Rare Earth Doped Optical Fibers with Multi-section Core

Summary

The gain bandwidth of a single-mode fiber is limited by the atomic transitions of one rare earth gain element. Here we overcome this long-standing challenge by designing a new single-mode fiber with multi-section core, where each section is doped with different gain element. We theoretically propose and experimentally demonstrate that this configuration provides a gain bandwidth well beyond the capability of conventional design, whereas the inclusion of multiple sections does not compromise single-mode operation or the quality of the transverse modal profile. This new fiber will be beneficial in realizing all fiber laser systems with few-cycle pulse duration or octave tunability.

Graphical Abstract

Highlights

• •A theoretical study of the fiber with asymmetric gain profile is presented
• •A multi-section core fiber is demonstrated with unique manufacturing strategy
• •This fiber greatly extends gain bandwidth while maintaining a good beam quality

Optics; Fiber Optics; Optical Materials

Introduction

The invention and development of rare earth doped optical fibers led to a revolution in the design of robust and compact light sources with excellent beam quality and high conversion efficiency (Agrawal, 2007). These fiber-based sources have become essential parts in a wide range of applications, including telecommunications, nonlinear microscopy, optical coherent tomography, and material processing (Richardson, 2010, Jackson, 2012, Geng and Jiang, 2014). As the demand for better performances continually grows, fiber light sources with shorter pulse duration, wider spectrum spanning, and larger tunable range are increasingly desirable. To achieve such sources, active fibers with broader gain bandwidth are critical (Digonnet, 2001). By optimizing active ion concentration, adding co-doping ions, or adjusting host glass compositions, the emission wavelength span can be increased to some degree. However, the allowable atomic transitions of rare earth dopants impose a physical limit on the maximum gain bandwidth that can be reached (Koechner, 2006).

In fact, a gain medium with broad emission band is not only a goal being pursued by the fiber community for a long time but also a subject of great interest in semiconductors. By stacking active nanomaterials with different emission wavelengths together, several groups have demonstrated spectrally broadband light sources (Gmachl et al., 2002, Rösch et al., 2015, Fan et al., 2015). In contrast to the development in semiconductor materials, to date, the core of single-mode fiber has been limited to only one kind of gain material and thus limited bandwidth. Some previous efforts combine multiple cores in one fiber to obtain multi-color emission (Bookey et al., 2007), but such designs can only generate discrete waveband from each core and are incompatible with the fibers that are routinely used. In another approach, a mixture of different granulated rare earth oxides is melted together and forms a single core (Di Labio et al., 2008). From laser media point of view, this core is actually made of one material, in which the rare earth ions have strong interactions with each other. As a result, undesirable energy transfers occur and quench certain radiative transitions, limiting laser emission wavelengths. To isolate each dopant from other active ions and local environment, nanoparticle-based approaches have been developed and explored (Kucera et al., 2009). The nanoparticles can establish shields outside the rare earth dopants and provide the physical separation, thereby reducing the ion interaction. Although this approach seems promising compared with previous ones, it is very difficult to control the morphology of rare earth nanoparticles and maintain their integrity in the multiple thermal steps of fiber fabrication, especially when two or more different dopants are present. Therefore, it remains a significant challenge to greatly extend the gain bandwidth of a single-mode gain fiber. Alternatively, researchers have to design complex optical cavities to alleviate the material constraint (Krauss et al., 2010, Chong et al., 2012), with increasing volume and cost of the overall system.

