both common and split paths), inter-amplifier-stage fiber-coupled Faraday isolators and 0.6 nm linewidth band-pass filters (with a nominal 2.5 dB insertion loss per stage) are used to suppress backward propagating light and remove amplified spontaneous emission (ASE) near the 1030 nm gain peak. In the final stage LMA PM-YDFA, the core diameter tapered adiabatically from 25 μm at the input to 40 μm at the exit, so as to preserve near diffraction limited beam quality. Each tapered fiber amplifier stage was terminated by a fusion-spliced beam expanding end-cap and produced a pulse energy ~250 μJ at 1 ns pulsewidths, corresponding to ~250 kW peak power (see Section 3.2).

The two 250 μJ pulse energy outputs were collimated, geometrically combined on a 50/50 beamsplitter in a Mach-Zehnder configuration, and phase-locked using a variant of the gated heterodyne technique [6

6. E. C. Cheung, M. Weber, and R. R. Rice, “Phase locking of a pulsed fiber amplifier,” in Advanced Solid-State Photonics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper WA2.

]. Similar multi-dither approaches require no external reference beam and for CW lasers have been shown to be scalable to up to 16 channels [11

11. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]

, 12

12. A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO:2011- Laser Applications to Photonic Applications, 2011 OSA Technical Digest Series (Optical Society of America, 2011), paper CFE3.

]. The piston phase of one of the two channels was dithered by applying ~0.1 rad. modulation depth at 40 MHz to its EO-FM. The fiber active and passive lengths were matched within 1 mm and fiber taps utilized to ensure that the output powers were matched through each of the gain stages. Fine adjustments in the path length matching were accomplished by inserting mm thickness anti-reflection coated windows into one of the free-space optical paths after collimation.

Samples of the combined beam were sent to the free space diagnostics (near field camera, large area photodiode, M2 meter, power meter) with a portion re-coupled into a passive SM PM 10 μm core fiber. This fiber coupled beam was split again for the phase control loops, optical spectrum analyzer and high speed photodiode. In the beam used for phase control, the pulse was attenuated by a second AO-AM, enabling detection of the weak inter-pulse coherent CW leakage. The detected beats were demodulated using lock-in detection and processed by digital electronics to generate the EO-FM drive signal for the piston phase feedback loop. This piston control loop is based on a combination of locking of optical coherence by single-detector electronic-frequency tagging (LOCSET) [13

13. T. M. Shay, “Self-reference locking of optical coherence by single-detector electronic-frequency tagging,” US Air Force, US Patent 7,233,433 (2007).

] and heterodyne coherent leakage with CW reference piston phase control (HCL-CWR) [6

6. E. C. Cheung, M. Weber, and R. R. Rice, “Phase locking of a pulsed fiber amplifier,” in Advanced Solid-State Photonics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper WA2.

] techniques modified specifically for low PRF pulsed systems (see section 3.3). The intra-pulse chirp was measured/controlled using the HCL-CWR technique (see Sections 3.3.1 and 3.6), which consists of frequency-shifting with a fiber coupled 40 MHz AO modulator the CW reference beam tapped off the MO (see Fig. 1), then mixing it with the output pulse on a high speed photodiode. Separate phase locking of this arm was necessary to provide a stable homodyne trace and due to non-common optical paths it used a separate phase modulator and control circuit. Although the intra-pulse phase control could in principle be done autonomously, for the experiments presented here the intra-pulse chirps were measured, reconstructed, convolved with the transfer function and programmed into the AWG in a stepwise fashion.

All fiber amplifiers in Fig. 2 were diode-pumped at ~976 nm using fused couplers, which results in an end-to-end all-fiber architecture. For the two parallel amplifier stages (stages 3 and 4) a single pump diode was utilized to provide matched 976 nm pump sources. This was accomplished with a custom in-fiber multi-mode 50/50 splitter. This pumping scheme ensures the same amplitude and spectral pump variations for each parallel stage so that the optical gain, noise and nonlinearities are well correlated. Tests performed with separate pump diode sources for the final tapered amplifier showed reduced phasing efficiency thereby verifying the utility of this approach in the high B-integral regime.

