Simulation of an erbium-doped chalcogenide micro-disk mid-infrared laser source

doi:10.1364/OE.19.011951

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Simulation of an erbium-doped chalcogenide micro-disk mid-infrared laser source

Faleh Al Tal, Clara Dimas, Juejun Hu, Anu Agarwal, and Lionel C. Kimerling »View Author Affiliations

Optics Express, Vol. 19, Issue 13, pp. 11951-11962 (2011)
http://dx.doi.org/10.1364/OE.19.011951

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– Abstract
1. Introduction
2. Simulation model
3. Simulation results
4. Conclusion
– References and links

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Abstract

The feasibility of mid-infrared (MIR) lasing in erbium-doped gallium lanthanum sulfide (GLS) micro-disks was examined. Lasing condition at 4.5 µm signal using 800 nm pump source was simulated using rate equations, mode propagation and transfer matrix formulation. Cavity quality (Q) factors of 1.48 × 10⁴ and 1.53 × 10⁶ were assumed at the pump and signal wavelengths, respectively, based on state-of-the-art chalcogenide micro-disk resonator parameters. With an 80 µm disk diameter and an active erbium concentration of 2.8 × 10²⁰ cm⁻³, lasing was shown to be possible with a maximum slope efficiency of 1.26 × 10⁻⁴ and associated pump threshold of 0.5 mW.

1. Introduction

Chalcogenide glasses (ChGs) are distinguished for having chemical durability, photosensitivity, high refractive index, low phonon energy, low melting temperature, and broad infrared transparency [1

B. J. Eggleton, “Chalcogenide photonics: fabrication, devices and applications. Introduction,” Opt. Express 18(25), 26632–26634 (2010). [CrossRef] [PubMed]

–3

A. Zakery, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]

]. Such characteristics make this family of glass attractive for the development of infrared integrated optical devices [4

N. Carlie, J. D. Musgraves, B. Zdyrko, I. Luzinov, J. Hu, V. Singh, A. Agarwal, L. C. Kimerling, A. Canciamilla, F. Morichetti, A. Melloni, and K. Richardson, “Integrated chalcogenide waveguide resonators for mid-IR sensing: leveraging material properties to meet fabrication challenges,” Opt. Express 18(25), 26728–26743 (2010). [CrossRef] [PubMed]

–6

K. Richardson, L. Petit, N. Carlie, B. Zdyrko, I. Luzinov, J. Hu, A. Agarwal, L. Kimerling, T. Anderson, and M. Richardson, “Progress on the fabrication of on-chip, integrated chalcogenide glass (ChG)-based sensors,” J. Nonlinear Opt. Phys. Mater. 19(01), 75–99 (2010). [CrossRef]

]. Integration of multiple monolithic components on a single substrate is beneficial for minimization of size and cost by enabling systems-on-chip applications. A key enabler for such systems is the demonstration of monolithic light sources emitting in various wavelength regimes.

Rare earth (RE) elements are incorporated as active emission centers in passive crystalline and amorphous materials. Many RE transitions are generally quenched in hosts such as phosphate and silica glasses which have high phonon energies that can bridge low energy gaps and cause large multi-phonon relaxation rates [7

M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).

A. Kenyon, “Recent Developments in rare-earth doped materials for optoelectronics,” Prog. Quantum Electron. 26(4-5), 225–284 (2002). [CrossRef]

]. On the other hand, ChGs have relatively low phonon energies which reduce the possibility of these non-radiative relaxations and enable emission of long wavelengths.

RE elements have been incorporated into bulk ChGs and thin films to emit near-infrared, mid-infrared and far-infrared light [9

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(25), 26704–26719 (2010). [CrossRef] [PubMed]

–15

J. Frantz, J. Sanghera, L. Shaw, G. Villalobos, I. Aggarwal, and D. Hewak, “Sputtered films of Er³⁺-doped gallium lanthanum sulfide glass,” Mater. Lett. 60(11), 1350–1353 (2006). [CrossRef]

]. Moreover, lasing in RE-doped ChGs fibers, waveguides, and micro-spheres has been reported. In particular, Nd-doped gallium lanthanum sulfide (GLS) fibers and laser written waveguides in bulk glass at 1080 nm [16

T. Schweizer, D. W. Hewak, D. N. Payne, T. Jensen, and G. Huber, “Rare-earth doped chalcogenide glass laser,” Electron. Lett. 32(7), 666–667 (1996). [CrossRef]

–19

A. K. Mairaj, A. M. Chardon, D. P. Shepherd, and D. W. Hewak, “Laser performance and spectroscopic analysis of optically written channel waveguides in neodymium-doped gallium lanthanum sulphide glass,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1381–1388 (2002). [CrossRef]

]; Nd and Tm-doped tellurite micro-spheres at 1060 nm and 2 µm, respectively [20

K. Sasagawa, K. Kusawake, J. Ohta, and M. Nunoshita, “Nd-doped tellurite glass microsphere laser,” Electron. Lett. 38(22), 1355–1357 (2002). [CrossRef]

–22

J. Wu, S. Jiang, T. Qua, M. Kuwata-Gonokami, and N. Peyghambarian, “2 μm lasing from highly thulium doped tellurite glass microsphere,” Appl. Phys. Lett. 87(21), 211118 (2005). [CrossRef]

]; and most recently Nd-doped GLS micro-sphere at 1080 nm [23

G. R. Elliott, G. S. Murugan, J. S. Wilkinson, M. N. Zervas, and D. W. Hewak, “Chalcogenide glass microsphere laser,” Opt. Express 18(25), 26720–26727 (2010). [CrossRef] [PubMed]

]. Also, a theoretical study showed the feasibility of lasing at 4.5 µm in erbium-doped photonic crystal fibers [24

F. Prudenzano, L. Mescia, L. A. Allegretti, M. De Sario, T. Palmisano, F. Smektala, V. Moizan, V. Nazabal, and J. Troles, “Design of Er³⁺-doped chalcogenide glass laser for MID-IR application,” J. Non-Cryst. Solids 355(18-21), 1145–1148 (2009). [CrossRef]

]. However, to date, no monolithic ChG laser has been demonstrated or investigated.

In this paper, we present our simulation results toward developing a monolithic MIR laser source, utilizing erbium-doped GLS glass. Bulk erbium-doped GLS showed MIR photoluminescence emission at 4.5 µm through the transition between ⁴I_9/2 and ⁴I_11/2 energy levels [25

T. Schweizer, D. Brady, and D. W. Hewak, “Fabrication and spectroscopy of erbium doped gallium lanthanum sulphide glass fibres for mid-infrared laser applications,” Opt. Express 1(4), 102–107 (1997). [CrossRef] [PubMed]

]. Compared to other ChG glasses, GLS is capable of hosting relatively high erbium concentrations (2.8 × 10²⁰ ions/cm³) without being affected by luminescence quenching [25

]. Nevertheless, the considered transition is characterized by a small emission cross section of 2.5 × 10⁻²¹ cm². This limits the maximum possible gain to less than 4 dB/cm. For lasing to be possible under this gain limitation, resonators with minimum quality (Q) factors of 3.5 × 10⁴ are required.

