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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 24 — Nov. 24, 2008
  • pp: 19649–19666
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Growth, processing, and optical properties of epitaxial Er2O3 on silicon

C. P. Michael, H. B. Yuen, V. A. Sabnis, T. J. Johnson, R. Sewell, R. Smith, A. Jamora, A. Clark, S. Semans, P. B. Atanackovic, and O. Painter  »View Author Affiliations


Optics Express, Vol. 16, Issue 24, pp. 19649-19666 (2008)
http://dx.doi.org/10.1364/OE.16.019649


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Abstract

Erbium-doped materials have been investigated for generating and amplifying light in low-power chip-scale optical networks on silicon, but several effects limit their performance in dense microphotonic applications. Stoichiometric ionic crystals are a potential alternative that achieve an Er3+ density 100×greater. We report the growth, processing, material characterization, and optical properties of single-crystal Er 2O3 epitaxially grown on silicon. A peak Er3+ resonant absorption of 364 dB/cm at 1535nm with minimal background loss places a high limit on potential gain. Using high-quality microdisk resonators, we conduct thorough C/L-band radiative efficiency and lifetime measurements and observe strong upconverted luminescence near 550 and 670 nm.

© 2008 Optical Society of America

Significant progress in the last decade has been made developing passive and active silicon optical components; however, efficient generation of light within a Si platform remains a technical and commercial challenge [1

1. L. Pavesi and D. J. Lockwood, eds., Silicon Photonics (Springer-Verlag, Berlin, 2004).

]. Efforts to incorporate Er 3+ into the Si material system, with erbium’s emission in the 1550-nm telecommunications band, have met with limited success.

Amorphous Er3+-doped glass waveguides on Si provide insufficient gain (<4 dB/cm [2

2. J. V. Gates, A. J. Bruce, J. Shmulovich, Y. H. Wong, G. Nykolak, M. R. X. Barros, and R. N. Ghosh, “Fabrication of Er doped glass films as used in planar optical waveguides,” Mater. Res. Soc. Symp. Proc. 392, 209–216 (1995). [CrossRef]

, 3

3. Y. C. Yan, A. J. Faber, H. de Waal, P. G. Kik, and A. Polman, “Erbium-doped phosphate glass waveguide on silicon with 4.1 dB/cm gain at 1.535 µm,” Appl. Phys. Lett. 71, 2922–2924 (1997). [CrossRef]

]) for dense photonic integration, while doped silicon allotropes are limited by other effects such as Auger recombination [4

4. P. G. Kik, M. J. A. de Dood, K. Kikoin, and A. Polman, “Excitation and deexcitation of Er3+ in crystalline silicon,” Appl. Phys. Lett. 70, 1721–1723 (1997). [CrossRef]

] and free-carrier absorption [5

5. R. D. Kekatpure, A. R. Guichard, and M. L. Brongersma, “Free-carrier absorption in Si nanocrystals probed by microcavity photoluminescence,” in Conference on Lasers and Electro-Optics (CLEO), p. CTuJ3 (Optical Society of America, San Jose, CA, 2008).

]. Here we describe the characterization of stoichiometric single-crystal Er2O3-on-Si (EOS) grown by atomic layer epitaxy. We measure a peak resonant absorption of 364 dB/cm at 1535nm and negligible background absorption (<3 dB/cm). The observed radiative efficiency from 1520–1650nm is 0.09% with cooperative upconversion producing strong green and red emission for Er 3+ excitation levels as low as 2%. Further development of EOS as multi-component rare-earth oxides, and their superlattices with Si, may allow for tailored emission spectra, controlled upconversion, and electrically injected light emission.

Spurred by the growing power consumption of high-speed electrical interconnects for multicore processors [6

6. J. D. Meindl, J. A. Davis, P. Zarkesh-Ha, C. S. Patel, K. P. Martin, and P. A. Kohl, “Interconnect opportunities for gigascale integration,” IBM J. Res. & Dev. 46, 245–263 (2002). [CrossRef]

], optical networks have become an attractive option to achieve Tb/s on-chip bandwidth [7

7. M. J. Kobrinsky, B. A. Block, J.-F. Zheng, B. C. Barnett, E. Mohammed, M. Reshotko, F. Roberton, S. List, I. Young, and K. Cadien, “On-chip optical interconnects,” Intel Tech. Jour. 8, 129–141 (2004).

]. Following the initial demonstration of silicon waveguide devices [8

8. R. Soref and J. Larenzo, “All-silicon active and passive guided-wave components for λ=1.3 and 1.6 µm,” IEEE J. Quantum Electron. 22, 873–879 (1986). [CrossRef]

], there has been significant development in adding optical functionality to silicon microelectronics and, similarly, applying the efficiency and infrastructure of modern CMOS processing to optical telecommunication components. While silicon exhibits low loss across the 1300-nm and 1550- nm telecommunication windows, unstrained silicon lacks any significant Pockels coefficient and produces little emission from its 1.1 eV indirect bandgap [1

1. L. Pavesi and D. J. Lockwood, eds., Silicon Photonics (Springer-Verlag, Berlin, 2004).

]. Free-carrier dispersion and four-wave mixing provide some inherent active functionality such as modulation with rates exceeding 1GHz [9

9. A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu, and M. Paniccia, “A high-speed silicon optical modulator based on a metal-oxide-semiconductor capacitor,” Nature 427, 615–618 (2004). [CrossRef] [PubMed]

] and wavelength conversion [10

10. M. A. Foster, A. C. Turner, J. E. Sharping, B. S. Schmidt, M. Lipson, and A. L. Gaeta, “Broad-band optical parametric gain on a silicon photonic chip,” Nature (London) 441, 960–963 (2006). [CrossRef]

], but considerable research, especially concerning light emission and detection, has focused on integrating silicon with other optical materials such as SiGe [11

11. L. Colace, G. Masini, F. Galluzzi, G. Assanto, G. Capellini, L. D. Gaspare, E. Palange, and F. Evangelisti, “Metal-semiconductor-metal near-infrared light detector based on epitaxial Ge/Si,” Appl. Phys. Lett. 72, 3175–3177 (1998). [CrossRef]

, 12

12. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. B. Miller, and J. S. Harris, “Strong quantum-confined Stark effect in germanium quantum-well structures on silicon,” Nature (London) 437, 1334–1336 (2005). [CrossRef]

] and the III–Vs [13

13. A. W. Fang, H. Park, O. Cohen, R. Jones, M. J. Paniccia, and J. E. Bowers, “Electrically pumped hybrid AlGaInAs-silicon evanescent laser,” Opt. Express 14, 9203–9210 (2006). [CrossRef] [PubMed]

, 14

14. H. Park, A. W. Fang, R. Jones, O. Cohen, O. Raday, M. N. Sysak, M. J. Paniccia, and J. E. Bowers, “A hybrid AlGaInAs-silicon evanescent waveguide photodetector,” Opt. Express 15, 6044–6052 (2007). [CrossRef] [PubMed]

]. In this work we describe the growth, processing, and optical properties of single-crystal Er2O3-on-Si (EOS). Similar to stoichiometric polycrystalline Er3+ materials [15

15. A. Kasuya and M. Suezawa, “Resonant excitation of visible photoluminescence form an erbium-oxide overlayer on Si,” Appl. Phys. Lett. 71, 2728–2730 (1997). [CrossRef]

20

20. K. Suh, J. H. Shin, S.-J. Seo, and B.-S. Bae, “Large-scale fabrication of single-phase Er2SiO5 nanocrystal aggregates using Si nanowires,” Appl. Phys. Lett. 89, 223102 (2006). [CrossRef]

], EOS allows for a 100-fold increase in Er 3+ concentration over conventional Er-doped glasses [21

21. E. Desurvire, Erbium-doped Fiber Amplifiers: Principles and Applications (John Wiley & Sons, Inc., New York, 2002).

], making it an attractive material for on-chip emission and amplification in the 1550-nm wavelength band. Developed simultaneously for optoelectronic [22

22. P. B. Atanackovic, “Rare earth-oxides, rare earth-nitrides, rare earth-phosphides, and ternary alloys with silicon,” U.S. Patent 7199015 (Dec. 28, 2004).

] and high-κ dielectric [23

23. R. Xu, Y. Y. Zhu, S. Chen, F. Xue, Y. L. Fan, X. J. Yang, and Z. M. Jiang, “Epitaxial growth of Er2O3 films on Si(001),” J. Cryst. Growth 277, 496–501 (2005). [CrossRef]

] applications, epitaxially grown Er 2O3 films can be incorporated into precisely controlled heterostructures and superlattices, which may also allow for efficient electrical injection. Oxides incorporating multiple cation species provide additional flexibility in designing the emission spectrum and dynamics as a number of rare-earth ions (Er3+, Yb3+, Nd3+, Dy3+, etc.) are interchangeable in the (RE)2O3 lattice [24

24. J. B. Gruber, J. R. Henderson, M. Muramoto, K. Rajnak, and J. G. Conway, “Energy levels of single-crystal erbium oxide,” J. Chem. Phys. 45, 477–482 (1966). [CrossRef]

26

26. R. P. Leavitt, J. B. Gruber, N. C. Chang, and C. A. Morrison, “Optical spectra, energy levels, and crystal-field analysis of tripositive rare-earth ions in Y2O3. II. Non-Kramers ions in C2 sites,” J. Chem. Phys. 76, 4775–4788 (1982). [CrossRef]

]. Beyond application to chip-based optical networks, the strong cooperative upconversion within these films may also be used for visible light generation in solid-state lighting and displays and infrared-to-visible energy conversion in photovolatics.