3.2 Experimental results for a single chain

One of the goals of this work is to develop an architecture composed of as many fiber or fiber coupled components as possible. To meet this end, we used an Yb-doped, longitudinally tapered, PM double-clad fiber (25/40μm input/output core diameter) manufactured by nLIGHT/Liekki as the final amplifier. The main distinguishing advantages of the fiber include its large output mode field diameter (which reduces nonlinearity), its slowly tapered profile (which helps retain a near diffraction limited beam quality), and its ability to be fusion-spliced to existing fiber components that provide good mode matching to upstream PM-YDFAs. A series of experiments were performed to verify the 25/40 um tapered fiber capabilities including power extraction, optical gain, efficiency, beam quality and its reproducibility and peak power handling capabilities. The results indicated that 250 kW peak power could be obtained without temporal pulse distortions and that a counter-pumped geometry reduced the spectral broadening by a factor of three, relative to the co-pumped configuration. The summary of the results obtained for a single amplifier chain are shown in Fig. 3
Fig. 3 Performance measurements for a single, multi-stage fiber amplifier chain (see text for details on the chain architecture) generating ~250 μJ pulse energy at 25 kHz PRF. (a) Pulsewidth, (b) Linewidth, (c) Output power (red: co-pumped, blue: counter-pumped), (d) Near-field intensity profile and beam quality measurement.
. This operational regime was maintained throughout the coherent phasing experiments. Higher peak powers could be obtained but were avoided, due to the onset of stimulated Raman scattering, which degraded the amplitude and spectral/phase quality of the pulses, thus reducing coherent phasing efficiencies.

3.3 Piston phase control

Piston phase control is necessary for correction of the pathlength differences between non-shared optical paths of the parallel fiber amplifier chains. Such differences result from mostly environmental disturbances such as local temperature fluctuations and acoustic vibrations. The pathlength differences are nulled by applying a correction signal to devices that change the optical path such as fiber stretchers based on piezo-electric transducers (PZT), EO-FM, or free space PZT-driven mirrors. For these experiments we use lithium niobate EO-FMs mainly due to their high speed and maturity as devices of environmentally proven telecom heritage. As described below, three different techniques were evaluated to determine the simplest, most robust and efficient piston locking methodology for low duty factor pulsed fiber arrays.

3.3.1 Heterodyne coherent leakage with CW reference piston phase control (HCL-CWR)

This approach phase-locks the individual channels by sampling the output of each chain and mixing it with an AO frequency-shifted CW reference beam, thereby extracting the piston phase via optical heterodyne detection (Fig. 4
Fig. 4 Schematic for heterodyne coherent leakage with CW reference piston phase control. MO: Master Oscillator; CW: Continuous Wave; RF: Radio Frequency; EO: Electro-Optic; AO: Acousto-Optic; DFB Fiber: Distributed Feedback Fiber Laser; PD: Photodiode. Red lines: Optical paths within the laser chains; Blue lines: Driving signals; Black lines: Detected signals.
). One problem with this technique is that the use of the AO pulse attenuator for recovering the inter-pulse coherent leakage results in non-shared paths between the output beam phasing plane at the 50/50 beamsplitter and the physical feedback point resulting in a passive fiber path that can drift on its own. Completely shared common path approaches analogous to LOCSET [11

11. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]

13

13. T. M. Shay, “Self-reference locking of optical coherence by single-detector electronic-frequency tagging,” US Air Force, US Patent 7,233,433 (2007).

] and hill climbing techniques [15

15. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). [CrossRef] [PubMed]

] were therefore investigated to obtain a better solution for piston locking. The HCL-CWR approach did, however, provide a means to generate a phase-locked homodyne signal which is necessary for the intra-pulse chirp measurement/control circuit (see Section 3.6).

