11 research outputs found
Compact Photonic Molecules Based On Internally Coupled Microring Resonators
We demonstrate compact planar photonic molecules based on multiple ring resonators internally coupled to a larger ring. Spectral engineering is demonstrated where doublets and quadruplets resonances with high Q are obtained due to degeneracy anti-bunching. © OSA 2013.Bertolotti, M., Driessen, A., Michelotti, F., Microresonators as building block for VLSI photonics (2004) American Institute of Physics, , NYBogaerts, W., Silicon microring resonators (2012) Laser Photonics Rev., 6, pp. 47-73Vlasov, Y., McNab, S., Losses in single-mode silicon-on-insulator strip waveguides and bends (2004) Opt. Exp., 12, pp. 1622-1631Boriskina, S.V., Photonic molecules and spectral engineering. (2010) Photonic microresonator research and applications, pp. 393-421. , Springer U
Observation Of Resonance Modes In Inas/ingaasp/inp Quantum Dot Microdisk Resonators
We present the development of quantum dot microdisk resonators grown by Chemical Beam Epitaxy (CBE). Two stacked layers of InAs Quantum Dots (QDs) embedded in a lattice-matched InGaAsP (λ g=1.4 μm) are grown on (100) InP substrate. Evidence of the presence of resonant modes are observed both by eletroluminescense and absorption spectra at room temperature. © The Electrochemical Society.141505509McCall, S.L., Levi, A.F.J., Slusher, R.E., Pearton, S.J., Logan, R.A., (1992) Appl. Phys. Lett, 60, p. 289Nishi, K., Saito, H., Sugou, S., Lee, J., (1999) Appl. Phys. Lett, 74, p. 1111Kiravittaya, S., Rastelli, A., Schmidt, O.G., (2005) Appl. Phys. Lett, 87Ustinov, V.M., Meleev, N.A., Zhukov, A.E., Kovsh, A.R., Egorov, A.Y., Lunev, A.V., Volovik, B.V., Bimberg, D., (1999) Appl. Phys. Lett, 74, p. 2815Barik, S., Tan, H.H., Jagadish, C., (2006) Nanotechnology, 17, p. 1867Saito, H., Nishi, K., Sugou, S., (2001) Appl. Phys. Lett, 78, p. 267Jeong, W.G., Dapkus, P.D., Lee, U.H., Lim, J.S., Lee, D., Lee, B.T., (2001) Appl. Phys. Lett, 78, p. 1171Wang, R.H., Stintz, A., Varangis, P.M., Newell, T.C., Li, H., Malloy, K.J., Lester, L.F., (2001) IEEE Photonics Technol. Lett, 13, p. 767Schwertberger, R., Gold, D., Reithmaier, J.P., Forchel, A., (2002) IEEE Photonics Technol. Lett, 14, p. 735Ni, C., Allen, Poole, P.J., Marshall, P., Fraser, J., Raymond, S., Fafard, S., (2002) Appl. Phys. Lett, 80, p. 3629Fafard, S., Wasilewski, Z., McCaffrey, J., Raymond, S., Charbonneau, S., (1996) Appl. Phys. Lett, 68, p. 991Li, H., Daniels-Race, T., Wang, Z., (1999) J. Cryst. Growth, 200, p. 321Poole, P.J., McCaffrey, J., Williams, R.L., Lefebvre, J., Chithrani, D., (2001) J. Vac. Sci. Technol. B, 19, p. 1467Xua, B., Wang, Z.G., Chen, Y.H., Jin, P., Ye, X.L., Liu, H.Y., Zhang, Z.Y., Liu, F.Q., (2004) IEEE 13th International Conference on Semiconducting and Insulating Materials, 113Nieto, L., Bortoleto, J.R.R., Cotta, M.A., Magalhães-Paniago, R., Gutiérrez, H.R., (2007) Appl. Phys. Lett, 91, p. 063122Allen, C.N., Finnie, P., Raymond, S., Wasilewski, Z.R., Fafard, S., (2001) Appl. Phys. Lett, 79, p. 2701Sztucki, M., Schülli, T.U., Metzger, T.H., Beham, E., Schuh, D., Chamard, V., (2004) Superlattices Microstruct, 36, p. 1
Ingaasp/inp Qw Microdisk Laser Fabricated By Focused Ion Beam
InGaAsP/InP quantum wells microdisk lasers were fabricated for the evaluation of Ga+ Focused Ion Beam milling of mirrors. Electrical and optical proprieties were investigated and the effects of the milling in the sidewalls were investigated. © 2009 Optical Society of America.Valhala, K.J., Optical Microcavities (2003) Nature, 424, p. 839Mialichi, J.R., Barea, L., von Zuben, A.A., Frateschi, N.C., "Observation of Resonance Modes in InAs/InGaAsP/InP Quantum Dot Microdisk Resonators" (2008), 505. , Electrochemical Society Transactions Microelectronics Technology and Devices. (Pennington NJ USA: Electrochemical Society), v. 