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We propose a novel all-solid rod-type fiber structure that presents a cylindrical symmetry and low refractive-index contrasts. Effectively single-mode propagation for the fundamental mode is ensured thanks to resonant couplings between Higher Order Modes (HOMs) and cladding modes. Numerical simulations demonstrate the possibility of achieving a fundamental mode effective area as large as 5000µm2 at a wavelength of 1.06μm in fibers ensuring a high leakage loss ratio (>100) between the HOMs and the fundamental mode while keeping the fundamental mode leakage losses at a level lower than 0.2dB/m. Further scaling to an effective area of 12,200µm2 at 1.06μm in an effectively single-mode fiber is also presented by exploiting the power delocalization of several HOMs on top of the high-leakage loss filtering.
©2013 Optical Society of America
1. Introduction
High-power fiber lasers have seen a dramatic progress over the last decade. A level of 10kW in continuous wave regime has been achieved in a diffraction limited beam in 2010 [1], only six years after the first demonstration of more than 1kW output power [2]. For a further increase of the output power, a current challenge lies in the scaling of the Effective Area (Aeff) within the fiber (in order to ensure non-linear effects mitigation), while maintaining a single-mode output (in order to ensure a good output beam quality).
Several fiber structures have been proposed to achieve single-mode operation and large fundamental mode Aeff, as low-NA step-index fibers (in which Higher Order Modes (HOMs) filtering is ensured thanks to controlled bending of the fiber) [3], Chirally Coupled Core fibers [4], tailored cladding fibers for HOMs suppression [5, 6], Bragg fibers [7], Photonic Bandgap Fibers [8], Photonic Crystal Fibers (PCF) [9], and Leakage Channel Fibers (LCF) [10]. However, the scaling of the Aeff in such fibers is limited due to detrimental bending effects [11]. For a further scaling, a promising approach consists of rod-type fibers [12], which are a few mm thick and cannot be bent. Despite losing the flexibility of conventional fiber laser, these structures present the assets of achieving ultra-large Aeff.
There are, mainly, three kinds of structures that have been proposed in the form of ultra-large Aeff for effective single-mode operation. First of all, PCFs have been reported for Aeff in the range 2000-5000µm2 at 1.06µm [12]. A further scaling of the Aeff up to 5000-10,000µm2 at 1.06µm has been achieved using careful excitation technique [13, 14] and several other common techniques to improve structure to ensure single-mode operation [15]. However these improved structures present considerable drawbacks and are difficult to fabricate. The second approach consists of LCFs in which an Aeff as large as 14,000µm2 in the case of a passive fiber and an Aeff around 3200µm2 in the case of an active fiber [16, 17] have been demonstrated around 1.04μm. The third approach, which was recently introduced, is constituted by Large Pitch Photonic Crystal Fibers (LPF) in which single-mode operation is ensured thanks to HOMs power delocalization [18]. These fibers have reached the value of 8600µm2 at 1.04μm for the Aeff in the case of active fibers and have shown higher power scaling capabilities than LCFs and PCFs [19]. The main drawbacks of all these three approaches are their difficult fabrication, due to the requirement of stack and draw technique, and a frequent hexagonal shape for the output beam. Another drawback of LPFs and PCFs consist of the presence of air holes which create further difficulties in terms of laser reliability [7, 10].
In this paper, we present a novel all-solid structure having a cylindrical symmetry that ensures single-mode operation with ultra large Aeff (>10,500μm2) at 1.06μm wavelength. Low-loss single-mode operation in fiber with a 100μm diameter core is first investigated by considering only differential leakage losses for HOMs filtering. Then the core diameter is scaled to 140μm, by exploiting also the small overlap of the HOMs with the doped area in the core as compared to the case of the fundamental core mode. Finally, an investigation of the impact of small core refractive-index variations is presented.