Recently, lift-off and thermal reflow process has been used to demonstrate ChG micro-disks with Q factors in excess of 10⁵ at 1.55 μm [26

J. Hu, N. N. Feng, N. Carlie, L. Petit, A. Agarwal, K. Richardson, and L. C. Kimerling, “Optical loss reduction in high-index-contrast chalcogenide glass waveguides via thermal reflow,” Opt. Express 18(2), 1469–1478 (2010). [CrossRef] [PubMed]

]. This is a catalyst for fabricating monolithic laser sources given the aforementioned specification requirements. In the subsequent text, lasing at 4.5 µm is examined with 800 nm pumping for erbium-doped GLS micro-disk. The rate equations of erbium, the pump, and signal disk modes were solved, and a transfer matrix formulation was used to estimate the output lasing power.

2. Simulation model

The developed model considers pump and signal modes that correspond to wavelengths of 800 nm and 4.5 µm, respectively. Separate bus waveguides introduce and collect the pump and signal light from the disk as illustrated in Fig. 1 . Also, the following constants and assumptions were used: 1) uniform erbium doping concentration of 2.8 × 10²⁰ cm⁻³; 2) disk structure of 80 µm diameter and 600 nm thickness; 3) refractive indices of 2.42 and 2.35 at the pump and signal wavelengths, respectively, were obtained by fitting experimental data to a Cauchy relation [27

H. Yayama, “Refractive index dispersion of gallium lanthanum sulfide and oxysulfide glasses,” J. Non-Cryst. Solids 239(1-3), 187–191 (1998). [CrossRef]

]; 4) transverse electric (TE) polarization modes, with dominant electric component parallel to the disk plane, were included; 5) Purcell cavity enhancement is neglected since the photon density in the cavity is high and the micro-disk structure has high order modes with large radiation; and 6) unidirectional mode propagation was considered.

Fig. 1 Laser configuration consists of a micro-disk with input pump waveguide and output signal waveguide. P is the pump power and S is the signal power at the positions indicated by the subscripts, κ² is the power coupling coefficient between the bus waveguides and the disk, and the subscripts P and S stand for the pump and signal, respectively.

We establish some useful considerations, to ease the development of our model. Since the disk has a relatively large diameter, the free spectral range will be less than the emission and absorption line-widths of erbium. Hence, resonance can be assumed for the pump and signal modes. Also, for the continuous wave (CW) case, steady state condition is imposed. With these assumptions and no input signal, the internal power in the disk can be related to the power in the pump and signal buses through the following relations [28

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

\frac{P_{1}}{P_{i n}} = \frac{κ_{P}^{2}}{{(1 - \sqrt{a_{P}^{2} (1 - κ_{P}^{2})})}^{2}} .

(1)

S_{o u t} = κ_{S}^{2} S_{2} .

(2)

where

a_{P}^{2}

is the round trip power absorption for the pump mode, P_i is the pump power and S_i is the signal power at the positions indicated by the subscripts,

κ_{P, S}^{2}

is the power coupling coefficient between the bus waveguides and the disk and the subscripts P and S stands for the pump and signal, respectively. We can also eliminate the inter-effect of the signal and pump bus waveguides on the disk pump and signal modes, respectively, by recognizing the following. The signal mode has much longer wavelength than the pump mode. Therefore, it possesses a greater evanescent tail length. Hence, the signal bus can be placed far from the pump mode tail which prevents pump out-coupling. In addition, since the pump light has a short wavelength, the pump bus can be designed with a width smaller than the signal cutoff. Hence, the pump bus will also have no coupling with the signal mode. Then, P₃ and S₁ will be equal to P₂ and S₄ , respectively. P₄ and S₂ are related to P₁ and S₃ by Beer–Lambert law and the signal coupling coefficient according to the following relations [28

H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).

,29

S. Hooker, Laser Physics (Oxford University Press, 2010). [PubMed]

P_{4} = P_{1} E x p (\int_{l_{1}}^{l_{4}} - α_{P}^{M} (l) . d l) .

(3)

\begin{matrix} S_{2} = S_{1} E x p (\int_{l_{1}}^{l_{2}} - α_{S}^{M} (l) + g_{S}^{M} (l) . d l), \\ S_{1} = S_{4} = S_{3} E x p (\int_{l_{3}}^{l_{4}} - α_{S}^{M} (l) + g_{S}^{M} (l) . d l) . \end{matrix}

(4)

S_{3} = S_{2} (1 - κ_{S}^{2}) .

(5)

where l is the azimuthal coordinate along the disk circumference,

α_{P / S}^{M} (l)

and

g_{S}^{M} (l)

are the absorption and gain coefficients of the pump (P) and signal (S) modes at l. From Eq. (4) and Eq. (5):

\int_{l_{3}}^{l_{4}} α_{S}^{M} (l) - g_{S}^{M} (l) . d l + \int_{l_{1}}^{l_{2}} α_{S}^{M} (l) - g_{S}^{M} (l) . d l = \ln (1 - κ_{S}^{2}) .

(6)

this equation defines the condition that should be satisfied for the steady state (CW) lasing case. The out coupled signal power should be exactly recovered by the round trip gain. For smaller gain, lasing is not possible, while higher gain values do not satisfy the steady state condition.

The energy evolution of erbium is described using the five-level model as elaborated in Fig. 2 [30

K. Kadono, “Rate equation analysis and energy transfer of Er³⁺-doped Ga₂S₃–GeS₂–La₂S₃ glasses,” J. Non-Cryst. Solids 331(1-3), 79–90 (2003). [CrossRef]

,31

M. Desario, L. Mescia, F. Prudenzano, F. Smektala, F. Deseveday, V. Nazabal, J. Troles, and L. Brilland, “Feasibility of Er³⁺-doped, Ga₅Ge₂₀Sb₁₀S₆₅ chalcogenide microstructured optical fiber amplifiers,” Opt. Laser Technol. 41(1), 99–106 (2009). [CrossRef]

]. The ion-ion and ion-photon interactions with the pump and signal light are calculated according to the subsequent rate equations:

\begin{matrix} \frac{d N_{1}}{d t} = C_{22} N_{2}^{2} - C_{14} N_{1}^{} N_{4}^{} + C_{33}^{} N_{3}^{2} - C_{16}^{} N_{1}^{} N_{5}^{} + C_{24}^{} N_{2}^{} N_{4}^{} \\ + (σ_{P}^{e} - σ_{P}^{a}) N_{1} \frac{I_{P}}{ℏ ω_{P}} + \sum_{i = 2}^{5} a_{i 1} N_{i} + W_{2} N_{2},_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{}_{}^{} \\ \frac{d N_{2}}{d t} = - 2 C_{22} N_{2}^{2} + 2 C_{14} N_{1}^{} N_{4}^{} + C_{16}^{} N_{1}^{} N_{5}^{} + C_{44}^{} N_{4}^{2} \\ {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{}_{}^{} + C_{24}^{} N_{2}^{} N_{4}^{} + \sum_{i = 5}^{3} a_{i 2} N_{i} - a_{21} N_{2} + W_{3} N_{3} - W_{2} N_{2}, \\ \frac{d N_{3}}{d t} = - 2 C_{33} N_{3}^{2} - σ_{S}^{a} N_{3}^{} \frac{I_{S}}{ℏ ω_{S}} + σ_{S}^{e} N_{4}^{} \frac{I_{S}}{ℏ ω_{S}} + \sum_{i = 4}^{5} a_{i 3} N_{i} - \sum_{i = 1}^{2} a_{3 i} N_{3} + W_{4} N_{4} - W_{3} N_{3}, \\ \frac{d N_{4}}{d t} = C_{22} N_{2}^{2} - C_{14} N_{1}^{} N_{4}^{} + C_{16} N_{1}^{} N_{5}^{} - 2 C_{44} N_{4}^{2} - C_{24} N_{2}^{} N_{4}^{} + (σ_{S}^{a} N_{3}^{} - σ_{S}^{e} N_{4}^{}) \frac{I_{S}}{ℏ ω_{S}} \\ + (σ_{P}^{a} N_{1}^{} - σ_{P}^{e} N_{4}^{}) \frac{I_{P}}{ℏ ω_{P}} + a_{54} N_{5} \sum_{i = 1}^{3} a_{4 i} N_{4} + W_{5} N_{5} - W_{4} N_{4},_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} {_{}^{}}_{}^{} \\ \frac{d N_{5}}{d t} = C_{33} N_{3}^{2} - C_{16} N_{1}^{} N_{5}^{} + C_{44} N_{4}^{2} + C_{24} N_{2}^{} N_{4}^{} - \sum_{i = 1}^{4} a_{5 i} N_{5} - W_{5} N_{5}, \\ \sum_{i = 1}^{5} N_{i} = N_{T o t a l} . \end{matrix}

