1. Introduction

Enhanced 2 µm mid-IR eye-safe lasers can open up new applications including high resolution spectroscopy, remote sensing, atmospheric monitoring, biomedical imaging, medical surgery, quality control, and has applications in the defense sector [1]. To obtain efficient lasers around 2 µm, glasses are doped with Tm³⁺ or Ho³⁺ rare earth ions [2]. The emission cross-section of Ho³⁺ at ∼ 2 µm is at least 4 times higher than that of the Tm³⁺ emission [3], combined with a long upper-state lifetime that is favorable for Q-switched laser applications.

2 µm laser emission in Ho³⁺ requires out of band pumping at either 900 nm or 1150 nm, or resonant in-band pumping at 1945nm (e.g. via a thulium fiber laser). The pump lasers operating at these wavelengths are expensive and commercially scarce hence the addition of a sensitizer ion along with the active ion helps utilize more readily available laser diodes (LDs) [2]. Relevant sensitizers include Tm³⁺ or Yb³⁺. In this study, Yb³⁺ is used as the sensitizer for two reasons. Firstly, Yb³⁺ has a strong absorption at 976 nm, which is a wavelength where high-power single-mode laser diodes are readily available. Secondly, the energy transfer coefficient from Yb³⁺ to Ho³⁺ was previously found to be high in silicate [4] and oxyfluoride [5] glasses.

Small-cavity mid-IR lasers (e.g. waveguide lasers) are targeted in this study as high optical gain and high efficiencies can be achieved. Besides this, monolithic devices can be manufactured by integrating waveguide lasers with other photonic devices on a single chip. Previous studies on small-cavity lasers have focused on silicate [6] and fluoride [7] glass hosts. Silicate glasses have high damage threshold and superior thermal stability compared to any other host glasses reported as waveguide lasers, however their transmission does not extend to the mid-IR. By contrast, fluorides have a wide transmission spectrum extending into the mid-IR region, however low thermal conductivity and mechanical strength limit the power scaling potential. Alternative glasses are heavy metal oxides including tellurite and germanate [8].

Lead-germanate glasses are promising host materials for 2 µm laser application due to their high chemical and thermal stability compared to other mid-IR transmitting glasses. One of the most widely investigated lead-germanate glasses has the molar composition of 56GeO₂-31PbO-4Ga₂O₃-9Na₂O (GPGN). The broad transmission spectrum of GPGN glass allows a wide range of laser wavelengths to be considered. GPGN glass is melted at a lower temperature of 1200°C-1250°C [9] compared to the extensively studied BaO-Ga₂O₃-GeO₂ germanate glass system, which melts at ∼1500°C [10]. This lower melting temperature allows convenient melting of GPGN in dry atmosphere using a glove-box based melting facility.

Lead-germanate glasses also possess a high refractive index compared to other glasses in the germanate family [11] which make them a suitable candidate for the fabrication of optical elements (eg. lenses). High refractive index is also useful for dispersion compensation and high-power non-linear applications (e.g. broadband supercontinuum generation and four-wave mixing). Another compelling feature of lead-germanate glass is its capacity to accommodate large concentrations of dopants unlike other glass hosts [12], making it a suitable candidate for single frequency laser operations, where short cavity lengths with sufficient net gain are required.

The Ho³⁺ based 2 µm laser properties have been investigated in singly doped and co-doped germanate glasses. Based on a Ho³⁺ singly doped lead-germanate glass with molar composition of 50GeO₂-5SiO₂-20PbO-20CaO-5K₂O, Ho³⁺ laser generation with 47% quantum efficiency was achieved using in-band pumping with a Tm³⁺ fiber laser at 1.94 µm [13]. A higher quantum efficiency of 79% was obtained in GeO₂- BaF₂-Ga₂O₃-LiF glass when co-doped with Yb³⁺ and pumped with 976 nm LD due to high energy transfer from Yb³⁺ to Ho³⁺ [14]. Several studies also revealed laser operation in Ho³⁺ doped and co-doped germanate glass fibers. These include a Ho³⁺ singly doped germanate fiber laser with similar composition as in [13]. resulting in a 35% laser slope efficiency when pumped at 1.94 µm [15]. A single frequency tunable laser operation in a 2 cm long Ho³⁺ doped germanate fiber was reported in [16] which also used a 1.94 µm in-band Tm³⁺ fiber laser pumping scheme. A low laser slope efficiency of 4.7% was observed in a BGG glass co-doped with Tm³⁺ using 796 nm LD pumping, with an energy transfer efficiency of 63% from Tm³⁺ to Ho³⁺ [17]. To the best of our knowledge, planar and channel waveguide lasers have yet to be demonstrated for Ho³⁺ singly doped or Yb³⁺/Ho³⁺ co-doped germanate glasses.