2. Multi-Trench Fiber presentation
We propose an optical fiber structure with a large core surrounded by a periodic cladding constituted of alternating low- and high-refractive index rings (as shown in Fig. 1 ). The high-index rings and the outer infinite cladding present the same refractive index as the core. Consequently, the structure is formed by the inclusion of the low-index rings (trenches) only and we call it: Multi-Trench Fiber (MTF). Figure 1(b) presents the notations used in this paper: rc is the core radius, t is the thickness of the low-index rings, d is the thickness of high-index ring, nc is the refractive index of the core, and Δn is the refractive index difference between the core and the low-index rings.
Fig. 1 (a) Schematic cross-section of the proposed fiber structure. Blue and white colours represent high and low-refractive index regions respectively. (b) Refractive index profile of the proposed optical fiber, where rc is the radius of the core, d is the thickness of the high-index rings (resonant rings), t is the thickness of the low-index rings (trenches), and Δn is the refractive-index difference between the resonant rings and the trenches.
Numerical simulations on these structures have been performed with a full-vectorial Finite Element Method (FEM), in which the domain truncation has been ensured by using circular anisotropic Perfectly Matched Layer (PML) [20].
3. Principle analysis
In a MTF, all the core modes are leaky in nature, due to the fact that the refractive index of the core is equal to those of the outer cladding. For the analysis of the working principle of Multi-Trench Fibers, we first study the case of a single-trench fiber formed by the three first layers of the multi-trench fiber (as shown in Fig. 2(a) ) with structural parameters rc = 50µm, t = 1.4µm, d = 31μm, and Δn = 0.001 at λ = 1.06μm. In the single-trench fiber, the core modes present very high leakage losses. Moreover, the leakage loss ratio between the first HOM (LP11) and the fundamental mode (LP01) is small (<4 at 1.06μm).
Fig. 2 Leakage losses spectrum of the fundamental core mode and the first HOM of: (a) the single trench fiber and (b) a fiber with three trenches. (c) Surface profile of the transverse electric field component of the fundamental and the first higher order mode(s) of the single and three trench fiber. (d) Transverse electric field component along the x-axis of the first higher mode of both fibers. The structural parameters are rc = 50µm, t = 1.4µm, d = 31μm, and Δn = 0.001 at λ = 1.06μm.
The inclusion of the additional trenches around the single-trench fiber has two main effects (as shown in Fig. 2(b)). First of all, the leakage losses of the fundamental core mode are significantly decreased. This is due to the reduction of the tunneling of its power towards the infinite outer cladding. Secondly, the ratio between the losses of the first HOM and the fundamental mode is increased (>100 at 1.06μm) thanks to resonant coupling between the first higher-order core mode of the single-trench fiber and the modes of the rings having same refractive index as the core (as shown in Fig. 2(c-d)) [21]. It is interesting to note that, for the specific case of the Fig. 2(b) (three -trenches fiber); three mode groups having the symmetry of a LP11 mode in the core coexist with a non-negligible amount of energy in the core and with a different level of leakage losses (cf. Figure 2(b-c)). This is due to the coupling between the LP11 core mode of the single-trench fiber and the LP11 modes of each of the two rings of same refractive index as the core (resonant rings). This is also applicable for other HOMs. For a straightforward study, we take into account the whole set of three modes groups.
4. Design of a MTF with a core diameter of 100µm
The leakage losses of the higher-order modes can be tuned by adjusting the thickness (d) of the resonant rings. Figure 3 illustrates this property for the case of a wavelength of 1.06μm and a 100μm-core diameter fiber having three trenches in which Δn = 1x10−3 and t = 1.4μm. In this figure, only the mode presenting the lowest leakage losses in the core for a given symmetry has been plotted. From Fig. 3, a range of thickness d (28-38μm) can be figured out for which the leakage losses of all the HOMs having the symmetry of a LP11, LP21 or LP02 mode are higher than 20dB/m, while the leakage losses of the fundamental mode are lower than 0.5dB/m. We have verified that the losses of the HOMs other than the above mentioned modes are also higher than 20dB/m for this range of thickness d. Therefore low-loss single-mode propagation for the fundamental mode can be ensured in this range. For an even stronger HOMs filtering, it is interesting to note that, for d in the range 30-33μm, all the HOMs have leakage losses higher than 30dB/m.
