Abstract

This paper presents a simulation-based assessment of the potential for improving the upconversion efficiency of β-NaYF4:Er3+ by embedding the upconverter in a one-dimensional photonic crystal. The considered family of structures consists of alternating quarter-wave layers of the upconverter material and a spacer material with a higher refractive index. The two photonic effects of the structures, a modified local energy density and a modified local density of optical states, are considered within a rate-equation-modeling framework, which describes the internal dynamics of the upconversion process. Optimal designs are identified, while taking into account production tolerances via Monte Carlo simulations. To determine the maximum upconversion efficiency across all realistically attainable structures, the refractive index of the spacer material is varied within the range of existing materials. Assuming a production tolerance of σ = 1 nm, the optimized structures enable more than 300-fold upconversion photoluminescence enhancements under one sun and upconversion quantum yields exceeding 15% under 30 suns concentration.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (5)

D. Zhou, D. Liu, W. Xu, X. Chen, Z. Yin, X. Bai, B. Dong, L. Xu, and H. Song, “Synergistic upconversion enhancement induced by multiple physical effects and an angle-dependent anticounterfeit application,” Chem. Mater. 29, 6799–6809 (2017).
[Crossref]

G. Gao, A. Turshatov, I. A. Howard, D. Busko, R. Joseph, D. Hudry, and B. S. Richards, “Up-conversion fluorescent labels for plastic recycling: a review,” Adv. Sustain. Syst.  1, 1600033 (2017).
[Crossref]

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

B. Shao, Z. Yang, J. Li, J. Yang, Y. Wang, J. Qiu, and Z. Song, “Au nanoparticles embedded inverse opal photonic crystals as substrates for upconversion emission enhancement,” J. Am. Ceram. Soc. 100, 988–997 (2017).
[Crossref]

2016 (8)

C. L. M. Hofmann, S. Fischer, C. Reitz, B. S. Richards, and J. C. Goldschmidt, “Comprehensive analysis of photonic effects on up-conversion of β-NaYF4:Er3+ nanoparticles in an organic-inorganic hybrid 1D photonic crystal,” Proc. SPIE 9885, 99851(2016).

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

S. Fischer, D. Kumar, F. Hallermann, G. V. Plessen, and C. Goldschmidt, “Enhanced upconversion quantum yield near spherical gold nanoparticles - a comprehensive simulation based analysis,” Opt. Express 24, A460–A475 (2016).
[Crossref] [PubMed]

C. L. M. Hofmann, B. Herter, S. Fischer, J. Gutmann, and J. C. Goldschmidt, “Upconversion in a Bragg structure: photonic effects of a modified local density of states and irradiance on luminescence and upconversion quantum yield,” Opt. Express 24, 14895–14914 (2016).
[Crossref] [PubMed]

M. You, M. Lin, S. Wang, X. Wang, G. Zhang, Y. Hong, Y. Dong, G. Jin, and F. Xu, “Three-dimensional quick response code based on inkjet printing of upconversion fluorescent nanoparticles for drug anti-counterfeiting,” Nanoscale. 8, 10096–10104 (2016).
[Crossref] [PubMed]

H. Wang, Z. Yin, W. Xu, D. Zhou, S. Cui, X. Chen, H. Cui, and H. Song, “Remarkable enhancement of upconversion luminescence on 2-D anodic aluminum oxide photonic crystals,” Nanoscale 8, 10004–10009 (2016).
[Crossref] [PubMed]

Y. Yang, P. Zhou, W. Xu, S. Xu, Y. Jiang, X. Chen, and H. Song, “NaYF4:Yb3+, Tm3+ inverse opal photonic crystals and NaYF4:Yb3+, Tm3+/TiO2 composites: synthesis, highly improved upconversion properties and NIR photoelectric response,” J. Mater. Chem. C 4, 659–662 (2016).
[Crossref]

Z. Yin, H. Li, W. Xu, S. Cui, D. Zhou, X. Chen, Y. Zhu, G. Qin, and H. Song, “Local field modulation induced three-order upconversion enhancement: combining surface plasmon effect and photonic crystal effect,” Adv. Mater. 28, 2518–2525 (2016).
[Crossref] [PubMed]

2015 (6)

J. H. Lin, H. Y. Liou, C.-D. Wang, C.-Y. Tseng, C.-T. Lee, C.-C. Ting, H.-C. Kan, and C. C. Hsu, “Giant enhancement of upconversion fluorescence of NaYF4:Yb3+, Tm3+ nanocrystals with resonant waveguide grating substrate,” ACS Photonics 2, 530–536 (2015).
[Crossref]

J. Liao, Z. Yang, J. Sun, S. Lai, B. Shao, J. Li, J. Qiu, Z. Song, and Y. Yang, “Preparation and upconversion emission modification of crystalline colloidal arrays and rare earth fluoride microcrystal composites,” Sci. Reports 5, 7636 (2015).
[Crossref]

J. C. Goldschmidt and S. Fischer, “Upconversion for photovoltaics–a review of materials, devices and concepts for performance enhancement,” Adv. Opt. Mater. 3, 510–535 (2015).
[Crossref]

S. Fischer, E. Favilla, M. Tonelli, and J. C. Goldschmidt, “Record efficient upconverter solar cell devices with optimized bifacial silicon solar cells and monocrystalline BaY2F8:30% Er3+ upconverter,” Sol. Energy Mater. Sol. Cells 136, 127–134 (2015).
[Crossref]

S.-M. Lee, W. Li, P. Dhar, S. Malyk, Y. Wang, W. Lee, A. Benderskii, and J. Yoon, “High-performance flexible nanostructured silicon solar modules with plasmonically engineered upconversion medium,” Adv. Energy Mater.  5, 1500761 (2015).
[Crossref]

A. Mereuta, A. Sirbu, A. Caliman, G. Suruceanu, V. Iakovlev, Z. Mickovic, and E. Kapon, “Fabrication and performance of 1.3-µm 10-Gb/s CWDM wafer-fused VCSELs grown by MOVPE,” J. Cryst. Growth 414, 210–214 (2015).
[Crossref]

2014 (11)

E. Yeganegi, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Local density of optical states in the band gap of a finite one-dimensional photonic crystal,” Phys. Rev. B 89, 045123 (2014).
[Crossref]

F. T. Rabouw, S. A. Den Hartog, T. Senden, and A. Meijerink, “Photonic effects on the Förster resonance energy transfer efficiency,” Nat. Commun.  5, 3610 (2014).
[Crossref]

S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
[Crossref]

S. K. W. MacDougall, A. Ivaturi, J. Marques-Hueso, K. W. Krämer, and B. S. Richards, “Broadband photoluminescent quantum yield optimisation of Er3+-doped β-NaYF4 for upconversion in silicon solar cells,” Sol. Energy Mater. Sol. Cells 128, 18–26 (2014).
[Crossref]

S. Fischer, B. Fröhlich, H. Steinkemper, K. W. Krämer, and J. C. Goldschmidt, “Absolute upconversion quantum yield of β-NaYF4 doped with Er3+ and external quantum efficiency of upconverter solar cell devices under broad-band excitation considering spectral mismatch corrections,” Sol. Energy Mater. Sol. Cells 122, 197–207 (2014).
[Crossref]