(7)

where N_i is the ion concentration at energy level i, I_S/P is the signal or pump beam intensity, ħω_S/P is the photon energy, C_ij are the energy transfer coupling coefficients that quantify the ion-ion interactions,

σ_{S / P}^{e / a}

is the emission (e) or absorption (a) cross section, a_ij is the spontaneous emission rate from level i to level j, W_i is the multi-phonon decay rate from level i to the next lower energy level, and N_Total is the total erbium doping concentration. The values of the energy transfer constants are obtained experimentally [30

K. Kadono, “Rate equation analysis and energy transfer of Er³⁺-doped Ga₂S₃–GeS₂–La₂S₃ glasses,” J. Non-Cryst. Solids 331(1-3), 79–90 (2003). [CrossRef]

]. The energy gap law is used to evaluate the multi-phonon decay rates [32

R. Quimby, “Multiphonon energy gap law in rare-earth doped chalcogenide glass,” J. Non-Cryst. Solids 320(1-3), 100–112 (2003). [CrossRef]

]. The spontaneous emission rate is obtained using Judd-Ofelt theorem [33

B. M. Walsh, “Judd-Ofelt theory: principles and practices,” in Advances in Spectroscopy for Lasers and Sensing , B. Bartolo and O. Forte, eds. (Kluwer Academic Publishers, 2006), pp. 403–433.

]. Finally, McCumber and Füchtbauer-Ladenburg relations are used to calculate the emission and absorption cross sections at the pump and signal wavelengths [34

D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134(2A), A299–A306 (1964). [CrossRef]

,35

J. G. Solé, L. E. Bausá, and D. Jaque, An Introduction to the Optical Spectroscopy of Inorganic Solids (John Wiley and Sons, Ltd., 2005).

]. The values of these parameters are provided in the appendix (Table 2 ).

Fig. 2 Erbium energy levels and ion-ion interaction parameters (C_ij ). 800 nm pump source excites the ions from the ground state to ⁴I_9/2. The excited ions decay to ⁴I_11/2 to emit 4.5 µm signal light.

Table 2 Rate Equations Parameters of Erbium-Doped GLS System

Emission and absorption cross sections		Multi-phonon decay rate (parameters are found in [ 40 T. Schweizer, “Rare-earth-doped gallium lanthanum sulphide glasses for mid-infrared fibre lasers,” University of Southampton, Faculty of Engineering and Applied Science, Department of Electronics and Computer Science, Doctoral Thesis (2000). ])
$σ_{S}^{e}$	2.5 × 10⁻²¹ cm² [25 T. Schweizer, D. Brady, and D. W. Hewak, “Fabrication and spectroscopy of erbium doped gallium lanthanum sulphide glass fibres for mid-infrared laser applications,” Opt. Express 1(4), 102–107 (1997). [CrossRef] [PubMed] ]	W₂	0
$σ_{P}^{a}$	3 × 10⁻²¹ cm² [25 T. Schweizer, D. Brady, and D. W. Hewak, “Fabrication and spectroscopy of erbium doped gallium lanthanum sulphide glass fibres for mid-infrared laser applications,” Opt. Express 1(4), 102–107 (1997). [CrossRef] [PubMed] ]	W₃	0
$σ_{S}^{a}$	2.5 × 10⁻²¹ cm² (Mc-Cumber)	W₄	800
$σ_{P}^{e}$	0.3 × 10⁻²¹ cm² (Mc-Cumber)	W₅	25

Spontaneous emission rate obtained by Judd-Ofelt (s⁻¹) [ 41 C. Ye, “Spectral properties of Er³⁺-doped gallium lanthanum sulphide glass,” J. Non-Cryst. Solids 208(1-2), 56–63 (1996). [CrossRef] ]		Energy transfer parameters (cm³/s) [ 30 K. Kadono, “Rate equation analysis and energy transfer of Er³⁺-doped Ga₂S₃–GeS₂–La₂S₃ glasses,” J. Non-Cryst. Solids 331(1-3), 79–90 (2003). [CrossRef] , 31 M. Desario, L. Mescia, F. Prudenzano, F. Smektala, F. Deseveday, V. Nazabal, J. Troles, and L. Brilland, “Feasibility of Er³⁺-doped, Ga₅Ge₂₀Sb₁₀S₆₅ chalcogenide microstructured optical fiber amplifiers,” Opt. Laser Technol. 41(1), 99–106 (2009). [CrossRef] ]
a₂₁	546.4	C₃₃	22.5 × 10⁻¹⁸
a₃₁	559	C₁₄	5 × 10⁻¹⁸
a₃₂	96	C₁₆	5 × 10⁻¹⁸
a₄₁	744.3	C₄₄	2 × 10⁻¹⁸
a₄₂	174.2	C₂₂	35 × 10⁻¹⁸
a₄₃	8	C₂₄	2 × 10⁻¹⁸
a₅₁	7076.1
a₅₂	332.3
a₅₃	268
a₅₄	29

Rosenbrock iterative method was used to find the steady state population distribution of the ions. The signal gain coefficient (g_S ), and the pump absorption coefficient due to erbium (α_P,Er ), are functions of the pump and signal intensities. These coefficients are given, per unit area, by the following equations [29

S. Hooker, Laser Physics (Oxford University Press, 2010). [PubMed]

g_{S} = σ_{S}^{e} N_{4}^{} - σ_{S}^{a} N_{3}^{}

(8)

α_{P, E r}^{} = σ_{P}^{a} N_{1}^{} - σ_{P}^{e} N_{4}^{}

(9)

The cavity modes were calculated for the disk cross section in Fig. 3 . A CaF₂ substrate was assumed for its low absorption in the MIR regime. As moisture can be trapped in CaF₂, a GLS thin film to coat the entire substrate was taken into account. To reduce the signal radiation losses, a large diameter of 80 microns was assumed. Reducing the thickness of the disk minimizes scattering from the side walls while it increases the signal radiation losses. Signal radiation was found to be insignificant for a disk thickness of 0.6 µm and a substrate coating layer of 0.1 µm thickness. A full-vectorial finite difference mode solver on FIMMWAVE was used to calculate the disk mode profiles at the signal and pump wavelengths [36

FIMMMWAVE: Waveguides solver (Photon Design, 34 Leopold Street, Oxford, OX41TW, U.K.).

