2. Combining efficiency
Our experimental device, shown in Fig. 2
, consists of two independent Erbium doped fiber amplifiers which are core pumped by two pigtailed laser diodes emitting at 980nm with a power up to 100mW. The Er-fibers (EDF) had lengths of ~17m corresponding to almost complete pump absorption. The two arms of the active interferometer were spliced to two 50/50 couplers. One of the output ports of the back coupler (C2) is spliced to a chirped fiber Bragg gratings (CFBG) with high reflectivity (≥98%) at 1550nm and 2nm bandwidth. The other output port is angle cleave to avoid light feedback in the cavity. The output coupler of the MZFL has a 4% reflectivity by cleaving the fiber of one input port of the other 50/50 coupler (C1). The second input port of the coupler was angle cleaved to avoid any reflection. We control the interferometer path length difference with a mechanical delay line (DL).
Fig. 2. Experimental set-up of the Mach-Zehnder Fiber Laser (MZFL)LD1, LD2: 980nm Pump laser diodes; EDF: Erbium doped fiber; CFBG: Chirped fiber Bragg grating @ 1550nm; WDM: Wavelength-division multiplexer; PC: Polarization controller.
We first measured the conversion efficiency of the MZFL, and then compared the performances obtained with the MZFL with those obtained with an individual fiber laser (IFL). IFL is based on the components forming one branch of the MZFL. Figure 3
shows that the MZFL threshold (Thr) of 20mW was twice the MZFL one. This is due to the fact that in each arm of the MZFL, the population inversion occurred at the same pumping level than in the IFL. The MZFL and the IFL had almost the same slope efficiency (ηL
) of 44%. This means that the combining efficiency was maximum, and was confirmed by the very low power leakage measured on the angle cleave outputs (Fig. 2
). For the highest pumping level of 2×100mW, the MZFL delivered Pout
= 79mW, almost twice the output power of an IFL (40mW). In that case, the leakage power Pleak
is lower than a milliwatt which corresponds to a combining efficiency η = Pout
) ≈ 99%. The laser output was not polarized, indicating that in the coupler, the two polarization states from each fiber arm were independently combined. The combining efficiency is not very sensitive to the intensity imbalance. This can be explained by a purely linear analysis, considering the interference contrast in each 50/50 coupler. In that way, the output power is Pout
)/2 when the leakage power is Pleak
)/2 ; Pi
is the emitted power of the individual fiber laser i, equivalent to that forming the laser arm i. By fixing P1
to its maximum value and P2
, K varying from 0 to 1, one can rewrite Pout
)/2 ; Pleak
)/2. We define the combining efficiency as η = Pout
) = 1/2+K/2+(K)1/2
/(1+K). Figure 4
shows theoretical and experimental variations of the combining efficiency as a function of the K factor. Experimentally, we fix P1
at its maximum value (maximum pumping) when P2
varies. One can note that individual laser combining is not greatly dependent upon power imbalance; even a 50% difference decreases the combining efficiency by only 3%.
Fig. 3. Power characteristics of the different fiber laser configurations: the individual fiber laser (IFL) the Mach-Zehnder fiber laser (MZFL), the 4-arm fiber laser (4AFL) ; Thr: threshold ; ηL: slope efficiency.
Fig. 4. Theoretical and experimental MZFL combining efficiency versus the power ratio (K=P2/P1) in the two arms.
3. Spectral behavior of the Mach-Zehnder fiber laser
We measured the MZFL spectrum with an Anritsu optical spectrum analyzer (MS9710B) of 0.07nm spectral resolution. Experimentally, we observe some spectrum modulations which correspond to the spectral filtering of period Δν = c/ΔL. However, the large homogeneous linewidth of Erbium doped fiber at room temperature prevents simultaneous oscillations of closely spaced wavelengths [5
5. E. Desurvire, D. Bayart, B. Desthieux, and S. Bigo, Erbium-Doped Fiber Amplifiers (Wiley, New York, 2002), chap. 4.
]. Thus, the path length difference ΔL must be large enough to get several modulation periods Δν in a bandwidth as small as 0.3nm.