14Kim, Y.K., Danner, A.J., Raftery, Jr.J.J., Choquette, K.D., "Focused ion beam nanopatterning for optoelectronic device fabrication," (2005) IEEE J. Sel. Topics Quantum Electron., 11, pp. 1292-1298Schrauwen, J., Van Lysebettens, J., Claes, T., De Vos, K., Bienstman, P., Van Thourhout, D., Baets, R., "Focused-ion-beam fabrication of slots in silicon waveguides and ring resonators" (2008) IEEE Photonics Technol. Lett., 20, pp. 2004-2006Vallini, F., Figueira, D.S.L., Jarschel, P.F., Barea, L.A.M., von Zuben, A.A.G., Filho, A.S., Frateschi, N.C., ".Effects of Ga+ milling on InGaAsP Quantum Well Laser with mirrors etched by Focused Ion Beam" in arXiv:0904.096
Photonic Molecules For Optical Signal Processing
We demonstrate how CMOS compatible photonic molecules (PM) can break the fundamental interdependence among quality factor (Q), channel spacing and size of microring resonators. Different PM architectures are presented for efficient and compact optical signal processing.5455Barea, L.A.M., Vallini, F., De Rezende, G.F.M., Frateschi, N.C., Spectral engineering with cmos compatible soi photonic molecules (2013) IEEE Photonics J., 5 (6), pp. 2202717-2202717Barea, L.A.M., Val Lini, F., Jarschel, P.F., Frateschi, N.C., Silicon technology compatible photonic molecules for compact optical signal processing (2013) Appl. Phys. Lett, 103 (20), p. 201102. , NovSouza, M.C.M.M., Barea, L.A.M., Vallini, F., Rezende, G.F.M., Wiederhecker, G.S., Frateschi, N.C., Embedded coupled microrings with high-finesse and close-spaced resonances for optical signal processing (2014) Opt. Express, 22 (9), pp. 10430-10438. , MayTzuang, L.D., Soltani, M., Lee, Y.H.D., Lipson, M., High rf carrier frequency modulation in silicon resonators by coupling adjacent free-spectral-range modes (2014) Opt. Lett, 39 (7), pp. 1799-1802. , AprXu, Q., Almeida, V.R., Lipson, M., Micrometer-scale all-optical wavelength converter on silicon (2005) Opt. Lett, 30 (20), pp. 2733-2735. , OctLi, Q., Zhang, Z., Liu, F., Qiu, M., Su, Y., Dense wavelength conversion and multicasting in a resonance-split silicon microring (2008) Appl. Phys. Lett, 93 (8), p. 081113. , Au
Enhanced Q With Internally Coupled Microring Resonators
We demonstrate fourfold quality factor (Q) enhancement with microring resonators internally coupled to larger microring resonator. Q ~ 37,000 is obtained for a 5 μm radius microring in a 40 μm x 40 μm footprint device. © OSA 2013.Vlasov, Y., McNab, S., Losses in single-mode silicon-on-insulator strip waveguides and bends (2004) Opt. Exp., 12, pp. 1622-1631Bogaerts, W., Silicon microring resonators (2012) Laser Photonics Rev., 6, pp. 47-73Xu, Q., Schmidt, B., Shakya, J., Lipson, M., Cascaded silicon micro-ring modulators for WDM optical interconnection (2006) Opt. Express, 14, pp. 9431-9435Su, B., Wang, C., Kan, Q., Chen, H., Compact Silicon-on-Insulator Dual-Microring Resonator Optimized for Sensing (2011) JLT, 29, pp. 1535-1541Heyn, P.D., Silicon-on-Insulator All-Pass Microring Resonators Using a Polarization Rotating Coupling Section (2012) PTL, 24, pp. 1176-117
Stadium Cavity Optical Resonator Fabricated By Focused Ion Beam
We have fabricated micro-disk and micro-stadium optical resonators based on conventional InGaAsP/InP multi-quantum well laser epitaxial structures, using a hybrid process by Focused Ion Beam milling and selective wet chemical etching. Resonators with very smooth walls were obtained allowing the observation of optical modes of the stadia with a 15 nm separation. This modal separation is an evidence of the beating between stadium scar modes. © The Electrochemical Society.231455460Del'Haye, P., Schliesser, A., Arcizet, O., (2007) Nature, 450 (7173), p. 1214Heller, (1984) PRL, 53, p. 1515Bogomolny, (1988) PhysicaD, 31, p. 169Gmachl, C., (1998) Science, 280, p. 1556Munoz, S.N., VonZuben, A.A.G., Frateschi", N.C., (2009) JAP, 105, p.
