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Abstract
Optimization of an Fe2+-doped chalcogenide fiber is considered for mid-IR lasing. The concept of using a chalcogenide glass as a fiber matrix to support optically active Fe2+ ions in ZnSe crystal particles requires use of a protective shell to prevent dissolution of the ZnSe particles. Here, we investigate the effect that the shell has on optical scattering and subsequently the relative gain and loss for a range of particle size, shell thickness and loading fraction of the ZnSe particles. Scattering loss depends on the particle size and is found to be acceptably low for fiber lasing for sizes larger than a threshold size. Furthermore, upon considering collective scattering from the particle group, increasing the concentration is shown to reduce the scattering loss and to be helpful in improving the gain coefficient to scattering loss coefficient ratio. Proper optimization is expected to result in a viable Fe2+ mid-IR fiber laser.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Mid-infrared (Mid-IR) light (1.5-5 $\mu$m) is of interest for a number of industrial, scientific, military, commercial, and medical applications including environmental sensing, astronomy, medical imaging, medical diagnostics, wireless communication, and infrared countermeasures [1–4]. Transition metal (TM) ions such as Ti$^{3+}$, Cr$^{3+}$, Cr$^{2+}$ and Fe$^{2+}$ substitutionally doped into crystalline lattices are well known and available commercially as laser gain media [5]. In these materials the crystalline lattice provides the symmetry needed to provide appropriate electronic energy level splittings. To achieve appropriate mid-IR splittings requires that the TM ion be located at a site with tetrahedral symmetry of anions around it. Thus chalcogenide crystals such as sulfides, selenides, and tellurides (group 16 element), have been demonstrated as viable hosts for TM ions.
Fiber lasers offer considerable advantages in terms of size, weight, insensitivity to thermal and vibrational effects, beam quality, flexibility in beam direction and ease of power scaling. However, development of mid-IR fiber lasers is significantly lacking compared with 1 $\mu$m and 2 $\mu$m silica-glass fiber lasers which are routinely operated at multi-kW average powers [6,7]. Of course silica-based glasses cannot be used as hosts because they are no longer transmissive at wavelengths beyond 2 $\mu$m.
To date, however, no demonstration of any high power, high efficiency TM-doped optical fiber-based laser source has been reported in the literature. To meet the needs of the aforementioned applications, laser sources with at least Watt level average powers are likely required. Among the laser technologies described herein, each has associated obstacles which must be overcome to realize efficient light generation. Towards the goal of a high power, tunable, mid-IR fiber laser, we report here considerations needed to achieve optimization of a specific example of a TM fiber laser, namely Fe$^{2+}$-doped ZnSe particles suspended in a chalcogenide glass fiber.
2. Problem
TM ions can substitutionally replace the cation, for example, Fe$^{2+}$ substitutes for Zn$^{2+}$ in ZnSe to form a tunable laser material. Substitution is limited due to concentration quenching of optical activity, levels less than $10^{19}/$cm$^3$ for Fe$^{2+}$ [8]. Unfortunately, doping TM ions into a glass has not, to our knowledge, resulted in optical emission and lasing, Since a glass is amorphous, it has a variety of local symmetries about a cation site with a variety of crystal field strengths at these sites. Optical excitation is likely being quenched by nonradiative relaxation. Thus directly doping TM ions into any type of amorphous material as a candidate host is not a promising technique for achieving TM-based fiber lasing.
3. Solution?
3.1 Previously explored concepts
Several concepts have been investigated to achieve guided wave lasing of TM ions. Pulsed laser deposition of a Cr$^{2+}$:ZnSe film on sapphire achieved random lasing [9]. Cr$^{2+}$:ZnSe deposited on the inner surface of a hollow-core silica fiber via high pressure chemical vapor deposition (HPCVD) achieved laser operation [10]. Similarly, continuous wave laser operation was achieved with an Fe$^{2+}$:ZnSe core composition also fabricated via HPCVD [11]. By using non-oxide glass chemistry, Cr$^{2+}$:ZnSe particles have been embedded in a chalcogenide glass (ChG) fabricated from powders using hot uniaxial pressing (HUP) and melt-quenching methods to achieve Cr$^{2+}$ emission [12]. The optical properties of Fe$^{2+}$-doped ZnSe microspheres prepared using a solvo-thermal method were investigated but no lasing was reported [13]. Ultra-broadband emission covering the 2.5-5.5 $\mu$m has also been observed from Ni$^{2+}$-doped chalcohalide glass ceramics [14]. However, none of these approaches has yet achieved robust high power fiber laser operation.