In this article, we present a new class of single-mode fibers with gain bandwidth well beyond the limit of a single laser material. Our fibers comprise multi-section core, with each section made of a different gain material (Figure 1A). There are two main challenges that have prevented the consideration and demonstration of this class of fibers previously. First, it is essential for fiber systems to maintain single-mode operation and the quality of the modal profile. Thus, all existing rare-earth-doped fibers have a cylindrical symmetric structure. An optical fiber typically comprises a central core surrounded by a cladding with lower refractive index. When doped with rare earth elements, the fiber is given optical gain that enables light amplification. The vast majority of rare-earth-doped fibers employ a uniform gain area overlapping with the circular core completely (Figure 1B). In some cases, the doping area is reduced smaller than the core (Figure 1C). Although the gain is no longer homogeneous in the core, it still follows a circular symmetric distribution to avoid mode distortion. Despite the large amount of research on optical fibers, so far little attention has been paid to the fibers with asymmetric gain profiles. It is not clear, without symmetric gain, whether a fiber such as shown in Figure 1A can still achieve good mode quality. Second, there are also intrinsic difficulties in experimentally achieving asymmetric structures with conventional modified chemical vapor deposition (MCVD) method, because the vapor mixtures are passed through and deposited on an axially rotated silica glass tube in the MCVD process (Li, 1985). In addition, it is not easy to precisely control and match the indices of the resultant glasses due to the limited controllability of the metal halide vapor stream.

Figure 1.

Comparison of Active Fiber Configurations

(A) The fiber with asymmetric gain.

(B) Conventional fibers with uniform gain filling their core.

(C) Conventional fibers with reduced gain area.

Our work addresses the two main challenges as outlined above. Theoretically, we conducted systematic analysis to understand the mode behavior with the presence of asymmetric gain profiles, complementing current fiber mode theory (Snyder and Love, 1983, Siegman, 2003, Siegman, 2007) and extending it to the complex space. Experimentally, the manufacture challenge was overcome through the rod-in-tube technique (Geng et al., 2014). Instead of conventional silica-based glasses, we demonstrated the fiber with multi-component silicate glasses, which allow us to precisely control the doping concentrations and refractive indices over a wider range than that can be achieved in silica glasses. The results show that, by weakly breaking the symmetry of the gain profile, a new degree of freedom is created and enables fibers with unprecedented performance.

Results and Discussion

We first explore mode properties of optical fibers having asymmetric gain. Figure 1A depicts a fiber that, like conventional fibers, has a round core surrounded by a cladding, but its core is divided into two sections. For simplicity, we assume that only one of the regions has gain. When a light wave propagates in the core region, it will see a complex refractive index distribution $n=n_0+n_R+i{n}_I$, where n₀ represents a constant background index and n_R is the real index profile of the structure. The gain component n_I has a uniform value n_I,1 = g for the doped region, whereas the other section is n_I,2 = 0. Then the light field $A\left(\stackrel{\rightharpoonup }{r}\right)=\varphi \left(x,y,z\right)e^{-ikz}$ in a fiber can be described by the equation

$${\nabla }^{2}A\left(\stackrel{\rightharpoonup }{r}\right)+k_0^2{n}^2\left(\stackrel{\rightharpoonup }{r}\right)A\left(\stackrel{\rightharpoonup }{r}\right)=0$$ (Equation 1)

where k = k₀n₀ with k₀ = 2π/λ and λ the wavelength of light in vacuum. Substitution of A into the equation and making the paraxial approximation yield

$$-i\frac{\partial \varphi }{\partial z}+\frac{1}{2k}\left(\frac{{\partial }^2}{\partial x^2}+\frac{{\partial }^2}{\partial y^2}\right)\varphi +k_0\left(n-n_0\right)\varphi =0$$ (Equation 2)

If we assume the field in the form $\varphi =\psi \left(x,y\right)e^{-i\mu z}$, the equation can be further simplified to

$$\frac{1}{2k}\left(\frac{{\partial }^2}{\partial x^2}+\frac{{\partial }^2}{\partial y^2}\right)\psi +\left[k_0\left(n-n_0\right)-\mu \right]\psi =0$$ (Equation 3)

where μ is related to propagation constant β by the equation β = k + μ.

