Abstract

The mid-infrared (MIR) emission behavior of Tb3+-doped Ge–As–Ga–Se bulk glasses (500, 1000, and 1500 ppmw Tb3+) and unstructured fiber (500 ppmw Tb3+) is investigated when pumping at 2.013 μm. A broad emission band is observed at 4.3–6.0 μm corresponding to F57F67, with an observed emission lifetime of 12.9 ms at 4.7 μm. The F47 level is depopulated nonradiatively and so it is proposed that Tb3+-doped Ge–As–Ga–Se fiber may operate as a quasi-three-level MIR fiber laser. Underlying glass-impurity vibrational absorption bands are numerically removed to give the true Tb3+ absorption cross section, as required for Judd–Ofelt (J–O) analysis. Radiative transition rates calculated from J–O theory are compared with measured lifetimes. A numerical model of the three-level Tb3+-doped fiber laser is developed for Tb3+ doping of 8.25×1024  ionsm3 (i.e., 500 ppmw) and dependence of laser performance on fiber length, output coupler reflectivity, pump wavelength, signal wavelength, and fiber background loss is calculated. Results indicate the feasibility of an efficient three-level MIR fiber laser operating within 4.5–5.3 μm, pumped at either 2.013 or 2.95 μm.

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1. INTRODUCTION

Selenide-chalcogenide glasses have a phonon energy of 300  cm1, a theoretical low optical-loss window of 100  dBkm1 across 310  μm in the mid-infrared (MIR) spectral region, and large refractive indices (2.52.8). Hence, rare earth (RE) ions doped in a selenide glass host exhibit long radiative lifetimes and large absorption and emission cross sections [1]. Recently, we demonstrated small-core Pr3+-doped, selenide glass, step-index fibers (SIFs) in which the Pr3+ lifetime remained the same (i.e., 7.8 ms at 4.7 μm, when pumped at 1.55 μm) as in the parent Pr3+-doped bulk glass, demonstrating a resistance to both RE-clustering and glass devitrification during the heat-treatment processing to make SIF [2]. Moreover, an exhaustive high-resolution transmission electron microscopy study found no glass devitrification in the fiber core and core/cladding interface. However optical loss, due to extrinsic scattering and absorption, must still be reduced. MIR fiber lasing has not yet been demonstrated beyond 3.9 μm [3]. One problem is the long lifetimes of adjacent RE electronic levels, in a selenide glass host, which tend to self-terminate, precluding lasing [4]. We have identified Tb3+ as potentially not suffering from this problem. We show that in Tb3+-doped Ge–As–Ga–Se glasses, when pumping into the F47 level, the emission transitions from F47, F37, F27, F17, or F07 levels are expected to be quenched and quickly relax to the long-lived F57 manifold; quasi-MIR three-level laser action is then possible for the F57F67 transition, i.e., from the first excited state to the ground state.

Tb3+-doped chalcogenide-glass emission was first reported in 2001 [5]. Judd–Ofelt (J–O) modeling was applied in [6,7], assuming that the excited state F47 was radiatively depopulated. However, experimental observation of strong emission has not been reported, to the best of our knowledge. Here, we have fabricated and measured absorption and emission of Tb3+-doped Ge–As–Ga–Se bulk-glass samples (500, 1000, and 1500 ppmw Tb3+) and fibers (500 ppmw Tb3+) when pumping at 2.013 μm. In the transparent window of selenide glasses, near-infrared (NIR) and MIR fundamental vibrational absorption due to glass impurities tends to underlie, and be obscured by, the RE electronic absorption. The effect is compounded because the extinction coefficients of fundamental vibrational absorption bands are some 105× higher than for NIR overtone and combination vibrational absorption. Here, the true Tb3+ absorption cross section was deconvoluted and used in (J–O) modeling [8]. Radiative transition rates and lifetimes, calculated from J–O theory, were compared with the experimentally observed lifetimes. Numerical modeling of the quasi-three-level Tb3+-doped Ge–As–Ga–Se fiber laser was carried out to find the performance dependence on fiber length, output coupler reflectivity, pump wavelength, emission wavelength, and fiber baseline loss. Results indicated the feasibility of efficient three-level MIR fiber lasing within 4.5–5.3 μm, pumping at either 2.013 or 2.95 μm in Tb3+-doped Ge–As–Ga–Se.

2. EXPERIMENTAL PROCEDURE

A. Glass Melting

A 500 ppmw Tb3+-doped Ge–As–Ga–Se glass rod was prepared and drawn directly to unstructured fiber of around 300–400 μm OD (outside diameter). Ge (5N purity, Materion), As (7N5, Furakawa Denshi, prior heat treated at 103  Pa), and Se (5N Materion, prior heat treated at 103  Pa) were batched inside a glovebox (MBraun: <0.1  ppm H2O and <0.1  ppm O2) and melted at 850°C/12 h in a silica glass ampoule (prior air-baked and then vacuum-baked, each at 1000°C/6 h) before being quenched. Then gallium (Ga) (5N, Testbourne Ltd.) and terbium foil (3N, Alfa Aesar) were added and the glass remelted at 850°C/2 h in a silica glass ampoule (prior air-baked then vacuum-baked, each at 1000°C/6 h) before being quenched and annealed. The 1500 ppmw Tb3+-doped bulk glass was prepared similarly, but the 1000 ppmw Tb3+-doped bulk glass was prepared by one melting of all batched elements at 850°C/12 h. Actual parts per million by weight (ppmw) were within ±20  ppmw of the stated value.

B. Linear Optical Properties

Absorption spectra across 0.6–10 μm of Tb3+-doped Ge–As–Ga–Se bulk samples of a few millimeter optical path length, with input and exit faces ground parallel and polished to a 1 μm finish, were collected in a Bruker IFS 66/S Fourier Transform MIR Spectrometer, which had been purged to remove CO2 and H2O.

An improved Swanepoel method was used to measure the refractive index of thin films (30 μm thick) of the 500 ppmw Tb3+-doped Ge–As–Ga–Se glass [9,10]. The thin film was prepared by hot pressing under vacuum (105  Pa) of the 500 ppmw Tb3+-doped Ge–As–Ga–Se glass fiber, annealing, and cooling. Therefore, the thin film was of the same glass composition as the bulk glass and the drawn fiber. However, the quenching rate affects glass density and hence refractive index. Therefore, we have calibrated our refractive index measurements; we have found agreement to within 0.65% for the same selenide glass composition, but in different forms, of a hot-pressed film (measured by the improved Swanepoel method) when compared to the minimum-deviation method using a polished prism of bulk glass at 12 wavelengths within the 1454–1574 μm band, at 10 nm intervals (Agilent fiber-coupled diode), and at 3.109 μm [interband cascade laser (ICL), NRL, USA].

C. Emission Properties

Emission spectra were recorded at 300 K over 3–6.5 μm of Tb3+-doped Ge–As–Ga–Se bulk glass and fiber, pumped at 2.013 μm, with a Tm:silica fiber laser (capable of 10 W output, LISA Laser) or at 1.940 μm, with a 500 mW multimode laser diode (BA-1940-E0500-MMF200 M2K). The fluorescence signal was modulated with a chopper (Scitec Instruments). The collected luminescence was focused onto the slit of a motorized Spex MiniMate monochromator with a diffraction grating blazed at 6 μm (51034 Jobian Yvon). Detection of the signal was achieved with a lock-in amplifier (EG&G Brookdeal 9503-SC), a room temperature MCT detector (Vigo System PVI-6), a preamplifier for the detector (Judson PA-6), a data acquisition card (NI USB-6008 National Instruments), and a computer. Emission was collected from bulk glasses across a polished sharp glass corner orthogonal to the pump and <1  mm from the incident pump beam, and to minimize photon trapping, using a distorted emission cross section and false elongation of emission-decay lifetimes [11]. The emission-decay lifetime at 4.7 μm in the Tb3+-doped Ge–As–Ga–Se bulk glasses was collected with direct modulation of the 2.013 μm wavelength pump laser. Time evolution of the emission was monitored with a digital oscilloscope. The simplest single exponential fit was applied; we expect lifetime errors of <10%.