Induced Optical Losses In Optoelectronic Devices Due Focused Ion Beam Damages
A study of damages caused by gallium focused ion beam (FIB) into III-V compounds is presented. Potential damages caused by local heating, ion implantation, and selective sputtering are presented. Preliminary analyzes shows that local heating is negligible. Gallium implantation is shown to occur over areas tens of nanometers thick. Gallium accumulation as well as selective sputtering during III-V compounds milling is expected. Particularly, for GaAs, this effect leads to gallium segregation and formation of metallic clusters. Microdisks resonators are fabricated using FIB milling with different emission currents to analyze these effects on a device. It is shown that for higher emission current, thus higher implantation doses, the cavity quality factor rapidly decreases due optical scattering losses induced by implanted gallium atoms.728791Vallini, F., Figueira, D.S.L., Jarschel, P.F., Barea, L.A.M., von Zuben, A.A.G., Filho, A.S., Frateschi, N.C., Effects of Ga + milling on InGaAsP quantum well laser with mirrors milled by focused ion beam (2009) J. Vac. Sci. Technol. B, 27, pp. L25Barea, L.A.M., Vallini, F., Vaz, A.R., Mialichi, J.R., Frateschi, N.C., Low-roughness active microdisk resonators fabricated by focused ion beam (2009) J. Vac. Sci. Technol. B, 27, p. 6Chen, H., McKay, H.A., Feenstra, R.M., Aers, G.C., Poole, P.J., Williams, R.L., Charbonneau, S., Mitchell, I.V., InGaAs/InP quantum well intermixing studied by cross-sectional scanning tunneling microscopy (2001) J. Appl. Phys, 89, p. 4815Ziegler, J.F., Biersack, J.P., Littmark, U., (1984) The Stopping and Range of Ions In Solids, 1. , Pergamon Press, New YorkFrateschi, N.C., Levi, A.F.J., The spectrum of microdisk lasers (1996) J. Appl. Phis, 80, p. 2Koren, U., Miller, B.I., Su, Y.K., Koch, T.L., Bowers, J.E., Low Internal Loss Separate Confinement Heterostructure InGaAs/InGaAsP Quantum Well Laser (1987) Appl. Phys. Lett, 51, p. 1744. , p
Low-power Four-channel Wavelength Multicasting In Embedded Microring Resonators
We demonstrate four-channel all-optical wavelength multicasting using only 1 mW of pump power and channel spacing of 40-60 GHz. Our device is based on a compact embedded microring design fabricated on a scalable SOI platform. © 2014 OSA.Bogaerts, W., De Heyn, P., Van Vaerenbergh, T., De Vos, K., Kumar Selvaraja, S., Claes, T., Dumon, P., Baets, R., Silicon microring resonators (2012) Laser Phot. Rev., 6, pp. 47-73Barea, L.A.M., Vallini, F., de Rezende, G.F.M., Frateschi, N.C., Spectral Engineering with CMOS Compatible SOI Photonic Molecules (2013) IEEE Photonics J., 5, p. 2202717Almeida, V.R., Barrios, C.A., Panepucci, R.R., Lipson, M., All-optical control of light on a silicon chip (2004) Nature, 431, p. 1081Li, Q., Zhang, Z., Liu, F., Qiu, M., Su, Y., Dense wavelength conversion and multicasting in a resonance-split silicon microring (2008) Appl. Phys. Lett., 93, p. 081113Preble, S.F., Xu, Q., Schmidt, B.S., Lipson, M., Ultrafast all-optical modulation on a silicon chip (2005) Opt. Lett., 30, p. 2891Waldow, M., Plötzing, T., Gottheil, M., Först, M., Bolten, J., Wahlbrink, T., Kurz, H., 25ps all-optical switching in oxygen implanted silicon-on-insulator microring resonator (2008) Opt. Exp., 16, p. 769
Analysis Of Focused Ion Beam Damages In Optoelectronic Devices Fabrication