P. Huang, W. Zheng, S. Zhou, D. Tu, Z. Chen, H. Zhu, R. Li, E. Ma, M. Huang, and X. Chen, “Lanthanide-doped LiLuF4 upconversion nanoprobes for the detection of disease biomarkers,” Angewandte Chemie Int. Ed. 53, 1252–1257 (2014).
[Crossref]

G. Chen, H. Qiu, P. N. Prasad, and X. Chen, “Upconversion nanoparticles: design, nanochemistry, and applications in theranostics,” Chem. Rev. 114, 5161–5214 (2014).
[Crossref] [PubMed]

S. Fischer, R. Martín-Rodríguez, B. Fröhlich, K. W. Krämer, A. Meijerink, and J. C. Goldschmidt, “Upconversion quantum yield of Er3+-doped β-NaYF4 and GdO2S: the effects of host lattice, Er3+ doping, and excitation spectrum bandwidth,” J. Lumin. 153, 281–287 (2014).
[Crossref]

L. Tao, W. Xu, Y. Zhu, L. Xu, H. Zhu, Y. Liu, S. Xu, P. Zhou, and H. Song, “Modulation of upconversion luminescence in Er3+, Yb3+-codoped lanthanide oxyfluoride (YOF, GdOF, LaOF) inverse opals,” J. Mater. Chem. C 2, 4186–4195 (2014).
[Crossref]

S. Xu, W. Xu, Y. Wang, S. Zhang, Y. Zhu, L. Tao, L. Xia, P. Zhou, and H. Song, “NaYF4:Yb, Tm nanocrystals and TiO2 inverse opal composite films: a novel device for upconversion enhancement and solid-based sensing of avidin,” Nanoscale. 6, 5859–5870 (2014).
[Crossref] [PubMed]

W. Niu, L. T. Su, R. Chen, H. Chen, Y. Wang, A. Palaniappan, H. Sun, and A. I. Y. Tok, “3-dimensional photonic crystal surface enhanced upconversion emission for improved near-infrared photoresponse,” Nanoscale.  6, 817–824 (2014).
[Crossref]

2013 (6)

Z. Yin, Y. Zhu, W. Xu, J. Wang, S. Xu, B. Dong, L. Xu, S. Zhang, and H. Song, “Remarkable enhancement of upconversion fluorescence and confocal imaging of PMMA Opal/NaYF4:Yb3+, Tm3+/Er3+ nanocrystals,” Chem. Commun. 49, 3781–3783 (2013).
[Crossref]

C. Johnson, P. Reece, and G. Conibeer, “Theoretical and experimental evaluation of silicon photonic structures for enhanced erbium up-conversion luminescence,” Sol. Energy Mater. Sol. Cells 112, 168–181 (2013).
[Crossref]

X. Huang, S. Han, W. Huang, and X. Liu, “Enhancing solar cell efficiency: the search for luminescent materials as spectral converters,” Chem. Soc. Rev. 42, 173–201 (2013).
[Crossref]

J. Gutmann, H. Zappe, and J. C. Goldschmidt, “Quantitative modeling of fluorescent emission in photonic crystals,” Phys. Rev. B 88, 205118 (2013).
[Crossref]

L. M. Goldenberg, V. Lisinetskii, and S. Schrader, “Fast and simple fabrication of organic bragg mirrors–application to plastic microchip lasers,” Laser Phys. Lett.  10, 055808 (2013).
[Crossref]

B. Herter, S. Wolf, S. Fischer, J. Gutmann, B. Bläsi, and J. C. Goldschmidt, “Increased upconversion quantum yield in photonic structures due to local field enhancement and modification of the local density of states - a simulation-based analysis,” Opt. Express 21, A883–A900 (2013).
[Crossref]

2012 (3)

S. Fischer, F. Hallermann, T. Eichelkraut, G. V. Plessen, W. Karl, D. Biner, H. Steinkemper, M. Hermle, and J. C. Goldschmidt, “Plasmon enhanced upconversion luminescence near gold nanoparticles - simulation and analysis of the interactions,” Opt. Express 20, 271–282 (2012).
[Crossref] [PubMed]

C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic control of the Förster resonance energy transfer efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
[Crossref]

S. Fischer, H. Steinkemper, P. Löper, M. Hermle, and J. C. Goldschmidt, “Modeling upconversion of erbium doped microcrystals based on experimentally determined Einstein coefficients,” J. Appl. Phys. 111, 13109 (2012).
[Crossref]

2011 (2)

C. M. Johnson, P. J. Reece, and G. J. Conibeer, “Slow-light-enhanced upconversion for photovoltaic applications in one-dimensional photonic crystals,” Opt. Lett. 36, 3990–3992 (2011).

I. Leonidov, V. Zubkov, A. Tyutyunnik, N. Tarakina, L. Surat, O. Koryakova, and E. Vovkotrub, “Upconversion luminescence in Er3+/Yb3+ codoped Y2CaGe4O12,” J. Alloy. Compd. 509, 1339–1346 (2011).
[Crossref]

2010 (3)

F. Zhang, Y. Deng, Y. Shi, R. Zhang, and D. Zhao, “Photoluminescence modification in upconversion rare-earth fluoride nanocrystal array constructed photonic crystals,” J. Mater. Chem. 20, 3895–3900 (2010).
[Crossref]

J.-C. Boyer and F. C. Van Veggel, “Absolute quantum yield measurements of colloidal NaYF4:Er3+, Yb3+ upconverting nanoparticles,” Nanoscale 2, 1417–1419 (2010).
[Crossref] [PubMed]

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

2009 (2)

Z.-X. Li, L.-L. Li, H.-P. Zhou, Q. Yuan, C. Chen, L.-D. Sun, and C.-H. Yan, “Colour modification action of an upconversion photonic crystal,” Chem. Commun. 43, 6616–6618 (2009).
[Crossref]

E. Verhagen, L. Kuipers, and A. Polman, “Field enhancement in metallic subwavelength aperture arrays probed by erbium upconversion luminescence,” Opt. Express 17, 14586–14598 (2009).
[Crossref] [PubMed]

2007 (5)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D: Appl. Phys. 40, 2666 (2007).
[Crossref]

R. L. Puurunen, J. Saarilahti, and H. Kattelus, “Implementing ALD layers in MEMS processing,” ECS Transactions 11, 3–14 (2007).
[Crossref]

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved gersten and nitzan model,” Phys. Rev. B 76, 115123 (2007).
[Crossref]

C. Strümpel, M. McCann, G. Beaucarne, V. Arkhipov, A. Slaoui, V. Švrček, C. Del Cañizo, and I. Tobias, “Modifying the solar spectrum to enhance silicon solar cell efficiency - an overview of available materials,” Sol. Energy Mater. Sol. Cells 91, 238–249 (2007).
[Crossref]

B. S. Richards and A. Shalav, “Enhancing the near-infrared spectral response of silicon optoelectronic devices via up-conversion,” IEEE Trans. Electron Devices 54, 2679–2684 (2007).
[Crossref]

2006 (1)