1. Growth

As shown in Fig. 1(a), single-crystal stoichiometric Er2O3 can be grown via atomic layer epitaxy on Si(111) or Si(100) on-axis wafers without a buffer layer. Like most trivalent lanthanide oxides [27

27. H. J. Osten, E. Bugiel, M. Czernohorsky, Z. Elassar, O. Kirfel, and A. Fissel, “Molecular Beam Epitaxy of Rare-Earth Oxides,” in Rare Earth Oxide Thin Films, M. Fanciulli and G. Scarel, eds. (Springer-Verlag, Berlin, 2007).

], the film has a bixbyite crystal structure oriented along Er 2O3(111) [Er2O3(110)] on Si(111) [Si(100)] [28

28. The Er2O3(111) orientation is rotated 180° about the Si(111) surface normal.

]. To minimize both erbium silicide formation and native SiO x growth, the O2:Er ratio during deposition is 1:5. High growth temperatures between 650–900 °C result in more homogeneous films [measured by transmission electron microscopy (TEM) and x-ray diffraction (XRD)], smoother surfaces [~1 nm roughness by atomic force microscopy (AFM), TEM, and reflection high-energy electron diffraction (RHEED)], and stronger C-band [29

29. The short wavelengths (S), conventional (C), and long wavelengths (L) telecommunications windows (bands) are relative to the region of lowest optical loss in silica fiber (λ ≈ 1550 nm) and occur at 1460–1530 nm, 1530–1565 nm, and 1565–1625 nm, respectively. These designations are not strictly applied in this report as that the absorption extends into the E-band (extended, 1360–1460 nm) and the emission in Fig. 8 continues through the U-band (ultralong wavelengths, 1625–1675 nm).

] photoluminescence with a narrower linewidth at 1536nm [Fig. 2(a)]. Films on Si(111) are consistently higher quality and have been grown up to 200nm thick. We observe no evidence of erbium clustering using TEM or visible upconversion [30

30. H. Isshiki, T. Ushiyama, and T. Kimura, “Demonstration of ErSiO superlattice crystal waveguide toward optical amplifiers and emitters,” Phys. Stat. Sol. A 205, 52–55 (2008). [CrossRef]

]. In post-growth XRD analysis, the dominant peaks in Fig. 1(b) are due to the substrate’s Si{111} and film’s Er 2O3{111} planes. Lesser peaks are associated with additional lines from the X-ray source (Kβ, W) and with dif- fraction from minority Er2O3 phases; there is no XRD evidence of erbium silicates or silicides at the Er2O3-Si interface [23

23. R. Xu, Y. Y. Zhu, S. Chen, F. Xue, Y. L. Fan, X. J. Yang, and Z. M. Jiang, “Epitaxial growth of Er2O3 films on Si(001),” J. Cryst. Growth 277, 496–501 (2005). [CrossRef]

,31

31. H. Ono and T. Katsumata, “Interfacial reactions between thin rare-earth-metal oxide films and Si substrates,” Appl. Phys. Lett. 78(13), 1832–1834 (2001). [CrossRef]

]. The {211}, {442}, and {822} families of peaks correspond to slightly strained volumes with surfaces nearly parallel to the dominant (111) surface. Given the EOS films’ homogeneousTEM cross sections and the relative intensities of the secondary XRD peaks, the minority phases compose a small fraction of the material. In addition to growth of Er2O3 on Si substrates, we have also demonstrated growth on the top Si device layer of (100)- oriented silicon-on-insulator substrates, as shown in Fig. 1(d).

Fig. 1. Er2O3 Growth and Processing. (a) TEM image of Er2O3-Si interface. (b) XRD spectrum for Er2O3 on Si(111) and a reference Si(111) sample; the (★) peaks designate strained layers (see §A.1). (c) SEM image of Er2O3 microdisk edge prior to the SF6 undercut. (d) Hybrid Er2O3-Si microdisk (78 nm Er2O3, 188 nm Si, 1 µm SiOx) after the final HF undercut of the buried oxide.

2. Processing

To fabricate Er2O3 microdisk resonators, a 400-nm low-stress SiNx hard mask is grown on the Er2O3-Si wafer by plasma enhanced chemical vapor deposition. The microdisk patterns are defined using electron-beam lithography and resist reflow [33

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

] and then are transferred to the SiNx using a C4F8:SF6 RIE. We then mill the Er2O3 with an Ar+ plasma. The Ar+ mill exhibits approximately 1:1 selectivity with the SiNx hard mask; the resulting side walls [Fig. 1(c)] feature mild striations due to magnification of residual roughness in the EOS. Finally, an isotropic SF6 dry etch simultaneously partially undercuts the silicon substrate and removes the remaining SiNx mask. Processing hybrid Er2O3-Si resonators from Er2O3-SOI wafers, as in Fig. 1(d), employs the same SiNx hard mask and Ar+ mill. With the Er2O3 layer acting as a mask, we etch the silicon device layer with an anisotropic C4F8:SF6 RIE and undercut the buried oxide with concentrated HF. Many samples are prepared to optimize the process parameters at each step in order to minimize the microdisk side wall roughness. The measurements described here concern ~150-nm thick Er2O3 on Si(111) and Er2O3 microdisks with a radius of ~20µm.

3. Optical properties

Once the SiNx is removed and the disks are undercut, the emission and absorption properties of Er2O3 are investigated using dimpled fiber taper waveguides [34

34. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15(8), 4745–4752 (2007). [CrossRef] [PubMed]

]. Mounted to a three-axis 50- nm encoded stage, placing the taper in the near field of the disk produces controllable and stable cavity-waveguide coupling. A bank of tunable diode lasers (spanning 963–993nm and 1420–1625 nm, linewidth <300 kHz) were used to characterize the disks’ WGMs and excite the Er 3+ optical transitions. The fiber taper also offers high photoluminescence collection efficiency [35

35. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

]. Once fiber coupled, the pump and emission can be easily demuxed for sensitive pump-probe and pulsed measurements. Extensive details are available in §A.2–A.3.

3.1. 4I13/2→4I15/2 absorption and emission spectra

Since the crystal fields are needed to mix states of opposite parity for electric-dipole transitions, ions on the low-symmetry lattice sites (C 2, 24 of 32 sites/unit cell) are optically active while the remaining high-symmetry sites (C3i) experience weaker magnetic-dipole transitions [24

24. J. B. Gruber, J. R. Henderson, M. Muramoto, K. Rajnak, and J. G. Conway, “Energy levels of single-crystal erbium oxide,” J. Chem. Phys. 45, 477–482 (1966). [CrossRef]

]. To observe the Stark-split structure for the 4I 13/2→4I 15/2 transitions in this crystalline host, we measure both the room temperature photoluminescence (PL) and absorption spectra. We obtain the emission spectrum by placing the fiber taper in contact with an undercut part of the film and pumping at λ=981.4 nm. The fiber-collected luminescence [Fig. 2(a)] displays little inhomogeneous broadening of the Er3+ transitions compared to amorphous hosts, and is qualitatively similar to the spectrum reported for polycrystalline Er 2O3 deposited by pulsed-laser ablation [19

19. A. M. Grishin, E. V. Vanin, O. V. Tarasenko, S. I. Khartsev, and P. Johansson, “Strong broad C-band roomtemperature photoluminescence in amorphous Er2O3 film,” Appl. Phys. Lett. 89, 021114 (2006). [CrossRef]

]. In comparison to large crystals of Er 2O3 and dilute Er-doped Y2O3 produced by flame fusion [24

24. J. B. Gruber, J. R. Henderson, M. Muramoto, K. Rajnak, and J. G. Conway, “Energy levels of single-crystal erbium oxide,” J. Chem. Phys. 45, 477–482 (1966). [CrossRef]

, 36

36. J. B. Gruber, K. L. Nash, D. K. Sardar, U. V. Valiev, N. Ter-Gabrielyan, and L. D. Merkle, “Modeling optical transitions of Er3+(4f11) in C2 and C3i sites in polycrystalline Y2O3,” J. Appl. Phys. 104(2), 023101 (2008). [CrossRef]

], the low temperature PL spectrum of EOS exhibits more broadening, also shown in Fig. 2(a).