In this paper, we investigate the potential of a new, in-house fabricated Yb³⁺/Ho³⁺ co-doped lead-germanate glass for 2 µm waveguide laser application. The main aim of the study was to develop a small cavity laser system that can be pumped with readily available high-power 976 nm LD source and efficiently emit at 2 µm. This study was also undertaken to validate the 2 µm laser performance in Yb³⁺/Ho³⁺: GPGN based on the experimentally measured/calculated spectroscopic parameters. The rare-earth (RE) concentrations were chosen to address our longer-term aim to develop a high efficiency waveguide cavity laser. For short cavity laser operation, we selected 3 mol% of sensitizer ion (Yb³⁺) to achieve efficient pump absorption (97% in 5 mm). A relatively low concentration (0.8 mol%) of active ion (Ho³⁺) was selected due to: (i) Ho³⁺ is efficient even at low concentrations and (ii) to avoid the very common ion clustering in Ho³⁺ doped materials. Based on absorption and emission measurements combined with Judd-Ofelt analysis, we determined a range of spectroscopic parameters (absorption and emission cross sections, fluorescence lifetime and energy transfer microparameter) for 2 µm waveguide laser simulations using rate equation modelling. Energy transfer efficiency of ∼ 94% for Yb³⁺:²F_5/2→Ho³⁺:⁵I₆ was estimated using the rate equations. A high Ho³⁺:⁵I₇→⁵I₈ quantum efficiency of 76% and a measured Ho³⁺:⁵I₇ lifetime of (7.74 ± 0.03) ms were determined for the glass.

2. Experimental procedures

The fabricated Yb³⁺/Ho³⁺ co-doped GPGN glass has a mol% composition of (56-x)GeO₂ - (31−y)PbO - 4Ga₂O₃ - 9Na₂O with x=1.5Yb₂O₃ and y=0.4Ho₂O₃, and was synthesized by a conventional melt-quench technique described in [18]. This glass sample is henceforth referred to as Yb³⁺/Ho³⁺:GPGN. This specific composition of lead-germanate glass was selected as GPGN possesses higher thermal stability against crystallization (previously demonstrated in [9]) compared to other lead-germanate glasses [11]. The 20 g batch was physically mixed and placed in a platinum crucible for melting at a temperature of ∼ 1250°C for 70 min under dry melting environment (80% N₂ and 20% O₂) in a glove-box. The molten glass was poured into a pre-heated brass mold and placed in the annealing furnace for ∼15 hours (∼ 390$^{\circ}{\textrm C})$ below the glass transition temperature (${T_g}$∼ 390°C) resulting in a glass block with dimensions of 20×15×5 mm³.

A spectrophotometer (Agilent Cary 5000) was used to collect the absorption spectrum of the optically polished glass block to measure its ground state absorption bands. The fluorescence emission spectrum of the sample was collected with a near infrared spectrometer (Ocean Optics NIRQUEST) using a CW 976 nm LD for excitation. All measurements were taken at room temperature. The fluorescence lifetime for the fabricated glass was measured using a spectrofluorimeter (Edinburgh Instruments FLS980). The density of the glass was measured using Archimedes’ Principle.

3. Results and discussion

3.1 Yb³⁺/Ho³⁺: GPGN spectroscopic analysis

3.1.1 Density and Refractive index

The density of the Yb³⁺/Ho³⁺:GPGN glass was measured to be 5.60 ± 0.02 g/cm³. Based on this value and the doping concentration, the ion density of Yb³⁺ and Ho³⁺ was determined as ${N_{Yb}}$ = 6.94×10²⁰ ion/cm³ and ${N_{Ho}}$ = 1.85×10²⁰ ions/cm³, respectively.