3.3.2 Coherent leakage pulsed LOCSET (CLP-LOCSET)

The CLP-LOCSET technique combines HCL-CWR presented above with a slightly modified version of self-referenced LOCSET previously used for coherently combining CW fiber amplifier arrays. In LOCSET, the one beam which serves as the reference is phase modulated with an EO-FM and a lock-in amplifier detects the modulation when mixed with the second channel. Advantages of this approach include an all common path design, even with the required AO pulse attenuator, and feedback rates that can be significantly higher than the laser PRF. CLP-LOCSET phase-modulates the low level (< −95 dB) inter-pulse coherent CW leakage and is not applied during the pulse so there are no intra-pulse modulation effects produced by the piston phase locking control loop. A schematic for CLP-LOCSET is shown in Fig. 5
Fig. 5 Schematic for coherent leakage pulsed (CLP) LOCSET piston phase control. MO: Master Oscillator; CW: Continuous Wave; RF: Radio Frequency; EO: Electro-Optic; AO: Acousto-Optic; DFB: DFB Fiber: Distributed Feedback Fiber Laser; PD: Photodiode. Red lines: Optical paths within the laser chains; Blue lines: Driving signals; Black lines: Detected signals. In this scheme, the CW reference is not used for piston phase control.
. CLP-LOCSET proved to have the best continuous coherent combination efficiencies and was utilized for the piston beam combination results presented in this work.

3.3.3 Hill climbing (HC)

The HC technique simply maximizes the output of the interferometer by dithering the relative phase between the channels with a gradient steepest climb algorithm [16

16. A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15(10), 2745–2758 (1998). [CrossRef]

] and is shown in Fig. 6
Fig. 6 Schematic for hill climbing piston phase control. MO: Master Oscillator; CW: Continuous Wave; RF: Radio Frequency; EO: Electro-Optic; AO: Acousto-Optic; DFB Fiber: Distributed Feedback Fiber Laser; PD: Photodiode. Red lines: Optical paths within the laser chains; Blue lines: Driving signals; Black lines: Detected signals. Similar to the case of CLP-LOCSET (see Fig. 5), the CW reference is not used for piston phase control in this scheme.
. Although HC is extremely useful for phase locking of CW amplifier chains [15

15. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). [CrossRef] [PubMed]

], several issues made it difficult to transition to a low PRF regime. The first is that the feedback can only take place at rates equal to or lower than the laser PRF of 25 kHz. When a two pulse average was adopted to minimize pulse to pulse fluctuations, the resulting 12.5 kHz feedback rate was not sufficient to compensate the piston phase noise of the unpackaged laser system in the laboratory environment. Two pulse fluctuations of piston phase errors of up to 14% produced a reduction in the phase combination efficiency. A second issue is that HC is susceptible to amplitude fluctuations so either stable pulse energy is necessary or pulse amplitude normalization methods are required to improve feedback robustness.

Figure 7
Fig. 7 Piston phase locking experimental results (a) The AO pulse attenuator is used to reduce the contrast between the CW coherent leakage and pulse for the piston phase control electronics. (b) Two pulse moving average for the relative piston phase errors using the HC technique. (c) Phase locking demonstration using HCL-CWR showing the heterodyne signal modulated by the 40 MHz offset (see Media 1 and Media 2). (d) Phase modulation scheme utilized for CLP-LOCSET.
shows experimental measurements made for the piston control feedback loops which illustrate (a) the AO pulse attenuation technique with the coherent leakage signal, (b) HC feedback signal derived from a BOXCAR integrator using a two pulse average, (c) phase locking of a pulse and CW reference using the HCL-CWR approach and (d) the modified CLP-LOCSET scheme which blanks-out the phase modulation around the pulse. Videos showing the heterodyne signal (pink scope trace, in the video) and the piston control clock (green trace, in the video) in the phase-unlocked and -locked regimes (the latter being characterized by synchronization of the heterodyne signal to the clock) are added to Fig. 7c (Media 1 and Media 2, respectively). Since the phase control clock provides the frequency source for both the AO frequency-shifter and the frequency demodulator, a phase error that is stable relative to the phase control clock signifies piston locking loop closure.