3.2 Particles in a glass matrix approach
Recently, we proposed an approach [15] that consisted of grinding up Fe$^{2+}$ or Cr$^{2+}$ doped polycrystalline ZnSe bulk samples using mortar and pestle, separating out 25 $\mu$m diameter particles using appropriate sieves and mixing them with chalcogenide glass particles of similar size. Smaller particle sizes needed for single mode fibers are possible using smaller sieve holes. The mixture was then heated to melt the glass particles without presumably melting the much higher melting point ZnSe particles. Upon cooling a bulk chalcogenide matrix with suspended TM-doped ZnSe particles should result (See Fig. 1). This should retain the TM ions in the required tetrahedral crystal symmetry while also allowing the composite material to be drawn into fiber.
Fig. 1. Conceptual diagram of Fe$^{2+}$-doped ZnSe particles surrounded by an alumina shell suspended in chalcogenide glass. Dimensions and colors are not literal.
One immediate concern was the potentially large scattering that could result for the difference in refractive index between ZnSe and the chalcogenide matrix. However, a mixture of $As_2S_3$ and $As_2Se_3$ can achieve a match to the refractive index of ZnSe at least over a given wavelength range and temperature range. Measurements of a $As_2S_3{(94.6{\% })}As_2Se_3(5.4{\% })$ ternary mixture provided an excellent match to the refractive index of ZnSe over the 2-5 $\mu$m range at room temperature [15].
Investigation of the suspension of Fe:ZnSe particles in a chalcogenide glass matrix showed no sign of Fe$^{2+}$ optical emission [15]. Further investigations indicated that heating the mixture of Fe:ZnSe particles and ChG particles to ChG melting temperatures resulted in the dissolution of ZnSe. Under cooling the majority of the Zn ions recrystallized as ZnS since there is much more sulfur than selenium in the ChG composition. The Fe$^{2+}$ ions apparently did not relocate into the ZnS crystalline particles but remained in the ChG with unfavorable crystal symmetry for optical activity.
A solution was found in depositing an alumina shell around the Fe:ZnSe particles using atomic layer deposition (ALD) [16]. Proof that Fe$^{2+}$ ions remained in the ZnSe particles was shown by observing chaeracteristic Fe$^{2+}$ emission when pumped with a 3 $\mu$m Er laser [17]. This protective shell of alumina has a significantly different refractive index (1.6682) compared to ZnSe (2.4254) at 4 $\mu$m so the issue of optical scattering must be considered.
4. Optimization of a Fe:ZnSe-ChG composite fiber as a laser gain medium
4.1 Application requirements and practical limitations
The requirements to achieve optimum laser performance must be carefully considered with trade-offs made between numerous, sometimes conflicting, requirements. Choice of ChG composition is restricted by refractive index matching. Alumina coating thickness must be thick enough to protect the ZnSe particles from dissolution at ChG melting temperatures. But deposition time and cost increases with film thickness. Also, increased shell thickness is expected to cause more scattering (see Section 4.2). TM doping must be as high as reasonable without significant concentration quenching. ZnSe particle size must be smaller than the selected fiber core size; but smaller particle size requires more particle grinding time and possible complications as larger fractions of Fe$^{2+}$ ions are exposed to surface effects such as broken tetrahedral crystal symmetry. Single-mode ChG fiber of our composition requires a core diameter of 12 $\mu$m with an As$_2$S$_3$ cladding and smaller particle sizes, perhaps 4 $\mu$m. However, even for a 4 $\mu$m particle diameter with an estimated 10 nm thick layer of inactive Fe$^{2+}$ ions, less than 1.5${\% }$ of the ions would be inactive. Only when one goes to nanoparticle sizes do surface effects become significant. Fibers with 200 $\mu$m diameter and 25 $\mu$m ZnSe particle size were successfully drawn from matrix preforms by Angela Seddon’s group at Nottingham University, although issues with bubbles in the preform resulted in high transmission loss. Finally, we require the total loss from all sources (absorption, scattering and resonator losses) to be less than the gain of the TM ions present in the matrix material to achieve laser threshold.
4.2 Mie scattering cross-section calculation
To estimate the total loss along the fiber, we use Mie theory to calculate the extinction cross-sections from a "gain-bubble", i.e., a core-shell particle suspended in a medium with refractive index equal to that of the core. We start by calculating the elements of the amplitude scattering matrix [18] of the bubble,
Since the particles are approximated as being spherical, $S_3 (\theta )=S_4 (\theta )=0$ and only $S_1 (\theta )$ and $S_2 (\theta$) characterize the scattering process. We calculate $S_1 (\theta )$ and $S_2 (\theta )$ using [19] and then evaluate the extinction cross-section $(\sigma _{ext})$ using the optical theorem [18] as
The scattering diagrams for a typical gain bubble and extinction cross-sections are shown in Fig. 2(a-c).