T. Trupke, A. Shalav, B. Richards, P. Würfel, and M. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90, 3327–3338 (2006).
[Crossref]

2005 (2)

M. De Dood, J. Knoester, A. Tip, and A. Polman, “Förster transfer and the local optical density of states in erbium-doped silica,” Phys. Rev. B 71, 115102 (2005).
[Crossref]

M. Barth, A. Gruber, and F. Cichos, “Spectral and angular redistribution of photoluminescence near a photonic stop band,” Phys. Rev. B 72, 085129 (2005).
[Crossref]

2004 (1)

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16, 1244–1251 (2004).
[Crossref]

2001 (1)

2000 (2)

P. Andrew and W. L. Barnes, “Förster energy transfer in an optical microcavity,” Science. 290, 785–788 (2000).
[Crossref] [PubMed]

M. Pollnau, D. Gamelin, S. Lüthi, H. Güdel, and M. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).

1999 (1)

S. John and K. Busch, “Photonic bandgap formation and tunability in certain self-organizing systems,” J. Light. Technol. 17, 1931 (1999).
[Crossref]

1997 (1)

K. W. Krämer, H. U. Güdel, and R. N. Schwartz, “Infrared-to-visible upconversion in LaCl3:1% Er3+: energy-level and line-strength calculations,” Phys. Rev. B 56, 13830 (1997).
[Crossref]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).

1995 (1)

1992 (1)

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46, 612 (1992).
[Crossref] [PubMed]

1966 (1)

R. E. Thoma, H. Insley, and G. M. Hebert, “The sodium fluoride-tanthanide trifluoride systems,” Inorg. Chem. 5, 1222–1229 (1966).
[Crossref]

1961 (1)

W. Shockley and H. J. Queisser, “Detailed balance limit of efficiency of p-n junction solar cells,” J. Appl. Phys. 32, 510–519 (1961).

Andrew, P.

P. Andrew and W. L. Barnes, “Förster energy transfer in an optical microcavity,” Science. 290, 785–788 (2000).
[Crossref] [PubMed]

Arkhipov, V.

C. Strümpel, M. McCann, G. Beaucarne, V. Arkhipov, A. Slaoui, V. Švrček, C. Del Cañizo, and I. Tobias, “Modifying the solar spectrum to enhance silicon solar cell efficiency - an overview of available materials,” Sol. Energy Mater. Sol. Cells 91, 238–249 (2007).
[Crossref]

Bai, X.

D. Zhou, D. Liu, W. Xu, X. Chen, Z. Yin, X. Bai, B. Dong, L. Xu, and H. Song, “Synergistic upconversion enhancement induced by multiple physical effects and an angle-dependent anticounterfeit application,” Chem. Mater. 29, 6799–6809 (2017).
[Crossref]

Balling, P.

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

Barnes, W. L.

P. Andrew and W. L. Barnes, “Förster energy transfer in an optical microcavity,” Science. 290, 785–788 (2000).
[Crossref] [PubMed]

Barth, M.

M. Barth, A. Gruber, and F. Cichos, “Spectral and angular redistribution of photoluminescence near a photonic stop band,” Phys. Rev. B 72, 085129 (2005).
[Crossref]

Bauer, G.

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

Beaucarne, G.

C. Strümpel, M. McCann, G. Beaucarne, V. Arkhipov, A. Slaoui, V. Švrček, C. Del Cañizo, and I. Tobias, “Modifying the solar spectrum to enhance silicon solar cell efficiency - an overview of available materials,” Sol. Energy Mater. Sol. Cells 91, 238–249 (2007).
[Crossref]

Benderskii, A.

S.-M. Lee, W. Li, P. Dhar, S. Malyk, Y. Wang, W. Lee, A. Benderskii, and J. Yoon, “High-performance flexible nanostructured silicon solar modules with plasmonically engineered upconversion medium,” Adv. Energy Mater.  5, 1500761 (2015).
[Crossref]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).

Biner, D.

S. Fischer, F. Hallermann, T. Eichelkraut, G. V. Plessen, W. Karl, D. Biner, H. Steinkemper, M. Hermle, and J. C. Goldschmidt, “Plasmon enhanced upconversion luminescence near gold nanoparticles - simulation and analysis of the interactions,” Opt. Express 20, 271–282 (2012).
[Crossref] [PubMed]

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16, 1244–1251 (2004).
[Crossref]

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

Bläsi, B.

Blum, C.

C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic control of the Förster resonance energy transfer efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
[Crossref]

Bowden, C. M.

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46, 612 (1992).
[Crossref] [PubMed]

Boyer, J.-C.

J.-C. Boyer and F. C. Van Veggel, “Absolute quantum yield measurements of colloidal NaYF4:Er3+, Yb3+ upconverting nanoparticles,” Nanoscale 2, 1417–1419 (2010).
[Crossref] [PubMed]

Brüggemann, R.

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

Bu, W.

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

Busch, K.

S. John and K. Busch, “Photonic bandgap formation and tunability in certain self-organizing systems,” J. Light. Technol. 17, 1931 (1999).
[Crossref]

Busko, D.

G. Gao, A. Turshatov, I. A. Howard, D. Busko, R. Joseph, D. Hudry, and B. S. Richards, “Up-conversion fluorescent labels for plastic recycling: a review,” Adv. Sustain. Syst.  1, 1600033 (2017).
[Crossref]

Cai, W.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

Caliman, A.

A. Mereuta, A. Sirbu, A. Caliman, G. Suruceanu, V. Iakovlev, Z. Mickovic, and E. Kapon, “Fabrication and performance of 1.3-µm 10-Gb/s CWDM wafer-fused VCSELs grown by MOVPE,” J. Cryst. Growth 414, 210–214 (2015).
[Crossref]

Carter, K.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

Chen, C.

Z.-X. Li, L.-L. Li, H.-P. Zhou, Q. Yuan, C. Chen, L.-D. Sun, and C.-H. Yan, “Colour modification action of an upconversion photonic crystal,” Chem. Commun. 43, 6616–6618 (2009).
[Crossref]

Chen, G.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

G. Chen, H. Qiu, P. N. Prasad, and X. Chen, “Upconversion nanoparticles: design, nanochemistry, and applications in theranostics,” Chem. Rev. 114, 5161–5214 (2014).
[Crossref] [PubMed]

Chen, H.

W. Niu, L. T. Su, R. Chen, H. Chen, Y. Wang, A. Palaniappan, H. Sun, and A. I. Y. Tok, “3-dimensional photonic crystal surface enhanced upconversion emission for improved near-infrared photoresponse,” Nanoscale.  6, 817–824 (2014).
[Crossref]

Chen, R.

W. Niu, L. T. Su, R. Chen, H. Chen, Y. Wang, A. Palaniappan, H. Sun, and A. I. Y. Tok, “3-dimensional photonic crystal surface enhanced upconversion emission for improved near-infrared photoresponse,” Nanoscale.  6, 817–824 (2014).
[Crossref]

Chen, X.