Fig. 2. Emission and absorption spectra. (a) Thin-film PL spectrum at 300 K and 8K while pumping at 981 nm. The dominant peaks at 8K are presented off the scale to make smaller features more visible. Emission is observed for ions on both C2 and C3i sites; the peaks at 1535.8 nm and 1548.6 nm correspond to the transition between the lowest Stark levels of the 4I 13/2 and 4I 15/2 manifolds on the C2 and C3i sites, respectively [24, 36, 37]. (b) Composite absorption spectrum. Different color ×’s correspond to the intrinsic linewidths for modes of different microdisks; the ★’s correspond to absorption peaks inferred from non-Lorentzian cavity resonances (see §A.3).

3.2. Upconversion behavior

While the 1450–1650nm band is most useful for hybrid Er 3+-silicon optical networks, upconversion into visible transitions is also present and has been partly investigated for polycrystalline EOS [15

15. A. Kasuya and M. Suezawa, “Resonant excitation of visible photoluminescence form an erbium-oxide overlayer on Si,” Appl. Phys. Lett. 71, 2728–2730 (1997). [CrossRef]

, 18

18. S. Saini, K. Chen, X. Duan, J. Michel, L. C. Kimerling, and M. Lipson, “Er2O3 for high-gain waveguide amplifiers,” J. Electron. Mater. 33, 809–814 (2004). [CrossRef]

]. We determine the upconversion spectrum by transferring a small piece (~2µm2×150 nm) of Er2O3 onto the fiber taper and pumping with <3mW at 1536.7 nm. The taper-collected PL is then measured in a spectrometer with a silicon CCD camera. The visible PL contains emission from many levels with significant emission near 550nm and 670nm and exhibits little inhomogeneous broadening, as in Fig. 2(a). The pump-power dependence [Fig. 3(c)] of the three primary upconversion bands provides insight into the specific upconversion mechanism [Fig. 3(d)]. The nearly quadratic dependence of the 800nm emission suggests pair-wise upconversion out of the 4I 13/2 multiplet followed by excited-state absorption or a second upconversion event (4I 9/2+4I 13/2→2H11/2) to produce the nearly cubic dependence at 550nm and 670 nm. Subsequent absorption or energy transfer then connects 2H11/2/4S3/2 to even higher levels with energies in the near UV.

3.3. Effective 4I13/2 lifetime

Depopulation of 4I 13/2 by cooperative upconversion adds an additional complication to measuring the 4I 13/2→4I 15/2 lifetime. To mitigate the upconversion effects, fluorescence decay measurements are performed by uniformly exciting a fundamental WGM at 1473.4nm with 10-ns square pulses and a peak absorbed power of 21.7µW. Because of the weak PL signal, we apply a pulse-delay technique and a single photon counter to sample the C/L-band fluorescence decay curve [Fig. 4]. To reduce dark counts, InGaAs/InP avalanche photodiodes (APDs) are only gated above the breakdown voltage for a short time (~50 ns), which is not suitable for decay curves with 10-6-10-2 s life-times. To circumvent the APD’s narrow gate width, we use the 50-ns window to discretely sample the decay curve. Centering the arrival of a pump pulse in the detection window simultaneously acquires the PL’s rise and initial decay due to the Nth pulse along with the decay associated with the (N-1)th pulse. The appearance of the Nth pulse serves as a marker for sampling the (N-1)th decay curve at a fixed delay-i.e. the pulse period separates the (N-1)th peak from its tail just before the Nth pulse. Several histograms (128 ps/bin resolution) with varying delays are used to construct the fluorescence decay in Fig. 4. As the pulse period approaches the PL lifetime, the data deviates from a single exponential curve because decay from multiple pulses contributes to the PL tail prior to the N th pulse’s arrival. Data at longer periods is limited by a constant noise floor linked to the small portion of pump laser spontaneous emission that is not blocked by the filters. For τ eff ≈ 10µs, probabilistic simulation suggests that a fitting region of 10–20µs gives the greatest confidence unbiased estimate of the decay lifetime. Fitting the points in this range gives an effective lifetime of 5.7±0.9µs for a peak excitation of 21.7µW and ±2σ uncertainty. With the effective lifetime much lower than the measured 8±0.5ms (7.8±2.2ms calculated) radiative lifetime in lightly Er3+-doped bulk Y2O3 [39

39. M. J. Weber, “Radiative and multiphonon relaxation of rare-earth ions in Y2O3,” Phys. Rev. 171, 283–291 (1968). [CrossRef]

], nonradiative relaxation is a major concern.

Fig. 3. Upconversion behavior. (a,b) Fiber-taper collected Er2O3 upconversion spectrum while pumping at 1536.7 nm; spectroscopic identifications are made by comparison to known Er3+ transitions back to 4I 15/2 [24]. NB: the scale is varied across the spectrum to make weaker transitions more visible. The relative intensities in (a,b) may not reflect the actual strength of each transition because we are unable to correct for the unknown taper collection efficiency across the visible range. (c) Pump-power dependence for the integrated PL in the 550 nm, 670 nm, and 800 nm bands. The data sets are offset vertically for clarity. (d) Proposed upconversion path.

The nonradiative decay of rare-earth ions was extensively investigated during the early development of inorganic gain crystals for solid-state lasers, and accurate phenomenological models have been established to describe the two principal mechanisms: multiphonon relaxation and cooperative relaxation (also known as concentration quenching) [40

40. L. A. Riseberg and M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, vol. XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1976).

]. For multiphonon emission, the high yield of the 4I 13/2→4I 15/2 transition in low Er3+-density samples is because the 0.8 eV (6500cm-1) energy gap is too large for fast depopulation. Using parameters from Er 3+ relaxation in Y2O3 at low temperature [39

39. M. J. Weber, “Radiative and multiphonon relaxation of rare-earth ions in Y2O3,” Phys. Rev. 171, 283–291 (1968). [CrossRef]

, 41

41. L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968). [CrossRef]

] and the close similarity of the Er 2O3 and Y2O3 vibrational spectra [42

42. G. Schaack and J. A. Koningstein, “Phonon and electronic Raman spectra of cubic rare-earth oxides and isomorphous yttrium oxide,” J. Opt. Soc. Am. 60, 1110–1115 (1970). [CrossRef]

], we estimate an effective lifetime of 4.2 s for relaxation at 300K via emission of 12 phonons (~550cm-1). Cooperative relaxation encompasses several decay and sensitizing mechanisms where the excitation is nonradiatively transfered between ions through multipole or exchange interactions-we will limit the discussion to processes involving a single ion species. Self-quenching, where a donor ion decays to an intermediate level by exciting a low-level transition in another, is significant for higher levels in Er 3+ (e.g. 4S 3/2) [43

43. L. G. V. Uitert and L. F. Johnson, “Energy transfer between rare-earth ions,” J. Chem. Phys. 44, 3514–3522 (1966). [CrossRef]

], but it is inactive for the first excited level (4I 13/2). The most probable relaxation path in Er2O3 is the loss of energy to quenching (acceptor) sites either from direct transfer or from resonant excitation migration through multiple ions [44

44. D. L. Dexter and J. H. Schulman, “Theory of concentration quenching in inorganic phosphors,” J. Chem. Phys. 22, 1063–1070 (1954). [CrossRef]

]. Acceptors are usually nonluminescent impurities (1–10ppm of Fe, W, and Re and >10ppm of Ta are present in the erbium source, impurity levels in the final Er2O3 films are unknown) and/or perturbed electronic states near surfaces or dislocations. At time scales shorter than the radiative lifetime in high purity crystals at 300 K, diffusion via electric dipole-dipole interactions becomes extremely rapid and >10 5 transfers are possible before reaching an acceptor [45

45. W. B. Gandrud and H.W. Moos, “Rare-earth infrared lifetimes and exciton migration rates in trichloride crystals,” J. Chem. Phys. 49, 2170–2182 (1968). [CrossRef]

,46

46. M. J. Weber, “Luminescence decay by energy migration and transfer: Observation of diffusion-limited relaxation,” Phys. Rev. B 4, 2932–2939 (1971). [CrossRef]

]. Although transfer through (Y1-xTbx)3Al5O12 (0.1≤x≤1.0) was consistent with dipole-dipole coupling [47

47. J. P. van der Ziel, L. Kopf, and L. G. Van Uitert, “Quenching of Tb3+ luminescence by direct transfer and migration in aluminum garnets,” Phys. Rev. B 6, 615–623 (1972). [CrossRef]

], high donor concentrations, as in Er2O3, may further the increase migration rate through short-range exchange and/or electric quadrupole-quadrupole interactions [48

48. R. J. Birgeneau, “Mechanisms of energy transport between rare-earth ions,” Appl. Phys. Lett. 13, 193–195 (1968). [CrossRef]

]. This transfer rate and the nonradiative relaxation can be slowed by increasing the mean Er-Er separation. Assuming the decay is diffusion-limited due to a low density of acceptors and conservatively assuming dipole-dipole interactions, the nonradiative decay rate is proportional to the Er3+ concentration [46

46. M. J. Weber, “Luminescence decay by energy migration and transfer: Observation of diffusion-limited relaxation,” Phys. Rev. B 4, 2932–2939 (1971). [CrossRef]

, 49

49. E. Okamoto, M. Sekita, and H. Masui, “Energy transfer between Er3+ ions in LaF3,” Phys. Rev. B 11, 5103–5111 (1975). [CrossRef]

].

