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Abstract
We demonstrate operation of a cladding-pumped hybrid ytterbium-doped HOM fiber amplifier and reconversion of the HOM output to Gaussian-like beam by using an axicon based reconversion system. The amplifier was constructed by concatenating single-mode and HOM ytterbium-doped double clad fibers, and was excited by a common multimode pump source. A continuous wave (cw) input signal of 97mW was amplified to 100W at the amplifier output, which yielded a gain of more than 30dB. The LP0,10 output of the HOM amplifier could be converted to a Gaussian-like beam with 67% conversion efficiency. We present, both analytically and numerically, the effects of scaling the beam size on axicon’s apex angle, and how shape imperfections affect the mode converter’s performance.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Coherent optical sources based on higher-order-mode (HOM) guidance in optical fiber have drawn a great deal of interest in the past years due to a number of unique and potentially beneficial attributes, such as ultra-large effective-area allowing high peak-power pulse generation, greater bend-resistance facilitating compact design, and unique optical nonlinear and chromatic-dispersion properties enabling ultrawideband wavelength-conversion [1–6].
Specialty optical fibers have been developed that allow for propagation of light in a specific HOM with minimal coupling to the neighboring modes allowing for robust operation [1–3]. Furthermore, methods for exciting a specific HOM in optical fibers have also been realized, which may include the use of a long-period-grating (LPG) inscribed within the HOM fiber [1,2] or a spatial phase modulator [7,8].
Like conventional fibers, the HOM fibers can be doped with rare-earth ions for use as a gain medium to amplify signal propagating in these modes. HOM fiber amplifiers can be configured either with core- or cladding-pumping. In a core-pumped HOM amplifier, pump radiation is effectuated to propagate in the same HOM as the signal to maximize the overlap between the pump and the signal fields within the doped core. On the other hand, in cladding-pumped amplifier, the pump is applied as a multimoded wave through the entire fiber cross-section, uniformly exciting the doped region, whereas the signal is still guided within a specific HOM to obtain a single-mode operation.
In the past, a core-pumped Er-doped-fiber HOM amplifier with 6000 μm2 effective area, for the amplification of both continuous-wave and nanosecond pulsed light has been demonstrated [2]. As well, there have been research efforts towards the development of ytterbium-doped HOM amplifiers aimed at applications within the 1μm wavelength region. In the Yb-doped fiber amplifiers, however, instead of the core-pumping, the cladding-pumping is preferred because of the availability of low-cost high-power 975 nm multimode pump laser diodes [4,6].
A challenge with the cladding pumping of a Yb:HOM amplifier is that the large doped core (~100μm in diameter) tends to produce an excessive amount of amplified spontaneous emission (ASE) noise due to the presence of hundreds of modes supported by the core. This could result in a severely reduced slope efficiency of the amplifier. One way to suppress the ASE is to use a relatively high-power input signal, in the order of several Watts [4]. Another approach towards achieving a high slope efficiency is to use a longer gain fiber that can facilitate the reabsorption of the forward propagating ASE for further amplification of the HOM-signal [6]. This approach, however, was not found to be effective in suppressing backward propagating ASE.
Recently, we reported a cladding-pumped hybrid-amplifier structure that consisted of cascaded single-mode and HOM gain fibers, with an intermediate LPG for converting the signal in to a large-effective-area HOM. The hybrid-amplifier design offered the advantage of pre-amplification of the weak signal in the single-mode gain fiber so that the signal could outgrow the ASE within the subsequent HOM-fiber section. The hybrid-amplifier structure also afforded the isolation of the ASE noise between the two amplifier stages via the spatial-filtering effect provided by the intermediate LPG [9,10]. Using a cladding-pumped Yb:HOM amplifier, we were able to operate the amplifier for pulsed operation (8 ns, 250 kHz, wavelength λ = 1064 nm) using only 115-mW input signal, and obtained 52 W of amplified output (26 dB gain) in a higher-order-mode, with an overall slope efficiency of 57% [9].