3. EXPERIMENTAL RESULTS

A. Refractive Index Dispersion for Tb3+-Doped Ge–As–Ga–Se Glass

Figure 1 shows the refractive index dispersion of 500 ppmw Tb3+-doped Ge–As–Ga–Se thin film fitted to the Sellmeier formula:

n2=1.485+4.942λ2λ20.29232+1.124λ2λ239.232,
where n is the refractive index and λ is the wavelength. The sum of the standard error of the Sellmeier fit was 9.7445×105 and r2=0.9991.

 

Fig. 1. Refractive index dispersion of 500 ppmw Tb3+-doped Ge–As–Ga–Se (blue points are data points from the improved Swanepoel method, and the black curve is the Sellmeier fit to the data points).

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B. True Absorption Cross Section of Tb3+

Figure 2(b) shows the electronic energy levels of Tb3+-doped into the Ge–As–Ga–Se host based on the observed MIR absorption spectrum shown in Fig. 2(a) of the 500 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass, comprising six electronic absorption bands, centered at 1.5, 1.8, 2.0, 2.3, 2.95, and 4.65 μm, respectively, each originating from ground state, F67, absorption of the Tb3+  ions, to upper manifolds: F07, F17, F27, F37, F47, and F57, respectively. The Tb3+ F67F07 and F67F17 absorption bands overlapped and were separated using Gaussian fitting [5].

 

Fig. 2. (b) Simplified energy-level diagram for Tb3+-doped chalcogenide glass proposed here according to (a) the absorption bands observed for Tb3+ bulk samples using FTIR.

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The observed MIR absorption spectra of 500, 1000, and 1500 ppmw Tb3+-doped Ge–As–Ga–Se bulk glasses (Fig. 3) belie the fact that hidden beneath the RE absorption bands is intrinsic and extrinsic absorption and scattering optical loss due to the host glass matrix and impurities. Sanghera et al. [12] have modeled intrinsic loss mechanisms of chalcogenide glasses and extrinsic loss mechanisms have been studied by the group of Churbanov (e.g., [13]). Underlying the Tb3+ ground-state absorption, F67F47, assumed centered at 2.95 μm, was found to be vibrational extrinsic absorption due to hydroxyl, i.e., -[O–H] contamination at 2.72.9  μm. This hydroxyl tends to be bonded into the glass matrix in two ways, absorbing at two slightly different wavelengths (i) as hydroxide, e.g., [GeOH], and (ii) as -[O–H] of molecular water, [H–O–H]. Underlying the Tb3+ ground state absorption, F67F57, assumed centered at 4.65 μm, was found to be vibrational extrinsic absorption due to [H–Se]- known to be centered at 4.6 μm [1].

 

Fig. 3. Experimentally measured absorption spectra of 500, 1000, and 1500 ppmw Tb3+: Ge–As–Ga–Se bulk glasses. The upper transition state is identified in each case.

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It is well known that the accuracy of J–O modeling is critically dependent on the accuracy of the absorption cross sections of the RE ion in the host concerned. That means the need to know the area under exclusively the RE electronic absorption bands in the absorption spectrum of the RE-doped host. However, here, in the case of Tb3+-doped Ge–As–Ga–Se glasses, we know that the F67F57 and F67F47 transitions overlie and obscure from view the vibrational absorption due to -[O–H] and [H–Se]- contamination, respectively. Furthermore, it is known that the extrinsic vibrational absorption cross sections are greater in the case of the Tb3+-doped chalcogenide glasses than in the undoped chalcogenide host glass with no Tb present because the Tb precursor chemical brings added anionic impurities into the glass. The manufacturer’s stated purity of the Tb precursor is 4×9  s, but this refers exclusively to cationic not anionic impurities. Therefore, it was imperative here to separate out the true contribution of electronic absorption due solely to Tb3+ from the observed absorption spectrum of the Tb3+-doped selenide-chalcogenide glass, which incorporated not only electronic absorption due solely to Tb3+ but also vibrational extrinsic absorption bands due to unwanted anionic impurities in the glass host matrix. To obtain the true Tb3+ -absorption cross section, we followed the detailed method presented in [8], which is described below.

  1. Step 1. The absorption spectrum of the Tb3+-doped Ge–As–Ga–Se glass was collected.
  2. Step 2. The Tb3+ electronic absorption bands were identified.
  3. Step 3. Known anionic impurities in chalcogenide glasses were considered, and one absorption band of one impurity was selected for analysis—for the sake of argument, here the impurity [H–Se]- vibrational absorption band centered at 4.6 μm wavelength was selected.
  4. Step 4. The absorption spectrum of Dy3+-doped Ge–As–Ga–Se glass was collected as Dy3+ has no electronic ground-state absorption at around 4.6 μm wavelength.
  5. Step 5. Gaussian bands were fixed in ratio to fix the band shape of the [H–Se]- absorption centered around 4.6 μm wavelength in the absorption spectrum collected for Dy3+-doped Ge–As–Ga–Se glass in Step 4.
  6. Step 6. The entire combined absorption band of {Tb3++[HSe]} in the 3.0–5.5 μm wavelength region of the absorption spectrum of the Tb3+-doped Ge–As–Ga–Se bulk glass was Gaussian fitted using (i) the fixed ratio for [H–Se]− (found in Step 5) and allowing the H–Se− bands to vary in intensity but remain in fixed ratio to each other and (ii) the minimum of other Gaussian bands to optimize the fitting to the combined absorption band of {Tb3++[HSe]}.
  7. Step 7. The observed absorption coefficient band shape of the combined {Tb3++[HSe]} absorption band was then deconvoluted into its component parts of [H–Se]- vibrational absorption and the true Tb3+ absorption cross section.
  8. Step 8. Steps 1–7 were repeated for the impurity −[O–H] vibrational absorption band centered close to 2.95 μm wavelength.

In this way, the true absorption cross sections of the Tb3+ ground-state transitions F67F47 and F67F57 were calculated [see Figs. 4(a) and 4(b)].

 

Fig. 4. (a) Absorption spectrum of the F67F47 transition in 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass. The solid line indicates the measured absorption spectrum of the F67F47 transition, which is comprised of both the Tb3+ absorption and the OH impurity absorption bands. The dashed line represents the true absorption spectrum of the F67F47 transition after calculation to remove the OH contribution. The dotted line represents the calculated contribution of the OH impurity to absorption in the 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass. (b) Absorption spectrum for the F67F57 transition of 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass. The solid line indicates the measured absorption spectrum of the F67F57 transition, which is comprised of both the Tb3+ absorption and the Se–H impurity absorption bands. The dashed line represents the true absorption spectrum of the F67F57 transition after calculation to remove the Se–H contribution. The dotted line represents the calculated contribution of the Se–H impurity to absorption in the 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass.

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The calculated absorption and emission cross sections for Tb3+-doped 1000 ppmw Ge–As–Ga–Se chalcogenide glass are presented in Fig. 5. The absorption cross sections (σabs) were directly obtained from the corrected absorption spectrum using the following formula:

σabs=α(λ)N,
where N is Tb3+ the ion density equal to 1.65×1025  ions/m3, which corresponds to 1000 ppmw Tb3+-doped glass Ge–As–Ga–Se, and α(λ) is the absorption coefficient of the 1000 ppmw Tb3+-doped glass Ge–As–Ga–Se.

 

Fig. 5. Absorption cross section for the F67F57 transition (solid curve, measured but with removal of the contribution of the Se–H impurity band). Emission cross section for the transition F57F67 (dashed curve, calculated using McCumber theory from the corrected absorption cross section). The absorption cross section was calculated for 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass.