Fig. 4. Measurement of 4I 13/2 lifetime. Pulse period measurement of the lifetime for C/Lband emission. Fitting the data in the shaded area gives a lifetime of 5.7±0.9 µs; this uncertainty and the dashed curves mark ±2σ confidence for the fit. Inset: sample histogram for a pulse period of 9.89 µs (101.1 kHz repetition rate).

3.4. Power-dependent radiative efficiency

τoτrad=ηscl=ηobsβobs.
(1)
Fig. 5. Radiative efficiency of the 4I 13/2→4I 15/2 transition vs. absorbed pump power. The marker color indicates the pump-mode wavelength from blue (1460.9 nm) to dark red (1494.5 nm) while (∘) and (+) designate first- and second-order radial pump modes, respectively. Black markers represent data from devices on another wafer processed with wet chemical etching and using first- and second-order pump modes (spanning 1437.6–1490.9 nm). The inset shows green upconverted luminescence from a fundamental cavity mode.

With τo=8ms and ηobs=3.4×10-5, we find ηscl=9.0×10-4 and β obs=0.038, which is consistent with estimates of β obs based on the cavity mode spectrum and negligible Purcell enhancement of τrad (see §A.5). Finally, at 204µW, upconversion reduces the lifetime to τeff=12 τo and gives ~3×1020 ions/cm3 in 4I 13/2. Based on the more rigorous analysis of Nikonorov et al. [50

50. N. Nikonorov, A. Przhevuskii, M. Prassas, and D. Jacob, “Experimental determination of the upconversion rate in erbium-doped silicate glasses,” Appl. Opt. 38, 6284–6291 (1999). [CrossRef]

], we estimate the cooperative upconversion coefficient (C up) to be

Cup=2hcVλpτo2Pup=(5.1±2.1)×1016cm3/s,
(2)

where V=20.1µm3 is the volume of Er2O3 excited by the cavity mode, λ p≈1480nm is the pump wavelength, and P up=204±47µWis the power when the nonradiative and upconversion rates are equal. This upconversion coefficient is extremely large and similar to that found in co-sputtered Er2O3/Al2O3 [51

51. P. G. Kik and A. Polman, “Cooperative upconversion as the gain-limiting factor in Er doped miniature Al2O3 optical waveguide amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003). [CrossRef]

].

4. Conclusions

Due to upconversion and nonradiative relaxation, rate equation estimates suggest significant power is required to invert the 4I 15/2 manifold in these 20-µm microdisk cavities (see §A.6).

Since the large upconversion rate prevents transparency in the C-band until most of the electrons are sequestered in higher states, individual upper levels (e.g. 2H 11/2) may be the first to invert relative to the ground state, making Er2O3 upconversion green lasers a possibility [52

52. S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986). [CrossRef]

54

54. P. Xie and S. C. Rand, “Visible cooperative upconversion laser in Er:LiYF4,” Opt. Lett. 17, 1198–1200 (1992). [CrossRef] [PubMed]

]. EOS might also be developed into an incoherent visible emitter-rough estimates based on the camera’s sensitivity give a green radiative efficiency on the order of 5% for an absorbed power density of 0.15mW/µm3. Additionally, we are investigating the potential of Er2O3 to upconvert infrared radiation into the visible spectrum for use in multijunction silicon solar cells.

To achieve technological maturity for its original application to waveguide amplifiers and lasers for on-chip optical networks, we are working to address the material’s optical inefficiencies (upconversion and nonradiative relaxation) and to develop methods for electrical injection. We are exploring the growth of ternary alloys with Y and Gd to slow the upconversion and nonradiative processes by increasing the inter-ion separation-e.g. (Y 0.9Er0.1)2O3 may exhibit resonant absorption on the order of 36 dB/cm with significantly improved C/L-band radiative efficiency. Detailed studies (as in Ref. [49

49. E. Okamoto, M. Sekita, and H. Masui, “Energy transfer between Er3+ ions in LaF3,” Phys. Rev. B 11, 5103–5111 (1975). [CrossRef]

]) of high quality Er 2O3 and (Y1-xErx)2O3 films will be necessary to characterize the energy migration and quenching sites, but this information is necessary to optimize the Er3+ concentration for performance of on-chip amplifiers (gain, efficiency, etc.). We are also working to grow (RE)2O3-Si superlattices and to determine how the Er3+ 4 f -levels align relative to the Si bands. As in III–V systems, high quality epitaxy will become crucial in controlling the material’s structure and optical properties while moving toward CMOS-compatible electroluminescence and photodetection.

A. Appendix

This document contains details for (A.1) x-ray diffraction analysis, (A.2) fiber-taper measurements of microdisk cavity transmission and photoluminescence while (de)muxing the pump and emission wavelengths, (A.3) fitting cavity loss rates and non-Lorentzian resonances, (A.4) determining the radiative efficiency for cavity-mode coupled emission using measured parameters, (A.5) estimating the ratio of free-space and cavity-coupled emission, and (A.6) our toy three-state rate equation model.

A.1. X-ray diffraction analysis

We employ two configurations for XRD analysis using a standard Cu Kα source: (1) a low angular resolution configuration that is sensitive to more material phases and (2) a high angular resolution configuration. The low-resolution setup utilizes a mirror to provide a wider angular divergence and higher intensity (shorter integration times) for the X-rays. With the 〈110〉 wafer flat of the Si(111) substrate 30° misaligned from the X-ray beam, this measurement is sensitive to more secondary material phases as in Fig. 1(b). The high resolution setup aligns the wafer flat parallel to the X-ray beam and uses a monochromator to narrow the beam’s angular divergence. High-resolution XRD spectra only include the Si{111} and Er 2O3{111} peaks.

A.2. Experimental setups for taper-based measurements

All the major optical measurements in this work are diagramed in Fig. 6. While these configurations are fairly self-evident, there are a few points that may need clarification.

• Two complementary VOAs are used to maintain a constant optical power at the photodetector (to give a constant electronic noise level) while the power at the device can be varied over 60 dB [55

55. M. Borselli, T. J. Johnson, and O. Painter, “Accurate measurement of scattering and absorption loss in microphotonic devices,” Opt. Lett. 32, 2954–2956 (2007). [CrossRef] [PubMed]

]. To avoid any nonlinear effects or absorption saturation while acquiring transmission spectra, the lasers are usually attenuated to give ~200nW at the taper, of which ~10% is coupled into the microdisk cavity.

• We employ a fiber-based MZI for sub-picometer calibration of narrow cavity linewidths.

Fig. 6. Testing arrangements for measuring (a) cavity transmission spectra and visible upconversion, (b) C/L-band photoluminescence and radiative efficiency, and (c) 4I 13/2→4I 15/2 effective lifetime. Abbreviations: variable optical attenuator (VOA), fiber polarization controller (FPC), Mach-Zehnder interferometer (MZI), photodetector (PD), short-pass filter (SPF, pass 1460–1500 nm, reflect 1527–1610 nm), long-pass filter (LPF, pass 1527–1610 nm, reflect 1455–1500 nm), optical spectrum analyzer (OSA), digital communications analyzer (DCA), electro-optic modulator (EOM), and InGaAs/InP avalanche photodiode (APD). Black lines represent optical fiber; blue lines designate coaxial cable. Dashed lines correspond to alternative connections.

• A fourth laser (spanning 1480–1580nm) is used to study any resonances at the boundaries of the primary lasers’ sweep ranges (i.e. near 1495nm and 1565 nm).

• Utilizing wide band-pass filters, S-band transmission and C/L-band emission can be observed simultaneously [Fig. 6(b)]-all cavity-based PL measurements are pumped on resonance with a WGM. The long-pass and short-pass filters separate their pass bands (PCM ports) and reflection bands (RCM ports) with high directivity (>55 dB) and low insertion loss (<1 dB). By collecting and filtering PL in the cavity’s “reflection” channel, we achieve >100dB isolation at the pump wavelength. Some residual spontaneous emission from the laser diode does bleed through the filters and produces a ~10pW signal at 1519nm with our pump near maximum power.

• For cryogenic experiments, the fiber-taper waveguide and the sample are mounted on piezo-electric stages within a continuous flow 4He cryostat [57

57. K. Srinivasan and O. Painter, “Optical fiber taper coupling and high-resolution wavelength tuning of microdisk resonators at cryogenic temperatures,” Appl. Phys. Lett. 90, 031114 (2007). [CrossRef]

].

• During pulsed emission measurements in Fig. 6(c), two polarization controllers are needed to independently match the polarizations of the EOM and the cavity resonance. To optimize the modulator bias voltage and input polarization, we constantly monitor our extinction ratio (>35 dB) and pulse shape (square pulse, 100 ps rise time, 120 ps fall time) with an OSA and a DCA.