Figures 2A–2E show the modal fields ψ in the cross section of a single-mode fiber when different amounts of gain are applied. A conventional single-mode optical fiber (n_I,1 = n_I,2 = constant) only supports the LP01 mode (Agrawal, 2007, Snyder and Love, 1983). As shown in Figure 2A, this mode has an intensity distribution that is similar to that of a Gaussian beam. Figure 2B shows the mode intensity profile with relatively low gain in the left section. In this case, the fiber still possesses a Gaussian-like distributed mode intensity, just like its conventional counterparts. If the gain keeps increasing, the mode intensity starts showing asymmetry with more energy residing in the doped section, as displayed in Figure 2C. As the gain coefficient g increases and exceeds a critical value, the fundamental mode will be confined in the left section (Figure 2D). Also, one can find that another new mode appears in the undoped section (Figure 2E).

Figure 2.

The Fiber Modes with Asymmetric Gain

(A–E) Typical behavior of modal field when gain coefficient is (A) zero, (B) low, (C) medium, and (D and E) high.

(F) Real and (G) imaginary parts of the propagating modes in the complex ${\tilde{V}}^2-b$ space. The transformation $\frac{\mathit{b}}{\mathit{\left|}\mathit{b}\mathit{\right|}}\mathit{log}\left(\mathit{1}\mathit{+}\mathit{\left|}\mathit{b}\mathit{\right|}\right)$ is used to better visualize data. For the projections shown in the ${\tilde{V}}^2$ plane, no localized states exist in the gray region; orange region, only fundamental modes exist; pink region, fundamental modes and higher-order modes coexist; blue region, each fundamental mode bifurcates into two separate modes; the region beyond blue, bifurcated higher-order modes.

See also Figure S1.

The physics behind this phenomenon can be explained by noting the imaginary parts of the refractive index imposing on ψ. Both real and imaginary refractive indices can create optical potentials confining light field. When the amount of gain is small, light can be freely exchanged between core sections; hence the mode field distribution in the core is just like conventional fibers. With the increasing gain gradually creating stronger imaginary potentials, the energy flow between two sections begins to be reduced and light field starts to be trapped in the two potentials. As the imaginary potential strength increases beyond the threshold, the weaker energy flow is no longer able to sustain the integrity of the field, and, as such, the fundamental mode becomes two isolated modes in each site.

To give a broader insight into the modes supported by the fibers with asymmetric gain, we further present an analysis in the complex ${\tilde{V}}^2-b$ space, where mathematical transformations are taken to make the results independent of particular fiber parameters. These transformations will not change the system's action. If we define a contrast factor $\Delta n_I=\left(n_{I,1}-n_{I,2}\right)/2$, gauge transformation can be established by $\varphi ={\varphi }^{\prime }\exp \left[-k_0\left(n_{I,1}-\Delta n_I\right)z\right]$ or ${\varphi }^{\text{'}}\exp \left[-k_0\left(\Delta n_I+n_{I,2}\right)z\right]$. The real and imaginary parts of the complex-valued index are expressed in the dimensionless forms (Siegman, 2003, Siegman, 2007).

$$\Delta n={\left(\frac{2\pi a}{\lambda }\right)}^{2}2n_0{n}_R$$ (Equation 4)

$$\Delta \alpha ={\left(\frac{2\pi a}{\lambda }\right)}^{2}2n_0\Delta n_I$$ (Equation 5)

where a is the radius of the fiber core. With these definitions the conventional fiber V parameter takes on the complex-valued form

$${\tilde{V}}^2=\Delta n+i\Delta \alpha$$ (Equation 6)

The normalized propagation constant b is defined as (Gloge, 1971)

$$b=\frac{n_{eff}^2-n_0^2}{{\left(n_0+n_R\right)}^2-n_0^2}\simeq \frac{n_{eff}-n_0}{n_R}$$ (Equation 7)

where n_eff is the effective index of each mode in the fiber.