]. Having azimuthal symmetry, the two-dimensional solution was calculated for the disk cross section along the radial and planar directions.

Fig. 3 The micro-disk material cross section showing a CaF₂ substrate, and erbium-doped GLS coating layer and disk. A CaF₂ substrate was considered for its low absorption in the MIR regime. As moisture can be trapped in CaF₂, a GLS coating layer was sandwiched between the disk and the substrate (dimensions not drawn to scale for clarity).

For optical cavities, the Q factor (Q) is used to quantify the power loss relative to the stored internal energy. An equivalent absorption coefficient (α_eq ) is obtained using the following equation [37

R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993). [CrossRef]

α_{e q} = \frac{2 π n_{g}}{Q λ} .

(10)

where n_g is the group velocity of the mode, and λ is the free space wavelength. Volume current formulation was used to estimate the mode scattering losses [38

M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]

]. The Q factors were evaluated based on preliminary experimental roughness parameters (10 nm roughness amplitude and 150 nm correlation length) of the demonstrated high Q (due to thermal reflow) ChG micro-disk [26

]. Future fabrication and characterization studies will fine tune these parameters. The radiation losses were quantified using a perfectly matched layer. The bulk absorption coefficient of GLS (0.035 cm⁻¹ at 800 nm, and 0.006 cm⁻¹ at 4.5 µm [39

Data Sheet, “Gallium lanthanum sulphide optical material—internal transmission,” ChG Southampton Ltd., University of Southampton, Highfield, Southampton, SO17 1BJ, U.K. (2010).

]) was multiplied by the mode confinement factor to arrive at the mode absorption losses. The signal mode gain coefficient and pump mode absorption coefficient can be obtained using:

g_{S}^{M} = \int_{\begin{array}{l} D i s k \\ A r e a \end{array}} g_{S}^{} (I_{S} (x, y), I_{P} (x, y)) \times f_{S}^{} (x, y) . d x d y .

(11)

α_{P, E r}^{M} = \int_{\begin{array}{l} D i s k_{} \\ A r e a \end{array}} α_{P, E r}^{} (I_{S} (x, y), I_{P} (x, y)) \times f_{P}^{} (x, y) . d x d y .

(12)

where (x,y) is a coordinate point on the disk cross section, f_S/P is the signal or pump mode power profile normalized to 1 W. This detailed model was used to simulate the micro-disk laser system under consideration. The simulation results are given in the next section.

3. Simulation results

Including the initial transient evolution of the mode powers and ion populations would require large simulation time. For this reason, we developed a route which utilizes the previously explained model to find a self-consistent steady state solution. Initially, the signal gain was calculated as a function of the signal and pump intensities using Eq. (7) and Eq. (8) (Fig. 4 ). Linear interpolation was used later to find the gain for the intermediate points. The data range was chosen to cover the saturation limits. This range was discretized such that the maximum interpolation error is less than 0.2%. Erbium absorption of the pump light was also calculated in the same way using Eq. (9).

Fig. 4 Steady state signal gain as a function of the pump and signal intensity for erbium doped GLS with concentration of 2.8 × 10²⁰ cm⁻³.

The solutions of the fundamental signal mode and the first eight pump radial modes were calculated, as shown in Fig. 5 . For the different pump modes, there are several competing factors affecting the obtained signal mode gain. First, the signal mode gain can be maximized by using the pump mode for which the maximum signal intensity overlaps the area having the maximum gain, i.e. highest pump intensity. However, as shown, the gain can decrease drastically as the signal intensity increases. In addition, concentrating most of the pump power at the signal intensity peak is of no benefit in the saturation region. Using the residual power to pump larger area of the signal mode would result in higher signal mode gain. Since it is not straightforward to identify the pump mode that results in the highest signal gain, the signal gain values associeated with the considered pump modes should be identified and compared.

Fig. 5 Intensity distribution of the signal (S) and pump (P) modes with the total mode power normalized to 1W. Polarization indicated by the subscripts. The first number is the planar index while the second is the radial index.

The signal mode gain was calculated as a function of the internal pump (P_i ) and signal (S_i ) power using Eq. (11). The mode intensity profiles were discretized into 50 segments per micron which results in negligible error in estimating the intensity at each grid point. The gain was interpolated at each grid point using the data obtained in Fig. 4. A comparison between the obtained signal gain by exciting several pump modes is shown in Fig. 6 . It is clear that pumping the first order mode does not result in the highest possible gain. Higher values can be achieved by pumping higher order modes. However, going beyond the 8th order mode (not shown) minimizes the pump signal overlap (Fig. 5) and hence minimizes the signal mode gain.

Fig. 6 Signal mode gain obtained by exciting several pump modes with different radial orders. The gain is computed as a function of the internal signal (S_i ) and pump (P_i ) modes powers.

The passive cavity Q factors and the equivalent absorption coefficients (Eq. (10)) of the TE11 pump and signal modes are summarized in Table 1 . As listed, the losses for both cases are dominated by scattering. This loss is much greater for the pump mode due to its relatively small wavelength. As explained in [38

M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]

], the scattering losses are directly related to the mode power amplitude within the scattering volume. For the considered pump modes, the difference in this value was found very small (less than 1%). The pump modes also have ignorable absorption and radiation losses similar to TE11. Consequently, these modes have close to equal Q factors. For this reason and because the 7th order mode gives the highest possible gain, it was chosen to pump the disk. Erbium absorption for the pump mode light was quantified using Eq. (12) and found to be small at operational pumping power levels.

Table 1 Q factors and Equivalent Absorption Coefficients for the Fundamental Pump and Signal Modes

Loss type	Q Factor		Equivalent absorption coefficient (dB/cm)
Loss type	Pump	Signal	Pump	Signal
Absorption	4.85 × 10⁶	6.10 × 10⁶	0.1607	0.0217
Radiation	1.79 × 10⁸	3.00 × 10⁷	0.0043	0.0043
Scattering	1.50 × 10⁴	2.20 × 10⁶	52.115	0.0565
Total	1.48 × 10⁴	1.53 × 10⁶	52.289	0.0825

The signal power in the disk was calculated as a function of the internal pump power and the signal coupling coefficient. Due to high internal pump losses, the pump power, and hence the signal gain, would show high variations along the disk circumference. Therefore, the disk was discretized azimuthally into 1µm length segments at the disk circumference. The modes were propagated through these segments, starting from P₁ and S₁ in Fig. 1 and using Eqs. (3)–(5). The bisectional method was used to search for the signal power (S₁ ) that satisfies the steady state lasing conditions given by Eq. (6). The condition was tested for a maximum tolerance of 0.1%. With the calculated Q factors and the maximum achievable signal gain, the error in estimating the calculated power is not significant and therefore can be ignored.

The round trip pump power absorption, caused by erbium and the passive cavity losses, was found to be ~75%. Based on Eq. (1), a pump coupling coefficient of 0.25 would maximize the pump power accumulation in the disk (P₁/P_in ) and minimize the needed input pump power (Fig. 7(a) ). This coupling value was used in Eq. (1) to find the input pump power (P_in ) that corresponds to P₁ . Due to the high scattering losses, the maximum power accumulation is limited to 4. This could be elevated by two orders of magnitude if the scattering losses in the disk were eliminated as shown in Fig. 7(b).