show the measured spectra where ΔL is respectively 27, 20.3 and 12.2mm. Smaller ΔL leads to a laser spectrum with one or two groups of resonant frequencies, as shown in Figs. 5(c)
. We also observed that the MZFL spectrum bandwidth broadens when ΔL is decreased so that at least one resonant frequency group is always emitted. The laser gain bandwidth boundaries are given by the chirp fiber Bragg grating characteristics (2nm bandwidth at 1550nm). The MZFL resonant frequencies randomly shift inside the bandwidth due to the external perturbations which slightly change the interferometer path length difference. The condition for shifting a maximum spectrum modulation towards its neighbor is the following: ν.[(ΔL + δ1)/c] = ν.(ΔL/c) = 1 i.e.
δ1 = λ. This small value is easily reachable in non protected environment taking into account the long lengths of the interferometer arms (~ 20m). This phenomenon is critical when the spectrum modulation period Δν is of the same order or larger than the laser gain bandwidth. The fluctuations of the laser output power then increase rapidly as ΔL tends to zero.
Fig. 5. Spectra of the MZFL obtained with different arm length detuning ΔL.
Fig. 6. Power fluctuations of the MZFL versus the path length difference ΔL compared with those of an Individual Fiber Laser (IFL).
shows the evolution of power fluctuations obtained with the MZFL versus the optical path difference ΔL by comparison with that of a standard individual fiber laser (Fabry Perot cavity). Power fluctuations have been measured during one second with a fast InGaAs photodiode of 1GHz bandwidth. Output power fluctuations are significant when ΔL is lower than 2mm which corresponds to a spectrum modulation period Δλ = 1.2nm to be compared to the 2nm of the Bragg grating bandwidth.
Nevertheless, and despite the MZFL being based on an interferometric architecture, it operates without any output power instabilities if the two arms of the active interferometer have a sufficiently high difference in length (Fig. 6
4. Coherent combining of widely tunable laser sources
The broad emission bandwidth of rare-earth doped fiber allows the achievement of widely tunable laser sources. In the past, many tunable fiber laser systems have been experimented either using fiber Bragg gratings [6
6. W.H. Loh, B.N. Samson, L. Dong, G.J. Cowle, and K. Hsu, “High Performance Single Frequency Fiber Grating-Based Erbium:Ytterbium-Codoped Fiber Lasers,” J. Lightwave Technol. 16, 114, (1998). [CrossRef]
], liquid crystals [7
7. P. Mollier, V. Armbruster, H. Porte, and J.P. Goedgebuer, “Electrically tunable Nd 3+ -doped fibre laser using nematic liquid crystals,” Elect. Lett. 31, 1248–1250, (1995). [CrossRef]
] or diffraction grating as dispersive elements [8
8. M. Auerbach, D. Wandt, C. Fallnich, H. Welling, and S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441, (2001). [CrossRef]
]. However, the output power obtained was only a few milliwatts. The coherent combining method used in the MZFL leads to a spectrum modulation Δν = c/ΔL which is not dependent on the laser wavelength. So, we have experimentally demonstrated that power scaling of all-fiber laser is compatible with wavelength tuning in the interferometric fiber laser.
Fig. 7. Experimental set-up of the tunable Mach-Zehnder fiber laser; LD1, LD2: 980nm Pump laser diodes; EDF: Erbium doped fiber; WDM: Wavelength-division multiplexer; PC: Polarization controller.