The refractive index n for undoped GPGN glass [9] was used for Fresnel reflection based absorbance subtraction and Judd-Ofelt calculations. The index at 1.5 µm is n = 1.8222 ± 0.0004. The refractive index as a function of wavelength is defined by the Sellmeier equation of the form given in Eq. (1)

By fitting Eq. (1) to the measured index values of GPGN given in [9], the Sellmeier coefficients of GPGN glass were calculated to be A=2.029, B=1.267, C=5.4×10⁻², D=4.4×10⁻⁴ and E=0.2993.

3.1.2 Rare-earth and OH^- absorption spectrum

The absorbance spectrum was collected to determine the ground state absorption bands of the doped rare earth ions and the absorption band of the fundamental vibration of OH groups in the Yb³⁺/Ho³⁺:GPGN glass fabricated. The baseline of the measured absorbance spectrum (i.e. the absorbance of the glass excluding rare earth ion and OH absorption bands) consists of the absorbance due to Fresnel reflections (E₀) at the glass sample surfaces, absorbance due to scattering at surface imperfections and absorbance due to impurities and defects in the glass volume. For high-purity glass samples with an optically flat surface finish, the absorbance from surface imperfections, impurities and defects is negligible. The E₀ component of absorbance E(λ) as a function of wavelength was determined using log₁₀((n²(λ) + 1)/2n(λ)). The absorption coefficient, α(λ), was then obtained by subtracting the Fresnel based absorbance E₀(λ) from the measured absorbance E(λ) and diving it by the sample’s thickness L= (1.61 ± 0.05) mm using the expression α (λ) = ln10 (E(λ)-E₀(λ))/L (Fig. 1(a)).

 

Fig. 1. (a) Absorption coefficient spectrum for Yb³⁺/Ho³⁺:GPGN glass from 400 nm – 2500nm representing different absorption bands of Ho³⁺ and Yb³⁺. Inset to the Fig. is the OH absorption coefficient spectrum peaking at ∼3100 nm in Yb³⁺/Ho³⁺:GPGN. (b) Comparison of Yb³⁺ absorption in GPGN with silica [19] and ZBLAN [20].

Download Full Size | PDF

The Ho³⁺ absorption peaks are shown in Fig. 1(a) and centered at 418 nm (⁵G₅), 450 nm (⁵F₁+⁵G₆), 540 nm (⁵F₄+⁵S₂), 642 nm (⁵F₅), 1150 nm (⁵I₆) and 1945nm (⁵I₇). The absorption cross section, ${\sigma _{abs\; }}(\lambda )$ of Ho³⁺ in Yb³⁺/Ho³⁺:GPGN was calculated using the absorption coefficient, α(λ), divided by the ion density of Ho³⁺ $({{N_{Ho}}} )$. ${\sigma _{abs\; }}$ for the Ho³⁺:⁵I₇ absorption band was estimated as 4.5×10⁻²¹ cm².

The Yb³⁺ absorption band (²F_5/2) shown in Fig. 1(a) ranges from ∼ 870 nm to 1100 nm, with distinct peaks at 905 nm and 976 nm. The 905 nm peak is narrower, and blue shifted compared to other hosts such as silica and fluoride, where the peak is located at ∼ 920 nm (Fig. 1(b)). The Yb³⁺ absorption band in Yb³⁺/Ho³⁺:GPGN can be fitted with 5 peaks at locations 905 nm, 932 nm, 950 nm, 976 nm and 1020 nm, unlike silica with 3 peaks (920 nm, 974 nm and 1020 nm) and ZBLAN with 4 peaks (925 nm, 942 nm, 976 nm and 1010 nm).

The broad absorption band covering 2800 nm – 3300 nm with a peak at 3100 nm (Fig. 1(a)) is due to the fundamental vibration of OH groups, which are usually observed in heavy metal oxide glasses. These OH groups are known to quench mid-IR fluorescence transitions [15], including Ho³⁺:⁵I₆→⁵I₇ (2.8 µm) and Ho³⁺:⁵I₇→⁵I₈ (2 µm) and, therefore, the estimation of the OH content is required to predict the OH quenching rate. The OH concentration (${N_{OH}}$) in terms of number of OH groups per cm³ is usually determined from the OH absorption coefficient at the peak wavelength of the OH absorption band at 3 µm using Eq. (2) [21].