D. Zhou, D. Liu, W. Xu, X. Chen, Z. Yin, X. Bai, B. Dong, L. Xu, and H. Song, “Synergistic upconversion enhancement induced by multiple physical effects and an angle-dependent anticounterfeit application,” Chem. Mater. 29, 6799–6809 (2017).
[Crossref]

H. Wang, Z. Yin, W. Xu, D. Zhou, S. Cui, X. Chen, H. Cui, and H. Song, “Remarkable enhancement of upconversion luminescence on 2-D anodic aluminum oxide photonic crystals,” Nanoscale 8, 10004–10009 (2016).
[Crossref] [PubMed]

Y. Yang, P. Zhou, W. Xu, S. Xu, Y. Jiang, X. Chen, and H. Song, “NaYF4:Yb3+, Tm3+ inverse opal photonic crystals and NaYF4:Yb3+, Tm3+/TiO2 composites: synthesis, highly improved upconversion properties and NIR photoelectric response,” J. Mater. Chem. C 4, 659–662 (2016).
[Crossref]

Z. Yin, H. Li, W. Xu, S. Cui, D. Zhou, X. Chen, Y. Zhu, G. Qin, and H. Song, “Local field modulation induced three-order upconversion enhancement: combining surface plasmon effect and photonic crystal effect,” Adv. Mater. 28, 2518–2525 (2016).
[Crossref] [PubMed]

P. Huang, W. Zheng, S. Zhou, D. Tu, Z. Chen, H. Zhu, R. Li, E. Ma, M. Huang, and X. Chen, “Lanthanide-doped LiLuF4 upconversion nanoprobes for the detection of disease biomarkers,” Angewandte Chemie Int. Ed. 53, 1252–1257 (2014).
[Crossref]

G. Chen, H. Qiu, P. N. Prasad, and X. Chen, “Upconversion nanoparticles: design, nanochemistry, and applications in theranostics,” Chem. Rev. 114, 5161–5214 (2014).
[Crossref] [PubMed]

Chen, Z.

P. Huang, W. Zheng, S. Zhou, D. Tu, Z. Chen, H. Zhu, R. Li, E. Ma, M. Huang, and X. Chen, “Lanthanide-doped LiLuF4 upconversion nanoprobes for the detection of disease biomarkers,” Angewandte Chemie Int. Ed. 53, 1252–1257 (2014).
[Crossref]

Christiansen, J.

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

Cichos, F.

M. Barth, A. Gruber, and F. Cichos, “Spectral and angular redistribution of photoluminescence near a photonic stop band,” Phys. Rev. B 72, 085129 (2005).
[Crossref]

Conibeer, G.

C. Johnson, P. Reece, and G. Conibeer, “Theoretical and experimental evaluation of silicon photonic structures for enhanced erbium up-conversion luminescence,” Sol. Energy Mater. Sol. Cells 112, 168–181 (2013).
[Crossref]

Conibeer, G. J.

Cui, H.

H. Wang, Z. Yin, W. Xu, D. Zhou, S. Cui, X. Chen, H. Cui, and H. Song, “Remarkable enhancement of upconversion luminescence on 2-D anodic aluminum oxide photonic crystals,” Nanoscale 8, 10004–10009 (2016).
[Crossref] [PubMed]

Cui, S.

H. Wang, Z. Yin, W. Xu, D. Zhou, S. Cui, X. Chen, H. Cui, and H. Song, “Remarkable enhancement of upconversion luminescence on 2-D anodic aluminum oxide photonic crystals,” Nanoscale 8, 10004–10009 (2016).
[Crossref] [PubMed]

Z. Yin, H. Li, W. Xu, S. Cui, D. Zhou, X. Chen, Y. Zhu, G. Qin, and H. Song, “Local field modulation induced three-order upconversion enhancement: combining surface plasmon effect and photonic crystal effect,” Adv. Mater. 28, 2518–2525 (2016).
[Crossref] [PubMed]

Cui, Z.

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

De Dood, M.

M. De Dood, J. Knoester, A. Tip, and A. Polman, “Förster transfer and the local optical density of states in erbium-doped silica,” Phys. Rev. B 71, 115102 (2005).
[Crossref]

Del Cañizo, C.

C. Strümpel, M. McCann, G. Beaucarne, V. Arkhipov, A. Slaoui, V. Švrček, C. Del Cañizo, and I. Tobias, “Modifying the solar spectrum to enhance silicon solar cell efficiency - an overview of available materials,” Sol. Energy Mater. Sol. Cells 91, 238–249 (2007).
[Crossref]

Den Hartog, S. A.

F. T. Rabouw, S. A. Den Hartog, T. Senden, and A. Meijerink, “Photonic effects on the Förster resonance energy transfer efficiency,” Nat. Commun.  5, 3610 (2014).
[Crossref]

Deng, Y.

F. Zhang, Y. Deng, Y. Shi, R. Zhang, and D. Zhao, “Photoluminescence modification in upconversion rare-earth fluoride nanocrystal array constructed photonic crystals,” J. Mater. Chem. 20, 3895–3900 (2010).
[Crossref]

Dhar, P.

S.-M. Lee, W. Li, P. Dhar, S. Malyk, Y. Wang, W. Lee, A. Benderskii, and J. Yoon, “High-performance flexible nanostructured silicon solar modules with plasmonically engineered upconversion medium,” Adv. Energy Mater.  5, 1500761 (2015).
[Crossref]

Dong, B.

D. Zhou, D. Liu, W. Xu, X. Chen, Z. Yin, X. Bai, B. Dong, L. Xu, and H. Song, “Synergistic upconversion enhancement induced by multiple physical effects and an angle-dependent anticounterfeit application,” Chem. Mater. 29, 6799–6809 (2017).
[Crossref]

Z. Yin, Y. Zhu, W. Xu, J. Wang, S. Xu, B. Dong, L. Xu, S. Zhang, and H. Song, “Remarkable enhancement of upconversion fluorescence and confocal imaging of PMMA Opal/NaYF4:Yb3+, Tm3+/Er3+ nanocrystals,” Chem. Commun. 49, 3781–3783 (2013).
[Crossref]

Dong, Y.

M. You, M. Lin, S. Wang, X. Wang, G. Zhang, Y. Hong, Y. Dong, G. Jin, and F. Xu, “Three-dimensional quick response code based on inkjet printing of upconversion fluorescent nanoparticles for drug anti-counterfeiting,” Nanoscale. 8, 10096–10104 (2016).
[Crossref] [PubMed]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structures,” Phys. Rev. E 53, 4107–4121 (1996).

J. P. Dowling and C. M. Bowden, “Atomic emission rates in inhomogeneous media with applications to photonic band structures,” Phys. Rev. A 46, 612 (1992).
[Crossref] [PubMed]

Eichelkraut, T.

Eriksen, E.

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

Fan, Q.

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

Favilla, E.

S. Fischer, E. Favilla, M. Tonelli, and J. C. Goldschmidt, “Record efficient upconverter solar cell devices with optimized bifacial silicon solar cells and monocrystalline BaY2F8:30% Er3+ upconverter,” Sol. Energy Mater. Sol. Cells 136, 127–134 (2015).
[Crossref]

Fischer, S.