depicts the experimental set-up which is used to investigate the MZFL tuning characteristics. The device is based on the Mach-Zehnder-type configuration described previously (figure2
). The two input ports of the coupler C2
were now angle cleaved. The output beam from one of them was collimated (lens of 11mm focal length) and was then sent onto a diffraction grating operating at the Littrow angle. The MZFL wavelength tuning was achieved by rotation of the grating. The diffraction grating had 830 gr/mm with a gold coating. The diffraction efficiency of the grating was close to 90% for p polarization and only 35% for the s polarization. Therefore, the diffraction grating acted as a polarizer and the radiation emitted by the MZFL was strongly linearly polarized with an extinction ratio of 50:1. Combining efficiency and intracavity losses were optimized thanks to the polarization controller (PC) in connection with the grating. The MZFL is tunable on a wide spectral range of 60nm from 1520nm to 1580nm which matches the whole gain bandwidth of the erbium doped fiber. Figure 8
shows different emission spectra obtained by rotating the diffraction grating. A maximum output power of 63mW at 1550nm was reached with a total leakage power lower than 2mW measured at the output of the angle cleaved fibers. It has to be noted that the fibers used in the MZFL had a low intrinsic birefringence with a beat length of ~1m. The orientation of the output beam polarization only rotates by a few degrees when the laser wavelength was tuned over the complete gain bandwidth. The combining efficiency optimized by adjusting the polarization controller at a given emission wavelength does not require additional adjustments at other wavelengths. Experimental results show a very small output power difference between the results obtained by optimizing the polarization controller at each wavelength in comparison with those obtained by only optimizing the PC at 1550nm (Fig. 9
, red and blue curves respectively).
Fig. 8. Few typical spectra of the tunable Mach-Zehnder fiber laser obtained for five different adjustments of the grating orientation.
Fig. 9. Output power versus laser wavelength. The red curve was obtained by optimizing the output power with the polarization controller at each wavelength, whereas the output power was optimized only at 1550 nm for the blue curve.
These last results demonstrate, for the first time to our knowledge, that coherent combining of lasers is compatible with wavelength tuning. The technique represents an alternative method making a widely tunable fiber laser source of high power.
5. N-arm interferometer resonator
We have also investigated the scaling of the method, for the combining of several elementary fiber lasers, only using standard 50/50 couplers. In a first step, we have successfully demonstrated the coherent combining of four fiber lasers. The experimental set-up, shown in figure 10
, is a Mach-Zehnder tree architecture in which the coherent combining is achieved with 50/50 couplers in a cascading arrangement. Each EDFA is core pumped by a pigtailed laser diode emitting at 980nm with a power up to 100mW. One input port of the coupler C5
is cleaved in order to achieve the output coupler of the laser with a reflectivity of 4%. The end mirror of the laser is realized by splicing a chirped fiber Bragg grating with a high reflectivity (≥98%) at 1550 and 2nm bandwidth. In contrast, all the other coupler’s input ports were angle cleaved to avoid any reflection in the laser resonator.
Fig. 10. Experimental set-up of the 4-arm fiber laser (4AFL).
We have measured the conversion efficiency of the 4-arm fiber laser (4AFL) to be compared with those obtained with the MZFL and an individual fiber laser (IFL). Figure 3
shows that the 4AFL threshold (Thr) was twice the MZFL one. In each arm of the interferometric laser, the population inversion occurs at the same pumping level as in the IFL. The 4AFL, the MZFL and the IFL had almost the same slope efficiency (ηL
) of 44%. This means that the combining efficiency was maximum which was confirmed by the very low power leakage measured on the angle cleave output (<1mW). At the highest pumping level of 4 × 100mW, the 4AFL output power reached 152mW, almost four times the output power of an IFL (40mW).
Finally, we theoretically investigated the resonator critical parameters in order to efficiently combine a high number of lasers in a single multi-arm cavity. The principle of coherent combining method is based on the use of an interferometric resonator configuration. The spectral response of such resonators determines the resonance frequencies of lowest losses which achieved a high efficient coherent combining. The multi-arm laser only amplifies these resonance frequencies. So, we have studied the spectral response of a N-arm interferometer resonator by using the circulating field theory [9
9. C. Pedersen and T. Skettrup, “Laser modes and threshold conditions in N-mirror resonators,” J. Opt. Soc. Am. B 13, 926–937, (1996). [CrossRef]
10. C. Pedersen and T. Skettrup, “Signal-flow graphs in coupled laser resonator analysis,” J. Opt. Soc. Am. A 14, 1791–1798, (1997). [CrossRef]
]. In that way, one can estimate the intracavity losses and so the combining efficiency of the multi-interferometer resonator.