Since most applications involving high-power lasers require a beam with a low M2-value, it is important to convert the HOM output to a Gaussian-like mode. Various methods have been proposed to re-convert the HOM, including the use of a reciprocal LPG inscribed at the output end of the HOM fiber [1], as well as by external means such as using bulk optic axicon [11], binary phase plate etc. To ensure high efficiency of mode re-conversion, it is important to maintain modal purity of the HOM at the amplifier output, which requires proper engineering of the HOM fiber for robust mode-propagation and amplification, as well as an appropriate design of the amplifier-system.
In this paper, we report on the operation of a cladding-pumped hybrid Yb:HOM amplifier and reconversion of the HOM output using a bulk optic axicon-lens. CW amplification properties of the hybrid amplifier, and the general design principles of optical-mode reconversion using axicon-lens are presented. This work demonstrates the performance of a high-power HOM-hybrid-amplifier system operated with a low-power input signal and provides a roadmap for the design of future systems that involve manipulation of the electric-field-distribution of light.
2. Ytterbium-doped HOM fiber
Yb-doped HOM gain fiber, which is the key element of the amplifier, consists of three concentric regions of glass—a single-mode inner core, a rare-earth doped outer core, and a surrounding cladding. The cross-sectional view of the HOM fiber is shown in Fig. 1(a). The diameters of the inner and outer cores are ~8 μm (2a1) and 110 μm (2a2), while the numerical apertures (NA) are 0.085 and 0.138, respectively. Optical signal can be launched into the inner core as a fundamental (LP0,1) mode, which can be subsequently converted in to a desired HOM by a long period grating inscribed directly within the gain fiber. The cladding (diameter: 356 μm) is coated with a low index polymer and has an octagonal shape for guiding and efficient mixing of the multimode pump radiation. The core is doped with ytterbium to yield a cladding pump absorption of ~40 dB/m, at a wavelength ~975 nm.
Fig. 1 (a) Cross-sectional view of the Yb:HOM fiber used in the amplifier, (b) The normalized electric field amplitude distribution of the LP0,1 and LP0,10 modes plotted in relation to the refractive index profile, RIP (not drawn to scale).
The outer core, which has a V-number of 44.7 (at wavelength of 1064nm), can support as many as 14 (~V/π) symmetric linearly polarized modes, LP0,N. In our amplifier design, we choose LP0,10 mode that exhibits enhanced stability towards bending. The refractive index profile and the normalized intensity distribution of the LP0,1 and LP0,10 modes are depicted in Fig. 1(b). The effective area of the chosen mode LP0,10 (3140 μm2) is 41 times larger than that of the fundamental mode, which has an effective area of 76 μm2.
3. Cladding-pumped Hybrid Yb:HOM amplifier
The schematic diagram of a cladding pumped hybrid amplifier is shown in Fig. 2(a). It was constructed from a short length (~0.6 m) of an11-μm-mode-field diameter (MFD), 200-µm-cladding single-mode ytterbium-doped double-clad fiber (YDF, 2.46 dB/m cladding absorption at 975 nm) and a 3.1m long HOM ytterbium-doped double-clad fiber. A tapered fiber bundle (TFB) was used to combine the (single-mode) signal and the (multimode) pump beams.
Fig. 2 (a) Schematic of a cladding-pumped hybrid Yb:HOM amplifier employing single-mode and higher-order mode gain fiber, (b) Beam profile of the HOM mode, LP0,10, at the amplifier output.
The MFD of the TFB output fiber, the YDF, and the Yb:HOM fiber were all ~11 μm, and the fibers were fusion-spliced with low-loss to create a cladding pumped amplifier. To covert the LP0,1 mode to LP0,10 mode, an LPG, 2-cm in length, was inscribed close to the input end of the Yb:HOM fiber using standard UV laser inscription technique. The conversion efficiency of the LPG was estimated from the transmission loss of light in LP0,1 mode in the Yb:HOM fiber measured before and after the grating inscription. The conversion efficiency of the LPG module used in the experiment was 98%. Nine multimode fiber-pigtailed pump laser diodes (975 nm, 26 W), were spliced to the TFB pump input ports delivering a maximum pump power of 235 W.