A study of the damages caused by gallium focused ion beam (FIB) is presented. Potential damages caused by local heating, ion implantation, and selective sputtering are presented. Preliminary analysis shows that local heating is negligible. Gallium implantation is shown to occur over areas tens of nanometers thick. Gallium accumulation as well as selective sputtering during III-V compound milling is expected. Particularly, for GaAs, this effect leads to gallium segregation and the formation of metallic clusters. Microdisks resonators are fabricated using FIB milling of different emission currents. It is shown that for higher emission current, thus higher implantation doses, the cavity quality factor rapidly decreases. © The Electrochemical Society.391299305Electronics and Photonics,IEEE/EDS,ECS,Brazilian Computer Society,Brazilian Microelectronics SocietyVallini, F., Figueira, D.S.L., Jarschel, P.F., Barea, L.A.M., Von Zuben, A.A.G., Filho, A.S., Frateschi, N.C., (2009) J. Vac. Sci. Technol. B, 27, pp. L25Barea, L.A.M., Vallini, F., Vaz, A.R., Mialichi, J.R., Frateschi, N.C., Low-roughness active microdisk resonators fabricated by focused ion beam (2009) J. Vac. Sci. Technol. B, 27, p. 6Chen, H., McKay, H.A., Feenstra, R.M., Aers, G.C., Poole, P.J., Williams, R.L., Charbonneau, S., Mitchell, I.V., (2001) J. Appl. Phys., 89, p. 4815Ziegler, J.F., Biersack, J.P., Littmark, U., (1984) The Stopping and Range of Ions in Solids, 1. , Pergamon Press, New YorkKoren, U., Miller, B.I., Su, Y.K., Koch, T.L., Bowers, J.E., Low-internal-loss separate confinement heterostructure InGaAs/InGaAsP quantum well laser (1987) Appl. Phys. Lett., 51, p. 1744. , TFrateschi, N.C., Levi, A.F.J., The Spectrum of Microdisk Lasers (1996) J. Appl. Phis, 80, p.
A-siox<er> Active Photonic Crystal Resonator Membrane Fabricated By Focused Ga+ Ion Beam
We have fabricated thin erbium-doped amorphous silicon suboxide (a-SiOx) photonic crystal membrane using focused gallium ion beam (FIB). The photonic crystal is composed of a hexagonal lattice with a H1 defect supporting two quasi-doubly degenerate second order dipole states. 2-D simulation was used for the design of the structure and full 3-D FDTD (Finite-Difference Time-Domain) numerical simulations were performed for a complete analysis of the structure. The simulation predicted a quality factor for the structure of Q = 350 with a spontaneous emission enhancement of 7. Micro photoluminescence measurements showed an integrated emission intensity enhancement of ∼2 times with a Q = 130. We show that the discrepancy between simulation and measurement is due to the conical shape of the photonic crystal holes and the optical losses induced by FIB milling. © 2012 Optical Society of America.20171877218783Pavesi, L., Lockwood, D.J., Silicon photonics (2004) Topics in Applied Physics, , SpringerEnnen, H., Scheneider, J., Pomrenke, G., Axmann, A., 1.54m luminescence of erbium?implanted III?V semiconductors and silicon (1983) Appl. Phys. Lett., 43 (10), pp. 943-945Tessler, L.R., Erbium in a-Si:H (1999) Braz. J. Phys., 29 (4), pp. 616-622Bradley, J.D.B., Pollnau, M., Erbium-doped integrated waveguide amplifiers and lasers (2011) Laser Photon. Rev., 5 (3), pp. 368-403Painter, O., Vuckovic, J., Scherer, A., Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab (1999) J. Opt. Soc. Am. B, 16 (2), pp. 275-285Makarova, M., Sih, V., Warga, J., Li, R., Dal Negro, L., Vuckovic, J., Enhanced light emission in photonic crystal nanocavities with erbium-doped silicon nanocrystals (2008) Appl. Phys. Lett., 92 (16), p. 161107Gong, Y., Makarova, M., Yerci, S., Li, R., Stevens, M.J., Baek, B., Nam, S.W., Dal Negro, L., Linewidth narrowing and Purcell enhancement in photonic crystal cavities on an Er-doped silicon nitride platform (2010) Opt. Express, 18 (3), pp. 2601-2612Gong, Y., Makarova, M., Yerci, S., Li, R., Stevens, M.J., Baek, B., Nam, S.W., Vuckovic, J., Observation of transparency of erbium-doped silicon nitride in photonic crystal nanobeam cavities (2010) Opt. Express, 18 (13), pp. 13863-13873Quan, Q., Burgess, I.B., Tang, S.K.Y., Floyd, D.L., Loncar, M., High-Q, low index-contrast polymeric photonic crystal nanobeam cavities (2011) Opt. Express, 19 (22), pp. 22191-22197Gong, Y., Vukovi, J., Photonic crystal cavities in silicon dioxide (2010) Appl. Phys. Lett., 96 (3), p. 031107Gong, Y., Ishikawa, S., Cheng, S., Gunji, M., Nishi, Y., Vukovi, J., Photoluminescence from silicon dioxide photonic crystal cavities with embedded silicon nanocrystals (2010) Phys. Rev. B, 81 (23), p. 235317Kreuzer, C., Riedrich-Möller, J., Neu, E., Becher, C., Design of photonic crystal microcavities in diamond films (2008) Opt. Express, 16 (3), pp. 1632-1644Barth, M., Nüsse, N., Stingl, J., Löchel, B., Benson, O., Emission properties of high-Q silicon nitride photonic crystal heterostructure cavities (2008) Appl. Phys. Lett., 93 (2), p. 021112Makarova, M., Vuckovic, J., Sanda, H., Nishi, Y., Silicon based photonic crystal nanocavity light emitters (2006) Appl. Phys. Lett., 89 (22), p. 221101Hennessy, K., Högerle, C., Hu, E., Badolato, A., Imamolu, A., Tuning photonic nanocavities by atomic force microscope nano-oxidation (2006) Appl. Phys. Lett., 89 (4), p. 041118Nozaki, K., Kita, S., Baba, T., Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser (2007) Opt. Express, 15 (12), pp. 7506-7514Figueira, D.S.L., Mustafa, D., Tessler, L.R., Frateschi, N.C., Resonant structures based on amorphous silicon sub-oxide doped with Er3+ with silicon nanoclusters for an efficient emission at 1550 nm (2009) J. Vac. Sci. Technol. B, 27 (6), pp. L38-L41Lang, R., Figueira, D.S.L., Vallini, F., Frateschi, N.C., Highly luminescent a-SiOx/SiO2/Si multilayer structure (2012) IEEE Photon. J., 4 (4), pp. 1115-1123Tandaechanurat, A., Iwamoto, S., Nomura, M., Kumagai, N., Arakawa, Y., Increase of Q-factor in photonic crystal H1-defect nanocavities after closing of photonic bandgap with optimal slab thickness (2008) Opt. Express, 16 (1), pp. 448-455Babinec, T.M., Choy, J.T., Smith, K.J.M., Khan, M., Lonar, M., Design and focused ion beam fabrication of single crystal diamond nanobeam cavities (2011) J. Vac. Sci. Technol. B, 29 (1), p. 010601Riedrich-Möller, J., Kipfstuhl, L., Hepp, C., Neu, E., Pauly, C., Mücklich, F., Baur, A., Becher, C., One- and two-dimensional photonic crystal microcavities in single crystal diamond (2011) Nat. Nanotechnol., 7 (1), pp. 69-74Chelnokov, A., Wang, K., Rowson, S., Garoche, P., Lourtioz, J.