3.1.3 Judd-Ofelt analysis for intensity parameter calculations

Judd-Ofelt (JO) intensity parameters Ω₂, Ω₄ and Ω₆ play an important part in the prediction of the spectroscopic properties of rare earth ions in a host material. According to the JO theory, the absorption line strength of an electric-dipole transition from initial manifold J to the excited manifold $J^{\prime}$ is given by Eq. (3)

The electric $({{S_{ed}}} )$ and the magnetic dipole $({{S_{md}}} )$ line strengths are associated with the integral of the absorption coefficient, $\alpha (\lambda )$, for a specific absorption band and are represented by Eq. (4)

Six absorption bands with peaks at 1945nm (⁵I₇), 1150 nm (⁵I₆), 642 nm (⁵F₅), 540 nm (⁵F₄+⁵S₂), 448 nm (⁵F₁+⁵G₆) and 418 nm (⁵G₅) were considered in this study. Multiple regression of all these bands resulted in the intensity parameters to be Ω₂ = 3.0×10⁻²⁰ cm², Ω₄ = 1.2×10⁻²⁰ cm² and Ω₆ = 2.0×10⁻²⁰ cm². Small RMS value indicates that the ${S_{ed}}$ values predicted through the multiple regression are in close approximation to the measured values. The calculated and measured electric dipole line strengths for the ground state absorption bands of Ho³⁺ in Yb³⁺/Ho³⁺:GPGN are presented in Table 1.

Table 1. Measured and calculated electric dipole line strengths (S_ed) and refractive index values for respective transition bands of Ho³⁺ and the JO intensity parameters Ω₂, Ω₄ and Ω₆ in Yb³⁺/Ho³⁺:GPGN. ^* represents the electric (A_ed) and magnetic (A_md) contributions for Ho³⁺:⁵I₇→⁵I₈ radiative transition probability.

View Table | View all tables in this article

The radiative transition probability for a specific energy level is related to the electric (${S_{ed}})$ and magnetic (${S_{md}}$) line strengths for the respective absorption bands and is represented by Eq. (6). For the given Ho³⁺:⁵I₇→⁵I₈ transition, ${A_r}$ was evaluated as 99 s^-1.

3.1.4 Emission spectrum and lifetime measurements

The emission cross-section $({{\sigma_{ems}}(\lambda )} )$ plays an important role in the estimation of laser transition probability and the laser performance. For 2 µm laser emission in Yb³⁺/Ho³⁺:GPGN, the peak emission cross-section $({{\sigma_{ems}}} )$ was calculated using the Füchtbauer-Ladenburg Eq. (7)

The emission spectrum I(λ) in Eq. (7) was collected using the configuration shown in Fig. 2(a), where the collimated beam from a 976 nm LD strikes the edge of the sample and the fluorescence is collected orthogonally to avoid fluorescence being reabsorbed by the ground state. I(λ) was collected from 950 nm to 2400 nm (Fig. 2(b)). The broad fluorescence up to 1150 nm in Fig. 2(b) is due to the Yb³⁺ in Yb³⁺/Ho³⁺:GPGN [25]. This broadening is attributed to the large stark splitting of Yb³⁺ in germanate glass [26].

 

Fig. 2. (a) Experimental setup to collect fluorescence data from the edge of the Yb³⁺/Ho³⁺:GPGN using 976 nm pumping source (b) Fluorescence spectrum I(λ).

Download Full Size | PDF

The fluorescence decay curves were measured for Ho³⁺ and Yb³⁺ in Yb³⁺/Ho³⁺:GPGN as well as for Yb³⁺ in GPGN glass of the same composition but singly doped with Yb³⁺ (Yb³⁺:GPGN), which was fabricated in our previous work [25]. The fluorescence decay curves were fitted to a single coefficient exponential equation, thus allowing the lifetimes of the respective ions to be determined (decay to 1/e), and then to be used to estimate the energy transfer efficiency from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆, which is discussed in 3.1.5.

The measured fluorescence lifetime of Ho³⁺:⁵I₇ in the Yb³⁺/Ho³⁺:GPGN glass is (7.74 ± 0.03) ms (Fig. 3(a)), similar to the Ho³⁺:⁵I₇ lifetime (7.68 ms) reported in GeO₂-BaF₂-Ga₂O₃-LiF germanate glass [14].