It is worth mentioning that for a core-pumped HOM amplifier, the LPG is required to be operated at the turn around point (TAP) of the phase matching curve for the spectrum to be sufficiently broad in order to convert both the pump and signal in to HOM mode [2,12]. It is no longer a requirement for the cladding-pumped architecture, as we need to convert only the signal wave into the desired HOM. Lifting of such restrictions provides additional freedom in choosing an HOM that exhibits greater stability during propagation in the HOM fiber.
We used an in-house built ytterbium doped fiber ASE source operating in the cw-mode at a wavelength of 1064 nm as the provider of the input signal. The 3dB-bandwidth was 0.6 nm and the noise floor was below −52dB (measured with a resolution bandwidth of 1 nm).
The single-mode YDF was relatively short in length (<1m) and when pumped at high power (with a few tens to a few hundreds of watts, to attain high population inversion), it served as a high gain pre-amplifier. The launched multimode pump, after a small fraction being absorbed in the single-mode YDF section, entered the HOM gain fiber, where the signal could be amplified to several tens of watt to over 100 W of average power.
Before operating the hybrid amplifier structure, we first tested the amplification properties of the single-mode YDF amplifier alone, with the output end polished at an angle of 10 degrees. The signal output power from the amplifier and the amount of unabsorbed pump are plotted in Figs. 3(a) and 3(b). It may be noted that an input signal was amplified from 79 mW (power launched into the single mode YDF) to 5.7 W average-power in the 0.5m long single-mode YDF using 180W of pump radiation, while yielding 168 W of unabsorbed pump to perform further amplification of the signal in the Yb:HOM fiber section.
Fig. 3 CW amplification characteristics of the cladding-pumped 0.5-m long single mode gain fiber, studied experimentally (a) Signal output power vs pump power, (b) Residual pump vs incident pump power.
In cladding-pumped Yb:HOM fiber amplifiers, in addition to the specified higher-order-mode, a fraction of the signal with arbitrary modes distribution may co-propagate with the signal and get amplified in the similar way as the desired HOM. This may, as a consequence, degrade the modal purity of the output signal. The power in these arbitrary modes depends on the imperfections in the TFB and the extent of the splice-loss between the single-mode and HOM gain fibers. The fraction of power in random modes that results from imperfections in TFB, however, eventually gets suppressed relative to the signal propagating in the fundamental-mode due to amplification in the single-mode YDF.
To minimize mode quality degradation due to splice, we needed to carefully optimize the splicing recipe between the single-mode and the HOM gain fibers. We were able to attain a fundamental-mode-launch efficiency > 95% (corresponding to a splice loss less than 0.22 dB). This efficiency was estimated by launching a 1170 nm light (transparent to ytterbium absorption and outside of LPG conversion band) into the single mode ytterbium doped fiber and measuring the fraction of light in the LP0,1 mode by imaging at the output of HOM fiber. As a result, the amplified HOM signal with high contrast between peaks and nulls of the optical-field-rings was obtained for the cladding-pumped hybrid fiber amplifier – see Fig. 2(b) for the near-field image of the amplified signal, recorded on a charge-coupled-device (CCD) camera.
The powers of the output signal, ASE and the residual pump at the output of the HOM fiber were measured using a set of dielectric optical filters (long pass and band-pass), and the values are plotted as a function of the pump power in Fig. 4. For an input signal of 97 mW (input power to the TFB), an output power of 100.3 W was obtained from the hybrid-amplifier using 180W of pump power, yielding an overall gain of 30dB. The slope efficiency was 66%, whereas the ASE in the forward direction was less than 5W.
Another noteworthy point is that the LPG provides isolation between the two stages as regards to the ASE propagation. Any broadband and multimoded ASE (except for ASE in LP0,10 mode) from the HOM gain fiber, that propagates in the backward direction, enters the single mode gain fiber as is and thus experiences minimal gain. Again, the forward propagating ASE from single mode gain fiber that resides mostly out of band of LPG, enters the HOM as an LP0,1 mode and thus remains relatively unchanged.