Figures 2F and 2G plot the propagation regions and boundaries for the LP01 and LP11 modes in the complex ${\tilde{V}}^2-b$ space. With the presence of increasing asymmetric gain, the modes lose their circular symmetry. When $\Delta \alpha$ goes beyond a critical value, the propagation constants bifurcate into a complex conjugated pair. This behavior is related to the parity-time phase transition in coupled waveguide system (Guo et al., 2009) (see Figure S1 for further details). To achieve good mode quality, currently almost all fibers employ circular symmetric or at least rotational symmetric refractive index profiles. Remarkably, Figures 2F and 2G also indicate the existence of a nontrivial regime, where $\Delta \alpha \ll \Delta n$ ($\Delta \alpha /\Delta n$ smaller than roughly 10⁻² level). As a crossover from exact symmetry to strong asymmetry, the fibers in this regime, though having asymmetric gain, admit confined modes, which are almost the same as conventional fibers. Hence, their circular symmetry of the wave functions can be approximately preserved. This feature gives us a new degree of freedom with which we can tailor the gain spectra of fibers.

Therefore, we propose a single mode-fiber whose core incorporates two gain materials. Such fiber combines the gain spectra of different laser media, whereas its modal profile maintains circular symmetry. A model based on the rate equations is used to evaluate the performance of this new fiber (see Transparent Methods). Simulation results confirm our anticipation that gain bandwidth can be significantly extended (see Figures S2–S4).

On the basis of the theoretical analysis, we demonstrated a proof-of-concept fiber combining the spectra of thulium (Tm) and holmium (Ho) together. To fabricate a core with multiple sections, the fiber preform was made by the rod-in-tube technique (Figure 3A) rather than by the conventional MCVD method, by which gases are deposited on an axially rotated silica tube. Therefore, it would be very difficult, if not impossible, for the MCVD method to form an asymmetric structure. Another important advantage of the rod-in-tube method is that it supports multi-component silicate glasses, which allows access to high rare-earth-doping concentration and precise and independent control of refractive indices of the core and cladding (Lee et al., 2015). To simplify pump scheme, Tm ions were added to the Ho-doped glass. In this way, both sections can be excited by the same pump source at ∼793 nm. Note that for the Tm-Ho codoped glass, Tm is not the active ion but a kind of sensitizer, which transfers energy to the activator. Thus the emission spectrum of Tm-Ho codoped glass cannot fully cover the range of Tm singly doped glass. The detail of the manufacturing process is provided in Transparent Methods.

Figure 3.

Fabrication and Characterization of Multi-section Core Fiber

(A) Schematic diagram of the rod-in-tube technique.

(B) The optical image of the fiber facet.

(C–E) The ASE spectrum from (C) proposed fiber, (D) Tm-doped fiber, and (E) Tm-Ho-codoped fiber.

An image of the cleaved fiber facet is shown in Figure 3B. The fiber has a double-clad structure with a 150-μm outer polymer cladding, a 110-μm inner cladding with a numerical aperture (NA) of ∼0.6, and a 8.5-μm circular core with a NA of 0.14, which allows single-mode operation at wavelengths above ∼1.6 μm. The loss is measured to be 5 dB/m at 2,097 nm. It is known that Tm generates emission centered at ∼1.9 μm and Ho at ∼2.1 μm. By doping one section of the bisected core with Tm ions and the other with Ho ions, two gain spectra from two sections are shared within the core, so a broadband amplified spontaneous emission (ASE) can be generated. As shown in Figure 3C, the ASE spectrum of 0.9 m proposed fiber exhibits a 3-dB bandwidth of ∼160 nm, which, to the best of our knowledge, is the broadest ASE bandwidth directly from a gain fiber. By using the identical experimental setup, the ASE spectra from regular Tm-doped and Tm-Ho-codoped silicate fibers have a bandwidth of only ∼90 and ∼60 nm, respectively (Figures 3D and 3E).

To examine the mode quality, we built a laser amplifier comprising the proposed fiber, as shown in Figure 4A. Two seed lasers at 1,940 nm and 2,050 nm were used, respectively. Figure 4B shows the measurement of the output beam profiles at 1,940 and 2,050 nm. The Gaussian-like shape profile further confirms the single-mode feature predicted by the simulation. Therefore the introduction of asymmetric imaginary index does not compromise the transverse mode profile but enables the fabrication of fibers with better performance.