3.4 Coherent beam combination results

The beam combination results are shown in Fig. 8
Fig. 8 Combined spatial profiles for in-phase (a, Media 3) and out-of-phase (b, Media 4) piston locking using CLP-LOCSET (the in-phase/out-of-phase transition can viewed in Media 5). (c) Combining efficiency vs. total combined pulse energy.
where the combination efficiency is defined as the in-phase beam power divided by the total power. Combination efficiencies greater than 95% were obtained for pulse energies of up to 80 μJ and this dropped to 79% at 10.6 W combined power (corresponding to 424 μJ combined pulse energy). The in-phase combined beam quality was near-diffraction limited at all powers with M2 = 1.05.

At higher peak powers the efficiency roll-over could be correlated to non-coincident pulse chirp between the two chains. Videos showing the beam spatial profile in the CBC locked and unlocked regimes, as well the transition between these regimes, can be also viewed in Fig. 8 (Media 3, Media 4, and Media 5, respectively).

The decreased efficiency, due to the temporal chirp mismatch, can be seen in the out-of-phase intensity profiles in Fig. 9(a)
Fig. 9 Temporal intensity profiles for in-phase and out-of-phase terms at (a) 40 μJ/pulse per beam and (b) 250 μJ/pulse per beam. Purple trace: Time reference; TC: Temporal Coherence.
and 9(b) respectively, with the degree of temporal coherence (TC) measured by comparing the integral of the in-phase and out-of-phase contribution to the measured signals. In these measurements, a time reference signal derived from one of the AWG markers, serves as a stable trigger source for the oscilloscope.

3.5 Nonlinear chirp measurement and reconstruction

Intra-pulse chirp mainly arises from phase modulation imparted by the EO-AM, Kerr-induced SPM, population induced phase (PIP) dynamics where the inversion is depleted by nanosecond pulse as well as other four wave mixing (FWM) interactions. The chirp was measured via a homodyne-mixing of a phase-locked CW reference field E0(t) that is sampled upstream of the MO pulse-slicer with a portion of the output pulse field E1(t) to generate a temporal interferogram or homodyne signal S(t) = |E0(t) + E1(t)|2 = I0(t) + I1(t) + 2[I0(t)I1(t)]1/2cos[ϕ(t)], where I0(t) = |E0(t)|2 and I1(t) = |E1(t)|2 are the optical intensity profiles associated with the two fields. The CW field E0(t) notation is used in this instance since the experimentally collected CW reference contains noise which varies in time. The intra-pulse chirp ϕ(t) is then algebraically extracted through Eq. (1) with the phase ambiguities unfolded to determine the total chirp profile.

ϕ(t)=cos1(S(t)I1(t)I0(t)2I1(t)I0(t))
(1)

Experimentally the homodyne signal S(t), the pulse intensity signal I1(t) and the CW reference I0(t) were collected on separate data runs using a 18 ps FWHM high speed photodiode and 20 GHz real time oscilloscope, as shown in Fig. 10
Fig. 10 Simplified schematic for collection of the signals required for nonlinear chirp reconstruction. All three signals (S(t), I1(t) and Io(t)) were collected without altering the optical path by using an in-line variable fiber tap coupler. CW: Continuous Wave, EO: Electro-Optic, AO: Acousto-Optic, YDFA: Ytterbium Doped Fiber Amplifier, FWHM: Full Width at Half maximum, PD: Photodiode, GS: Giga-Samples, Ch: Channel, Mk: Marker.
. An in-fiber variable 2x2 tap coupler was utilized to switch between S(t), I1(t) and Io(t) so as to minimize temporal shifts between the data runs. The homodyne signals for the 40 uJ and 250 uJ/pulse data are shown in Fig. 11
Fig. 11 Measured homodyne signals for (a) 40 uJ/pulse and (b) 250 uJ/pulse from the taper fiber amplifier system.
.