• A variable electronic delay is necessary to synchronize the APD with the arrival of the PL pulse and to avoid effects associated with ringing in the gate voltage as in Ref. [58

58. C. Zinoni, B. Alloing, C. Monat, V. Zwiller, L. H. Li, A. Fiore, L. Lunghi, A. Gerardino, H. de Riedmatten, H. Zbinden, and N. Gisin, “Time-resolved and antibunching experiments on single quantum dots at 1300 nm,” Appl. Phys. Lett. 88, 131102 (2006). [CrossRef]

].

A.3. Cavity mode spectra and lineshapes

ddtacw=iΔωacw12(γ1+γe)acw+κs
(3)

where Δω=ω-ω0 is the detuning; γi=γassrad+… is the intrinsic power loss rate due to the sum of losses from absorption (γ a), surface scattering (γss), radiation (γrad), etc.; γe is the extrinsic coupling rate to the waveguide; and s is the amplitude of the waveguide field. The intrinsic and loaded cavity quality factor (Qi and Ql) are given by ω0i and ω0/(γie), respectively. Under a weak coupling approximation, time reversal symmetry and conservation of power require the coupling coefficient (κ) to satisfy κ=iγe.. Ignoring any parasitic loading [65

65. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]

], the normalized cavity-waveguide transmission (Tcav) in steady state is

Tcav=1+iγe(acws)2=1γeiΔω+12(γ1+γe)2.
(4)
Fig. 7. (a) Microdisk transmission spectrum for quasi-TE modes; the fundamental radial-order WGMs are highlighted (grey). (b) Sample Lorentzian fit. (c) Sample non-Lorentzian fit (solid line) of an asymmetric cavity resonance. The inferred absorption peak and a Lorentzian fit (dashed line) to the same data are also included.

To obtain the best estimate for γ i, we weakly load the cavity (~10% contrast) and fit the data with Eq. (4) to find {ω0ie}, as in Fig. 7. For a fixed taper position, WGMs across the S/C/L bands exhibit different coupling depths because of the Er 3+ absorption spectrum. On the edges of the absorption band (near 1420nm and 1620 nm), γ iγ e, and the resonances are significantly over coupled. In the center of the band, γ iγ e, and the modes are near critical coupling.

Since there are several loss mechanisms that contribute to γ i, radiation and surface scattering losses must be accounted for when using cavity modes to determine the absorption spectrum (similar to [66

66. C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett. 90, 051108 (2007). [CrossRef]

]). By choosing appropriate cavity dimensions, the calculated γ rad is negligible for the fundamental modes: γ rad<82MHz=0.026cm-1. Since Rayleigh scattering increases towards longer wavelengths [59

59. B. E. Little and S. T. Chu, “Estimating surface-roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390–1392 (1996). [CrossRef] [PubMed]

,67

67. M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693 (2004). [CrossRef]

], scattering losses can be bounded as less than the minimum intrinsic loss rate near 1625 nm: γss≾min(γ i)=2.5GHz=0.79 cm-1. This 2.5GHz likely has a small absorption component as 4I 13/2→4I 15/2 emission into WGMs is observed out to ~1660 nm. Therefore scattering accounts for less than 1% of the peaks, and γ iγ a except in the spectral tails. The second-order microdisk resonances exhibit slightly greater γ i’s due to mode coupling between the Er2O3 WGMs and the lossy WGMs of the Si pedestal. Because we are unable to bound this additional loss rate, the second-order modes are not used to establish the 4I 15/2→4I 13/2 absorption spectrum.

Due to the small inhomogeneous broadening of the Er 3+ transitions, it is possible for an underlying absorption peak to change appreciably across a cavity linewidth. In this case, the resulting non-Lorentzian cavity resonance can be fit [Fig. 7(c)] using Eq. (4) and including a Lorentzian absorption profile

γiγa(ω)=γ0(δωa2)2(ωωa)2+(δωa2)2
(5)

where ωa, δω a, and γ0 are the center, full width at half-maximum, and amplitude of the absorption peak. For the observed resonances, it has been unnecessary to include the absorption peak’s effect on the real part of the refractive index through the Kramers-Kronig relation. The inferred absorption peaks from fitting these asymmetric resonances around 1457.3, 1462.8, 1478.8, 1545.6, and 1556.9nm agree well with the data from nearby Lorentzian resonances.

A.4. Radiative efficiency measurement

Because the fiber taper offers adjustable waveguide coupling and a low-loss method for PL excitation and collection [35

35. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

], the efficiency for emission into the cavity modes can be empirically determined. The cavity-coupled radiative efficiency (ηobs) is given by the ratio of the total power emitted into the cavity modes divided by the absorbed pump power. This measurement requires careful characterization of the pump mode along with all modes in the desired emission band. For these c-Er2O3 microdisks, surface scattering and radiation losses are negligible compared to the Er3+ absorption, and the absorbed power (Pa) is nearly equal to the dropped power (Pd)

Pa=γaγiPdPd=(1Tcav)PinTt
(6)

where Tcav is the cavity-waveguide transmission at the pump wavelength, Tt is the end-to-end fiber taper transmission, and P in is the pump power measured at the fiber taper input. Equation (6) assumes the taper’s loss is symmetric about the taper-device coupling region. While transmission loss in fiber tapers is usually dominated by bending loss in the taper mount which is symmetric about the coupling region, small bits of dust on the taper will scatter light from the fundamental mode and produce asymmetric loss. In this case, Tt is replaced by the one-sided waveguide transmission (T 1), which can be found from Tt and the ratio of another quantity that depends on P d (e.g. thermo-optic wavelength shift, peak PL yield, etc.) when using either end of the waveguide as the input. For these measurements, Tt=0.68 with symmetric losses. Using the collected emission [P(λ)] spectrum as in Fig. 8, the total power emitted into the cavity modes (P cav) is given by

Pcav=28λrbwTt[n(γi,n+γe,nγe,n)Pn(λ)Tf(λ)dλ]
(7)

where the summation is over the cavity modes at λ>1520nm and δλ rbw is the resolution bandwidth of the detector. The factor of 2 compensates for equal emission into the degenerate clockwise and counter-clockwise traveling-wave modes of the disk and hence into the forward and backward propagating modes of the waveguide. While the C/L-band transmission [Tf(λ)] is fairly flat for the filters used to (de)mux the PL and the pump beam, the transmission does slowly decrease at longer wavelengths. In the emission band, Tt=0.66 with symmetric loss. To establish and correct for the fraction of the PL in the WGMs that is collected by the taper, we find the total cavity loss rate for each cavity mode in the emission band by measuring the γ i,n under weak loading and γe,n at the fixed taper position used during PL collection. Then the fraction of P cav coupled into the forward propagating mode is the ratio of the loss rate into the waveguide (γe,n) over the loss rate into all channels (γ i,n+γe,n), which gives a correction factor of (γi,n+γe,n)/γe,n. Since the ratio of the intensity of individual WGMs over the total emitted power is constant at P d≾4mW, the total integrated PL is proportional to the intensity of the strongest emission line. Using this proportionality, the radiative efficiency measurement can be extended to excitation levels low enough that the largest PL peak is just above the noise floor.

Fig. 8. Observed cavity-coupled photoluminescence spectrum for the device in Fig. 7(a); the fundamental WGMs are highlighted (grey).

A.5. β -factor calculation

In laser physics, the β -factor is the ratio near the lasing threshold of the spontaneous emission into the lasing mode to the emission into all modes, and it can range from 10-6-10-5 for large gas lasers to nearly 100 for few quantum-dot microcavity lasers [68

68. S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]

]. In this work, we modify this definition so β is the ratio of emitted power into a chosen subset of modes (P′c,T) over the total power emitted into free-space (Pf s,T) and cavity modes (Pc,T):

β=Pc,TPfs,T+Pc,T.
(8)

From Fermi’s Golden rule, the total emitted power (PT) in a given spectral range is approximately

PT=2πρfψfĤintψi2NErωidωi
(9)

where ρf is the density of final states and NEr is the number of excited Er3+ ions. We express the final density of states as a product of the density of electronic states (ρe) per energy per ion and the density of emission modes (ρm) per unit frequency. Using a semiclassical electricdipole interaction Ĥint=-qE⃗·r⃗ and averaging over all polarizations and wave vectors for a fixed dipole orientation, PT can be expressed as

PT=2π3ρfE(ωi)2μ(ωi)2NErωidωi
(10)

where 〈E⃗(ωi)〉 is the time-averaged electric-field strength per emitted photon and µ⃗(ωi)=-q 〈Ψf|x⃗|Ψi is the |Ψi〉→|Ψf〉 transition’s dipole moment. For emission into free-space modes, ρm and 〈E⃗(ωi)〉 are given by

ρm=ρfs(ωi)=Vbωi2n3π2c3
(11)
E(ωi)=ωi2n2εoVb
(12)

where Vb is the volume of the “box” containing the free-space modes and n≈2.0 is the refractive index of Er2O3. Since Eq. (10) for the free-space modes is proportional to the measured photoluminescence spectrum from the unpatterned film, the spectral dependence of ρei)|µ⃗(ωi)|2 is known without obtaining its explicit form.