 

Fig. 3. Measured fluorescence decay curves in blue (dotted lines). Single coefficient best fit exponential decay curves are given in brown (solid lines) for (a) Ho³⁺:⁵I₇ in Yb³⁺/Ho³⁺: GPGN with τ_m= 7.74 ms. (b) Yb³⁺:²F_5/2 in Yb³⁺:GPGN with τ_Yb = 1.76 ms.

Download Full Size | PDF

The lifetime of the upper state of Yb³⁺:²F_5/2 in the singly doped Yb³⁺:GPGN glass is (1.76 ± 0.01) ms (Fig. 3(b)), whereas in co-doped Yb³⁺/Ho³⁺:GPGN glass, this lifetime is reduced to 0.1 ms.

Using the integrated emission spectrum 1800nm – 2200 nm and the measured lifetime of Ho³⁺:⁵I₇ in Eq. (7), the peak emission cross section, σ_ems, at ∼ 2 µm is calculated to be 4.2×10⁻²¹ cm² (Fig. 4). In comparison, the σ_ems of Ho³⁺ is 4.9×10⁻²¹ cm² in GeO₂-BaF₂-Ga₂O₃-LiF glass [14] and 3.1×10⁻²¹ cm² in La₂O₃-Al₂O₃-GeO₂ glass [27].

 

Fig. 4. Absorption (blue) and emission (brown) cross sections for the Ho³⁺:⁵I₇→⁵I₈ transition at ∼2 µm. The fluorescence emission spectrum was obtained by exciting the sample with a 976 nm LD.

Download Full Size | PDF

Quantum efficiency plays an important role to estimate the laser performance in a gain medium. It is defined as the product of measured lifetime and the radiative transition probability (τ_m${\times} $ A_r). The quantum efficiency for the Ho³⁺:⁵I₇→⁵I₈ transition in Yb³⁺/Ho³⁺:GPGN was predicted to be 76%, which is larger compared to phosphate glass (51%), LiF₃ crystal (64%) or in another lead-germanate glass type (47%) [13]. This high predicted quantum efficiency in Yb³⁺/Ho³⁺:GPGN indicates that the glass is a promising candidate for efficient 2 µm laser application.

3.1.5 2 µm energy transfer pathway

This section investigates the energy transfer pathway from Yb³⁺ (donor ion, D) to Ho³⁺ (acceptor ion, A). The Yb³⁺ ions in the ground state (²F_7/2) are excited to the upper state (²F_5/2) when pumped with a 976 nm LD. Based on this excitation wavelength, three energy transfers (ET) were observed from Yb³⁺:²F_5/2 to three different states of Ho³⁺ (Fig. 5). (i) ET₁ is the phonon assisted energy transfer to Ho³⁺:⁵I₆ that populates the upper laser level ⁵I₇ via multi-phonon decay process from where it depopulates to the ground state. (ii) ET₂ is the up-conversion energy transfer to Ho³⁺:⁵F₅ transition that leads to unwanted red fluorescence and (iii) ET₃ is the up-conversion energy transfer to Ho³⁺:⁵F₄ that leads to unwanted green fluorescence.

 

Fig. 5. Energy transfers (ET) pathways in Yb³⁺/Ho³⁺:GPGN. Solid transfer lines represent dominating processes.

Download Full Size | PDF

For the 2 µm laser model, we are only considering the phonon assisted ET₁ and ignoring ET₂ and ET₃ because the measured decay rates of Ho³⁺:⁵F₄ (${\tau _1}$ = 52 µs) and Ho³⁺:⁵F₅ (${\tau _2}\; \,$=115 µs) are fast compared to the decay rate of Ho³⁺:⁵I₇ (${\tau _m}$=7.7 ms). This makes ET₂ and ET₃ negligible compared to the dominating ET₁ process. For the phonon assisted ET₁, the energy gap between Yb³⁺:²F_5/2 and Ho³⁺:⁵I₆ is ∼ 1200 cm^-1. Thus, 1 or 2 phonons are required to take part in the transfer as the phonon energy of the lead-germanate glass is ∼ 800 cm^-1 [28]. The rate of this energy transfer (W_ET) is given in Eq. (8)