The I1(t) data set was fit to analytic asymmetric Gaussian profiles, since noise in the experimentally collected signal that oscillated through zero at the beginning and end of the curve would result in “divide-by-zero” singularities in the reconstructed phase (see Eq. (1). The exact functional form of the fit is not overly important to the phase reconstruction algorithm as long as it is only positively valued and is well correlated to the experimental data.

As a self-consistency check in timing consistencies, I1(t) was also calculated directly from S(t) envelope functions where there are no uncertainties in the relative timing. This calculation showed good agreement between experimental and derived I1(t)s with the upper (green curve) and lower (purple curve) enveloped homodyne signals shown in Fig. 12(b)
Fig. 12 Method utilized to extract the intra-pulse chirp profile from the experimental measurements. (a) Representative experimental data for the homodyne S(t) and the intensity I(t) signals. Similar data sets were collected as a function of output pulse energy (b) Analytic fits of experimental signals to asymmetric Gaussian profile (green-upper SU(t) envelope fit, purple-lower SL(t) envelope fit, red- I(t) calculated from S(t)). (c) Extracted phase ϕ(t). (d) Stacked chirp profiles with potential paths and the best fit chirp profile (red). (e) Nonlinear chirp decomposed into PIP and SPM terms.
along with the calculated intensity signal (red curve).

Taking the inverse of cosϕ(t), results in phase values between 0 and λ/2 (Fig. 12(c)) and phase unwrapping is necessary to identify the best path amongst the multi-valued solutions. Representative possible phase paths are shown in Fig. 12(d) with stacking of several vertically π-shifted profiles of ϕ(t). The best path was selected based on continuity, the evolution of the chirp as a function of pulse energy (starting at chirp levels that are less than π where the solution is single valued) and by similarity with theoretical predictions. Such predictions were based on an in-house developed pulse fiber amplifier numerical model, which includes linear and nonlinear contributions (absorption, emission, stimulated Brillouin scattering, Raman scattering, amplified spontaneous emission, and SPM) to the in-fiber pulse amplitude and phase evolution. The result was decomposed into effects due to the EO-AM induced chirp, population induced phase (PIP) and SPM terms based on fits of the homodyne signals as a function of pulse energy (in this case six different pulse energies were utilized) with the PIP and the SPM terms with linear and quadratic dependences respectively (Fig. 12(e)). The EO-AM homodyne signal was measured independently by mixing the pulse and CW reference beams and subtracted before the PIP and SPM decomposition. The fits followed theoretical predictions except that the magnitude of the experimental PIP term was a factor of 8 larger than expected using the Kramers-Kronig (KK) relation. This discrepancy could result from the fact that the KK relation only applies to fully equilibrated electronic and thermal populations which is not a valid assumption on a nanosecond timescale. Further efforts are underway to understand this more fully as well as better refine the phase measurement and reconstruction technique so that no assumptions are necessary to obtain the correct phase path.

3.6 Intra-pulse phase control

There are advanced active sensing techniques that could benefit from phase control of the pulse itself [17

17. W. F. Buell, N. J. Marechal, R. P. Dickinson, D. Kozlowski, T. J. Wright, J. R. Buck, and S. M. Beck, “Synthetic aperture imaging ladar: lab demo and signal processing,” Proceedings of the 2003 Military Sensing Symposia: Active EO Systems (2003).

]. For chirped-pulse amplification of broadband, femtosecond duration pulses, it is straightforward to control intra-pulse chirp using active pulse shaping in the spectral domain [18

18. A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000). [CrossRef]

].