For emission into the microdisk cavity modes, ρm is

ρm=ρc(ωi)=j2L(ωi,ωj,δωj)
(13)

where 𝕃(ωij,δωj) is a lorentzian with a center at the jth cavity mode (ωj) and full-width at half-max (δω j) given by the mode’s loaded linewidth (γei); 𝕃(ωij,δωj) is normalized such that ∫+∞-∞𝕃(ωi)i=1. The factor of 2 accounts for the degenerate clockwise and counterclockwise traveling wave modes. Since the cavity field is not spatially uniform, the average field strength per photon in the jth cavity mode experienced by the ions is

E(ωi)j=ωiϑj2n2εoVc,j
(14)

where Vc, j is the cavity mode volume and 𝜗j accounts for the overlap between the jth emission mode and the distribution of excited ions. Because the excited ion distribution depends on the intensity of the pump mode and Eq. (10) includes |〈E⃗(ωi)j|2, 𝜗j is a scalar integral over the cavity volume

ϑj=Ej2Ep2dVmax(Ej2)Ep2dV
(15)

with the field components of the pump mode (E⃗p) and jth emission mode (E⃗j) computed with finite-element models.

Using the thin film PL data and the cavity mode parameters, the β -factor can be calculated for any individual or collection of modes. While Pc,T in Eq. (8) includes a summation over all cavity modes (both observed and unobserved [69

69. The higher order quasi-TE modes have large bending losses (Q<100) and are poorly phase-matched to the taper waveguide. Since they cannot be observed in transmission or taper-collected PL, all necessary parameters are obtained through finite element simulations.

]), the 𝜗j/Vc, j factor heavily weights the contribution of the modes with low radial order. In this analysis we include the quasi-TE modes of the first 8 radial families; the quasi-TM modes are poorly confined and have little overlap with the Er3+ ions. For first and second radial-order emission modes at λ>1520nm as in the radiative efficiency measurement, we estimate β obs=0.091 which is in reasonable agreement with the experimental value of 0.038. Increasing the sum to include all observed modes across the S/C/Lbands (Fig. 7) gives β 12=0.127. By including all the cavity modes in P′c,T, βT=0.227 is the fraction of the total 4I 13/2→4I 15/2 photoluminescence that is emitted into the microdisk WGMs.

A.6. Three-state rate equation model

To model the upconversion and nonradiative relaxations of the 4I 13/2 population, we solve a three-state system of rate equations in the steady state:

N1=NErN2N3
(16)
dN2dt=N2τoCupN22+sΦ(N1rN2)
(17)
dN3dt=N3τo+12CupN22.
(18)

The populations {N1,N2,N3} represent densities for ions in the {4I 15/2, 4I 13/2, 4I 9/2} states, respectively; higher states are neglected because we lack reasonable estimates for the appropriate upconversion and/or excited-state absorption coefficients. For simplicity, the Stark-split structure for all levels is ignored. The total ion density on C2 lattice sites (NEr) is 2.0×1022 cm-3, and we use our estimated value for the cooperative upconversion coefficient C up=5.1×10-16 cm-3/s. We assume the 4I 13/2 and 4I 9/2 lifetimes are approximately equal (τo=7.2µs) because both transitions to the ground state are dipole forbidden and likely subject to similar nonradiative relaxation-spontaneous and stimulated emission are both excluded from this analysis. The pump photon flux within the cavity is given by Φ, and r is the ratio of the emission and absorption cross sections at the pump wavelength. For Er 3+-doped silica, r≈1/3 at 1480nm [70

70. P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundementals and Technology, Optics and Photonics (Academic Press, San Diego, 1999).

]. The adjustable parameter s=2.5×10-12 encompasses a number of factors including the value of the absorption cross section; it is set to give N2≈2.0×1020 cm-3 at P d=204µW-corresponding to the inferred values from our radiative efficiency measurements. This model for the Er3+ transitions is then applied to a microdisk cavity (20-µm radius, 20.1-µm3 active volume).

Solutions to these rate equations give only a rough estimate for the pump powers at which N2N3 and at which these transitions near transparency. By P d≈0.6mW, there are ~5×1020 ions/cm3 in both the 4I 13/2 and 4I 9/2 levels. These microdisks approach transparency for 4I 9/2→4I 15/2 (λ≈800 nm) and 4I 13/2→4I 15/2 (λ≈1480 nm) with pump powers of P d≈18mW and P d≈130mW, respectively. To more accurately represent the system, this model should, at least, include higher energy levels. Since the upconverted luminescence is most intense around λ≈550 nm, the combined upconversion-emission path for 4I 9/22H11/2/4S3/2→4I15/2 may provide a fast route back to the ground state. A fast green relaxation would increase the transparency thresholds and may make the 4I 9/2→4I 15/2 relaxation a secondary process. In summary, the upconversion processes close to transparency may be quick enough to produce substantial populations in every level up to and including 2H 11/2, which greatly increases the number of spontaneous and stimulated relaxations that must be considered.

Acknowledgments

This work was funded by the DARPA EPIC program. We would like to thank Q. Lin for his fabrication assistance, and CPM would like to thank the Moore Foundation and the NSF for fellowship support.

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N. C. Chang, J. B. Gruber, R. P. Leavitt, and C. A. Morrison, “Optical spectra, energy levels, and crystal-field analysis of tripositive rare earth ions in Y2O3. I. Kramers ions in C2 sites,” J. Chem. Phys. 76, 3877–3889 (1982). [CrossRef]

26.

R. P. Leavitt, J. B. Gruber, N. C. Chang, and C. A. Morrison, “Optical spectra, energy levels, and crystal-field analysis of tripositive rare-earth ions in Y2O3. II. Non-Kramers ions in C2 sites,” J. Chem. Phys. 76, 4775–4788 (1982). [CrossRef]

27.

H. J. Osten, E. Bugiel, M. Czernohorsky, Z. Elassar, O. Kirfel, and A. Fissel, “Molecular Beam Epitaxy of Rare-Earth Oxides,” in Rare Earth Oxide Thin Films, M. Fanciulli and G. Scarel, eds. (Springer-Verlag, Berlin, 2007).

28.

The Er2O3(111) orientation is rotated 180° about the Si(111) surface normal.

29.

The short wavelengths (S), conventional (C), and long wavelengths (L) telecommunications windows (bands) are relative to the region of lowest optical loss in silica fiber (λ ≈ 1550 nm) and occur at 1460–1530 nm, 1530–1565 nm, and 1565–1625 nm, respectively. These designations are not strictly applied in this report as that the absorption extends into the E-band (extended, 1360–1460 nm) and the emission in Fig. 8 continues through the U-band (ultralong wavelengths, 1625–1675 nm).

30.

H. Isshiki, T. Ushiyama, and T. Kimura, “Demonstration of ErSiO superlattice crystal waveguide toward optical amplifiers and emitters,” Phys. Stat. Sol. A 205, 52–55 (2008). [CrossRef]

31.

H. Ono and T. Katsumata, “Interfacial reactions between thin rare-earth-metal oxide films and Si substrates,” Appl. Phys. Lett. 78(13), 1832–1834 (2001). [CrossRef]

32.

B. J. Ainslie, “A Review of the fabrication and properties of Erbium-doped fibers for optical amplifiers,” IEEE J. Lightwave Technol. 9, 220–227 (1991). [CrossRef]

33.

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

34.

C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, “An optical fiber-taper probe for wafer-scale microphotonic device characterization,” Opt. Express 15(8), 4745–4752 (2007). [CrossRef] [PubMed]

35.

K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, “Photoluminescence measurements of quantum-dot-containing semiconductor microdisk resonators using optical fiber taper waveguides,” Phys. Rev. B 72, 205318 (2005). [CrossRef]

36.

J. B. Gruber, K. L. Nash, D. K. Sardar, U. V. Valiev, N. Ter-Gabrielyan, and L. D. Merkle, “Modeling optical transitions of Er3+(4f11) in C2 and C3i sites in polycrystalline Y2O3,” J. Appl. Phys. 104(2), 023101 (2008). [CrossRef]

37.

J. B. Gruber, R. P. Leavitt, C. A. Morrison, and N. C. Chang, “Optical spectra, energy levels, and crystal-field analysis of tripositive rare-earth ions in Y2O3. IV. C3i sites,” J. Chem. Phys. 82, 5373–5378 (1985). [CrossRef]

38.

The intrinsic loss rate (γi) and loss coefficient (αi) are related through the material- and device-dependent group velocity (vg): αi =γi/vg.

39.

M. J. Weber, “Radiative and multiphonon relaxation of rare-earth ions in Y2O3,” Phys. Rev. 171, 283–291 (1968). [CrossRef]

40.