Fig. 2. : Scattering properties of the gain bubbles. (a) Normalized scattering diagram of a gain bubble with a 40 $\mu$m core diameter and 30 nm shell thickness, (b) extinction cross-sections for various core diameters and shell thicknesses; white dot is $\sigma _{ext}$ for the parameters used in panel (a), (c) scattering cross-sections for gain bubbles of 40 $\mu$m core-diameter as a function of shell thickness and 30 nm shell thickness as a function of core-diameters.
Since the size of the particle is significantly larger than the wavelength, the scattering phase function is peaked in the forward direction. From Figs. 2(b) and (c), it is seen that in this regime of sizes, the extinction cross-section does not oscillate with increasing core diameters and shell thicknesses but monotonically increases. From Fig. 2(c), note that the increase in $\sigma _{ext}$ when the shell thickness is increased by 0.09 $\mu$m is comparable to when the core-diameter is increased by 100 $\mu$m, a consequence of a bubble-like particle.
Within our parameter range, we note that $\sigma _{ext}\sim D_{core}^{2.1}$ where $D_{core}$ is the core-diameter of the particle. The exponent is slightly greater than the expected value of 2 [18] since not all particle sizes in our parameter range can be considered as being much larger than the wavelength. At a given volume fraction, the number of particles, $N_{par}$ is $\sim {D_{core}^{-3}}$. Hence, the total extinction for all particles at a given concentration follows $N_{par}\sigma _{ext}\sim D_{par}^{-0.9}$, suggesting that the total extinction for larger particles is lower than that for smaller particles.
4.3 Concentration induced reduction of the effective extinction cross-section
The results presented until now were calculated from the field scattered by a single isolated particle. However, it is known that, under temporally coherent illumination, the scattering properties of a single particle are modified due to its environment [20–27]. In our system, as more particles are introduced, the center-to-center distances between the particles are no longer uniformly randomly distributed, i.e., certain center-to-center distances become more probable than others [23,27]. Consequently, the total scattered field along a given direction is impacted by constructive or destructive interference due to the modification of the probability distribution of the center-to-center distances. The impact of this effect on the total scattered intensity can be accounted for by calculating the extinction cross-section as
For the numerical integration, we discretize $\theta$ in steps of $0.02^{\circ }$, which is such that $\tilde {\sigma }_{ext}$ calculated from numerical integration and the optical theorem deviate within $10^{-6}$. We quantify the impact of concentration induced structure on the single particle extinction cross-section by $\Delta \sigma (f_V)=(\tilde {\sigma }_{ext} (f_V )-{\sigma }_{ext})/{\sigma }_{ext},$ which is the relative difference between the extinction cross-section at a given concentration and that for an isolated particle. The results are summarized in Fig. 3.
Fig. 3. Concentration induced reduction of the extinction cross-section for (a) 6.87% and (b) 13.74% volume fraction. (c) Reduction in extinction cross sections for various shell thicknesses of a 25 $\mu$m core diameter and for different core diameters with a 30 nm shell thickness particles at different concentrations.
Note that the concentration induced structure reduces the extinction cross-section of the gain bubble within our parameter range. The reduction increases at higher concentrations, reaching values of up to −44% at volume concentrations of 13.7%. While the magnitude of reduction increases as the shell thickness increases, an opposite trend is observed when the core diameter increases, as seen in Fig. 3(c).
While both $\sigma _{ext}$ and $\tilde {\sigma }_{ext}$ increase with shell thickness, the latter increases slower. This happens because $\tilde {\sigma }_{ext}$ is impacted by the concentration-induced structure, which, in turn, is affected by the overall increase in the size of the particle. The impact, however, is relatively small, since adding a few tens of nanometers to the shell thickness represents only a minor change in the overall particle size (on the order of microns) leading eventually to a weak dependence of $\Delta \sigma$ on the shell thickness.