Fig. 7 Pump power accumulation as a function of the power coupling coefficient: (a) the continuous line shows the basic case with the scattering losses included (Pump Q = 1.48 × 10⁴) (b) the dashed line shows the case with no scattering losses taken into account (Pump Q = 4.85 × 10⁶).

Equation (2) was used to find the signal power out-coupled from the disk to the signal bus. As mentioned previously, the laser performance is tightly related to the signal coupling coefficient. Figure 8(a) shows the signal output power of the disk for the cavity with the scattering losses taken into account. The threshold power varies directly with the signal coupling. For coupling coefficient higher than 2 × 10⁻³, lasing is not possible since the signal gain is not sufficient to recover the internal and external disk losses. For low signal coupling, the lasing threshold shows saturation at a minimum of 0.2 mW. However, the slope efficiency decreases drastically by decreasing the coupling to that level.

Fig. 8 Output signal power as a function of the pump power and the signal coupling coefficient. Lasing is only possible with signal coupling smaller than 2 × 10⁻³. The peak output power is obtained at signal coupling of 4 × 10⁻⁴. (a) For the case of including scattering losses, pump Q = 1.48 × 10⁴, signal Q = 1.53 × 10⁶ and pump coupling coefficient = 0.25, a maximum slope efficiency of 1.26 × 10⁻⁴ with threshold of 0.5 mW is obtained. (b) For the case of excluding scattering losses, pump Q = 4.8 × 10⁶, signal Q = 6 × 10⁶ and pump coupling coefficient = 0.0025, a maximum efficiency of 0.025 with 0.02mW threshold can be achieved.

The output power peaks at a signal coupling of 4 × 10⁻⁴. This value of signal coupling gives an optimized performance for the micro-disk device as it maximizes the slope efficiency (1.26 × 10⁻⁴) with a lasing threshold of 0.5 mW. Higher coupling values result in small signal accumulation. On the other hand, decreasing coupling below that level will increase the accumulation but only a small fraction of the internal signal power couples to the output bus.

Simulated efficiency of erbium-doped ChG fiber, can achieve ~15% [24

]. However, fiber lasers require long lengths (tens of centimeters) and do not offer suitable solution for on-chip applications. In contrast, the predicted slope efficiency of the micro-disk is very small but it offers a compact platform for on-chip applications. The low slope efficiency for the micro-disk case is caused by the high pump scattering from the sidewall roughness. This results in a small pump accumulation in addition to a relatively high lasing threshold. Progress is taking place to reduce these losses [26

], for which there is a vast untapped opportunity to enhance lasing characteristics by two orders of magnitude (Fig. 8(b)).

4. Conclusion

We developed a model to simulate MIR lasing for erbium-doped GLS micro-disk. The optimal coupling coefficients for the signal and pump waveguides were identified. Lasing at 4.5 µm signal using 800 nm pump was shown to be possible with the recently reported chalcogenide micro-disk quality factor characteristics [26

]. With 80 µm disk diameter, 0.6 µm thickness and erbium concentration of 2.8 × 10²⁰ cm⁻³, lasing is possible with a maximum slope efficiency of 1.26 × 10⁻⁴ and threshold of 0.5 mW for pump and signal coupling coefficients of 0.25 and 2 × 10⁻³, respectively. The efficiency could be improved to ~0.025 if scattering losses are eliminated.

Appendices

Appendix

Acknowledgments

The authors gratefully acknowledge contributions of Michiel Vanhoutte, from the department of materials science and engineering at Massachusetts Institute of Technology. This study was supported by a grant from Masdar Institute of Science and Technology (Abu Dhabi, UAE), project number 400200.