L. A. Riseberg and M. J. Weber, “Relaxation phenomena in rare-earth luminescence,” in Progress in Optics, vol. XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1976).

41.

L. A. Riseberg and H. W. Moos, “Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals,” Phys. Rev. 174, 429–438 (1968). [CrossRef]

42.

G. Schaack and J. A. Koningstein, “Phonon and electronic Raman spectra of cubic rare-earth oxides and isomorphous yttrium oxide,” J. Opt. Soc. Am. 60, 1110–1115 (1970). [CrossRef]

43.

L. G. V. Uitert and L. F. Johnson, “Energy transfer between rare-earth ions,” J. Chem. Phys. 44, 3514–3522 (1966). [CrossRef]

44.

D. L. Dexter and J. H. Schulman, “Theory of concentration quenching in inorganic phosphors,” J. Chem. Phys. 22, 1063–1070 (1954). [CrossRef]

45.

W. B. Gandrud and H.W. Moos, “Rare-earth infrared lifetimes and exciton migration rates in trichloride crystals,” J. Chem. Phys. 49, 2170–2182 (1968). [CrossRef]

46.

M. J. Weber, “Luminescence decay by energy migration and transfer: Observation of diffusion-limited relaxation,” Phys. Rev. B 4, 2932–2939 (1971). [CrossRef]

47.

J. P. van der Ziel, L. Kopf, and L. G. Van Uitert, “Quenching of Tb3+ luminescence by direct transfer and migration in aluminum garnets,” Phys. Rev. B 6, 615–623 (1972). [CrossRef]

48.

R. J. Birgeneau, “Mechanisms of energy transport between rare-earth ions,” Appl. Phys. Lett. 13, 193–195 (1968). [CrossRef]

49.

E. Okamoto, M. Sekita, and H. Masui, “Energy transfer between Er3+ ions in LaF3,” Phys. Rev. B 11, 5103–5111 (1975). [CrossRef]

50.

N. Nikonorov, A. Przhevuskii, M. Prassas, and D. Jacob, “Experimental determination of the upconversion rate in erbium-doped silicate glasses,” Appl. Opt. 38, 6284–6291 (1999). [CrossRef]

51.

P. G. Kik and A. Polman, “Cooperative upconversion as the gain-limiting factor in Er doped miniature Al2O3 optical waveguide amplifiers,” J. Appl. Phys. 93, 5008–5012 (2003). [CrossRef]

52.

S. A. Pollack, D. B. Chang, and N. L. Moise, “Upconversion-pumped infrared erbium laser,” J. Appl. Phys. 60, 4077–4086 (1986). [CrossRef]

53.

P. Xie and S. C. Rand, “Continuous-wave, pair-pumped laser,” Opt. Lett. 15, 848–850 (1990). [CrossRef] [PubMed]

54.

P. Xie and S. C. Rand, “Visible cooperative upconversion laser in Er:LiYF4,” Opt. Lett. 17, 1198–1200 (1992). [CrossRef] [PubMed]

55.

M. Borselli, T. J. Johnson, and O. Painter, “Accurate measurement of scattering and absorption loss in microphotonic devices,” Opt. Lett. 32, 2954–2956 (2007). [CrossRef] [PubMed]

56.

K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, “Single quantum dot spectroscopy using a fiber taper waveguide near-field optic,” Appl. Phys. Lett. 91, 091102 (2007). [CrossRef]

57.

K. Srinivasan and O. Painter, “Optical fiber taper coupling and high-resolution wavelength tuning of microdisk resonators at cryogenic temperatures,” Appl. Phys. Lett. 90, 031114 (2007). [CrossRef]

58.

C. Zinoni, B. Alloing, C. Monat, V. Zwiller, L. H. Li, A. Fiore, L. Lunghi, A. Gerardino, H. de Riedmatten, H. Zbinden, and N. Gisin, “Time-resolved and antibunching experiments on single quantum dots at 1300 nm,” Appl. Phys. Lett. 88, 131102 (2006). [CrossRef]

59.

B. E. Little and S. T. Chu, “Estimating surface-roughness loss and output coupling in microdisk resonators,” Opt. Lett. 21, 1390–1392 (1996). [CrossRef] [PubMed]

60.

J. E. Heebner, T. C. Bond, and J. S. Kallman, “Generalized formulation for performance degradations due to bending and edge scattering loss in microdisk resonators,” Opt. Express 15, 4452–4473 (2007). [CrossRef] [PubMed]

61.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984).

62.

D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, “Splitting of high- Q Mie modes induced by light backscattering in silica microspheres,” Opt. Lett. 20, 1835–1837 (1995). [CrossRef] [PubMed]

63.

M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, “Rayleigh scattering in high-Q microspheres,” J. Opt. Soc. Am. B 17, 1051–1057 (2000). [CrossRef]

64.

K. Srinivasan and O. Painter, “Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity,” Phys. Rev. A 75, 023814 (2007). [CrossRef]

65.

S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, “Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics,” Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]

66.

C. P. Michael, K. Srinivasan, T. J. Johnson, O. Painter, K. H. Lee, K. Hennessy, H. Kim, and E. Hu, “Wavelength-and material-dependent absorption in GaAs and AlGaAs microcavities,” Appl. Phys. Lett. 90, 051108 (2007). [CrossRef]

67.

M. Borselli, K. Srinivasan, P. E. Barclay, and O. Painter, “Rayleigh scattering, mode coupling, and optical loss in silicon microdisks,” Appl. Phys. Lett. 85, 3693 (2004). [CrossRef]

68.

S. Strauf, K. Hennessy, M. T. Rakher, Y.-S. Choi, A. Badolato, L. C. Andreani, E. L. Hu, P. M. Petroff, and D. Bouwmeester, “Self-tuned quantum dot gain in photonic crystal lasers,” Phys. Rev. Lett. 96, 127404 (2006). [CrossRef] [PubMed]

69.

The higher order quasi-TE modes have large bending losses (Q<100) and are poorly phase-matched to the taper waveguide. Since they cannot be observed in transmission or taper-collected PL, all necessary parameters are obtained through finite element simulations.

70.

P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundementals and Technology, Optics and Photonics (Academic Press, San Diego, 1999).

OCIS Codes
(160.4760) Materials : Optical properties
(160.5690) Materials : Rare-earth-doped materials
(190.7220) Nonlinear optics : Upconversion
(230.5750) Optical devices : Resonators

ToC Category:
Materials

History
Original Manuscript: August 25, 2008
Revised Manuscript: November 6, 2008
Manuscript Accepted: November 8, 2008
Published: November 12, 2008

Citation
C. P. Michael, H. B. Yuen, V. A. Sabnis, T. J. Johnson, R. Sewell, R. Smith, A. Jamora, A. Clark, S. Semans, P. B. Atanackovic, and O. Painter, "Growth, processing, and optical properties of epitaxial Er2O3 on silicon," Opt. Express 16, 19649-19666 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-24-19649