The energy transfer microparameter, C_DA, from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆ is defined by W_ET = C_DA×N_Yb×N_Ho. In [14], an energy transfer coefficient, C_D, is defined as W_ET = C_D×N_Ho, with C_D = C_DA×N_Yb. To be able to compare C_DA of Yb³⁺/Ho³⁺:GPGN with that of Yb³⁺/Ho³⁺ co-doped GeO₂-BaF₂-Ga₂O₃-LiF (GBGL) glass in [14], we calculated C_DA from the C_D values given in [14]. As the Yb³⁺ concentration in [14] is only given in mol%, we calculated C_DA in unit cm³.mol%/s (Table 2). The plot of the energy transfer microparameter as a function of the Ho³⁺ concentration (Fig. 6) shows a linear dependence, which indicates that the energy transfer rate scales with N_Ho² for ≥ 0.1 mol% Ho₂O₃, i.e. W_ET = k_DA×N_Yb×N_Ho², where k_DA = C_DA/N_Ho is the slope of the line in Fig. 6. Further work is needed to understand the mechanism of the nonlinear dependence of the energy transfer rate on the Ho³⁺ concentration for ≥ 0.1 mol% Ho₂O₃.

 

Fig. 6. Linear dependence of energy transfer microparameter on the Ho³⁺ concentration (plotted using data in blue from [14] and this work (brown)). Data points > 0.1 mol% Ho₂O₃ were used for linear fitting (green).

Download Full Size | PDF

Table 2. Comparison of current study with published Yb³⁺/Ho³⁺ GBGL where the Yb³⁺ lifetime is measured for a range of Ho³⁺ concentrations.

View Table | View all tables in this article

3.1.6 Effect of OH on Ho³⁺:⁵I₇ lifetime:

The depopulation of the metastable state of Ho³⁺ (⁵I₇) is accompanied by the radiative decay rate, ${A_r}$, determined by the radiative lifetime, ${\tau _r}$, and the non-radiative decay rate having two contributions of (i) multi-phonon decay for Ho³⁺:⁵I₇→⁵I₈ (${W_{MP}}$) and (ii) energy transfer to the OH groups (${W_{OH}}$). ${\tau _m}$ is, therefore, given by Eq. (9)

W_MP in Eq. (9) is estimated using the well-known energy gap law defined in [29] where the non-radiative energy transfer within a host material follows an exponential decay path, ${W_{MP}} = a \times \exp[{ - b({\Delta E - 2\hbar \omega } )} ]$, where a and b are the non-radiative decay parameters that depend on the glass type. The values for germanate glass were taken from [29], $\Delta E$ is the energy gap between ⁵I₆ and ⁵I₇ (∼5000 cm^-1) and $\hbar \omega $ is the phonon energy of GPGN (∼ 820 cm^-1). Using these values, ${W_{MP}}$ is ∼ 12 s^-1.

With the calculated W_MP, as well as the known measured and radiative lifetime of the Ho³⁺:⁵I₇ level, Eq. (9) is used to calculate ${W_{OH}}$ to be 18 s^-1. To compare this value with other germanate glass, we consider the Ho³⁺-OH energy migration assisted energy transfer model in [13], which was adopted from the Er³⁺-OH migration assisted energy transfer model in [30]. This model is based on three main assumptions, (i) only a fraction of OH ions is coupled to Ho³⁺, (ii) the number of Ho³⁺ ions coupled to OH groups is proportional to the number of OH groups with the proportionality constant given by $\gamma $, (iii) the excited energy migrates between Ho³⁺ ions that are not coupled to OH to Ho³⁺ ions that are coupled to OH, and from these coupled Ho³⁺ ions fast energy transfer to their proximate OH groups occurs. According to this model, the rate of the overall Ho³⁺-OH energy transfer process, W_OH, is determined by the energy migration between Ho³⁺ ions, which depends on the total concentration of Ho³⁺ ions, and the energy transfer between coupled Ho³⁺ and OH, which depends on the OH concentration according to assumption (ii). This is given by Eq. (10), which is adapted from [30],

As the rate of the energy transfer between coupled Ho³⁺ and OH is much faster than that of the energy migration between Ho³⁺ ions, C_Ho is the microparameter of the energy migration, where Ho³⁺ is donor and acceptor. Hence, C_Ho is calculated using the experimentally determined emission and absorption cross sections of the Ho³⁺:⁵I₇→⁵I₈ transition at 2 µm, yielding 63 × 10⁻⁴⁰ cm⁶/s. Using this C_Ho value, W_OH = 18 s^-1 as calculated from Eq. (9), N_Ho and N_OH, Eq. (10) yields γ ∼ 0.15 in GPGN.