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The emission cross sections (σem) were calculated from the corrected observed absorption spectra using the McCumber method. In this case, we derived the emission cross section from a corrected observed absorption spectrum instead of using the measured photoluminescence spectrum, whose shape may be affected by the Se–H impurity band [8].

The emission cross section of the F57F67 transition was scaled using [14]

σem=λ48πn2cAjjrΔλ,
where Δλ=I(λ)/I(λ)dλ is the line shape of the emission band, and I(λ) is the emission intensity from F57F67, n is the refractive index (n2.53) (see Fig. 1), c is the speed of light in the vacuum, Ajjr is the spontaneous emission rate of the F57F67 transition (taken from Table 1), and λ is the central wavelength of the emission (4.7 μm) [14]. The emission cross section of the transition value from F57 to the ground state here was calculated to be 0.94×1024  m2 at 4.7 μm. This value is in good agreement with emission cross sections reported in the literature for other selenide-chalcogenide glasses [5]. The calculated emission cross section shows a maximum at a wavelength of 4.7 μm for the bulk glass sample, where the mid-infrared emission full width at half-maximum bandwidth is equal to 0.850 μm.

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Table 1. Calculated Spontaneous Emission Rates [Electronic (AED) and Magnetic (AMD)], Radiative Branching Ratios (βrad), and Radiative Lifetimes (τrad) for Emissions Observed Centered at Wavelength λ

C. Judd–Ofelt Modeling

Using the true absorption cross sections of Tb3+ in the Tb3+-doped Ge–As–Ga–Se glass, the emission cross sections derived from the true absorption cross sections and the measured refractive index of the Tb3+-doped Ge–As–Ga–Se glasses, the J–O parameters for this system were calculated as Ω2=(6.43±1.3)×1020  cm2, Ω4=(3.50±0.7)×1020  cm2, and Ω6=(2.92±0.58)×1020  cm2, and radiative rates, lifetimes, and branching ratios were calculated (Table 1).

The relative errors of J–O analysis can be as high as 30%–35% [15,16]. These errors result from the uncertainty, which is inherent to the determination of the integral absorption coefficients, error in estimation of Tb3+ concentration, and the accuracy of the refractive index measurement. The errors also depend on the accuracy with which the influence of impurities in the matrix host on the absorption cross section can be extracted. Therefore, radiative rates, the branching ratio, and absorption and emission cross sections are estimated with ±35% error.

Figure 6 shows the normalized decay of the luminescent intensity at 4.7 μm under 2.013 μm excitation, fitted most simply to a single exponential with time constant τm=12.9  ms. Reasonable agreement was found between the measured (τm=12.9  ms) and calculated lifetime (τrad=13.1  ms, Table 1) for the F57 radiative transition to ground state F67. If nonradiative decay solely due to intrinsic multiphonons alone is considered, then as the glass highest phonon energy is 300  cm1, the observed 4.7 μm emission should be mainly radiative, with a quantum efficiency close to 98.47%. We have

η=τmτrad,
where τm is a measured lifetime for the F57F67 transition (see Fig. 6) and τrad is a radiative lifetime calculated from J–O theory for the F57F67 transition (see Table 1).

 

Fig. 6. Decay time of the F57 excited level of 1000 ppmw Tb3+-doped chalcogenide selenide glass bulk sample measured at 4.7 μm after QCW (6–8 Hz) laser excitation at 2.013 μm. The best fit to the measured decay profile yields a single exponential decay with τm=12.9  ms.

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However, we suggest that there is a population of Tb3+  ions in the host matrix that is sited adjacent to [H–Se]- impurity, leading to resonant depopulation of the excited state of high probability and giving low quantum efficiency and radiative energy loss to heat [1]. Note that Churbanov et al. [17] found that the decay time of the F57 state of Tb3+-doped selenide-iodide chalcogenide glasses decreased with increasing (inferred) [H–Se]- contamination. A long decay time of τm=16.1  ms was observed for the purest (considering only [H–Se]- impurity bonds) sample.

Emission at 3.0 μm due to the F47F67 transition was not experimentally observed. We tentatively propose that this F47 manifold is depopulated in a nonradiative way. The energy gap (1265  cm1) of the F47F57 transition may be bridged effectively by only four host glass phonons. However, in addition, the F47F57 transition may be depopulated by the nonradiative transfer of energy to extrinsic molecular water (H2O) impurities in the selenide-chalcogenide glass matrix with vibrational absorption at 6.3 μm (H–O–H bending), which has a first overtone at 3  μm that is resonant with the F47F67 transition at 3  μm. Hence, from arguments found in [1], quenching of the F47F57 transition in Tb3+-doped Ge–As–Ga–Se glass due to nonradiative decay and concurrent stimulation of H–O–H bending vibration is expected to occur. Note that quenching of the F47F67 transition at 3  μm was also reported in [5], where the measured lifetime from F47F57 was approximately equal to 12 μs. Therefore, we propose that the F37, F27, F17, and F07 upper levels are depopulated nonradiatively (see Fig. 2). This result suggests that terbium (III) operating at 4.7 μm and pumped at 2.95 μm could operate as a three-level laser system like that of the erbium- (III) doped silica glass fiber amplifier operating at 1.55 μm when pumped at 0.98 μm [14].

The emission cross section and lifetime of the F57F67 transition (see Fig. 5) are in reasonable agreement with values for Tb3+-doped selenide-chalcogenide glass in [5].

σem×τm characterizes gain in RE-doped materials. For the F57F67 transition in the Tb3+-doped Ge–As–Ga–Se glasses here, σem×τm=12.1×1024  m2  ms and is, for instance, two orders of magnitude larger than in gallium lanthanum sulfide-oxide [GLS(O)] bulk glass [18] and is greater than in crystalline KPb2Br5 [19] (Table 2). A long decay lifetime for the KPb2Br5 crystal is a direct consequence of the low phonon energy of this material of 140  cm1.

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Table 2. Measured Luminescent Lifetimes (τm), Emission Cross Section (σem), and Product of Merit (σem×τm) of F57F67 in Tb3+-Doped Mid-Infrared Optical Materials

500 ppmw Tb3+-doped Ge–As–Ga–Se unstructured fiber and 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass when pumped at 2.013 μm into the F27 level gave emission across 4.15.9  μm (Fig. 7). Photoluminescence was collected from the fiber end opposite to the pump end. The fibers used in the experiment were 350  μm diameter and were 65 mm length. The host in each case was the selenide glass Ge–As–Ga–Se. This emission is attributed to the Tb3+ F57F67 transition, and the difference in band shape between the bulk glass and the fiber is attributed to photon migration [11], with the longer path length fiber causing band shape distortion.

 

Fig. 7. Measured MIR emission spectra of 1000 ppmw Tb3+: bulk sample and 500 ppmw Tb3+ glass fiber under excitation at 2.013 μm; spectra are normalized to 1. The emission intensities were corrected for the system response.