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References

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  18. S. Saini, K. Chen, X. Duan, J. Michel, L. C. Kimerling, and M. Lipson, "Er2O3 for high-gain waveguide ampli-fiers," J. Electron. Mater. 33, 809-814 (2004). [CrossRef]
  19. A. M. Grishin, E. V. Vanin, O. V. Tarasenko, S. I. Khartsev, and P. Johansson, "Strong broad C-band roomtemperature photoluminescence in amorphous Er2O3 film," Appl. Phys. Lett. 89, 021114 (2006). [CrossRef]
  20. K. Suh, J. H. Shin, S.-J. Seo, and B.-S. Bae, "Large-scale fabrication of single-phase Er2SiO5 nanocrystal aggregates using Si nanowires," Appl. Phys. Lett. 89, 223102 (2006). [CrossRef]
  21. E. Desurvire, Erbium-doped Fiber Amplifiers: Principles and Applications (John Wiley & Sons, Inc., New York, 2002).
  22. P. B. Atanackovic, "Rare earth-oxides, rare earth-nitrides, rare earth-phosphides, and ternary alloys with silicon," U.S. Patent 7199015 (Dec. 28, 2004).
  23. R. Xu, Y. Y. Zhu, S. Chen, F. Xue, Y. L. Fan, X. J. Yang, and Z. M. Jiang, "Epitaxial growth of Er2O3 films on Si(001)," J. Cryst. Growth 277, 496-501 (2005). [CrossRef]
  24. J. B. Gruber, J. R. Henderson, M. Muramoto, K. Rajnak, and J. G. Conway, "Energy levels of single-crystal erbium oxide," J. Chem. Phys. 45, 477-482 (1966). [CrossRef]
  25. N. C. Chang, J. B. Gruber, R. P. Leavitt, and C. A. Morrison, "Optical spectra, energy levels, and crystal-field analysis of tripositive rare earth ions in Y2O3. I. Kramers ions in C2 sites," J. Chem. Phys. 76, 3877-3889 (1982). [CrossRef]
  26. R. P. Leavitt, J. B. Gruber, N. C. Chang, and C. A. Morrison, "Optical spectra, energy levels, and crystal-field analysis of tripositive rare-earth ions in Y2O3. II. Non-Kramers ions in C2 sites," J. Chem. Phys. 76, 4775-4788 (1982). [CrossRef]
  27. H. J. Osten, E. Bugiel, M. Czernohorsky, Z. Elassar, O. Kirfel, and A. Fissel, "Molecular Beam Epitaxy of Rare-Earth Oxides," in Rare Earth Oxide Thin Films, M. Fanciulli and G. Scarel, eds. (Springer-Verlag, Berlin, 2007).
  28. The Er2O3(111) orientation is rotated 180. about the Si(111) surface normal.
  29. The short wavelengths (S), conventional (C), and long wavelengths (L) telecommunications windows (bands) are relative to the region of lowest optical loss in silica fiber (⌊¡Ö 1550 nm) and occur at 1460-1530 nm, 1530-1565 nm, and 1565-1625 nm, respectively. These designations are not strictly applied in this report as that the absorption extends into the E-band (extended, 1360-1460 nm) and the emission in Fig. 8 continues through the U-band (ultralong wavelengths, 1625-1675 nm).
  30. H. Isshiki, T. Ushiyama, and T. Kimura, "Demonstration of ErSiO superlattice crystal waveguide toward optical amplifiers and emitters," Phys. Stat. Sol. A 205, 52-55 (2008). [CrossRef]
  31. H. Ono and T. Katsumata, "Interfacial reactions between thin rare-earth-metal oxide films and Si substrates," Appl. Phys. Lett. 78(13), 1832-1834 (2001). [CrossRef]
  32. B. J. Ainslie, "A Review of the fabrication and properties of Erbium-doped fibers for optical amplifiers," IEEE J. Lightwave Technol. 9, 220-227 (1991). [CrossRef]
  33. M. Borselli, T. J. Johnson, and O. Painter, "Beyond the Rayleigh scattering limit in high-Q silicon microdisks: theory and experiment," Opt. Express 13, 1515 (2005). [CrossRef] [PubMed]
  34. C. P. Michael, M. Borselli, T. J. Johnson, C. Chrystal, and O. Painter, "An optical fiber-taper probe for wafer-scale microphotonic device characterization," Opt. Express 15(8), 4745-4752 (2007). [CrossRef] [PubMed]
  35. K. Srinivasan, A. Stintz, S. Krishna, and O. Painter, "Photoluminescence measurements of quantum-dotcontaining semiconductor microdisk resonators using optical fiber taper waveguides," Phys. Rev. B 72, 205318 (2005). [CrossRef]
  36. J. B. Gruber, K. L. Nash, D. K. Sardar, U. V. Valiev, N. Ter-Gabrielyan, and L. D. Merkle, "Modeling optical transitions of Er3+(4f11) in C2 and C3i sites in polycrystalline Y2O3," J. Appl. Phys. 104(2), 023101 (2008). [CrossRef]
  37. J. B. Gruber, R. P. Leavitt, C. A. Morrison, and N. C. Chang, "Optical spectra, energy levels, and crystal-field analysis of tripositive rare-earth ions in Y2O3. IV. C3i sites," J. Chem. Phys. 82, 5373-5378 (1985). [CrossRef]
  38. The intrinsic loss rate (©i) and loss coefficient (〈i) are related through the material- and device-dependent group velocity (vg): 〈i = ©i/vg.
  39. M. J. Weber, "Radiative and multiphonon relaxation of rare-earth ions in Y2O3," Phys. Rev. 171, 283-291 (1968). [CrossRef]
  40. L. A. Riseberg and M. J. Weber, "Relaxation phenomena in rare-earth luminescence," in Progress in Optics, vol. XIV, E. Wolf, ed. (North-Holland, Amsterdam, 1976).
  41. L. A. Riseberg and H. W. Moos, "Multiphonon orbit-lattice relaxation of excited states of rare-earth ions in crystals," Phys. Rev. 174, 429-438 (1968). [CrossRef]
  42. G. Schaack and J. A. Koningstein, "Phonon and electronic Raman spectra of cubic rare-earth oxides and isomorphous yttrium oxide," J. Opt. Soc. Am. 60, 1110-1115 (1970). [CrossRef]
  43. L. G. V. Uitert and L. F. Johnson, "Energy transfer between rare-earth ions," J. Chem. Phys. 44, 3514-3522 (1966). [CrossRef]
  44. D. L. Dexter and J. H. Schulman, "Theory of concentration quenching in inorganic phosphors," J. Chem. Phys. 22, 1063-1070 (1954). [CrossRef]
  45. W. B. Gandrud and H.W. Moos, "Rare-earth infrared lifetimes and exciton migration rates in trichloride crystals," J. Chem. Phys. 49, 2170-2182 (1968). [CrossRef]
  46. M. J. Weber, "Luminescence decay by energy migration and transfer: Observation of diffusion-limited relaxation," Phys. Rev. B 4, 2932-2939 (1971). [CrossRef]
  47. J. P. van der Ziel, L. Kopf, and L. G. Van Uitert, "Quenching of Tb3+ luminescence by direct transfer and migration in aluminum garnets," Phys. Rev. B 6, 615-623 (1972). [CrossRef]
  48. R. J. Birgeneau, "Mechanisms of energy transport between rare-earth ions," Appl. Phys. Lett. 13, 193-195 (1968). [CrossRef]
  49. E. Okamoto, M. Sekita, and H. Masui, "Energy transfer between Er3+ ions in LaF3," Phys. Rev. B 11, 5103-5111 (1975). [CrossRef]
  50. N. Nikonorov, A. Przhevuskii, M. Prassas, and D. Jacob, "Experimental determination of the upconversion rate in erbium-doped silicate glasses," Appl. Opt. 38, 6284-6291 (1999). [CrossRef]
  51. P. G. Kik and A. Polman, "Cooperative upconversion as the gain-limiting factor in Er doped miniature Al2O3 optical waveguide amplifiers," J. Appl. Phys. 93, 5008-5012 (2003). [CrossRef]
  52. S. A. Pollack, D. B. Chang, and N. L. Moise, "Upconversion-pumped infrared erbium laser," J. Appl. Phys. 60, 4077-4086 (1986). [CrossRef]
  53. P. Xie and S. C. Rand, "Continuous-wave, pair-pumped laser," Opt. Lett. 15, 848-850 (1990). [CrossRef] [PubMed]
  54. P. Xie and S. C. Rand, "Visible cooperative upconversion laser in Er:LiYF4," Opt. Lett. 17, 1198-1200 (1992). [CrossRef] [PubMed]
  55. M. Borselli, T. J. Johnson, and O. Painter, "Accurate measurement of scattering and absorption loss in microphotonic devices," Opt. Lett. 32, 2954-2956 (2007). [CrossRef] [PubMed]
  56. K. Srinivasan, O. Painter, A. Stintz, and S. Krishna, "Single quantum dot spectroscopy using a fiber taper waveguide near-field optic," Appl. Phys. Lett. 91, 091102 (2007). [CrossRef]
  57. K. Srinivasan and O. Painter, "Optical fiber taper coupling and high-resolution wavelength tuning of microdisk resonators at cryogenic temperatures," Appl. Phys. Lett. 90, 031114 (2007). [CrossRef]
  58. C. Zinoni, B. Alloing, C. Monat, V. Zwiller, L. H. Li, A. Fiore, L. Lunghi, A. Gerardino, H. de Riedmatten, H. Zbinden, and N. Gisin, "Time-resolved and antibunching experiments on single quantum dots at 1300 nm," Appl. Phys. Lett. 88, 131102 (2006). [CrossRef]
  59. B. E. Little and S. T. Chu, "Estimating surface-roughness loss and output coupling in microdisk resonators," Opt. Lett. 21, 1390-1392 (1996). [CrossRef] [PubMed]
  60. J. E. Heebner, T. C. Bond, and J. S. Kallman, "Generalized formulation for performance degradations due to bending and edge scattering loss in microdisk resonators," Opt. Express 15, 4452-4473 (2007). [CrossRef] [PubMed]
  61. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984).
  62. D. S. Weiss, V. Sandoghdar, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, "Splitting of high- Q Mie modes induced by light backscattering in silica microspheres," Opt. Lett. 20, 1835-1837 (1995). [CrossRef] [PubMed]
  63. M. L. Gorodetsky, A. D. Pryamikov, and V. S. Ilchenko, "Rayleigh scattering in high-Q microspheres," J. Opt. Soc. Am. B 17, 1051-1057 (2000). [CrossRef]
  64. K. Srinivasan and O. Painter, "Mode coupling and cavity-quantum-dot interactions in a fiber-coupled microdisk cavity," Phys. Rev. A 75, 023814 (2007). [CrossRef]
  65. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics," Phys. Rev. Lett. 91, 043902 (2003). [CrossRef] [PubMed]
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