We also see that the extinction cross-section for a smaller core diameter is reduced more than that for a larger core diameter. In order to explain this feature, we plot the scattering diagrams $(p(\theta )$, normalized to the maximum) and structure factors at 13.7% concentration for a 4 $\mu$m and 40 $\mu$m core diameter particle with a 30 nm shell as solid lines and dotted lines, respectively, in Fig. 4. Note that the initial angular range over which $S(\theta )$ has small values is wider for a 4 $\mu$m particle than it is for a 40 $\mu$m particle. Hence, from an energetic standpoint, the reduction in energy scattered around the forward direction is greater for a 4 $\mu$m particle than it is for a 40 $\mu$m particle, resulting in a greater reduction of the extinction cross section of the former.
Fig. 4. Size dependent concentration induced extinction cross-section reduction. The solid lines are the scattering diagram of an independent particle and dotted lines are the structure factors at 13.74% for a 4 $\mu$m and 40 $\mu$m core diameter particle with a 30 nm shell. Since the initial angular range of sub unity values of the structure factor is larger for a 4 $\mu$m particle than for a 40 $\mu$m particle, the forward scattered energy for a 4 $\mu$m particle is reduced more than that of a 40 $\mu$m particle.
The size dependent concentration induced extinction cross-section reduction could be an appealing design parameter. At a given volume concentration of matter in a medium, the amount of interface between the matter and medium is higher when the matter is composed of smaller particles than when it is composed of larger particles. Furthermore, from a fabrication standpoint, the surface roughness of a smaller particle is also expected to be higher than that of a larger particle. The interface can induce losses in the particle due to various mechanisms, such as, for instance, dangling bonds, and effectively increase the extinction cross-section per particle. However, this interface induced increase in extinction cross-section could be compensated for by the concentration induced reduction in extinction cross-section, as suggested from our results.
In the previous section, we concluded that since the total extinction varies as $N_{par}\sigma _{ext}\sim {D_{core}^{-0.9}}$, larger particles are a better choice for our purpose. Since this conclusion was made while neglecting any concentration effects, it is worth checking whether the same trend is followed when the calculations account for concentration induced modification of the scattering cross-section. We note that, within our parameter range, $\Delta \sigma$ is not too sensitive to the shell thickness and, for large core-diameters, it also becomes independent of the core diameter. Since $\tilde {\sigma }_{ext}=\sigma _{ext}(1+\Delta \sigma )$, and $\Delta \sigma$ does not depend on the core diameter and shell thickness, $\tilde {\sigma }_{ext}\sim D_{core}^{2.1}$ and the total extinction still follows $\sim D_{core}^{-0.9}$. Hence, even upon accounting for concentration induced modification of the extinction cross-section, a larger particle is a better choice for reducing the scattering losses.
4.4 Gain coefficient
With the ultimate objective of fabricating a fiber laser we calculated laser gain coefficient ($\alpha _g$) and scattering loss coefficient for a range of particle sizes and volume fractions. The gain coefficient can be calculated from the known Fe$^{2+}$ emission cross-section (Table 1), the loading level of Fe$^{2+}$:ZnSe particles in the ChG and the doping of Fe$^{2+}$ into the ZnSe particles. For example, a wt% loading of 5% (3.4% volume fraction), an Fe$^{2+}$ doping level of 1x10$^{19}$ cm$^{-3}$, and ZnSe particle diameter of 25 $\mu$m, the average Fe$^{2+}$ density in the matrix material is 3.4x10$^{17}$ cm$^{-3}$. For this case $\alpha _g$ = 0.47 cm$^{-1}$. This is the maximum gain since we have assumed that all Fe$^{2+}$ ions have been excited.
Table 1. Mie scattering input parameters.
In Fig. 5, loss coefficients and gain coefficients are plotted as a function of the core diameter for a 30 nm shell particle and for different volume fractions. Noting that $\alpha _g$ depends linearly on the volume fraction, we plot it as dashed lines for several volume fractions. Following the results presented in Figs. 2 and 3, we calculate the loss coefficient, $\tilde \alpha _{sc}$, and plot it as a function of core diameter and volume fractions as solid lines. As mentioned earlier, since the loss coefficient is a product of both the number density ($\propto D_{core}^{-3}$) and the extinction cross-section ($\propto D_{core}^{2.1}$), it decreases as the core diameter increases. Due to the concentration induced reduction of the scattering cross-section, the loss coefficient depends sub-linearly on the particle concentration. Hence, while both gain and loss coefficients increase with concentration, the gain increases faster than the loss. Consequently, the threshold core diameter at which gain exceeds loss reduces as the concentration increases. These results suggest that a minimum core diameter of $\sim$40 $\mu$m is required to observe lasing action at concentrations as low as 0.33%.