Fig. 3 Leakage losses of the fundamental mode and of HOMs of low order as a function of the resonant ring thickness (d) at a wavelength of 1.06µm for a fiber with Δn = 0.001, rc = 50µm, and t = 1.4µm. Inset shows the surface profile of the transverse component of the electric field for various modes at d = 31µm.
From the perspective of practical realization, we have studied the robustness of the single-mode operation of our proposed 100μm-diameter core structure to small variations of the depth of the trench (Δn) and its thickness (t). Figure 4 shows the variation of the leakage losses of the fundamental mode and the HOM which has the lowest losses among all the possible HOMs at 1.06μm for a 100µm diameter core as a function of d. Figure 4(a) and 4(b) show this variation for different t at constant Δn and for different Δn at constant t. For a fixed Δn of 0.001, a level of leakage losses higher than 20dB/m is obtained for all the HOMs, for d in the range 30-33µm and t in the range 1.2-1.6µm. For a fixed t of 1.4μm, same level of HOMs suppression is ensured for d in the range 30-33µm and Δn in the range 0.0008-0.001. The losses of the fundamental mode are maintained below 0.72dB/m for both of these cases. For these ranges of parameters, the Aeff of the fundamental core mode LP01 is higher than 5000μm2 at 1.06μm.
Fig. 4 (a) Leakage losses of the fundamental mode and lowest leakage losses level of the higher order mode as a function of d for a 100μm core diameter fiber at 1.06μm wavelength (a) at Δn = 0.001 for different t and (b) at t = 1.4μm for different Δn.
5. Mode area scaling
To further increase the Aeff, while maintaining a single-mode output for the fundamental mode, we have chosen a higher core diameter (140μm) and have taken into account the power delocalization for HOMs filtering. The Fig. 5(a) shows that, for the specifically chosen parameters (t = 1μm, Δn = 0.001), for a d value between 42μm to 45μm, a leakage loss level higher than 20dB/m can be ensured for all the HOMs except for the lowest loss mode having a symmetry of a LP11 mode that exhibits leakage losses higher than 15dB/m only. But, in this range, this mode is the result of couplings between core and ring modes and have a low percent of power in the core (<47%) (as shown in Fig. 5(b).). The overlap between this mode and the active area located in the core is thus small and a single-mode amplification of the fundamental mode (that has leakage losses lower than 0.19dB/m and a percent of power in the core higher than 93%) is thus achievable [6].
Fig. 5 (a) Leakage losses of the fundamental mode and of HOMs of low order as a function of d at λ = 1.06µm for a fiber with Δn = 0.001, rc = 70µm, and t = 1µm. (b) Fraction of power in the core for LP01 and LP11 modes as a function of d at λ = 1.06µm of the same fiber.
Figure 6 shows two ranges of structural parameters d = 42-45μm and t = 0.8-1.0µm at Δn = 0.001 and d = 42-45μm and Δn = 0.0008-0.001 at t = 1.0µm in which the lowest loss LP11 has leakage losses higher than 15dB/m with a percent of power in the core lower than 47%. The other HOMs has leakage losses higher than 20dB/m. In these ranges, the leakage losses of the fundamental mode are lower than 0.5dB/m. Therefore low loss single-mode operation is ensured for the fundamental mode. For these ranges, the Aeff of the fundamental mode ranges between 10,500μm2 to 12,200µm2.
Fig. 6 Leakage losses, at λ = 1.06µm, of the fundamental mode and lowest leakage loss level of the higher-order modes as a function of d for: (a) different t for a fixed Δn of 0.001 as well as for: (b) different Δn for a fixed t of 1μm for a 140µm-diameter core fiber.