Figure 4.

Mode Quality Examination

(A) Schematic of experimental setup.

(B) The output beam profiles at (i) 1,940 and (ii) 2,050 nm.

Besides significant extension of gain bandwidth, this fiber also opens up new possibilities for dual-wavelength lasers that can generate two widely separated wavelengths. Because a dual-wavelength laser can serve dual purposes with one single device, it is more cost effective and versatile when compared with lasers, which normally produce one single wavelength or two closely spaced wavelengths (Walsh, 2010). Dual-wavelength laser oscillators or amplifiers could be essential ingredients in many useful applications, such as remote sensing, optical communication, laser ranging, medical imaging, and spectroscopy (Walsh, 2010, Zhao et al., 2016, Xu and Wise, 2013), where multiple wavelengths are required for one device in a limited space. Therefore, compact dual-wavelength lasers are highly demanded.

We went further by constructing an all-fiber tunable dual-wavelength laser with the proposed fiber, as illustrated in the Figure 5A. Figure 5B shows the output spectra, where two laser wavelengths can be found simultaneously with one ranging from 1,912 to 1,927 nm and the other ranging from 2,049 to 2,064 nm. The tunable range is as large as 15 nm. The total output power varies from 10 to 21 mW as wavelengths change. To further confirm that the dual-wavelength operation was the contribution of the multi-section core fiber, it was replaced by regular Tm-doped and Tm-Ho-codoped silicate fibers with only one core section, whereas the other components and parameters remained the same. Owing to strong gain competition among limited excited Tm or Ho ions, only one wavelength was obtained. It should be noted that dual wavelength from conventional fibers is achievable if the cavity reflectivities are carefully adjusted to balance the ion transition of each wavelength. However, such balance is so delicate that it will be broken easily once the pump power or ambient temperature is changed. In addition, those dual-wavelength lasers have small wavelength separations and their output wavelengths are fixed. Our work offers a way to develop compact dual-wavelength lasers with high stability and wide tunability. It is an important step toward the realization of multi-wavelength and multi-functional fiber lasers.

Figure 5.

All-Fiber Tunable Dual-Wavelength Laser

(A) Schematic of the dual-wavelength fiber laser.

(B) Spectra of the dual-wavelength laser.

Although the above proof-of-concept fiber is based on Tm and Tm-Ho, this configuration can be extended to other rare earth combinations, such as Tm/Er, Er/Yb, and Yb/Nd. Further extension of emission wavebands can be achieved by including more core sections that are made of different rare earth dopants or host glasses. Simulations show that these fibers still possess a Gaussian-like transverse mode profile as displayed in Figure 6. In addition, this fiber configuration is compatible with other fiber designs. For example, one can introduce the multi-section core to photonic crystal fibers (Russell, 2003), which currently manipulate light flow through the microstructures in their cladding, and may open an avenue to versatile fibers with more intriguing properties.

Figure 6.

Several Examples of the Fibers with More Core Sections

In conclusion, we have presented a detailed theoretical study of the fiber with asymmetric gain profile and extended fiber mode theory to the complex space. Based on the analysis, we have proposed a new fiber configuration and experimentally demonstrated a multi-section core fiber with unique manufacturing strategy. Such fiber provides an effective approach of producing optical gain beyond that of a single laser material and should lead to breakthroughs in fiber light sources having broader bandwidth, shorter pulse width, and wider tunability.

Limitations of the Study

The all-fiber dual-wavelength laser showed relatively low output power. As the main purpose was to demonstrate stable and tunable dual-wavelength operation, no effort was made to optimize the output power in this experiment. We believe that the low power was caused by the relatively high losses of some intracavity components (tunable filter and isolator) and a large improvement can be obtained by reducing these losses.

Methods

All methods can be found in the accompanying Transparent Methods supplemental file.

Published: December 20, 2019