4. Conversion of HOM to Gaussian-shaped beam
Since most practical applications of high-power lasers demand a Gaussian-shaped beam that may allow diffraction-limited focusing, it is of great importance to convert the HOM output of the amplifier to a suitable Gaussian-like beam, with an M2-value close to 1. One convenient approach to achieve mode re-conversion is to use conical lens, known as axicon [11]. Axicons have been widely used to convert a Gaussian beam into a Bessel beam by modifying the radial phase distribution [13]. It has been shown that when an HOM beam (a truncated form of Bessel beam) diffracts upon propagation in free-space, the radial phase distribution is modified such that it could be nominally corrected by the linear phase imposed by an axicon-lens placed at an optimal location. There is an optimum value of the axicon-lens’ apex angle ‘α0’ that depends on the electric field distribution of the incident HOM beam. The overlap integral between the phase-corrected beam and a Gaussian-beam can be slightly over 80% for an ideal axicon [11].
In the following, we present a general analysis of converting an HOM beam into a Gaussian-like beam using an axicon-lens. We derive simple formulae to relate the given beam-parameters with the optimum values of axicon apex-angle and position to achieve the maximum efficiency of mode-conversion.
The schematic diagram of an axicon-based mode-converter is shown in Fig. 5. Let’s assume that the electric-field-distribution of the HOM beam at the exit of the fiber is u(ξ,η). As an example, the amplitude and phase distribution of the LP0,10 mode are shown in Fig. 6(a). As the HOM beam propagates in free-space, it undergoes diffraction, as shown in Fig. 6(b). The electric field at any distance z can be expressed under Fresnel approximation as [14],
Fig. 6 Electric field amplitude and phase distribution of HOM calculated at different locations within the reconversion system. (a) Exit of the HOM fiber, (b) right before the axicon.
The efficiency of reconversion can be calculated by comparing (i.e. by taking overlap integral of) the diffracted beam (after phase-correction by axicon) with an ideal Gaussian beam. The Fig. 7 shows the maximum overlap integral achieved by optimizing the apex angle α of an ideal axion, with a perfectly sharp tip, placed at different distances z. It can be seen that for the LP0,10 mode emanating from our Yb:HOM fiber, an overlap integral of 0.823 can be achieved when an axicon with an optimum apex angle (α0) of 11.71 deg is placed at an optimum distance z = Ζ0 of 0.7 mm. The electric field amplitude and phase distribution of the HOM electric field at z = Z0 is shown in Fig. 6(b), showing an almost linear phase distribution.
Fig. 7 Optimum apex angle and corresponding overlap integral (OI) plotted as a function of the position of the axicon.
Now, it is to be noted that the practical implementation of an optical setup for mode reconversion using an axicon with such sharp tip and such small gap can be a rather daunting task. A convenient way to circumvent this is to magnify the beam by an appropriate amount before mode reconversion, as shown in Fig. 8(a).
Fig. 8 (a) Schematic of reconversion of magnified HOM beam using axicon, (b) Optimum apex angle and position of axicon plotted as a function of beam magnification, calculated for LP0,10 mode of HOM fiber used in the experiment.
An HOM beam u(ξ, η) with size magnified by M, can be represented by u(ξ/M, η/M). When such magnified beam diffracts in free space, it can be shown that the amplitude and phase distribution at a distance z.M2 (from the input plane) is an exact replica of the field-distribution of an original beam u(ξ, η) that has propagated through a distance z; the only difference being that the former is radially magnified by a factor of M. This can be mathematically expressed as,
As a result, the optimum apex angle αM and the optimum distance ZM associated with M-fold magnified beam are related to α0, and Z0 as follows,
Figure 8(b) shows αM and ZM for the LP0,10 mode of the Yb:HOM fiber plotted as a function of M, using αo = 11.706 deg, Z0 = 0.7 mm, and the Eqs. 3(a) and 3(b). From the figure, we can see that if we employ an axicon with an apex angle of 1 deg, the required magnification will be M = 11.9, and the optimum axicon position will be ZM = 99.5 mm. As regards to the choice of magnification factor M, the smaller the value of M, the smaller will be the size of the diffracted beam being incident on the axicon. Thus, for smaller M, the adverse effect of rounding of the axicon tip will be more severe. On the other hand, choosing a large M, although will be beneficial in minimizing the effect of tip rounding, the length of the converter might be too large and inconvenient for practical application.