Fig. 11. Scheme and nomenclature of a) the Fabry-Perot resonator; b) the Michelson interferometer.
The well-known complex amplitude reflectivity req
of a Fabry-Perot cavity (see figure 11a
) is given by:
with the output coupler reflectivity r0 and the back mirror reflectivity
By replacing the back mirror reflectivity rk of the Fabry-Perot resonator by the equivalent complex reflectivity of a N-arm interferometer rkN, one can determine the spectral response of the N-arm interferometer resonator.
We first consider the case of the standard Michelson interferometer, which has a similar spectral behavior than the Mach-Zehnder device with two arms as depicted in Fig. 11b
. All the circulating fields used in the next equations are defined on the Fig. 11
. The circulating field expressions are:
rs and ts are respectively the reflectivity and the transmission of the 2×2 coupler.
They lead to:
We consider a balanced 2×2 coupler such that
Then, the complex reflectivity of the interferometer device is:
It has to be noted that the expression of rkN
does not depend on the position of the 2×2 couplers or of the fiber couplers in the tree architecture of the N-arm interferometer resonator. So, the whole 2×2 couplers of the experimental 4-arm fiber laser previously described could be replaced by a single 4×4 coupler operating in the same way [2
Fig. 12. Scheme and nomenclature of the N-arm interferometer resonator.
Finally, we replace the end mirror Mk
of the Fabry-Perot cavity by the N-arm interferometer (Fig. 12
). Then, the equivalent complex reflectivity of the N-arm interferometer resonator reqN
and the intensity spectral response of the N-arm interferometer resonator is: ReqN = ‖reqN‖2.
We numerically have investigated the spectral response of the multi-interferometer resonator. In order to control the minimal path length difference between all the arms of the resonator, they had a constant average length difference ΔL. A random length deviation δli was added such that the length Li of the elementary resonator i was defined as: Li = Lc + i.ΔL + δli. Lc was the minimal length of the elementary resonators. δli was chosen to take into account the difficulty to cut a long fiber at a precise length. The next calculus was obtained with the following data: Lc = 20m ; r02 = 0.04 ; -ΔL/10 ≤ δli ≤ ΔL/10 ; Δλ = 1nm, spectrum bandwidth centered on λ0 = 1550nm.
Fig. 13 Calculated intensity spectral response of a 20-arm interferometer resonator with an average length difference ΔL = 10cm.
An example of the ReqN
function plotted Fig. 13
is calculated by considering an interferometer resonator of 20 arms and ΔL = 10cm. One observes a predominant modulation of the spectrum due to the constant average length difference ΔL. The large number of modulations in the spectrum bandwidth must ensure both high combining efficiency and output power stability as previously discussed in the Michelson or Mach-Zehnder fiber laser. The intracavity losses are closely connected to the intensity reflectivity of the resonator spectral response. Indeed, only the resonance frequencies corresponding to the highest value of ReqN
are amplified in the multi-interferometer laser. The numerical results also show that the number N of arms has no influence on the combining efficiency of the multi-interferometer resonator. Figure 14
describes the evolution of the highest reflectivity max(ReqN
) in the spectrum as a function of the number of arms. Max(ReqN
) has small fluctuations around an high average value of ~ 94% for ΔL = 10cm. However, this average reflectivity decreases with the minimal arm length difference ΔL as shown figure 15
as and when the number of modulations due to ΔL decreases in the spectrum bandwidth. The intracavity losses are complementary to max(ReqN
). The numerical results of the figure 15
show that these losses become critical only for a very small value of ΔL which is not realistic experimentally.
These last experimental and numerical results demonstrate that the coherent coupling method is compatible with the combining of a large number of lasers without loss of efficiency.
Fig. 14. Calculated evolution of the highest reflectivity max(ReqN) of the spectral response, as function of the number of arms N for ΔL = 10cm.
Fig. 15. Calculated evolution of the highest reflectivity max(ReqN) of the spectral response, as function of the average arm length difference ΔL.