However, due to grating dispersion limitations this approach is not applicable for narrow linewidth nanosecond optical pulses presented in this work instead chirp correction is accomplished directly in the time domain through the use of high speed electronics.

The intra-pulse chirp compensation (IPC) method was demonstrated using one of the amplifier chains in a recursive configuration (Fig. 13(a)
Fig. 13 (a) Simplified schematic for validation (Θo(τ)) and implementation (Θi(τ)) for the IPC technique. (b) Recursive phase control generates a recirculating pulse to which a phase correction profile can be applied on each pass.
). Since the EO-FM amplitude was limited to only a small fraction of the total intra-pulse chirp, it was multi passed (period ΔT = 50 ns) by using a fiber loop constructed with tap couplers. Upon each of N passes, the AWG applied a fraction of the total required conjugate phase. The output of the recursive loop is a train of decaying pulses where all but the Nth optimally pre-compensated pulse is rejected by the pulse slicer. It should be noted that the AWG in general allows application of different phase correction profiles on each pass enabling an iterative process to converge to desired phase format.

In practice, the IPC method was first validated by compensating a sample of the output of the amplifier chain itself (Fig. 13(b)). This step was necessary due to the simultaneous requirements for precise timing and well matched chirp profiles. Fine timing adjustments were accomplished by a combination of shifting data in the AWG registry, differential cable lengths and calibrated fiber delay lines. The AWG correction function consisted of a series of pulses derived from the reconstructed chirp profile modified by a transfer function which compensated for the nonlinear response of the phase modulator and 40 GHz Mach-Zehnder (MZ) amplifier.

The results for this test are shown in Fig. 14
Fig. 14 Measured homodyne signals using the output IPC method without (a) and with (b) the applied correction. Measured homodyne signals using the input IPC method without (c) and with (d) the applied correction.
where the corrected profile was driven towards a flat phase (other phase profiles are of course possible). At 40 μJ output energy, the chirp was reduced from ~15 rad. to 1 rad., and this measured fidelity basically forms the best case expected for the input IPC loop. An analogous method was utilized for the input IPC but an additional AO AM was necessary to slice out the appropriate round-trip pulse from the train (typically the 5th pulse) for injection into the fiber amplifier chain. The amplitude reduction caused by the loop was compensated by increasing the gain of PM-YDFA stages 2 and 3 which only slightly modified the system total chirp. In this case, the AWG correction function was calculated using the extracted chirp profile and the transfer function in combination with the theoretical fiber model. The model calculates the phase profile which effectively acts as the conjugate of the extracted chirp when taking into account the contributions of the downstream fiber amplifiers. The results are shown in Fig. 14(c) and 14(d) where the output is again driven towards the same flat phase profile. It can be seen that the results for the output and input chirp compensation are similar. The residual chirp (~1-2 rad.) was dynamically varying on a pulse to pulse basis and is most likely due to pulse energy fluctuations which are converted into phase chirp via SPM. Improved chirp compensation is therefore expected through better pulse energy stability, implementation of a dynamic IPC loop or tailored input pulseshapes which reduce SPM effects.

4. Conclusions

CBC of two ~1ns pulsed all-fiber based PM amplifier chains was demonstrated in the high B-integral nonlinear regime, with 79% combining efficiency, 424 μJ output pulse energy, 10.6W average power and diffraction-limited beam quality at 25 kHz repetition rates. Combining efficiency was limited by non-common intra-pulse phase distortions generated in the fiber amplifier chains. By implementing recursive chirp pre-compensation, intra-pulse phasing errors were reduced from 15 rad. to 1-2 rad., recovering more transform-limited output pulses and providing a path towards full phase control of nanosecond pulse coherent all-fiber amplifier arrays.

Acknowledgments

References and links

1.

F. Di Teodoro, High-Power Laser Handbook (McGraw-Hill, 2011), pp. 463–498.

2.

L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, and O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011). [CrossRef] [PubMed]

3.