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4. NONRADIATIVE DECAY IN RARE-EARTH-ION-DOPED SELENIDE GLASSES

A. Intrinsic Multiphonon Depopulation of RE Excited States

The intrinsic phonon energy of the Tb3+-doped Ge–As–Ga–Se glass is assumed to be 300  cm1 [1]. The probability of intrinsic multiphonon relaxation, AMP, is [1,14]

AMP(T)=B(n(T)+1)pexp(αΔE),
where T is assumed as 300 K, α and B are experimentally determined parameters assumed constant for a given host glass and derived from fitting Eq. (5) to the experimentally determined AMP dependence against energy gap (ΔE), and p is the number of phonons required to bridge ΔE:
p=ΔEω,
where ω is the intrinsic multiphonon energy. In Eq. (5), n(T) is the Bose–Einstein number, which describes the phonon population as a function of temperature (T):
n(T)=1exp(ω/kT)1.
At low RE concentration levels and short path lengths, RE ion–ion interactions may be ignored and ideally the intrinsic multiphonon relaxation rate transition probability may be assumed equal to the nonradiative relaxation rate. The intrinsic multiphonon relaxation rate increases exponentially with the decrease in energy gap, ΔE, which must be bridged by the phonons. We have
AMP=ATAR,
where AT is the observed excited state decay rate, and AR is the radiative rate calculated from J–O theory. In this work, we used data from [5,20] to fit the AMP dependence on the energy gap (Fig. 8) giving α=0.0074  cm1 and B=6.82×107  s1 for the Ge–As–Ga–Se glass host. Selenide-chalcogenide glasses exhibit their lowest nonradiative rates within the 3 μm (3333  cm1) to 6 μm (1666  cm1) wavelength range. Emission >1265  cm1 (8  μm) is denied, supporting the proposal (Section 3) that the F47 level in Tb3+-doped Ge–As–Ga–Se glass is depopulated nonradiatively.

 

Fig. 8. Calculated dependence of the multiphonon relaxation rate on the energy gap for selenide-chalcogenide optical bulk glasses based on Ge–As–Ga–Se calculated based on the data presented in [5,20]. The black line indicates the best fit to calculated intrinsic multiphonon relaxation rates in rare-earth-doped selenide-chalcogenide glasses.

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Comparison between nonradiative rates for various optical fiber glass can be found in [21].

B. Intrinsic Multiphonon Depopulation of RE Excited States Versus Extrinsic Resonant and Overtone Depopulation of RE Excited States

Assuming that the maximum intrinsic phonon energy of Tb3+-doped Ge–As–Ga–Se is 300  cm1 [1], the emission transition F47F57, which has an energy gap of transition of 1265  cm1 (7.91 μm), is predicted to be depopulated fast and nonradiatively as the transition may be bridged by 4 host intrinsic phonons. On the other hand, impurity GeO- in the glass has vibrational absorption at 8  μm [1] and so resonant nonradiative emission via extrinsic vibrational photon-assisted depopulation is also possible [1]. Tb3+ electronic transitions from the upper levels F37, F27, F17, and F07 levels are expected to be host phonon assisted and resonant and overtone vibrational photon absorption from the electronic state can occur.

As stated in [1], in impure glasses it is more correct to count the Tb3+ population in the glass as composed of subpopulations where the ideal subpopulation is exposed only to the possibility of intrinsic multiphonon decay and then for the F57F67 transition radiative decay and lasing is possible. Nonideal subpopulations of the doped-in Tb3+ may be adjacent to oxide (such as =[As–O]-) with broadband fundamental absorption centered at 12 μm [13] and hydride (such as [H–Se]-) with broad fundamental absorption centered at 4.6 μm. Resonant nonradiative decay due to extrinsic vibrational absorption of the long-lived excited state F57F67 is very probable for the subpopulation of Tb3+  ions adjacent to [H–Se]-. Multiphoton (i.e., overtone absorption) nonradiative decay due to extrinsic vibrational absorption of the long-lived excited state F57F67 is quite probable for the subpopulation of Tb3+  ions adjacent to =[As–O]-. However, it is possible that the probability of nonradiative decay of the Tb3+ excited state decreases much more rapidly as the number of photons required to bridge the gap of the potentially radiative RE transition in extrinsically mediated multiphoton nonradiative decay than in intrinsically mediated multiphonon decay.

5. POPULATION INVERSION IN Tb3+ CHALCOGENIDE GLASS AND FIBER

Rate equations were employed here mimic the erbium-doped fiber amplifier operating as a continuous wave (CW) at 1.55 μm and pumped at 0.98 μm [14]:

dN3dt=WpaN1(Wpe+W31+W32)N3,
dN2dt=WsaN1(Wse+W21)N2+W32N3,
N=N1+N2+N3,
where Ni, i=1, 2, and 3, are the ion population of energy levels 1, 2, and 3, respectively, and Wxy are the transition rates between levels x and y. The transition rates are defined as follows: the absorption and emission rates Wpa, Wpe, Wsa, and Wse of the pump and signal, respectively.

In the steady state (dNidt=0), Eqs. (9)–(11) reduce to three algebraic equations.

In Eqs. (9)–(11), the stimulated emission or absorption rates are expressed by

Wxy=ΓxσxyλxPxAhc,
where Γx is the confinement factor, which defines the fraction of energy that propagates in the core to the total energy that propagates in the fiber (core and the clad) [14], σxy is the absorption or emission cross section for the xy transition, Px denotes the propagating signal and pump powers, respectively, A is the doping cross-section area, h is Planck’s constant, λx is the wavelength of signal or pump, and c is the speed of light in free space.

Total decay rates Wij are calculated by

Wij=Wijr+Wijmp+Wijimp,
where Wijr and Wijmp are radiative and host multiphonon decay rates from the level i to the level j, respectively, taken from Table 1 and Fig. 8. Note that Wijimp was defined in [1] as the decay rate due to impurity resonant and multiphoton depopulation of the excited state. This is an integral across many different vibrational absorption energies and extinction coefficients and represents the real situation; here this was ignored and the ideal situation was modeled.

The forward Px+ and reverse Px propagation of pump Pp and signal Ps powers along the active fiber are described by the following differential equations:

dPp±dz=±Γp(σpeN3σpaN1)Pp±αpPp±,
dPs±dz=±Γs(σ21eN2σ21aN1)Ps±αsPs±,
where “+” and “−” refer to forward and backward traveling waves, respectively, Pp±=Pp++Pp, and Ps±=Ps++Ps.

σpa, σpe, σ21a, and σ21e are the absorption and emission cross sections of the pump and signal, respectively. To find output power, the photon fluxes are integrated back/forth, subject to reflective boundary conditions imposed at each fiber end and repeated to get convergence of the photon flux (detailed in [7,14]), using the experimentally determined excited-state lifetimes of 12.9 ms for the F57 level (see Fig. 6) and 12 μs for the F47 level ([5]). The Tb3+ ion density in the Ge–As–Ga–Se host was 8.25×1024  ions/m3 (=500  ppmw). Table 3 lists the modeling parameters.

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Table 3. Tb3+-Doped Selenide-Chalcogenide Glass Fiber Laser Modeling Parameters

Figure 9 shows the calculated material gain (in 1/m) as a function of the pump intensity for a Ge–As–Ga–Se glass doped with Tb3+ at a level of 500 ppmw (8.25×1024  ions/m3) obtained by numerical solution of the steady state rate equations [Eqs. (9)–(13)] for pumping at 2.013 μm and 2.95 μm, respectively, and assuming nonradiative emission solely via the selenide-chalcogenide glass host intrinsic phonons.

 

Fig. 9. Calculated material gain ΔN=σemN2σabsN1 as a function of the pump intensity for different pumping wavelengths and for laser emission at 4.7 μm in Tb3+-doped Ge–As–Ga–Se.

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The material gain was obtained using the relation

ΔN=σemN2σabsN1,
where N2 and N1 are the populations of the F57 and F67 levels, respectively, and σabs and σem are the absorption and emission cross sections at 4.7 μm, respectively (Fig. 5). From Fig. 9, positive gain was found for F57F67 pumping at either 2.013 or 2.95 μm. The pump intensity necessary to render Tb3+-doped material transparent was determined to be 20  MW/m2 and 10.7  MW/m2 for a 2.013 μm pump and 2.95 μm pump, respectively. A high gain at 4.7 μm would help reduce the active fiber length required to achieve efficient laser action at 4.7 μm. The experimentally estimated power damage threshold for selenide glass fiber has been reported to be 250  MW/m2 [22]. On the other hand, it has also been shown that the power damage threshold can be significantly increased by operation in a quasi-continuous wave (QCW) regime [23].