C. L. M. Hofmann, S. Fischer, C. Reitz, B. S. Richards, and J. C. Goldschmidt, “Comprehensive analysis of photonic effects on up-conversion of β-NaYF4:Er3+ nanoparticles in an organic-inorganic hybrid 1D photonic crystal,” Proc. SPIE 9885, 99851(2016).

S. Fischer, D. Kumar, F. Hallermann, G. V. Plessen, and C. Goldschmidt, “Enhanced upconversion quantum yield near spherical gold nanoparticles - a comprehensive simulation based analysis,” Opt. Express 24, A460–A475 (2016).
[Crossref] [PubMed]

C. L. M. Hofmann, B. Herter, S. Fischer, J. Gutmann, and J. C. Goldschmidt, “Upconversion in a Bragg structure: photonic effects of a modified local density of states and irradiance on luminescence and upconversion quantum yield,” Opt. Express 24, 14895–14914 (2016).
[Crossref] [PubMed]

S. Fischer, E. Favilla, M. Tonelli, and J. C. Goldschmidt, “Record efficient upconverter solar cell devices with optimized bifacial silicon solar cells and monocrystalline BaY2F8:30% Er3+ upconverter,” Sol. Energy Mater. Sol. Cells 136, 127–134 (2015).
[Crossref]

J. C. Goldschmidt and S. Fischer, “Upconversion for photovoltaics–a review of materials, devices and concepts for performance enhancement,” Adv. Opt. Mater. 3, 510–535 (2015).
[Crossref]

S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
[Crossref]

S. Fischer, B. Fröhlich, H. Steinkemper, K. W. Krämer, and J. C. Goldschmidt, “Absolute upconversion quantum yield of β-NaYF4 doped with Er3+ and external quantum efficiency of upconverter solar cell devices under broad-band excitation considering spectral mismatch corrections,” Sol. Energy Mater. Sol. Cells 122, 197–207 (2014).
[Crossref]

S. Fischer, R. Martín-Rodríguez, B. Fröhlich, K. W. Krämer, A. Meijerink, and J. C. Goldschmidt, “Upconversion quantum yield of Er3+-doped β-NaYF4 and GdO2S: the effects of host lattice, Er3+ doping, and excitation spectrum bandwidth,” J. Lumin. 153, 281–287 (2014).
[Crossref]

B. Herter, S. Wolf, S. Fischer, J. Gutmann, B. Bläsi, and J. C. Goldschmidt, “Increased upconversion quantum yield in photonic structures due to local field enhancement and modification of the local density of states - a simulation-based analysis,” Opt. Express 21, A883–A900 (2013).
[Crossref]

S. Fischer, F. Hallermann, T. Eichelkraut, G. V. Plessen, W. Karl, D. Biner, H. Steinkemper, M. Hermle, and J. C. Goldschmidt, “Plasmon enhanced upconversion luminescence near gold nanoparticles - simulation and analysis of the interactions,” Opt. Express 20, 271–282 (2012).
[Crossref] [PubMed]

S. Fischer, H. Steinkemper, P. Löper, M. Hermle, and J. C. Goldschmidt, “Modeling upconversion of erbium doped microcrystals based on experimentally determined Einstein coefficients,” J. Appl. Phys. 111, 13109 (2012).
[Crossref]

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

Frei, G.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16, 1244–1251 (2004).
[Crossref]

Fröhlich, B.

S. Fischer, R. Martín-Rodríguez, B. Fröhlich, K. W. Krämer, A. Meijerink, and J. C. Goldschmidt, “Upconversion quantum yield of Er3+-doped β-NaYF4 and GdO2S: the effects of host lattice, Er3+ doping, and excitation spectrum bandwidth,” J. Lumin. 153, 281–287 (2014).
[Crossref]

S. Fischer, B. Fröhlich, H. Steinkemper, K. W. Krämer, and J. C. Goldschmidt, “Absolute upconversion quantum yield of β-NaYF4 doped with Er3+ and external quantum efficiency of upconverter solar cell devices under broad-band excitation considering spectral mismatch corrections,” Sol. Energy Mater. Sol. Cells 122, 197–207 (2014).
[Crossref]

S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
[Crossref]

Gamelin, D.

M. Pollnau, D. Gamelin, S. Lüthi, H. Güdel, and M. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).

Gao, G.

G. Gao, A. Turshatov, I. A. Howard, D. Busko, R. Joseph, D. Hudry, and B. S. Richards, “Up-conversion fluorescent labels for plastic recycling: a review,” Adv. Sustain. Syst.  1, 1600033 (2017).
[Crossref]

Geng, J.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

Glunz, S.

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

Glunz, S. W.

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

Goldenberg, L. M.

L. M. Goldenberg, V. Lisinetskii, and S. Schrader, “Fast and simple fabrication of organic bragg mirrors–application to plastic microchip lasers,” Laser Phys. Lett.  10, 055808 (2013).
[Crossref]

Goldschmidt, C.

Goldschmidt, J.

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

Goldschmidt, J. C.

C. L. M. Hofmann, S. Fischer, C. Reitz, B. S. Richards, and J. C. Goldschmidt, “Comprehensive analysis of photonic effects on up-conversion of β-NaYF4:Er3+ nanoparticles in an organic-inorganic hybrid 1D photonic crystal,” Proc. SPIE 9885, 99851(2016).

C. L. M. Hofmann, B. Herter, S. Fischer, J. Gutmann, and J. C. Goldschmidt, “Upconversion in a Bragg structure: photonic effects of a modified local density of states and irradiance on luminescence and upconversion quantum yield,” Opt. Express 24, 14895–14914 (2016).
[Crossref] [PubMed]

J. C. Goldschmidt and S. Fischer, “Upconversion for photovoltaics–a review of materials, devices and concepts for performance enhancement,” Adv. Opt. Mater. 3, 510–535 (2015).
[Crossref]

S. Fischer, E. Favilla, M. Tonelli, and J. C. Goldschmidt, “Record efficient upconverter solar cell devices with optimized bifacial silicon solar cells and monocrystalline BaY2F8:30% Er3+ upconverter,” Sol. Energy Mater. Sol. Cells 136, 127–134 (2015).
[Crossref]

S. Fischer, R. Martín-Rodríguez, B. Fröhlich, K. W. Krämer, A. Meijerink, and J. C. Goldschmidt, “Upconversion quantum yield of Er3+-doped β-NaYF4 and GdO2S: the effects of host lattice, Er3+ doping, and excitation spectrum bandwidth,” J. Lumin. 153, 281–287 (2014).
[Crossref]

S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
[Crossref]

S. Fischer, B. Fröhlich, H. Steinkemper, K. W. Krämer, and J. C. Goldschmidt, “Absolute upconversion quantum yield of β-NaYF4 doped with Er3+ and external quantum efficiency of upconverter solar cell devices under broad-band excitation considering spectral mismatch corrections,” Sol. Energy Mater. Sol. Cells 122, 197–207 (2014).
[Crossref]

B. Herter, S. Wolf, S. Fischer, J. Gutmann, B. Bläsi, and J. C. Goldschmidt, “Increased upconversion quantum yield in photonic structures due to local field enhancement and modification of the local density of states - a simulation-based analysis,” Opt. Express 21, A883–A900 (2013).
[Crossref]

J. Gutmann, H. Zappe, and J. C. Goldschmidt, “Quantitative modeling of fluorescent emission in photonic crystals,” Phys. Rev. B 88, 205118 (2013).
[Crossref]

S. Fischer, F. Hallermann, T. Eichelkraut, G. V. Plessen, W. Karl, D. Biner, H. Steinkemper, M. Hermle, and J. C. Goldschmidt, “Plasmon enhanced upconversion luminescence near gold nanoparticles - simulation and analysis of the interactions,” Opt. Express 20, 271–282 (2012).
[Crossref] [PubMed]

S. Fischer, H. Steinkemper, P. Löper, M. Hermle, and J. C. Goldschmidt, “Modeling upconversion of erbium doped microcrystals based on experimentally determined Einstein coefficients,” J. Appl. Phys. 111, 13109 (2012).
[Crossref]

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

Green, M.

