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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 13 — Jun. 20, 2011
  • pp: 11951–11962
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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

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.

© 2011 OSA

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

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

3

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

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

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

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

,8

8. 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

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

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

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

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

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

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

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

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 4I9/2 and 4I11/2 energy levels [25

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

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]

]. 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

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
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.
. 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

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.

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

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

]:

gS=σSeN4σSaN3
(8)
αP,Er=σPaN1σPeN4
(9)

The cavity modes were calculated for the disk cross section in Fig. 3
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).
. 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

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.

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
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.
). 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).

The solutions of the fundamental signal mode and the first eight pump radial modes were calculated, as shown in Fig. 5
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.
. 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.

The signal mode gain was calculated as a function of the internal pump (Pi) and signal (Si) 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
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 (Si) and pump (Pi) modes powers.
. 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.

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/Pin) and minimize the needed input pump power (Fig. 7(a)
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).
). This coupling value was used in Eq. (1) to find the input pump power (Pin) 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).

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

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, 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

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]

], 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

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]

]. 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.

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.

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

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

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

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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]

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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]

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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]

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J. Fick, “High photoluminescence in erbium-doped chalcogenide thin films,” J. Non-Cryst. Solids 272(2-3), 200–208 (2000). [CrossRef]

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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]

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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]

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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]

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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]

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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

  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]
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