In GeO₂-SiO₂-PbO-CaO-K₂O (GSPCK) germanate glass, linear regression of the non-radiative decay rate 1/τ_m-1/τ_r as a function of ${N_{Ho}} \times {N_{OH}}$ (Fig. 7(b)) according to Eq.(9) yielded W_MP=33 s^-1 from the intercept and γ = 0.24 from the slope [32]. The lower value of W_MP=12 s^-1 for GPGN is consistent with the absence of high phonon energy component SiO₂ in GPGN compared to GSPCK. It is important to note that the linear dependence of the non-radiative decay rate on ${N_{Ho}} \times {N_{OH}}$ (Figure 7(b)) indicates that γ is a characteristic parameter for a specific glass composition (Table 3 and Fig. 7(b)) and cannot be linked only to Ho³⁺ coupled to OH as assumed in the quenching model in [13]. The lower γ value in GPGN (0.15) compared to GSPCK (0.24) suggests reduced tendency of OH ions to cluster with Ho³⁺ ions. In comparison, for phosphate glasses, cluster formation between rare earth ions and OH groups was derived from energy transfer analysis [33] which is consistent with the high γ = 0.6 value for Er³⁺-OH energy migration assisted energy transfer in phosphate glass [30].

 

Fig. 7. (a) Simplified ET diagram for depopulation of ⁵I₇ energy state of Ho³⁺. (b) Non-radiative decay rate as a function of Ho³⁺ and OH concentrations for GSPCK and GPGN glass, with similar slope in both glasses.

Download Full Size | PDF

Table 3. Measured and calculated parameters for GPGN and GSPCK for different concentrations of Ho³⁺ and OH for the calculation of γ and the respective quantum efficiency (QE).

View Table | View all tables in this article

The presence of OH in GPGN quenched the lifetime of ⁵I₇ from 10.1 ms down to 7.74 ms. The quantum efficiency (QE) for ⁵I₇→⁵I₈ in GPGN using A_r/(A_r+W_MP+W_OH) =76% is much higher than that in [13] where it was 47% for the sample with high N_Ho and low N_OH (G6). This is because of enhanced energy migration to the Ho³⁺ ions coupled to the OH (fast W_OH) in G6 due to high Ho³⁺ concentration. In contrast, the QE in G1 with low Ho³⁺ concentration is 69% despite of high OH content due to low energy migration to the Ho³⁺ ions coupled to the OH (slow W_OH). It is, therefore, important to balance the proportion of both the Ho³⁺ and OH concentrations to minimize W_OH for maximizing the QE of the Ho³⁺ emission at 2 µm. The QE for GPGN can be further enhanced by reducing the OH content for same Ho³⁺ concentration via improved dehydration of the glass melt during the fabrication process.

4. 2 µm laser simulations

In this section we present the 2 µm waveguide laser simulation model using the RP fiber power software. This software is designed for laser simulations based on rate-equation modelling to assist in quantitative understanding of the laser performance. Adopting a waveguide mode confinement simplifies the laser model as it conveniently propagates the forward and backward laser signal through the fixed cylindrical gain volume where it remains confined to the waveguide core in the laser cavity. The simulations are based on the spectroscopic parameters obtained for Yb³⁺/Ho³⁺:GPGN in the previous sections including ${\sigma _{abs}}(\lambda )$, ${\sigma _{ems}}(\lambda )$, the lifetimes ${\tau _r}$, ${\tau _{Yb}}$, and ${\tau _D}$ for respective states, donor and acceptor ion densities ${N_{Yb}}$ and ${N_{Ho}}$, and the energy transfer microparameter, ${C_{DA}},$ from Yb³⁺:²F_5/2→Ho³⁺:⁵I₆.

Considering a simple energy model, only three states of Ho³⁺ were considered. 1 is allotted to ground state (⁵I₈), 2 is the metastable state (⁵I₇), and 3 is the excited state (⁵I₆) with ion populations described as ${N_{1(A )}}$, ${N_{2(A )}}$ and ${N_{3(A )}}$, respectively. The states 4 and 5 were allocated to the Yb³⁺ ground (²F_7/2) and excited (²F_5/2) states with ions populations ${N_{1(D )}}$ and ${N_{2(D )}}$, respectively. Equation (12) provided an estimate of the length of the gain medium by our previous measurement of the pump absorption. It can be observed from Fig. 8 that for a 1.5 mol % Yb₂O₃ concentration, ∼ 90% of the pump is predicted to be absorbed in 3 mm of Yb³⁺/Ho³⁺:GPGN.