L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, and P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36(5), 621–623 (2011). [CrossRef] [PubMed]

4.

X. L. Wang, P. Zhou, Y. X. Ma, H. T. Ma, X. J. Xu, Z. J. Liu, and Y. J. Zhao, “Coherent beam combining of pulsed fiber lasers with hybrid phase control,” Laser Phys. 20(6), 1453–1458 (2010). [CrossRef]

5.

E. Seise, A. Klenke, S. Breitkopf, M. Plötner, J. Limpert, and A. Tünnermann, “Coherently combined fiber laser system delivering 120 μJ femtosecond pulses,” Opt. Lett. 36(4), 439–441 (2011). [CrossRef] [PubMed]

6.

E. C. Cheung, M. Weber, and R. R. Rice, “Phase locking of a pulsed fiber amplifier,” in Advanced Solid-State Photonics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper WA2.

7.

C. Xu, L. Mollenauer, and X. Liu, “Compensation of nonlinear self-phase modulation with phase modulators,” Electron. Lett. 38(24), 1578–1579 (2002). [CrossRef]

8.

J. van Howe, G. Zhu, and C. Xu, “Compensation of self-phase modulation in fiber-based chirped-pulse amplification systems,” Opt. Lett. 31(11), 1756–1758 (2006). [CrossRef] [PubMed]

9.

G. Zhu, J. Edinberg, and C. Xu, “Nonlinear distortion free fiber-based chirped pulse amplification with self-phase modulation up to 2pi,” Opt. Express 15(5), 2530–2534 (2007). [CrossRef] [PubMed]

10.

G. D. Goodno, C. C. Shih, and J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]

11.

T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]

12.

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO:2011- Laser Applications to Photonic Applications, 2011 OSA Technical Digest Series (Optical Society of America, 2011), paper CFE3.

13.

T. M. Shay, “Self-reference locking of optical coherence by single-detector electronic-frequency tagging,” US Air Force, US Patent 7,233,433 (2007).

14.

L. Lago, D. Bigourd, A. Mussot, M. Douay, and E. Hugonnot, “High-energy temporally shaped nanosecond-pulse master-oscillator power amplifier based on ytterbium-doped single-mode microstructured flexible fiber,” Opt. Lett. 36(5), 734–736 (2011). [CrossRef] [PubMed]

15.

C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, and T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). [CrossRef] [PubMed]

16.

A. Vorontsov and V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15(10), 2745–2758 (1998). [CrossRef]

17.

W. F. Buell, N. J. Marechal, R. P. Dickinson, D. Kozlowski, T. J. Wright, J. R. Buck, and S. M. Beck, “Synthetic aperture imaging ladar: lab demo and signal processing,” Proceedings of the 2003 Military Sensing Symposia: Active EO Systems (2003).

18.

A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000). [CrossRef]

OCIS Codes
(140.3510) Lasers and laser optics : Lasers, fiber
(140.3298) Lasers and laser optics : Laser beam combining

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 11, 2012
Revised Manuscript: March 3, 2012
Manuscript Accepted: March 7, 2012
Published: March 16, 2012

Citation
Stephen Palese, Eric Cheung, Gregory Goodno, Chun-Ching Shih, Fabio Di Teodoro, Timothy McComb, and Mark Weber, "Coherent combining of pulsed fiber amplifiers in the nonlinear chirp regime with intra-pulse phase control," Opt. Express 20, 7422-7435 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-7-7422