For modeling the performance of a 500 ppmw (8.25×1024  ions/m3) Tb3+-doped Ge–As–Ga–Se fiber lasing in the F57F67 transition, a SIF structure was assumed, with core diameter=30  μm, NA=0.4 [2], loss <1  dBm1 at all considered wavelengths [4], and fiber Bragg gratings (FBGs) to control the cavity with reflectivity at the fiber-input FBG at pump and signal wavelengths of 0.05 and 0.95, respectively, and fiber-output FBG reflectivity at pump and signal wavelengths of 0.9 and 0.05, respectively. A fiber with a similar structure has already been reported in the literature by our group [2]. In this paper [2], we have shown that the spectroscopic properties achieved for a bulk sample are also sustained for a small-core step index fiber. Fiber-laser performance was analyzed using self-consistent numerical solution of the rate and propagation equations [Eqs. (9)–(16)].

Dependence of output power on the cavity length was assessed by a systematic increase of loss [Fig. 10(a)] for pump power=1  W and lasing and pump wavelengths of arbitrarily 4.7 μm and 2.95 μm, respectively. Maximum output power was 0.42 W for a 0.9 m cavity length and 1  dB/m fiber loss. For fiber loss fixed at 3  dB/m, the maximum output power was reduced to a maximum 0.26 W for a fiber length of 0.8 m. Rapid increase of the output power was observed with an increase in cavity length, reaching a maximum at 0.8 m and decreasing with increasing cavity length. This behavior is attributed to signal reabsorption, attenuation, and pump-power depletion. Figure 10(b) shows threshold pump power as a function of cavity length (fiber loss). The minimum threshold was 25 mW and 35 mW for 1  dB/m and 3  dB/m loss, respectively. Figure 10 indicates that fiber lasing is achievable in a three-level system rather than previously designed cascading systems reliant on multiple FBGs to offset long-lived levels leading to termination [4,24].

 

Fig. 10. (a) Calculated laser power (λs=4.7  μm) and (b) threshold pump powers as a function of fiber length with different levels of fiber background loss. The results were achieved with an input pump power Pp=1  W and pump wavelength set at 2.95 μm. Results are plotted for a fiber with a background loss of 1  dB/m and 3  dB/m.

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To investigate the influence of output coupling on fiber lasing, output power was plotted as a function of cavity length for different values of output coupler reflectance, R (Fig. 11). Figure 11 indicates that the maximum possible output power was reduced, and the position of maximum output power shifted to shorter length, for an increase in R, attributed to lower cavity loss at higher R and shorter fiber length needed for maximum output power.

 

Fig. 11. Calculated laser power (λs=4.7  μm) as a function of fiber length for different values of reflectivity of the output coupler. The results were achieved with an input pump power Pp=1  W and a pump wavelength set to 2.95 μm. Results are plotted for a fiber with a background loss of 1  dB/m.

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Figure 12 shows output power as a function of lasing wavelength, for two loss levels, for the pump wavelength and fiber length fixed at 2.95 μm and 0.9 m, respectively, and pump power=1  W. The results suggest that a Tb3+-doped Ge–As–Ga–Se fiber laser could efficiently lase within the range of 4.5–5.3 μm.

 

Fig. 12. Calculated output power as a function of lasing wavelength at a pump power of 1 W. The pump wavelength and fiber length are fixed at 2.95 μm and 0.9 m, respectively. Results are plotted for a fiber with a background loss of 1  dB/m and 3  dB/m, respectively.

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Investigating the output power dependence on pump wavelength in the range of 2.75–3.2 μm (Fig. 13), this pump wavelength region is provided with several, e.g., Er:YAG, solid-state lasers and semiconductor ICLs [25]. We define the optimum fiber length as the fiber length for which maximum output power occurs. The pump power and fiber background loss were set to 1 W and 1  dB/m, respectively. From Fig. 13, output power increases steeply with increasing pump wavelength, achieves a maximum of 0.42 W at 2.95 μm, and then decreases with further increase in pump wavelength. Also, the optimum fiber length rapidly decreases with an initial increase in the pump wavelength, reaching a minimum of 0.9 m for a pump wavelength of 2.95 μm and then increasing as pump wavelength is further increased. That the output power and optimum fiber length reach their respective maximum and minimum values at a pump wavelength of 2.95 μm is due to the maximum in absorption cross section at this wavelength [see Fig. 4(a)]. High values of pump absorption cross section ensure that pump power is more quickly absorbed, which results in a shorter fiber length and correspondingly smaller attenuation loss. Based on the results presented above, it can be concluded that the pump wavelength and fiber length should be optimized simultaneously in order to achieve the best laser performance.

 

Fig. 13. Calculated output power and optimum fiber length as a function of pumping wavelength. Results are plotted for a fiber with a background loss of 1  dB/m.

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To estimate the effect of fiber loss on fiber-laser operation, the output power was calculated as a function of input pump power for different values of fiber loss (Fig. 14). From Fig. 14, it can be seen that output-power and pump-power thresholds decrease and then increase gradually, from 0.42 W to 0.06 W and from 0.031 W to 0.08 W, respectively, as fiber loss increased from 1 to 9  dB/m. Naturally, to achieve MIR fiber lasing, good glass quality is key. Recently, our group has shown that in undoped Ge–As–Se fiber, background loss and loss due to the Se–H impurity vibration band absorption can be reduced to 0.1  dB/m and 1.6  dB/m, respectively [26].

 

Fig. 14. Calculated output power as a function of input pump power for different fiber background losses. Results were calculated for the signal wavelength and the pump wavelength set to 4.7 μm and 2.95 μm, respectively.

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6. CONCLUSIONS

We have demonstrated that quasi-three-level fiber lasing is feasible in Tb3+-doped Ge–As–Ga–Se glass, giving low optical loss of <1  dBm1 at all wavelengths of interest in the fiber. We observe strong MIR emission in the range of 4.3–6.0 μm and a lifetime of 12.9 ms for the F57F67 transition in Ge–As–Ga–Se bulk glass samples and fiber samples made in-house, viz., bulk glasses doped with 500, 1000, and 1500 ppmw Tb3+ and an unstructured optical fiber doped with 500 ppmw Tb3+. The F47F67 transition was not observed to emit radiatively at 3 μm wavelength, which is why Tb3+-doped Ge–As–Ga–Se has the potential to act as a quasi-three-level system laser; the upper pumping level F47 is depopulated in a fast, nonradiative manner to F57. We have modeled the fiber-laser performance and shown, using numerical modeling, that population inversion and gain within 4.5–5.3 μm may be achieved pumping at 2.013 or 2.95 μm. Laser action with 42% efficiency is projected for pumping at 2.95 μm.

Funding

Seventh Framework Programme (FP7) (317803); European Cooperation in Science and Technology (COST) (MP1401); Ministerstwo Nauki i Szkolnictwa Wyższego (MNiSW) (IP0441/IP2/2015/73); Engineering and Physical Sciences Research Council (EPSRC) (RDF/0312).

Acknowledgment

This research has been partly supported by the European Commission through the Seventh Framework Programme (FP7) project MINERVA (317803; http://minerva-project.eu) and by the EPSRC pump priming grant RDF/0312: Three level lasing host for mid-infrared (MIR) generation. The authors would like to acknowledge networking support from COST Action: MP1401. L. S. would like to acknowledge support by the Polish Ministry of Science and Higher Education under the project entitled “Iuventus Plus,” 2016–2018 (IP0441/IP2/2015/73).