 

Fig. 8. (a) Predicted pump absorption in Yb³⁺/Ho³⁺:GPGN sample with respect to the position. n₂ population in ⁵I₇ is ∼ 40% with no losses (b) Output power as function of wavelength for 2 W of input power.

Download Full Size | PDF

For all the above assumptions the ‘ideal’ ∼2 µm gain of the medium was predicted at 0.34 dB using the equation $G = [{\sigma _{ems}}(\lambda ){N_{2(A )}} - {\sigma _{abs}}(\lambda ){N_{1(A )}}$] if no other losses are considered. If more realistic estimate losses are considered, such as 0.7 dB Fresnel reflection loss, 0.7 dB of waveguide loss and assuming the absence of OH quenching losses, the gain drops to1.4 dB loss/ pass for the cavity. Using the waveguide laser model, the presence of OH losses affects the 2 µm laser efficiency by reducing the excited ion population in the ⁵I₇ state from 40% (without losses) to 20% for a total of 1.5 dB loss as can be observed from Fig. 8(a) and Fig. 9(a).

 

Fig. 9. (a) ⁵I₇ population in Yb³⁺/Ho³⁺:GPGN reduced to ∼ 20% with 1.8 dB cavity loss (b) Output power as function of wavelength for 2W of input power.

Download Full Size | PDF

For the Yb³⁺/Ho³⁺:GPGN glass as gain medium, the highest gain was predicted for a 6 mm length of the sample considering no cavity losses (Fig. 8(b)). By setting the loss to 1.8 dB, maximum laser efficiency was estimated for a 2 mm long sample (Fig. 9(b)). To simulate the 2 µm laser, a 30 µm mode diameter of the laser cavity was considered. The input coupler used in the simulation was T=100% @ 976 nm and HR near ∼ 2000 nm, while the output coupler was a R = 95% output-coupler with a broadband reflectively centered at 2000 nm. By assuming no losses in the medium, a laser efficiency of 20% was predicted with a low 200 mW laser threshold. For a 1 dB loss in the glass medium (including the Fresnel and the internal glass absorption loss) the laser efficiency reduces to 15% with an increase in the laser threshold to ∼ 500 mW. Laser efficiency further reduces with an increase in the laser threshold by also considering OH quenching loss. For intra-cavity losses higher than 1.8 dB, no laser action was observed (Fig. 10).

 

Fig. 10. 2 µm laser simulations in Yb³⁺/Ho³⁺:GPGN and the effect of losses on the laser efficiency and threshold. No laser action observed for a total cavity loss above 1.8 dB.

Download Full Size | PDF

5. Conclusion

The potential of a new co-doped lead-germanate glass (Yb³⁺/Ho³⁺:GPGN) for 2 µm waveguide laser application was presented. The intensity parameters were calculated as Ω₂ = 3.0×10⁻²⁰ cm², Ω₄ = 1.2×10⁻²⁰ cm² and Ω₆ = 2.0×10⁻²⁰ cm². The energy transfer efficiency from Yb³⁺:²F_5/2 to Ho³⁺:⁵I₆ was as high as 94% due to higher concentration of Yb³⁺ and Ho³⁺ in GPGN compared to the Yb³⁺/Ho³⁺ co-doped germanate glasses reported previously [3,12]. A quantum efficiency of 76% for 2 µm Ho³⁺ emission with a long measured radiative lifetime of Ho³⁺: ⁵I₇ = (7.74 ± 0.03) ms was observed compared to other lead-germanate glasses [2,3,12]. The energy transfer analysis from Ho³⁺ to OH in GPGN resulted in a low value of $\gamma $ (0.15) indicating reduced tendency of OH to cluster with Ho³⁺ compared to GSPCK (0.24) [2]. Using the spectroscopic data, the simulated waveguide laser results predict that for Yb³⁺/Ho³⁺:GPGN, >15% laser efficiency at 2 µm can be achieved for cavity losses ≤ 0.5 dB. The overall spectroscopic analysis and the laser simulations indicate that Yb³⁺/Ho³⁺:GPGN is a promising gain medium for 2 µm waveguide laser operation.