6. Impact of small variations of the core refractive index
In the above study, perfect index-matching has been assumed between the active ions doped core and the surrounding undoped cladding material (formed by the rings and the infinite cladding), that is very challenging to achieve during the fabrication of the fiber.
For the above presented MTFs, if the core presents a refractive index slightly larger than those of the surrounding undoped material, several HOMs are guided in the core with very low leakage loss. To avoid this configuration, it is possible to target a core refractive index that is lower than that of the surrounding undoped cladding material (i.e. a core refractive index depression Δnc) [22].
Figure 7(a) shows the impact of a core-refractive index depression of Δnc = −1x10−4 for the case of a three-trench fiber with rc = 50μm, t = 1.6μm and Δn = 0.001. In the case of a perfect core-cladding index matching, this fiber presents an Aeff of ~5000μm2 at 1.06μm, a reasonable level of fundamental mode leakage loss and a good HOM filtering for d = 30-33μm (cf. Fig. 4(a)). In the case of a core refractive index depression of Δnc = −1x10−4, the leakage loss of the fundamental mode are larger than 5dB/m for d = 30-33μm, that is not acceptable for most of rod-type fiber laser applications. It is worth noting that the beam quality remains however good, the M2–parameter of the fundamental mode has been indeed evaluated to ~1.35. Moreover, the Aeff remains larger than 4750µm2.
Fig. 7 Leakage losses, at λ=1.06µm and rc=50µm of (a) the fundamental mode at different Δnc at t=1.6µm and Δn=0.001 of (b) the fundamental mode and HOMs lowest leakage loss level for different t and Δn at Δnc=-1x10-4.
To ensure low leakage losses for the fundamental mode, it is possible to adjust the MTF cladding for compensating the effects of the index depression in the core. For the above mentioned fiber, such adjustment can be done by increasing the thickness of the trenches (cf. Fig. 7(b)). For example for Δnc = −1x10−4, a low-loss single-mode operation can be ensured for d = 37-39µm, t = 2.4-2.8μm, and Δn = 0.0008-0.001. Indeed, for appropriate combination of these parameters, the fundamental leakage losses remain lower than 2dB/m, the fundamental-mode power percent in the core is larger than 94%, and the HOMs leakage losses are larger than 23dB/m (cf. Fig. 7(b)). In this range of structural parameters, the Aeff is varying between 4850µm2 and 5120µm2. Moreover, thanks to the cylindrical symmetry of the structure, the beam-quality remains very good (M2≤1.35). Such MTF with adjusted cladding can be realized by fabricating separately the active core and the MTF cladding. Initial simulations suggest that, in depressed index core MTF, the Aeff can be scaled further to a value of ~10,000μm2, but it is intended to a future work.
It is worth noting that, in the case of depressed-core LPF, the fundamental mode M2 parameter is rapidly increasing with increasing Aeff [22]. Even a core index depression of Δnc = −0.2x10−4, leads to the deterioration of the M2 to a value larger than 1.35, for Aeff larger than 2500μm2 [22]. Moreover, for a core index depression of Δnc = −1x10−4, the best M2 values that can be achieved for an Aeff of 2500μm2 and 4000μm2 are respectively of 1.7 and 2. The MTF presents therefore a dramatically better robustness to core-index depression than LPF in terms of beam quality preservation.
7. Conclusion
All-solid low refractive index contrast optical fibers of 100µm and 140μm core diameter with Aeff higher than 5000µm2 and 10,500µm2 at 1.06µm respectively have been proposed. In these fibers, single mode operation is ensured by efficient HOMs filtering thanks to resonant couplings to the rings of the cladding. These fibers show a good potential for ultra-large mode operation and show certain advantages over LPFs and PCFs mainly constituted of easy fabrication and a good output beam quality. Furthermore, MTFs are all solid structure and are free from any problems due to air holes, which are encountered in LPFs and PCFs.
Acknowledgment
The work is supported by the EPSRC Centre for the Innovative manufacturing in Photonics EP/HO2607X/1.
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