T. Trupke, A. Shalav, B. Richards, P. Würfel, and M. Green, “Efficiency enhancement of solar cells by luminescent up-conversion of sunlight,” Sol. Energy Mater. Sol. Cells 90, 3327–3338 (2006).
[Crossref]

Gruber, A.

M. Barth, A. Gruber, and F. Cichos, “Spectral and angular redistribution of photoluminescence near a photonic stop band,” Phys. Rev. B 72, 085129 (2005).
[Crossref]

Güdel, H.

M. Pollnau, D. Gamelin, S. Lüthi, H. Güdel, and M. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).

Güdel, H. U.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16, 1244–1251 (2004).
[Crossref]

K. W. Krämer, H. U. Güdel, and R. N. Schwartz, “Infrared-to-visible upconversion in LaCl3:1% Er3+: energy-level and line-strength calculations,” Phys. Rev. B 56, 13830 (1997).
[Crossref]

Gutmann, J.

Hallermann, F.

Han, S.

X. Huang, S. Han, W. Huang, and X. Liu, “Enhancing solar cell efficiency: the search for luminescent materials as spectral converters,” Chem. Soc. Rev. 42, 173–201 (2013).
[Crossref]

Han, X.

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

He, X.-P.

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

Hebert, G. M.

R. E. Thoma, H. Insley, and G. M. Hebert, “The sodium fluoride-tanthanide trifluoride systems,” Inorg. Chem. 5, 1222–1229 (1966).
[Crossref]

Hehlen, M.

M. Pollnau, D. Gamelin, S. Lüthi, H. Güdel, and M. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).

Hehlen, M. P.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16, 1244–1251 (2004).
[Crossref]

Hermle, M.

S. Fischer, H. Steinkemper, P. Löper, M. Hermle, and J. C. Goldschmidt, “Modeling upconversion of erbium doped microcrystals based on experimentally determined Einstein coefficients,” J. Appl. Phys. 111, 13109 (2012).
[Crossref]

S. Fischer, F. Hallermann, T. Eichelkraut, G. V. Plessen, W. Karl, D. Biner, H. Steinkemper, M. Hermle, and J. C. Goldschmidt, “Plasmon enhanced upconversion luminescence near gold nanoparticles - simulation and analysis of the interactions,” Opt. Express 20, 271–282 (2012).
[Crossref] [PubMed]

S. Fischer, J. Goldschmidt, P. Löper, G. Bauer, R. Brüggemann, K. Krämer, D. Biner, M. Hermle, and S. Glunz, “Enhancement of silicon solar cell efficiency by upconversion: optical and electrical characterization,” J. Appl. Phys. 108, 044912 (2010).
[Crossref]

Herter, B.

Hofmann, C. L. M.

C. L. M. Hofmann, B. Herter, S. Fischer, J. Gutmann, and J. C. Goldschmidt, “Upconversion in a Bragg structure: photonic effects of a modified local density of states and irradiance on luminescence and upconversion quantum yield,” Opt. Express 24, 14895–14914 (2016).
[Crossref] [PubMed]

C. L. M. Hofmann, S. Fischer, C. Reitz, B. S. Richards, and J. C. Goldschmidt, “Comprehensive analysis of photonic effects on up-conversion of β-NaYF4:Er3+ nanoparticles in an organic-inorganic hybrid 1D photonic crystal,” Proc. SPIE 9885, 99851(2016).

Hong, H.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

Hong, Y.

M. You, M. Lin, S. Wang, X. Wang, G. Zhang, Y. Hong, Y. Dong, G. Jin, and F. Xu, “Three-dimensional quick response code based on inkjet printing of upconversion fluorescent nanoparticles for drug anti-counterfeiting,” Nanoscale. 8, 10096–10104 (2016).
[Crossref] [PubMed]

Howard, I. A.

G. Gao, A. Turshatov, I. A. Howard, D. Busko, R. Joseph, D. Hudry, and B. S. Richards, “Up-conversion fluorescent labels for plastic recycling: a review,” Adv. Sustain. Syst.  1, 1600033 (2017).
[Crossref]

Hsu, C. C.

J. H. Lin, H. Y. Liou, C.-D. Wang, C.-Y. Tseng, C.-T. Lee, C.-C. Ting, H.-C. Kan, and C. C. Hsu, “Giant enhancement of upconversion fluorescence of NaYF4:Yb3+, Tm3+ nanocrystals with resonant waveguide grating substrate,” ACS Photonics 2, 530–536 (2015).
[Crossref]

Huang, M.

P. Huang, W. Zheng, S. Zhou, D. Tu, Z. Chen, H. Zhu, R. Li, E. Ma, M. Huang, and X. Chen, “Lanthanide-doped LiLuF4 upconversion nanoprobes for the detection of disease biomarkers,” Angewandte Chemie Int. Ed. 53, 1252–1257 (2014).
[Crossref]

Huang, P.

P. Huang, W. Zheng, S. Zhou, D. Tu, Z. Chen, H. Zhu, R. Li, E. Ma, M. Huang, and X. Chen, “Lanthanide-doped LiLuF4 upconversion nanoprobes for the detection of disease biomarkers,” Angewandte Chemie Int. Ed. 53, 1252–1257 (2014).
[Crossref]

Huang, W.

X. Huang, S. Han, W. Huang, and X. Liu, “Enhancing solar cell efficiency: the search for luminescent materials as spectral converters,” Chem. Soc. Rev. 42, 173–201 (2013).
[Crossref]

Huang, X.

X. Huang, S. Han, W. Huang, and X. Liu, “Enhancing solar cell efficiency: the search for luminescent materials as spectral converters,” Chem. Soc. Rev. 42, 173–201 (2013).
[Crossref]

Hudry, D.

G. Gao, A. Turshatov, I. A. Howard, D. Busko, R. Joseph, D. Hudry, and B. S. Richards, “Up-conversion fluorescent labels for plastic recycling: a review,” Adv. Sustain. Syst.  1, 1600033 (2017).
[Crossref]

Iakovlev, V.

A. Mereuta, A. Sirbu, A. Caliman, G. Suruceanu, V. Iakovlev, Z. Mickovic, and E. Kapon, “Fabrication and performance of 1.3-µm 10-Gb/s CWDM wafer-fused VCSELs grown by MOVPE,” J. Cryst. Growth 414, 210–214 (2015).
[Crossref]

Insley, H.