References and links

1.	B. J. Eggleton, “Chalcogenide photonics: fabrication, devices and applications. Introduction,” Opt. Express 18(25), 26632–26634 (2010). [CrossRef] [PubMed]
2.	A. Seddon, “Chalcogenide glasses: a review of their preparation, properties and applications,” J. Non-Cryst. Solids 184, 44–50 (1995). [CrossRef]
3.	A. Zakery, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]
4.	N. Carlie, J. D. Musgraves, B. Zdyrko, I. Luzinov, J. Hu, V. Singh, A. Agarwal, L. C. Kimerling, A. Canciamilla, F. Morichetti, A. Melloni, and K. Richardson, “Integrated chalcogenide waveguide resonators for mid-IR sensing: leveraging material properties to meet fabrication challenges,” Opt. Express 18(25), 26728–26743 (2010). [CrossRef] [PubMed]
5.	C. Tsay, Y. Zha, and C. B. Arnold, “Solution-processed chalcogenide glass for integrated single-mode mid-infrared waveguides,” Opt. Express 18(25), 26744–26753 (2010). [CrossRef] [PubMed]
6.	K. Richardson, L. Petit, N. Carlie, B. Zdyrko, I. Luzinov, J. Hu, A. Agarwal, L. Kimerling, T. Anderson, and M. Richardson, “Progress on the fabrication of on-chip, integrated chalcogenide glass (ChG)-based sensors,” J. Nonlinear Opt. Phys. Mater. 19(01), 75–99 (2010). [CrossRef]
7.	M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).
8.	A. Kenyon, “Recent Developments in rare-earth doped materials for optoelectronics,” Prog. Quantum Electron. 26(4-5), 225–284 (2002). [CrossRef]
9.	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(25), 26704–26719 (2010). [CrossRef] [PubMed]
10.	J. S. Sanghera, L. Brandon Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009). [CrossRef]
11.	J. Sanghera, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 256–257, 6–16 (1999). [CrossRef]
12.	V. Nazabal, P. Němec, A. M. Jurdyc, S. Zhang, F. Charpentier, H. Lhermite, J. Charrier, J. P. Guin, A. Moreac, and M. Frumar, “Optical waveguide based on amorphous Er³⁺-doped Ga–Ge–Sb–S(Se) pulsed laser deposited thin films,” Thin Solid Films 518(17), 4941–4947 (2010). [CrossRef]
13.	J. Fick, “High photoluminescence in erbium-doped chalcogenide thin films,” J. Non-Cryst. Solids 272(2-3), 200–208 (2000). [CrossRef]
14.	V. Nazabal, A. M. Jurdyc, P. Němec, M. L. Brandily-Anne, L. Petit, K. Richardson, P. Vinatier, C. Bousquet, T. Cardinal, and S. Pechev, “Amorphous Tm³⁺ doped sulfide thin films fabricated by sputtering,” Opt. Mater. 33(2), 220–226 (2010). [CrossRef]
15.	J. Frantz, J. Sanghera, L. Shaw, G. Villalobos, I. Aggarwal, and D. Hewak, “Sputtered films of Er³⁺-doped gallium lanthanum sulfide glass,” Mater. Lett. 60(11), 1350–1353 (2006). [CrossRef]
16.	T. Schweizer, D. W. Hewak, D. N. Payne, T. Jensen, and G. Huber, “Rare-earth doped chalcogenide glass laser,” Electron. Lett. 32(7), 666–667 (1996). [CrossRef]
17.	T. Schweizer, B. N. Samson, R. C. Moore, D. W. Hewak, and D. N. Payne, “Rare-earth doped chalcogenide glass fibre laser,” Electron. Lett. 33(5), 414–416 (1997). [CrossRef]
18.	A. K. Mairaj, C. Riziotis, A. M. Chardon, P. G. R. Smith, D. P. Shepherd, and D. W. Hewak, “Development of channel waveguide lasers in Nd³⁺-doped chalcogenide (Ga:La:S) glass through photoinduced material modification,” Appl. Phys. Lett. 81(20), 3708–3710 (2002). [CrossRef]
19.	A. K. Mairaj, A. M. Chardon, D. P. Shepherd, and D. W. Hewak, “Laser performance and spectroscopic analysis of optically written channel waveguides in neodymium-doped gallium lanthanum sulphide glass,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1381–1388 (2002). [CrossRef]
20.	K. Sasagawa, K. Kusawake, J. Ohta, and M. Nunoshita, “Nd-doped tellurite glass microsphere laser,” Electron. Lett. 38(22), 1355–1357 (2002). [CrossRef]
21.	K. Sasagawa, Z.-o. Yonezawa, R. Iwai, J. Ohta, and M. Nunoshita, “S-band Tm³⁺-doped tellurite glass microsphere laser via a cascade process,” Appl. Phys. Lett. 85(19), 4325–4327 (2004). [CrossRef]
22.	J. Wu, S. Jiang, T. Qua, M. Kuwata-Gonokami, and N. Peyghambarian, “2 μm lasing from highly thulium doped tellurite glass microsphere,” Appl. Phys. Lett. 87(21), 211118 (2005). [CrossRef]
23.	G. R. Elliott, G. S. Murugan, J. S. Wilkinson, M. N. Zervas, and D. W. Hewak, “Chalcogenide glass microsphere laser,” Opt. Express 18(25), 26720–26727 (2010). [CrossRef] [PubMed]
24.	F. Prudenzano, L. Mescia, L. A. Allegretti, M. De Sario, T. Palmisano, F. Smektala, V. Moizan, V. Nazabal, and J. Troles, “Design of Er³⁺-doped chalcogenide glass laser for MID-IR application,” J. Non-Cryst. Solids 355(18-21), 1145–1148 (2009). [CrossRef]
25.	T. Schweizer, D. Brady, and D. W. Hewak, “Fabrication and spectroscopy of erbium doped gallium lanthanum sulphide glass fibres for mid-infrared laser applications,” Opt. Express 1(4), 102–107 (1997). [CrossRef] [PubMed]
26.	J. Hu, N. N. Feng, N. Carlie, L. Petit, A. Agarwal, K. Richardson, and L. C. Kimerling, “Optical loss reduction in high-index-contrast chalcogenide glass waveguides via thermal reflow,” Opt. Express 18(2), 1469–1478 (2010). [CrossRef] [PubMed]
27.	H. Yayama, “Refractive index dispersion of gallium lanthanum sulfide and oxysulfide glasses,” J. Non-Cryst. Solids 239(1-3), 187–191 (1998). [CrossRef]
28.	H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
29.	S. Hooker, Laser Physics (Oxford University Press, 2010). [PubMed]
30.	K. Kadono, “Rate equation analysis and energy transfer of Er³⁺-doped Ga₂S₃–GeS₂–La₂S₃ glasses,” J. Non-Cryst. Solids 331(1-3), 79–90 (2003). [CrossRef]
31.	M. Desario, L. Mescia, F. Prudenzano, F. Smektala, F. Deseveday, V. Nazabal, J. Troles, and L. Brilland, “Feasibility of Er³⁺-doped, Ga₅Ge₂₀Sb₁₀S₆₅ chalcogenide microstructured optical fiber amplifiers,” Opt. Laser Technol. 41(1), 99–106 (2009). [CrossRef]
32.	R. Quimby, “Multiphonon energy gap law in rare-earth doped chalcogenide glass,” J. Non-Cryst. Solids 320(1-3), 100–112 (2003). [CrossRef]
33.	B. M. Walsh, “Judd-Ofelt theory: principles and practices,” in Advances in Spectroscopy for Lasers and Sensing , B. Bartolo and O. Forte, eds. (Kluwer Academic Publishers, 2006), pp. 403–433.
34.	D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134(2A), A299–A306 (1964). [CrossRef]
35.	J. G. Solé, L. E. Bausá, and D. Jaque, An Introduction to the Optical Spectroscopy of Inorganic Solids (John Wiley and Sons, Ltd., 2005).
36.	FIMMMWAVE: Waveguides solver (Photon Design, 34 Leopold Street, Oxford, OX41TW, U.K.).
37.	R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993). [CrossRef]
38.	M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]
39.	Data Sheet, “Gallium lanthanum sulphide optical material—internal transmission,” ChG Southampton Ltd., University of Southampton, Highfield, Southampton, SO17 1BJ, U.K. (2010).
40.	T. Schweizer, “Rare-earth-doped gallium lanthanum sulphide glasses for mid-infrared fibre lasers,” University of Southampton, Faculty of Engineering and Applied Science, Department of Electronics and Computer Science, Doctoral Thesis (2000).
41.	C. Ye, “Spectral properties of Er³⁺-doped gallium lanthanum sulphide glass,” J. Non-Cryst. Solids 208(1-2), 56–63 (1996). [CrossRef]

OCIS Codes
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(140.3500) Lasers and laser optics : Lasers, erbium
(140.3580) Lasers and laser optics : Lasers, solid-state
(140.5680) Lasers and laser optics : Rare earth and transition metal solid-state lasers
(140.3945) Lasers and laser optics : Microcavities

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: March 14, 2011
Revised Manuscript: May 13, 2011
Manuscript Accepted: May 13, 2011
Published: June 6, 2011

Citation
Faleh Al Tal, Clara Dimas, Juejun Hu, Anu Agarwal, and Lionel C. Kimerling, "Simulation of an erbium-doped chalcogenide micro-disk mid-infrared laser source," Opt. Express 19, 11951-11962 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-11951