REFERENCES

1. A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010). [CrossRef]  

2. Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015). [CrossRef]  

3. J. Schneider, “Fluoride fibre laser operating at 3.9  μm,” Electron. Lett. 31, 1250–1251 (1995). [CrossRef]  

4. R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008). [CrossRef]  

5. L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001). [CrossRef]  

6. Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012). [CrossRef]  

7. S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015). [CrossRef]  

8. A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

9. R. Swanepoel, “Determining refractive index and thickness of thin films from wavelength measurements only,” J. Opt. Soc. Am. 2, 1339–1343 (1985). [CrossRef]  

10. Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

11. S. Kasap, “Influence of radiation trapping on spectra and measured lifetimes,” in The 7th International Conference on Optical, Optoelectronic and Photonic Materials and Applications (ICOOPMA) (IEEE, 2016), paper 16263756.

12. J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996). [CrossRef]  

13. G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009). [CrossRef]  

14. P. C. Becker, N. A. Olsson, and J. R. Simpson, “Erbium-doped fiber amplifiers—amplifier basics,” in Erbium-Doped Fiber Amplifiers, J. R. Simpson, ed. (Academic, 1999), pp. 131–152.

15. R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012). [CrossRef]  

16. V. G. Truong, A. M. Jurdyc, B. Jacquier, B. S. Ham, A. Q. Le Quang, J. Leperson, V. Nazabal, and J. L. Adam, “Optical properties of thulium-doped chalcogenide glasses and the uncertainty of the calculated radiative lifetimes using the Judd–Ofelt approach,” J. Opt. Soc. Am. B 23, 2588–2596 (2006). [CrossRef]  

17. M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003). [CrossRef]  

18. T. Schweizer, B. N. Samson, J. R. Hector, W. S. Brocklesby, D. W. Hewak, and D. N. Payne, “Infrared emission and ion–ion interactions in thulium- and terbium-doped gallium lanthanum sulfide glass,” J. Opt. Soc. Am. B 16, 308–316 (1999). [CrossRef]  

19. K. Rademaker, W. F. Krupke, R. H. Page, S. A. Payne, K. Petermann, G. Huber, A. P. Yelisseyev, L. I. Isaenko, U. N. Roy, A. Burger, K. C. Mandal, and K. Nitsch, “Optical properties of Nd3+- and Tb3+-doped KPb2Br5 and RbPb2Br5 with low nonradiative decay,” J. Opt. Soc. Am. B 21, 2117–2129 (2004). [CrossRef]  

20. H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014). [CrossRef]  

21. M. Pollnau and S. Jackson, “Advances in mid-infrared fiber lasers,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds. (Springer, 2008), pp. 315–346.

22. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

23. M. Bernier, V. Fortin, N. Caron, M. El-Amraoui, Y. Messaddeq, and R. Vallée, “Mid-infrared chalcogenide glass Raman fiber laser,” Opt. Lett. 38, 127–129 (2013). [CrossRef]  

24. J. Hu, C. R. Menyuk, C. Wei, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Highly efficient cascaded amplification using Pr3+-doped mid-infrared chalcogenide fiber amplifiers,” Opt. Lett. 40, 3687–3690 (2015). [CrossRef]  

25. S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6, 423–431 (2012). [CrossRef]  

26. Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015). [CrossRef]  

References

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  1. A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010).
    [Crossref]
  2. Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015).
    [Crossref]
  3. J. Schneider, “Fluoride fibre laser operating at 3.9  μm,” Electron. Lett. 31, 1250–1251 (1995).
    [Crossref]
  4. R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008).
    [Crossref]
  5. L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
    [Crossref]
  6. Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
    [Crossref]
  7. S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
    [Crossref]
  8. A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.
  9. R. Swanepoel, “Determining refractive index and thickness of thin films from wavelength measurements only,” J. Opt. Soc. Am. 2, 1339–1343 (1985).
    [Crossref]
  10. Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.
  11. S. Kasap, “Influence of radiation trapping on spectra and measured lifetimes,” in The 7th International Conference on Optical, Optoelectronic and Photonic Materials and Applications (ICOOPMA) (IEEE, 2016), paper 16263756.
  12. J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
    [Crossref]
  13. G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
    [Crossref]
  14. P. C. Becker, N. A. Olsson, and J. R. Simpson, “Erbium-doped fiber amplifiers—amplifier basics,” in Erbium-Doped Fiber Amplifiers, J. R. Simpson, ed. (Academic, 1999), pp. 131–152.
  15. R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012).
    [Crossref]
  16. V. G. Truong, A. M. Jurdyc, B. Jacquier, B. S. Ham, A. Q. Le Quang, J. Leperson, V. Nazabal, and J. L. Adam, “Optical properties of thulium-doped chalcogenide glasses and the uncertainty of the calculated radiative lifetimes using the Judd–Ofelt approach,” J. Opt. Soc. Am. B 23, 2588–2596 (2006).
    [Crossref]
  17. M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
    [Crossref]
  18. T. Schweizer, B. N. Samson, J. R. Hector, W. S. Brocklesby, D. W. Hewak, and D. N. Payne, “Infrared emission and ion–ion interactions in thulium- and terbium-doped gallium lanthanum sulfide glass,” J. Opt. Soc. Am. B 16, 308–316 (1999).
    [Crossref]
  19. K. Rademaker, W. F. Krupke, R. H. Page, S. A. Payne, K. Petermann, G. Huber, A. P. Yelisseyev, L. I. Isaenko, U. N. Roy, A. Burger, K. C. Mandal, and K. Nitsch, “Optical properties of Nd3+- and Tb3+-doped KPb2Br5 and RbPb2Br5 with low nonradiative decay,” J. Opt. Soc. Am. B 21, 2117–2129 (2004).
    [Crossref]
  20. H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
    [Crossref]
  21. M. Pollnau and S. Jackson, “Advances in mid-infrared fiber lasers,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds. (Springer, 2008), pp. 315–346.
  22. B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).
  23. M. Bernier, V. Fortin, N. Caron, M. El-Amraoui, Y. Messaddeq, and R. Vallée, “Mid-infrared chalcogenide glass Raman fiber laser,” Opt. Lett. 38, 127–129 (2013).
    [Crossref]
  24. J. Hu, C. R. Menyuk, C. Wei, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Highly efficient cascaded amplification using Pr3+-doped mid-infrared chalcogenide fiber amplifiers,” Opt. Lett. 40, 3687–3690 (2015).
    [Crossref]
  25. S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6, 423–431 (2012).
    [Crossref]
  26. Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
    [Crossref]

2015 (4)

2014 (1)

2013 (1)

2012 (3)

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6, 423–431 (2012).
[Crossref]

R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

2011 (1)

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

2010 (1)

2009 (1)

G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[Crossref]

2008 (1)

R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008).
[Crossref]

2006 (1)

2004 (1)

2003 (1)

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

2001 (1)

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
[Crossref]

1999 (1)

1996 (1)

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

1995 (1)

J. Schneider, “Fluoride fibre laser operating at 3.9  μm,” Electron. Lett. 31, 1250–1251 (1995).
[Crossref]

1985 (1)

R. Swanepoel, “Determining refractive index and thickness of thin films from wavelength measurements only,” J. Opt. Soc. Am. 2, 1339–1343 (1985).
[Crossref]

Adam, J. L.

Aggarwal, I. D.

J. Hu, C. R. Menyuk, C. Wei, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Highly efficient cascaded amplification using Pr3+-doped mid-infrared chalcogenide fiber amplifiers,” Opt. Lett. 40, 3687–3690 (2015).
[Crossref]

R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008).
[Crossref]

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
[Crossref]

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

Barney, E.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

Becker, P. C.

P. C. Becker, N. A. Olsson, and J. R. Simpson, “Erbium-doped fiber amplifiers—amplifier basics,” in Erbium-Doped Fiber Amplifiers, J. R. Simpson, ed. (Academic, 1999), pp. 131–152.

Benson, T. M.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015).
[Crossref]

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010).
[Crossref]

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Beres-Pawlik, E.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

Bernier, M.

Bowman, S. R.

R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012).
[Crossref]

Brocklesby, W. S.

Burger, A.

Caron, N.

Caspary, R.