R. E. Thoma, H. Insley, and G. M. Hebert, “The sodium fluoride-tanthanide trifluoride systems,” Inorg. Chem. 5, 1222–1229 (1966).
[Crossref]

Ivaturi, A.

S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
[Crossref]

S. K. W. MacDougall, A. Ivaturi, J. Marques-Hueso, K. W. Krämer, and B. S. Richards, “Broadband photoluminescent quantum yield optimisation of Er3+-doped β-NaYF4 for upconversion in silicon solar cells,” Sol. Energy Mater. Sol. Cells 128, 18–26 (2014).
[Crossref]

Janz, S.

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

Jeon, M.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

Jeppesen, B. R.

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

Ji, D.

H. Qiao, Z. Cui, S. Yang, D. Ji, Y. Wang, Y. Yang, X. Han, Q. Fan, A. Qin, T. Wang, X.-P. He, W. Bu, and T. Tang, “Targeting osteocytes to attenuate early breast cancer bone metastasis by theranostic upconversion nanoparticles with responsive plumbagin release,” ACS Nano 11, 7259–7273 (2017).
[Crossref] [PubMed]

Jiang, Y.

Y. Yang, P. Zhou, W. Xu, S. Xu, Y. Jiang, X. Chen, and H. Song, “NaYF4:Yb3+, Tm3+ inverse opal photonic crystals and NaYF4:Yb3+, Tm3+/TiO2 composites: synthesis, highly improved upconversion properties and NIR photoelectric response,” J. Mater. Chem. C 4, 659–662 (2016).
[Crossref]

Jin, G.

M. You, M. Lin, S. Wang, X. Wang, G. Zhang, Y. Hong, Y. Dong, G. Jin, and F. Xu, “Three-dimensional quick response code based on inkjet printing of upconversion fluorescent nanoparticles for drug anti-counterfeiting,” Nanoscale. 8, 10096–10104 (2016).
[Crossref] [PubMed]

Joannopoulos, J. D.

Johannsen, S. R.

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

John, S.

S. John and K. Busch, “Photonic bandgap formation and tunability in certain self-organizing systems,” J. Light. Technol. 17, 1931 (1999).
[Crossref]

Johnson, C.

C. Johnson, P. Reece, and G. Conibeer, “Theoretical and experimental evaluation of silicon photonic structures for enhanced erbium up-conversion luminescence,” Sol. Energy Mater. Sol. Cells 112, 168–181 (2013).
[Crossref]

Johnson, C. M.

Johnson, S. G.

Joseph, R.

G. Gao, A. Turshatov, I. A. Howard, D. Busko, R. Joseph, D. Hudry, and B. S. Richards, “Up-conversion fluorescent labels for plastic recycling: a review,” Adv. Sustain. Syst.  1, 1600033 (2017).
[Crossref]

Julsgaard, B.

H. Lakhotiya, A. Nazir, S. P. Madsen, J. Christiansen, E. Eriksen, J. Vester-Petersen, S. R. Johannsen, B. R. Jeppesen, P. Balling, A. N. Larsen, and B. Julsgaard, “Plasmonically enhanced upconversion of 1500 nm light via trivalent Er in a TiO2 matrix,” Appl. Phys. Lett. 109, 263102 (2016).
[Crossref]

Kan, H.-C.

J. H. Lin, H. Y. Liou, C.-D. Wang, C.-Y. Tseng, C.-T. Lee, C.-C. Ting, H.-C. Kan, and C. C. Hsu, “Giant enhancement of upconversion fluorescence of NaYF4:Yb3+, Tm3+ nanocrystals with resonant waveguide grating substrate,” ACS Photonics 2, 530–536 (2015).
[Crossref]

Kapon, E.

A. Mereuta, A. Sirbu, A. Caliman, G. Suruceanu, V. Iakovlev, Z. Mickovic, and E. Kapon, “Fabrication and performance of 1.3-µm 10-Gb/s CWDM wafer-fused VCSELs grown by MOVPE,” J. Cryst. Growth 414, 210–214 (2015).
[Crossref]

Karl, W.

Kattelus, H.

R. L. Puurunen, J. Saarilahti, and H. Kattelus, “Implementing ALD layers in MEMS processing,” ECS Transactions 11, 3–14 (2007).
[Crossref]

Kim, C.

Y. Zhang, H. Hong, B. Sun, K. Carter, Y. Qin, W. Wei, D. Wang, M. Jeon, J. Geng, R. J. Nickles, G. Chen, P. N. Prasad, C. Kim, J. Xia, W. Cai, and J. F. Lovell, “Surfactant-stripped naphthalocyanines for multimodal tumor theranostics with upconversion guidance cream,” Nanoscale. 9, 3391–3398 (2017).
[Crossref] [PubMed]

Knoester, J.

M. De Dood, J. Knoester, A. Tip, and A. Polman, “Förster transfer and the local optical density of states in erbium-doped silica,” Phys. Rev. B 71, 115102 (2005).
[Crossref]

Koenderink, A. F.

H. Mertens, A. F. Koenderink, and A. Polman, “Plasmon-enhanced luminescence near noble-metal nanospheres: comparison of exact theory and an improved gersten and nitzan model,” Phys. Rev. B 76, 115123 (2007).
[Crossref]

Koryakova, O.

I. Leonidov, V. Zubkov, A. Tyutyunnik, N. Tarakina, L. Surat, O. Koryakova, and E. Vovkotrub, “Upconversion luminescence in Er3+/Yb3+ codoped Y2CaGe4O12,” J. Alloy. Compd. 509, 1339–1346 (2011).
[Crossref]

Kramer, K.

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

Krämer, K.

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S. Fischer, B. Fröhlich, H. Steinkemper, K. W. Krämer, and J. C. Goldschmidt, “Absolute upconversion quantum yield of β-NaYF4 doped with Er3+ and external quantum efficiency of upconverter solar cell devices under broad-band excitation considering spectral mismatch corrections,” Sol. Energy Mater. Sol. Cells 122, 197–207 (2014).
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C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic control of the Förster resonance energy transfer efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
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J. Liao, Z. Yang, J. Sun, S. Lai, B. Shao, J. Li, J. Qiu, Z. Song, and Y. Yang, “Preparation and upconversion emission modification of crystalline colloidal arrays and rare earth fluoride microcrystal composites,” Sci. Reports 5, 7636 (2015).
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Lüthi, S. R.

K. W. Krämer, D. Biner, G. Frei, H. U. Güdel, M. P. Hehlen, and S. R. Lüthi, “Hexagonal sodium yttrium fluoride based green and blue emitting upconversion phosphors,” Chem. Mater. 16, 1244–1251 (2004).
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M. Pollnau, D. Gamelin, S. Lüthi, H. Güdel, and M. Hehlen, “Power dependence of upconversion luminescence in lanthanide and transition-metal-ion systems,” Phys. Rev. B 61, 3337–3346 (2000).