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References

B. J. Eggleton, “Chalcogenide photonics: fabrication, devices and applications. Introduction,” Opt. Express 18(25), 26632–26634 (2010). [CrossRef] [PubMed]
A. Seddon, “Chalcogenide glasses: a review of their preparation, properties and applications,” J. Non-Cryst. Solids 184, 44–50 (1995). [CrossRef]
A. Zakery, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]
N. Carlie, J. D. Musgraves, B. Zdyrko, I. Luzinov, J. Hu, V. Singh, A. Agarwal, L. C. Kimerling, A. Canciamilla, F. Morichetti, A. Melloni, and K. Richardson, “Integrated chalcogenide waveguide resonators for mid-IR sensing: leveraging material properties to meet fabrication challenges,” Opt. Express 18(25), 26728–26743 (2010). [CrossRef] [PubMed]
C. Tsay, Y. Zha, and C. B. Arnold, “Solution-processed chalcogenide glass for integrated single-mode mid-infrared waveguides,” Opt. Express 18(25), 26744–26753 (2010). [CrossRef] [PubMed]
K. Richardson, L. Petit, N. Carlie, B. Zdyrko, I. Luzinov, J. Hu, A. Agarwal, L. Kimerling, T. Anderson, and M. Richardson, “Progress on the fabrication of on-chip, integrated chalcogenide glass (ChG)-based sensors,” J. Nonlinear Opt. Phys. Mater. 19(01), 75–99 (2010). [CrossRef]
M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).
A. Kenyon, “Recent Developments in rare-earth doped materials for optoelectronics,” Prog. Quantum Electron. 26(4-5), 225–284 (2002). [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(25), 26704–26719 (2010). [CrossRef] [PubMed]
J. S. Sanghera, L. Brandon Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009). [CrossRef]
J. Sanghera, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 256–257, 6–16 (1999). [CrossRef]
V. Nazabal, P. Němec, A. M. Jurdyc, S. Zhang, F. Charpentier, H. Lhermite, J. Charrier, J. P. Guin, A. Moreac, and M. Frumar, “Optical waveguide based on amorphous Er3+-doped Ga–Ge–Sb–S(Se) pulsed laser deposited thin films,” Thin Solid Films 518(17), 4941–4947 (2010). [CrossRef]
J. Fick, “High photoluminescence in erbium-doped chalcogenide thin films,” J. Non-Cryst. Solids 272(2-3), 200–208 (2000). [CrossRef]
V. Nazabal, A. M. Jurdyc, P. Němec, M. L. Brandily-Anne, L. Petit, K. Richardson, P. Vinatier, C. Bousquet, T. Cardinal, and S. Pechev, “Amorphous Tm3+ doped sulfide thin films fabricated by sputtering,” Opt. Mater. 33(2), 220–226 (2010). [CrossRef]
J. Frantz, J. Sanghera, L. Shaw, G. Villalobos, I. Aggarwal, and D. Hewak, “Sputtered films of Er3+-doped gallium lanthanum sulfide glass,” Mater. Lett. 60(11), 1350–1353 (2006). [CrossRef]
T. Schweizer, D. W. Hewak, D. N. Payne, T. Jensen, and G. Huber, “Rare-earth doped chalcogenide glass laser,” Electron. Lett. 32(7), 666–667 (1996). [CrossRef]
T. Schweizer, B. N. Samson, R. C. Moore, D. W. Hewak, and D. N. Payne, “Rare-earth doped chalcogenide glass fibre laser,” Electron. Lett. 33(5), 414–416 (1997). [CrossRef]
A. K. Mairaj, C. Riziotis, A. M. Chardon, P. G. R. Smith, D. P. Shepherd, and D. W. Hewak, “Development of channel waveguide lasers in Nd3+-doped chalcogenide (Ga:La:S) glass through photoinduced material modification,” Appl. Phys. Lett. 81(20), 3708–3710 (2002). [CrossRef]
A. K. Mairaj, A. M. Chardon, D. P. Shepherd, and D. W. Hewak, “Laser performance and spectroscopic analysis of optically written channel waveguides in neodymium-doped gallium lanthanum sulphide glass,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1381–1388 (2002). [CrossRef]
K. Sasagawa, K. Kusawake, J. Ohta, and M. Nunoshita, “Nd-doped tellurite glass microsphere laser,” Electron. Lett. 38(22), 1355–1357 (2002). [CrossRef]
K. Sasagawa, Z.-o. Yonezawa, R. Iwai, J. Ohta, and M. Nunoshita, “S-band Tm3+-doped tellurite glass microsphere laser via a cascade process,” Appl. Phys. Lett. 85(19), 4325–4327 (2004). [CrossRef]
J. Wu, S. Jiang, T. Qua, M. Kuwata-Gonokami, and N. Peyghambarian, “2 μm lasing from highly thulium doped tellurite glass microsphere,” Appl. Phys. Lett. 87(21), 211118 (2005). [CrossRef]
G. R. Elliott, G. S. Murugan, J. S. Wilkinson, M. N. Zervas, and D. W. Hewak, “Chalcogenide glass microsphere laser,” Opt. Express 18(25), 26720–26727 (2010). [CrossRef] [PubMed]
F. Prudenzano, L. Mescia, L. A. Allegretti, M. De Sario, T. Palmisano, F. Smektala, V. Moizan, V. Nazabal, and J. Troles, “Design of Er3+-doped chalcogenide glass laser for MID-IR application,” J. Non-Cryst. Solids 355(18-21), 1145–1148 (2009). [CrossRef]
T. Schweizer, D. Brady, and D. W. Hewak, “Fabrication and spectroscopy of erbium doped gallium lanthanum sulphide glass fibres for mid-infrared laser applications,” Opt. Express 1(4), 102–107 (1997). [CrossRef] [PubMed]
J. Hu, N. N. Feng, N. Carlie, L. Petit, A. Agarwal, K. Richardson, and L. C. Kimerling, “Optical loss reduction in high-index-contrast chalcogenide glass waveguides via thermal reflow,” Opt. Express 18(2), 1469–1478 (2010). [CrossRef] [PubMed]
H. Yayama, “Refractive index dispersion of gallium lanthanum sulfide and oxysulfide glasses,” J. Non-Cryst. Solids 239(1-3), 187–191 (1998). [CrossRef]
H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
S. Hooker, Laser Physics (Oxford University Press, 2010). [PubMed]
K. Kadono, “Rate equation analysis and energy transfer of Er3+-doped Ga2S3–GeS2–La2S3 glasses,” J. Non-Cryst. Solids 331(1-3), 79–90 (2003). [CrossRef]
M. Desario, L. Mescia, F. Prudenzano, F. Smektala, F. Deseveday, V. Nazabal, J. Troles, and L. Brilland, “Feasibility of Er3+-doped, Ga5Ge20Sb10S65 chalcogenide microstructured optical fiber amplifiers,” Opt. Laser Technol. 41(1), 99–106 (2009). [CrossRef]
R. Quimby, “Multiphonon energy gap law in rare-earth doped chalcogenide glass,” J. Non-Cryst. Solids 320(1-3), 100–112 (2003). [CrossRef]
B. M. Walsh, “Judd-Ofelt theory: principles and practices,” in Advances in Spectroscopy for Lasers and Sensing, B. Bartolo and O. Forte, eds. (Kluwer Academic Publishers, 2006), pp. 403–433.
D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134(2A), A299–A306 (1964). [CrossRef]
J. G. Solé, L. E. Bausá, and D. Jaque, An Introduction to the Optical Spectroscopy of Inorganic Solids (John Wiley and Sons, Ltd., 2005).
FIMMMWAVE: Waveguides solver (Photon Design, 34 Leopold Street, Oxford, OX41TW, U.K.).
R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993). [CrossRef]
M. Borselli, T. J. Johnson, and O. Painter, “Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment,” Opt. Express 13(5), 1515–1530 (2005). [CrossRef] [PubMed]
Data Sheet, “Gallium lanthanum sulphide optical material—internal transmission,” ChG Southampton Ltd., University of Southampton, Highfield, Southampton, SO17 1BJ, U.K. (2010).
T. Schweizer, “Rare-earth-doped gallium lanthanum sulphide glasses for mid-infrared fibre lasers,” University of Southampton, Faculty of Engineering and Applied Science, Department of Electronics and Computer Science, Doctoral Thesis (2000).
C. Ye, “Spectral properties of Er3+-doped gallium lanthanum sulphide glass,” J. Non-Cryst. Solids 208(1-2), 56–63 (1996). [CrossRef]

Appl. Phys. Lett.