It is noteworthy that the axicons that are commercially available exhibits a tip with significant rounding due to the mechanical polishing during manufacturing. Such deviation from the ideal axicon can somewhat compromise the conversion efficiency and could also affect the optimum position of the axicon.
Figure 9(a) shows the phase delay introduced by a 1-degree ideal axicon and one that we used in our experiment, where a deviation due to the rounding of the tip can be clearly seen. In Fig. 9(b), we have plotted the overlap integral OI (representing the efficiency of mode-reconversion) and the corresponding optimum position of the axicon, for different values of beam magnification. In both cases, the largest OI can be achieved for a magnification-factor of 11.9. Due to the rounding of the tip, however, the maximum OI (0.76) for the commercially-available axicon is slightly lower than that achievable with an ideal axicon. Moreover, the optimum distance is found to be significantly longer (138 mm) compared with 99.5 mm for the ideal axicon case, which is again attributed to the rounding of the tip. Intuitively, this is quite expected, as the longer propagation distance Z0 helps expand the size of the HOM beam on the axicon compared with the rounded area of the tip.
Fig. 9 (a) Radial distribution of phase delay due to ideal and experimental 1-deg silica-glass axicon, (b) OI and optimum axicon location as a function of beam magnification.
When a beam is magnified by a factor M, the diffracted beam at M2.Z0 is simply a magnified image of the original beam at a distance of Z0. Due to this scaling effect, one would expect exactly the same conversion efficiency, regardless of the magnification factor. We can see from Figs. 7 and 9(b) that for both M = 1 and M = 11.9, OI remains the same at 0.823, provided that axicons are ideal. This is also in agreement with the simulation results shown in Fig. 3(b) of Ref [11].
It is worth noticing that as we magnify the beam by the desired amount before directing to the axicon, the phase distribution of the magnified HOM beam needs to be preserved as close to that at the HOM fiber output for an efficient reconversion of the mode using axicon. This can be effectively achieved using a pair of lenses with focal lengths of f1 and f2 arranged in a 4-f configuration, such that the f2/f1 becomes equal to the required M.
To confirm our theoretical predictions, we perform reconversion of the HOM output signal from by our hybrid amplifier system. The experimental setup used for HOM-beam reconversion using the axicon is shown in Fig. 10. We used a confocal image magnifier with two lenses f1 = 7.5 mm and f2 = 88.9 mm, yielding a magnification M = 11.85. The axicon was placed at a distance of ~138 mm from the image plane of the magnifier; the distance between the tip of the HOM fiber to the axicon was 330 mm. The beam after the axicon was focused using a lens with a focal length (f3) of 40 cm on to a CCD camera (Spiricon, SP620U), essentially yielding a far-field pattern of the reconverted beam. The HOM beam was efficiently reconverted to a Gaussian-shaped beam (shown in Fig. 11(a) with a very small background. Furthermore, M2-value of the reconverted beam was also measured using an M2-measuring instrument (Thorlabs: M2MS-BP209IR) for various levels of the beam transmission through a variable aperture that was placed at the focal plane of the f = 40-cm lens.
Fig. 10 Experimental setup of reconversion of HOM amplifier output using axicon. For beam profiling, camera is placed at the location of aperture.
Fig. 11 Reconversion of HOM amplifier output using axicon. (a) Far-field pattern of the reconverted beam, (b) M2 as a function of aperture transmission.
The measured M2 versus aperture transmission is plotted in Fig. 11(b), We obtained an M2 <1.1 for 67% aperture transmission, where the theoretically estimated OI was 75% for axicon with rounded tip, shown in Fig. 9(b). The small difference can be explained by the fact that a few percent of the output light may constitute modes other than the desired LP0,10 mode.
5. Conclusion
In conclusion, we have demonstrated a cladding pumped hybrid Yb:HOM fiber-amplifier emitting LP0,10 HOM output, and an efficient reconversion of the Bessel-like HOM-beam to a Gaussian-shaped beam using commercially available axicon and an appropriately designed 4-f image magnification system. A Gaussian-shaped beam was successfully obtained with small background and an M2-value that matched closely with the theoretical predictions. We have also shown simple equations to relate the parameters of converter for optimum mode conversion to the beam magnification.
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