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Churbanov, M. F.

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[Crossref]

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Cole, B.

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
[Crossref]

Condon, N. J.

R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012).
[Crossref]

Dianov, E. M.

G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[Crossref]

Eggleton, B. J.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

El-Amraoui, M.

Fang, Y.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Fay, M.

Fortin, V.

Furberg, P.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Furniss, D.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015).
[Crossref]

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010).
[Crossref]

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Galagan, B. I.

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Ham, B. S.

Hector, J. R.

Hewak, D. W.

Hu, J.

Huber, G.

Isaenko, L. I.

Jackson, S.

M. Pollnau and S. Jackson, “Advances in mid-infrared fiber lasers,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds. (Springer, 2008), pp. 315–346.

Jackson, S. D.

S. D. Jackson, “Towards high-power mid-infrared emission from a fibre laser,” Nat. Photonics 6, 423–431 (2012).
[Crossref]

Jacquier, B.

Jayasuriya, D.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Jurdyc, A. M.

Kasap, S.

S. Kasap, “Influence of radiation trapping on spectra and measured lifetimes,” in The 7th International Conference on Optical, Optoelectronic and Photonic Materials and Applications (ICOOPMA) (IEEE, 2016), paper 16263756.

Krupke, W. F.

Kryukova, E. B.

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Kung, F. H.

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

Lamrini, S.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Le Quang, A. Q.

Leperson, J.

Luther-Davies, B.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

Mandal, K. C.

Markos, C.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Menyuk, C. R.

Messaddeq, Y.

Milos, R. E.

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

Moneim, N. A.

Nazabal, V.

Neate, N.

Nguyen, V. Q.

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

Nitsch, K.

O’Connor, S. P.

R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012).
[Crossref]

Oladeji, A.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Olsson, N. A.

P. C. Becker, N. A. Olsson, and J. R. Simpson, “Erbium-doped fiber amplifiers—amplifier basics,” in Erbium-Doped Fiber Amplifiers, J. R. Simpson, ed. (Academic, 1999), pp. 131–152.

Page, R. H.

Payne, D. N.

Payne, S. A.

Petermann, K.

Phillips, A.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Plotnichenko, V. G.

G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[Crossref]

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Pollnau, M.

M. Pollnau and S. Jackson, “Advances in mid-infrared fiber lasers,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds. (Springer, 2008), pp. 315–346.

Pureza, P. C.

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

Pyrkov, Y. N.

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Quimby, R. S.

R. S. Quimby, N. J. Condon, S. P. O’Connor, and S. R. Bowman, “Excited state dynamics in Ho:KPb2Cl5,” Opt. Mater. 34, 1603–1609 (2012).
[Crossref]

R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008).
[Crossref]

Rademaker, K.

Richardson, K.

B. J. Eggleton, B. Luther-Davies, and K. Richardson, “Chalcogenide photonics,” Nat. Photonics 5, 141–148 (2011).

Roy, U. N.

Sakr, H.

Samson, B. N.

Sanghera, J. S.

J. Hu, C. R. Menyuk, C. Wei, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Highly efficient cascaded amplification using Pr3+-doped mid-infrared chalcogenide fiber amplifiers,” Opt. Lett. 40, 3687–3690 (2015).
[Crossref]

R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008).
[Crossref]

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
[Crossref]

J. S. Sanghera, V. Q. Nguyen, P. C. Pureza, R. E. Milos, F. H. Kung, and I. D. Aggarwal, “Fabrication of long lengths of low loss transmitting As40S(60-x)Sex glass fibers,” J. Lightwave Technol. 14, 743–748 (1996).
[Crossref]

Schneider, J.

J. Schneider, “Fluoride fibre laser operating at 3.9  μm,” Electron. Lett. 31, 1250–1251 (1995).
[Crossref]

Scholle, K.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Schweizer, T.

Scripachev, I. V.

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Seddon, A. B.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015).
[Crossref]

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010).
[Crossref]

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Shaw, L. B.

J. Hu, C. R. Menyuk, C. Wei, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Highly efficient cascaded amplification using Pr3+-doped mid-infrared chalcogenide fiber amplifiers,” Opt. Lett. 40, 3687–3690 (2015).
[Crossref]

R. S. Quimby, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Modeling of cascade lasing in Dy:chalcogenide glass fiber laser with efficient output at 4.5  μm,” IEEE Photon. Technol. Lett. 20, 123–125 (2008).
[Crossref]

L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
[Crossref]

Shiryaev, V. S.

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

G. E. Snopatin, V. S. Shiryaev, V. G. Plotnichenko, E. M. Dianov, and M. F. Churbanov, “High-purity chalcogenide glasses for fiber optics,” Inorg. Mater. 45, 1439–1460 (2009).
[Crossref]

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

Simpson, J. R.

P. C. Becker, N. A. Olsson, and J. R. Simpson, “Erbium-doped fiber amplifiers—amplifier basics,” in Erbium-Doped Fiber Amplifiers, J. R. Simpson, ed. (Academic, 1999), pp. 131–152.

Smetanin, S. V.

M. F. Churbanov, I. V. Scripachev, V. S. Shiryaev, V. G. Plotnichenko, S. V. Smetanin, E. B. Kryukova, Y. N. Pyrkov, and B. I. Galagan, “Chalcogenide glasses doped with Tb, Dy, and Pr ions,” J. Non-Cryst. Solids 326, 301–305 (2003).
[Crossref]

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[Crossref]

Sojka, L.

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Sójka, L.

Sujecki, S.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015).
[Crossref]

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010).
[Crossref]

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

Swanepoel, R.

R. Swanepoel, “Determining refractive index and thickness of thin films from wavelength measurements only,” J. Opt. Soc. Am. 2, 1339–1343 (1985).
[Crossref]

Tang, Z.

S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Z. Tang, D. Furniss, M. Fay, H. Sakr, L. Sójka, N. Neate, N. Weston, S. Sujecki, T. M. Benson, and A. B. Seddon, “Mid-infrared photoluminescence in small-core fiber of praseodymium-ion doped selenide-based chalcogenide glass,” Opt. Mater. Express 5, 870–886 (2015).
[Crossref]

Z. Tang, V. S. Shiryaev, D. Furniss, L. Sojka, S. Sujecki, T. M. Benson, A. B. Seddon, and M. F. Churbanov, “Low loss Ge–As–Se chalcogenide glass fiber, fabricated using extruded preform, for mid-infrared photonics,” Opt. Mater. Express 5, 1722–1737 (2015).
[Crossref]

H. Sakr, D. Furniss, Z. Tang, L. Sojka, N. A. Moneim, E. Barney, S. Sujecki, T. M. Benson, and A. B. Seddon, “Superior photoluminescence (PL) of Pr3+-In, compared to Pr3+-Ga, selenide-chalcogenide bulk glasses and PL of optically-clad fiber,” Opt. Express 22, 21236–21252 (2014).
[Crossref]

Ł. Sójka, Z. Tang, H. Zhu, E. Bereś-Pawlik, D. Furniss, A. B. Seddon, T. M. Benson, and S. Sujecki, “Study of mid-infrared laser action in chalcogenide rare earth doped glass with Dy3+, Pr3+ and Tb3+,” Opt. Mater. Express 2, 1632–1640 (2012).
[Crossref]

A. B. Seddon, Z. Tang, D. Furniss, S. Sujecki, and T. M. Benson, “Progress in rare-earth-doped mid-infrared fiber lasers,” Opt. Express 18, 26704–26719 (2010).
[Crossref]

Tang, Z. Q.

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

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L. B. Shaw, B. Cole, P. A. Thielen, J. S. Sanghera, and I. D. Aggarwal, “Mid-wave IR and long-wave IR laser potential of rare-earth doped chalcogenide glass fiber,” IEEE J. Quantum Electron. 37, 1127–1137 (2001).
[Crossref]

Truong, V. G.