A. K. Mairaj, C. Riziotis, A. M. Chardon, P. G. R. Smith, D. P. Shepherd, and D. W. Hewak, “Development of channel waveguide lasers in Nd3+-doped chalcogenide (Ga:La:S) glass through photoinduced material modification,” Appl. Phys. Lett. 81(20), 3708–3710 (2002). [CrossRef]
K. Sasagawa, Z.-o. Yonezawa, R. Iwai, J. Ohta, and M. Nunoshita, “S-band Tm3+-doped tellurite glass microsphere laser via a cascade process,” Appl. Phys. Lett. 85(19), 4325–4327 (2004). [CrossRef]
J. Wu, S. Jiang, T. Qua, M. Kuwata-Gonokami, and N. Peyghambarian, “2 μm lasing from highly thulium doped tellurite glass microsphere,” Appl. Phys. Lett. 87(21), 211118 (2005). [CrossRef]
R. E. Slusher, A. F. J. Levi, U. Mohideen, S. L. McCall, S. J. Pearton, and R. A. Logan, “Threshold characteristics of semiconductor microdisk lasers,” Appl. Phys. Lett. 63(10), 1310–1312 (1993). [CrossRef]

Electron. Lett.

T. Schweizer, D. W. Hewak, D. N. Payne, T. Jensen, and G. Huber, “Rare-earth doped chalcogenide glass laser,” Electron. Lett. 32(7), 666–667 (1996). [CrossRef]
T. Schweizer, B. N. Samson, R. C. Moore, D. W. Hewak, and D. N. Payne, “Rare-earth doped chalcogenide glass fibre laser,” Electron. Lett. 33(5), 414–416 (1997). [CrossRef]
K. Sasagawa, K. Kusawake, J. Ohta, and M. Nunoshita, “Nd-doped tellurite glass microsphere laser,” Electron. Lett. 38(22), 1355–1357 (2002). [CrossRef]

IEEE J. Sel. Top. Quantum Electron.

J. S. Sanghera, L. Brandon Shaw, and I. D. Aggarwal, “Chalcogenide glass-fiber-based mid-IR sources and applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009). [CrossRef]
A. K. Mairaj, A. M. Chardon, D. P. Shepherd, and D. W. Hewak, “Laser performance and spectroscopic analysis of optically written channel waveguides in neodymium-doped gallium lanthanum sulphide glass,” IEEE J. Sel. Top. Quantum Electron. 8(6), 1381–1388 (2002). [CrossRef]

J. Non-Cryst. Solids

F. Prudenzano, L. Mescia, L. A. Allegretti, M. De Sario, T. Palmisano, F. Smektala, V. Moizan, V. Nazabal, and J. Troles, “Design of Er3+-doped chalcogenide glass laser for MID-IR application,” J. Non-Cryst. Solids 355(18-21), 1145–1148 (2009). [CrossRef]
H. Yayama, “Refractive index dispersion of gallium lanthanum sulfide and oxysulfide glasses,” J. Non-Cryst. Solids 239(1-3), 187–191 (1998). [CrossRef]
K. Kadono, “Rate equation analysis and energy transfer of Er3+-doped Ga2S3–GeS2–La2S3 glasses,” J. Non-Cryst. Solids 331(1-3), 79–90 (2003). [CrossRef]
R. Quimby, “Multiphonon energy gap law in rare-earth doped chalcogenide glass,” J. Non-Cryst. Solids 320(1-3), 100–112 (2003). [CrossRef]
J. Sanghera, “Active and passive chalcogenide glass optical fibers for IR applications: a review,” J. Non-Cryst. Solids 256–257, 6–16 (1999). [CrossRef]
J. Fick, “High photoluminescence in erbium-doped chalcogenide thin films,” J. Non-Cryst. Solids 272(2-3), 200–208 (2000). [CrossRef]
A. Seddon, “Chalcogenide glasses: a review of their preparation, properties and applications,” J. Non-Cryst. Solids 184, 44–50 (1995). [CrossRef]
A. Zakery, “Optical properties and applications of chalcogenide glasses: a review,” J. Non-Cryst. Solids 330(1-3), 1–12 (2003). [CrossRef]
C. Ye, “Spectral properties of Er3+-doped gallium lanthanum sulphide glass,” J. Non-Cryst. Solids 208(1-2), 56–63 (1996). [CrossRef]

J. Nonlinear Opt. Phys. Mater.

K. Richardson, L. Petit, N. Carlie, B. Zdyrko, I. Luzinov, J. Hu, A. Agarwal, L. Kimerling, T. Anderson, and M. Richardson, “Progress on the fabrication of on-chip, integrated chalcogenide glass (ChG)-based sensors,” J. Nonlinear Opt. Phys. Mater. 19(01), 75–99 (2010). [CrossRef]

Mater. Lett.

J. Frantz, J. Sanghera, L. Shaw, G. Villalobos, I. Aggarwal, and D. Hewak, “Sputtered films of Er3+-doped gallium lanthanum sulfide glass,” Mater. Lett. 60(11), 1350–1353 (2006). [CrossRef]

Opt. Express

Opt. Laser Technol.

M. Desario, L. Mescia, F. Prudenzano, F. Smektala, F. Deseveday, V. Nazabal, J. Troles, and L. Brilland, “Feasibility of Er3+-doped, Ga5Ge20Sb10S65 chalcogenide microstructured optical fiber amplifiers,” Opt. Laser Technol. 41(1), 99–106 (2009). [CrossRef]

Opt. Mater.

V. Nazabal, A. M. Jurdyc, P. Němec, M. L. Brandily-Anne, L. Petit, K. Richardson, P. Vinatier, C. Bousquet, T. Cardinal, and S. Pechev, “Amorphous Tm3+ doped sulfide thin films fabricated by sputtering,” Opt. Mater. 33(2), 220–226 (2010). [CrossRef]

Phys. Rev.

D. McCumber, “Theory of phonon-terminated optical masers,” Phys. Rev. 134(2A), A299–A306 (1964). [CrossRef]

Prog. Quantum Electron.

A. Kenyon, “Recent Developments in rare-earth doped materials for optoelectronics,” Prog. Quantum Electron. 26(4-5), 225–284 (2002). [CrossRef]

Thin Solid Films

V. Nazabal, P. Němec, A. M. Jurdyc, S. Zhang, F. Charpentier, H. Lhermite, J. Charrier, J. P. Guin, A. Moreac, and M. Frumar, “Optical waveguide based on amorphous Er3+-doped Ga–Ge–Sb–S(Se) pulsed laser deposited thin films,” Thin Solid Films 518(17), 4941–4947 (2010). [CrossRef]

Other

M. Ebrahim-Zadeh and I. Sorokina, Mid-Infrared Coherent Sources and Applications (Springer, 2007).
B. M. Walsh, “Judd-Ofelt theory: principles and practices,” in Advances in Spectroscopy for Lasers and Sensing, B. Bartolo and O. Forte, eds. (Kluwer Academic Publishers, 2006), pp. 403–433.
Data Sheet, “Gallium lanthanum sulphide optical material—internal transmission,” ChG Southampton Ltd., University of Southampton, Highfield, Southampton, SO17 1BJ, U.K. (2010).
T. Schweizer, “Rare-earth-doped gallium lanthanum sulphide glasses for mid-infrared fibre lasers,” University of Southampton, Faculty of Engineering and Applied Science, Department of Electronics and Computer Science, Doctoral Thesis (2000).
H. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
S. Hooker, Laser Physics (Oxford University Press, 2010). [PubMed]
J. G. Solé, L. E. Bausá, and D. Jaque, An Introduction to the Optical Spectroscopy of Inorganic Solids (John Wiley and Sons, Ltd., 2005).
FIMMMWAVE: Waveguides solver (Photon Design, 34 Leopold Street, Oxford, OX41TW, U.K.).

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