Fig. 5. Core diameter optimization. Loss coefficients (solid lines) and gain coefficients (dashed lines) are plotted as a function of the core diameter for a 30 nm shell particle for different volume fractions. Note the core-diameters at which the loss and gain coefficients are equal (vertical lines). Due to the concentration induced reduction of the extinction cross-section, the minimum required core-diameter for lasing reduces as concentration increases.
As the concentration increases, the net gain per unit length will also increase. The reason for this is twofold. Firstly, disregarding the impact of structure on the extinction cross-section, the net gain for a given particle size $=\alpha _g-\alpha _{sc}\propto f_V$ and hence will increase linearly with concentration. Secondly, due to the concentration induced reduction of the extinction cross-section, the net gain will increase even more. For concentrations considered here, the gain and loss coefficients are tabulated in Table 2.
Table 2. Gain/loss coefficients and net gain at different volume fractions of particles of 40 $\mu$m core diameter and 30 nm shell thickness.
For the ranges of particle size and shell thickness considered here the light is highly forward scattered. For example, in Fig. 2(a) the forward scattering lobe has approximately 37% of the total scattered power. Such forward scattered photons could participate in the effective gain (if within the divergence of the laser beam) seen by a laser oscillator or amplifier. Thus the effective gain is likely to be larger than that shown in Table 2.
Careful purification of the starting materials has resulted in sulfide fibers with passive losses as low as 0.1-0.2 dB/m (0.00023-0.00046 cm$^{-1}$) [29]. Commercial sulfide fiber is advertised to have 0.05 dB/m @ 2.8 $\mu$m loss although impurities increase the loss to 1.3 dB/m at 4 $\mu$m. Even so, this loss is much less than the particle scattering loss and the Fe$^{2+}$ gain for expected configurations making the possibility of high power lasing in such fibers quite promising.
5. Discussions and conclusions
A tunable fiber laser operating at mid-IR wavelengths is desirable for advantages in terms of size, weight, insensitivity to thermal and vibrational effects, beam quality, flexibility in beam direction and ease of power scaling. The obvious procedure of doping TM ions into the core of a glass fiber, while conceptually straightforward, is not practically feasible. The inhomogeneous nature of glass randomizes the crystal field symmetries and strengths, which, in turn, affect the desired TM ion optical activity. Instead of directly doping TM ions into the fiber core, they can be doped into chalcogenide crystalline particles. Coated with a protective shell to prevent dissolution in the chalcogenide glass, a mixture of chalcogenide glass powder and TM-doped crystalline particles can then be heated to form an optically active matrix material that can be drawn as fiber. While this procedure enables the potential fabrication of a TM fiber laser, it also raises several optimization questions about the mechanical, chemical and optical impacts of such a structure. In this work, we answered some of these questions.
From the structural and chemical standpoints, a number of characteristics must be insured. First, maintaining the optical activity of TM ions requires that the desired crystal symmetry must be present. Second, the refractive index of the glass matrix must be close to the index of the suspended crystalline particles in order to minimize scattering losses. Finally, the need for a protective shell on the crystalline particles adds to scattering, an issue that we have thoroughly examined in this paper. We have not addressed the particle size influence on fiber drawing capability (tensile strength, diameter variability, bendability, etc.) other than noting that particle sizes approaching fiber diameter are more likely to cause problems.
From an optical design standpoint, we have answered three main questions. (i) Is the gain larger than the scattering induced losses? Mie calculations for core-shell particles indicate that the extinction cross-sections of the particles are small enough such that, when all the assumptions of our calculations are satisfied, a fiber laser based on the above mentioned approach could be practically implemented. (ii) To minimize scattering losses, what particle sizes should be used? Within the parameter range of our calculations, we conservatively estimate gain to dominate scattering losses for particle core diameters larger than 40 $\mu$m. The scattering induced losses are lower for larger particles than they are for smaller ones. Hence, particles larger than 40 $\mu$m and as large as can be accommodated within the core of the fiber without compromising the mechanical and chemical stability of the fiber should be used. (iii) What impact, if any, does the volume fraction of particles have on the scattering losses? Since a large number of finite size particles must be considered and because they are placed at random locations, a necessary spatial correlation occurs between their positions. This structural effect impacts the scattering efficiency and needs to be accounted for. Our calculations suggest that, due to this unavoidable structuring, the total loss along the fiber reduces upon increasing the volume fraction of particles. This reduction could be up to −44% for volume concentrations $\sim$13.7%.
Funding
Office of Naval Research (N00014-20-1-2789); Air Force Office of Scientific Research (FA9550-19-1-0127).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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