Vallée, R.

Wei, C.

Weston, N.

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[Crossref]

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[Crossref]

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[Crossref]

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S. Sujecki, A. Oladeji, A. Phillips, A. B. Seddon, T. M. Benson, H. Sakr, Z. Tang, E. Barney, D. Furniss, Ł. Sójka, E. Bereś-Pawlik, K. Scholle, S. Lamrini, and P. Furberg, “Theoretical study of population inversion in active doped MIR chalcogenide glass fibre lasers (invited),” Opt. Quantum Electron. 47, 1389–1395 (2015).
[Crossref]

Other (5)

A. B. Seddon, D. Furniss, Z. Q. Tang, Ł. Sojka, T. M. Benson, R. Caspary, and S. Sujecki, “True mid-infrared Pr3+ absorption cross section in a selenide-chalcogenide host-glass,” in 18th International Conference on Transparent Optical Networks (ICTON) (IEEE, 2016), paper 7550709.

M. Pollnau and S. Jackson, “Advances in mid-infrared fiber lasers,” in Mid-Infrared Coherent Sources and Applications, M. Ebrahim-Zadeh and I. Sorokina, eds. (Springer, 2008), pp. 315–346.

Y. Fang, L. Sojka, D. Jayasuriya, D. Furniss, Z. Q. Tang, C. Markos, S. Sujecki, A. B. Seddon, and T. M. Benson, “Characterising refractive index dispersion in chalcogenide glasses,” in Proceedings of 18th International Conference on Transparent Optical Networks (IEEE, 2016), paper 7550618.

S. Kasap, “Influence of radiation trapping on spectra and measured lifetimes,” in The 7th International Conference on Optical, Optoelectronic and Photonic Materials and Applications (ICOOPMA) (IEEE, 2016), paper 16263756.

P. C. Becker, N. A. Olsson, and J. R. Simpson, “Erbium-doped fiber amplifiers—amplifier basics,” in Erbium-Doped Fiber Amplifiers, J. R. Simpson, ed. (Academic, 1999), pp. 131–152.

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Figures (14)

Fig. 1.
Fig. 1. Refractive index dispersion of 500 ppmw Tb3+-doped Ge–As–Ga–Se (blue points are data points from the improved Swanepoel method, and the black curve is the Sellmeier fit to the data points).
Fig. 2.
Fig. 2. (b) Simplified energy-level diagram for Tb3+-doped chalcogenide glass proposed here according to (a) the absorption bands observed for Tb3+ bulk samples using FTIR.
Fig. 3.
Fig. 3. Experimentally measured absorption spectra of 500, 1000, and 1500 ppmw Tb3+: Ge–As–Ga–Se bulk glasses. The upper transition state is identified in each case.
Fig. 4.
Fig. 4. (a) Absorption spectrum of the F67F47 transition in 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass. The solid line indicates the measured absorption spectrum of the F67F47 transition, which is comprised of both the Tb3+ absorption and the OH impurity absorption bands. The dashed line represents the true absorption spectrum of the F67F47 transition after calculation to remove the OH contribution. The dotted line represents the calculated contribution of the OH impurity to absorption in the 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass. (b) Absorption spectrum for the F67F57 transition of 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass. The solid line indicates the measured absorption spectrum of the F67F57 transition, which is comprised of both the Tb3+ absorption and the Se–H impurity absorption bands. The dashed line represents the true absorption spectrum of the F67F57 transition after calculation to remove the Se–H contribution. The dotted line represents the calculated contribution of the Se–H impurity to absorption in the 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass.
Fig. 5.
Fig. 5. Absorption cross section for the F67F57 transition (solid curve, measured but with removal of the contribution of the Se–H impurity band). Emission cross section for the transition F57F67 (dashed curve, calculated using McCumber theory from the corrected absorption cross section). The absorption cross section was calculated for 1000 ppmw Tb3+-doped Ge–As–Ga–Se bulk glass.
Fig. 6.
Fig. 6. Decay time of the F57 excited level of 1000 ppmw Tb3+-doped chalcogenide selenide glass bulk sample measured at 4.7 μm after QCW (6–8 Hz) laser excitation at 2.013 μm. The best fit to the measured decay profile yields a single exponential decay with τm=12.9  ms.
Fig. 7.
Fig. 7. Measured MIR emission spectra of 1000 ppmw Tb3+: bulk sample and 500 ppmw Tb3+ glass fiber under excitation at 2.013 μm; spectra are normalized to 1. The emission intensities were corrected for the system response.
Fig. 8.
Fig. 8. Calculated dependence of the multiphonon relaxation rate on the energy gap for selenide-chalcogenide optical bulk glasses based on Ge–As–Ga–Se calculated based on the data presented in [5,20]. The black line indicates the best fit to calculated intrinsic multiphonon relaxation rates in rare-earth-doped selenide-chalcogenide glasses.
Fig. 9.
Fig. 9. Calculated material gain ΔN=σemN2σabsN1 as a function of the pump intensity for different pumping wavelengths and for laser emission at 4.7 μm in Tb3+-doped Ge–As–Ga–Se.
Fig. 10.
Fig. 10. (a) Calculated laser power (λs=4.7  μm) and (b) threshold pump powers as a function of fiber length with different levels of fiber background loss. The results were achieved with an input pump power Pp=1  W and pump wavelength set at 2.95 μm. Results are plotted for a fiber with a background loss of 1  dB/m and 3  dB/m.
Fig. 11.
Fig. 11. Calculated laser power (λs=4.7  μm) as a function of fiber length for different values of reflectivity of the output coupler. The results were achieved with an input pump power Pp=1  W and a pump wavelength set to 2.95 μm. Results are plotted for a fiber with a background loss of 1  dB/m.
Fig. 12.
Fig. 12. Calculated output power as a function of lasing wavelength at a pump power of 1 W. The pump wavelength and fiber length are fixed at 2.95 μm and 0.9 m, respectively. Results are plotted for a fiber with a background loss of 1  dB/m and 3  dB/m, respectively.
Fig. 13.
Fig. 13. Calculated output power and optimum fiber length as a function of pumping wavelength. Results are plotted for a fiber with a background loss of 1  dB/m.
Fig. 14.
Fig. 14. Calculated output power as a function of input pump power for different fiber background losses. Results were calculated for the signal wavelength and the pump wavelength set to 4.7 μm and 2.95 μm, respectively.

Tables (3)

Tables Icon

Table 1. Calculated Spontaneous Emission Rates [Electronic (AED) and Magnetic (AMD)], Radiative Branching Ratios (βrad), and Radiative Lifetimes (τrad) for Emissions Observed Centered at Wavelength λ

Tables Icon

Table 2. Measured Luminescent Lifetimes (τm), Emission Cross Section (σem), and Product of Merit (σem×τm) of F57F67 in Tb3+-Doped Mid-Infrared Optical Materials

Tables Icon

Table 3. Tb3+-Doped Selenide-Chalcogenide Glass Fiber Laser Modeling Parameters

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

n2=1.485+4.942λ2λ20.29232+1.124λ2λ239.232,
σabs=α(λ)N,
σem=λ48πn2cAjjrΔλ,
η=τmτrad,
AMP(T)=B(n(T)+1)pexp(αΔE),
p=ΔEω,
n(T)=1exp(ω/kT)1.
AMP=ATAR,
dN3dt=WpaN1(Wpe+W31+W32)N3,
dN2dt=WsaN1(Wse+W21)N2+W32N3,
N=N1+N2+N3,
Wxy=ΓxσxyλxPxAhc,
Wij=Wijr+Wijmp+Wijimp,
dPp±dz=±Γp(σpeN3σpaN1)Pp±αpPp±,
dPs±dz=±Γs(σ21eN2σ21aN1)Ps±αsPs±,
ΔN=σemN2σabsN1,

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