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References

  1. F. Di Teodoro, High-Power Laser Handbook (McGraw-Hill, 2011), pp. 463–498.
  2. L. Lombard, A. Azarian, K. Cadoret, P. Bourdon, D. Goular, G. Canat, V. Jolivet, Y. Jaouën, O. Vasseur, “Coherent beam combination of narrow-linewidth 1.5 μm fiber amplifiers in a long-pulse regime,” Opt. Lett. 36(4), 523–525 (2011). [CrossRef] [PubMed]
  3. L. Daniault, M. Hanna, L. Lombard, Y. Zaouter, E. Mottay, D. Goular, P. Bourdon, F. Druon, P. Georges, “Coherent beam combining of two femtosecond fiber chirped-pulse amplifiers,” Opt. Lett. 36(5), 621–623 (2011). [CrossRef] [PubMed]
  4. X. L. Wang, P. Zhou, Y. X. Ma, H. T. Ma, X. J. Xu, Z. J. Liu, Y. J. Zhao, “Coherent beam combining of pulsed fiber lasers with hybrid phase control,” Laser Phys. 20(6), 1453–1458 (2010). [CrossRef]
  5. E. Seise, A. Klenke, S. Breitkopf, M. Plötner, J. Limpert, A. Tünnermann, “Coherently combined fiber laser system delivering 120 μJ femtosecond pulses,” Opt. Lett. 36(4), 439–441 (2011). [CrossRef] [PubMed]
  6. E. C. Cheung, M. Weber, and R. R. Rice, “Phase locking of a pulsed fiber amplifier,” in Advanced Solid-State Photonics, 2008 OSA Technical Digest Series (Optical Society of America, 2008), paper WA2.
  7. C. Xu, L. Mollenauer, X. Liu, “Compensation of nonlinear self-phase modulation with phase modulators,” Electron. Lett. 38(24), 1578–1579 (2002). [CrossRef]
  8. J. van Howe, G. Zhu, C. Xu, “Compensation of self-phase modulation in fiber-based chirped-pulse amplification systems,” Opt. Lett. 31(11), 1756–1758 (2006). [CrossRef] [PubMed]
  9. G. Zhu, J. Edinberg, C. Xu, “Nonlinear distortion free fiber-based chirped pulse amplification with self-phase modulation up to 2pi,” Opt. Express 15(5), 2530–2534 (2007). [CrossRef] [PubMed]
  10. G. D. Goodno, C. C. Shih, J. E. Rothenberg, “Perturbative analysis of coherent combining efficiency with mismatched lasers,” Opt. Express 18(24), 25403–25414 (2010). [CrossRef] [PubMed]
  11. T. M. Shay, “Theory of electronically phased coherent beam combination without a reference beam,” Opt. Express 14(25), 12188–12195 (2006). [CrossRef] [PubMed]
  12. A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO:2011- Laser Applications to Photonic Applications, 2011 OSA Technical Digest Series (Optical Society of America, 2011), paper CFE3.
  13. T. M. Shay, “Self-reference locking of optical coherence by single-detector electronic-frequency tagging,” US Air Force, US Patent 7,233,433 (2007).
  14. L. Lago, D. Bigourd, A. Mussot, M. Douay, E. Hugonnot, “High-energy temporally shaped nanosecond-pulse master-oscillator power amplifier based on ytterbium-doped single-mode microstructured flexible fiber,” Opt. Lett. 36(5), 734–736 (2011). [CrossRef] [PubMed]
  15. C. X. Yu, S. J. Augst, S. M. Redmond, K. C. Goldizen, D. V. Murphy, A. Sanchez, T. Y. Fan, “Coherent combining of a 4 kW, eight-element fiber amplifier array,” Opt. Lett. 36(14), 2686–2688 (2011). [CrossRef] [PubMed]
  16. A. Vorontsov, V. P. Sivokon, “Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction,” J. Opt. Soc. Am. A 15(10), 2745–2758 (1998). [CrossRef]
  17. W. F. Buell, N. J. Marechal, R. P. Dickinson, D. Kozlowski, T. J. Wright, J. R. Buck, and S. M. Beck, “Synthetic aperture imaging ladar: lab demo and signal processing,” Proceedings of the 2003 Military Sensing Symposia: Active EO Systems (2003).
  18. A. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71(5), 1929–1960 (2000). [CrossRef]

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