-M., Near-infrared Yablonovitelike photonic crystals by focused-ion-beam etching of macroporous silicon (2000) Appl. Phys. Lett., 77 (19), pp. 2943-2945Barea, L.A.M., Vallini, F., Vaz, A.R., Mialichi, J.R., Frateschi, N.C., Low-roughness active microdisk resonators fabricated by focused ion beam (2009) J. Vac. Sci. Technol. B, 27 (6), pp. 2979-2981Vallini, F., Barea, L.A.M., Dos Reis, E.F., Von Zuben, A.A., Frateschi, N.C., Focused ion beam damages induced optical losses in optoelectronic devices JICS, , to be publishedWiederhecker, G.S., Manipatruni, S., Lee, S., Lipson, M., Broadband tuning of optomechanical cavities (2011) Opt. Express, 19 (3), pp. 2782-2790Chan, J., Alegre, T.P.M., Safavi-Naeini, A.H., Hill, J.T., Krause, A., Gröblacher, S., Aspelmeyer, M., Painter, O., Laser cooling of a nanomechanical oscillator into its quantum ground state (2011) Nature, 478 (7367), pp. 89-92Ryu, H., Park, H., Lee, Y., Two-dimensional photonic crystal semiconductor lasers: Computational design, fabrication, and characterization (2002) IEEE J. Sel. Top. Quant Electron., 8 (4), pp. 891-908Nomura, M., Kumagai, N., Iwamoto, S., Ota, Y., Arakawa, Y., Photonic crystal nanocavity laser with a single quantum dot gain (2009) Opt. Express, 17 (18), pp. 15975-15982Sridharan, D., Bose, R., Kim, H., Solomon, G.S., Waks, E., A reversibly tunable photonic crystal nanocavity laser using photochromic thin film (2011) Opt. Express, 19 (6), pp. 5551-5558Khorasani, S., Mehrany, K., Differential transfer-matrix method for solution of one-dimensional linear nonhomogeneous optical structures (2003) J. Opt. Soc. Am. B, 20 (1), pp. 91-96http://www.rsoftdesign.com/Tang, Y., Mintairov, A.M., Merz, J.L., Tokranov, V., Oktyabrsky, S., Characterization of 2D-Photonic Crystal Nanocavities by Polarization-Dependent and Near-Field Photoluminescence (2005) Proceedings of IEEE Conference on Nanotechnology, pp. 35-38. , Nagoya, JapanFigueira, D.S.L., Frateschi, N.C., Evidences of the simultaneous presence of bow-tie and diamond scars in rare-earth doped amorphous silicon microstadium resonators (2008) J. Appl. Phys., 103 (6), p. 063106Figueira, D.S.L., Frateschi, N.C., (2006) Rare-earth Doped Amorphous Silicon Microdisk Resonator Structures, , John Wiley & SonsShin, J.H., Serna, R., Hoven, G.N., Polman, A., Sark, W.G.J.H.M., Vrendenberg, A.M., Luminescence quenching in erbium?doped hydrogenated amorphous silicon (1996) Appl. Phys. Lett., 68 (1), pp. 46-48Kalkman, J., Tchebotareva, A., Polman, A., Kippengerb, T.J., Min, B., Vahala, K.J., Fabrication and characterization of erbium-doped toroidal microcavity lasers (2006) J. Appl. Phys., 99 (8), pp. 83103-83111Fredrickson, J.E., Waddell, C.N., Spitzer, W.G., Hubler, G.K., Effects of thermal annealing on the refractive index of amorphous silicon produced by ion implantation (1982) Appl. Phys. Lett., 40 (2), pp. 172-174Hoyland, J.D., Sands, D., Temperature dependent refractive index of amorphous silicon determined by timeresolved reflectivity during low fluence excimer laser heating (2006) J. Appl. Phys., 99 (6), p. 063516Vallini, F., Figueira, D.S.L., Jarschel, P.F., Barea, L.A.M., Zuben, A.A.G.V., Frateschi, N.C., Effects of Ga+ milling on InGaAsP Quantum Well Laser with mirrors etched by focused ion beam (2009) J. Vac. Sci. Technol. B, 27 (5), pp. 25-27Desurvire, E., (1994) Erbium Doped Fiber Amplifiers, pp. 207-306. , John WileyGayral, B., Gérard, J.M., Photoluminescence experiment on quantum dots embedded in a large purcell-factor microcavity (2008) Phys. Rev. B, 78 (23), p. 23530