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S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
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S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
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S. Fischer, A. Ivaturi, B. Fröhlich, M. Rüdiger, A. Richter, K. W. Krämer, B. S. Richards, and J. C. Goldschmidt, “Upconverter silicon solar cell devices for efficient utilization of sub-band-gap photons under concentrated solar radiation,” IEEE J. Photovolt. 4, 183–189 (2014).
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M. De Dood, J. Knoester, A. Tip, and A. Polman, “Förster transfer and the local optical density of states in erbium-doped silica,” Phys. Rev. B 71, 115102 (2005).
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E. Yeganegi, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Local density of optical states in the band gap of a finite one-dimensional photonic crystal,” Phys. Rev. B 89, 045123 (2014).
[Crossref]

J. Gutmann, H. Zappe, and J. C. Goldschmidt, “Quantitative modeling of fluorescent emission in photonic crystals,” Phys. Rev. B 88, 205118 (2013).
[Crossref]

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[Crossref]

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[Crossref]

K. W. Krämer, H. U. Güdel, and R. N. Schwartz, “Infrared-to-visible upconversion in LaCl3:1% Er3+: energy-level and line-strength calculations,” Phys. Rev. B 56, 13830 (1997).
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Phys. Rev. E (1)

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Phys. Rev. Lett. (1)

C. Blum, N. Zijlstra, A. Lagendijk, M. Wubs, A. P. Mosk, V. Subramaniam, and W. L. Vos, “Nanophotonic control of the Förster resonance energy transfer efficiency,” Phys. Rev. Lett. 109, 203601 (2012).
[Crossref]

Proc. SPIE (1)

C. L. M. Hofmann, S. Fischer, C. Reitz, B. S. Richards, and J. C. Goldschmidt, “Comprehensive analysis of photonic effects on up-conversion of β-NaYF4:Er3+ nanoparticles in an organic-inorganic hybrid 1D photonic crystal,” Proc. SPIE 9885, 99851(2016).

Sci. Reports (1)

J. Liao, Z. Yang, J. Sun, S. Lai, B. Shao, J. Li, J. Qiu, Z. Song, and Y. Yang, “Preparation and upconversion emission modification of crystalline colloidal arrays and rare earth fluoride microcrystal composites,” Sci. Reports 5, 7636 (2015).
[Crossref]

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Sol. Energy Mater. Sol. Cells (6)

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[Crossref]

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S. K. W. MacDougall, A. Ivaturi, J. Marques-Hueso, K. W. Krämer, and B. S. Richards, “Broadband photoluminescent quantum yield optimisation of Er3+-doped β-NaYF4 for upconversion in silicon solar cells,” Sol. Energy Mater. Sol. Cells 128, 18–26 (2014).
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S. Fischer, B. Fröhlich, H. Steinkemper, K. W. Krämer, and J. C. Goldschmidt, “Absolute upconversion quantum yield of β-NaYF4 doped with Er3+ and external quantum efficiency of upconverter solar cell devices under broad-band excitation considering spectral mismatch corrections,” Sol. Energy Mater. Sol. Cells 122, 197–207 (2014).
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S. Fischer, E. Favilla, M. Tonelli, and J. C. Goldschmidt, “Record efficient upconverter solar cell devices with optimized bifacial silicon solar cells and monocrystalline BaY2F8:30% Er3+ upconverter,” Sol. Energy Mater. Sol. Cells 136, 127–134 (2015).
[Crossref]

Other (2)

J. Gutmann, “Photonic luminescent solar concentrators,” Ph.D. thesis, Albert-Ludwigs University Freiburg, Technical Faculty (2014).

J. C. Goldschmidt, P. Loper, S. Fischer, S. Janz, M. Peters, S. W. Glunz, G. Willeke, E. Lifshitz, K. Kramer, and D. Biner, “Advanced upconverter systems with spectral and geometric concentration for high upconversion efficiencies,” in Conference on Optoelectronic and Microelectronic Materials and Devices (IEEE, 2008), pp. 307–311.

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Figures (9)

Fig. 1
Fig. 1 Structural sketches of the Bragg structure (a) and the reference structure (b). The Bragg structure consists of alternating quarter-wave layers, with respect to a design wavelength λD, of an active and a spacer material with refractive indices nlow and nhigh. The outermost layers have a reduced optical thickness of λD/(8n) and are assumed passive. The reference structure consists of a single, homogeneous layer containing the same amount of active material as the corresponding Bragg structure.
Fig. 2
Fig. 2 Schematic of the first seven energy levels in β-NaYF4:Er3+ included in the rate equation model, along with most important transitions for the UC process. The highest two energy levels are treated as one due to their close proximity. For the considered excitation of 1523 nm wavelength, the main UC emission lies at 984 nm.
Fig. 3
Fig. 3 (a) Average relative energy density ūrel across the active layers as a function of design wavelength λD for an exemplary Bragg structure with nhigh= 2.3 and #al = 25. The upper x -axis indicates the active layer thickness, dlow = λD/(4nlow). (b) Reflectance, R, for the example structure at the design wavelength yielding the maximum ūrel-value, λ D u max (marked by a black, shaded circle in panel a). (c) Spatial energy density distribution inside the structure for λ D = λ D u max. Additionally, the refractive index profile is shown. (d) Average relative energy density across the active layers as a function of nhigh and #al. The example structure considered in panels a, b and c is marked by a white, shaded circle.
Fig. 4
Fig. 4 Average relative energy density ūrel across the active layers of a Bragg structure as a function of #al and nhigh. ūrel is shown for four different production accuracies, simulated using a Monte Carlo method (see section 2.1). For each pixel, 50.000 separate calculations were carried out. The black contours indicate 99% (solid line) and 95% (dashed line) of the maximum. The panels show σ-values of 0.1 nm (a), 0.5 nm (b), 1.0 nm (c), and 5.0 nm (d).
Fig. 5
Fig. 5 Average relative energy density ūrel across the active layers of a Bragg structure as a function of #al for nhigh= 2.3. ūrel is shown for two different production accuracies, simulated using a Monte Carlo method (see section 2.1). For each data point, 50.000 separate calculations were carried out. The shadings indicate ± one standard deviation. The panels show σ-values of 0.5 nm (a), and 1.0 nm (b).
Fig. 6
Fig. 6 Illustration of the LDOS for two different high index materials, nhigh = 2.3 (a) and nhigh = 3.0 (b), along with the associated photonic band structure for k y = 0. The regions of nhigh and nlow (the active region) within the Wigner-Seitz unit cell are indicated on the top. The band gaps are marked by blue shadings. To avoid washing out features in the left panel, the scale is truncated at 2.0 even though the maximum value in the right panel is 2.5.
Fig. 7
Fig. 7 (a) LDOS ¯ rel for SPE31 (main UC emission) and SPE21 (loss emission), as well as their ratio for an example structure with nhigh= 2.3 as a function of the design wavelength λD. The shaded regions indicate where the respective transition falls within the first photonic bandgap (1PBG). (b) Ratio of LDOS ¯ rel for SPE31 and SPE21 as function of nhigh and λD. The solid lines indicate where the respective transition falls within the 1PBG.
Fig. 8
Fig. 8 UCQY as a function of incident irradiance I for exemplary families of Bragg structures with (a) nhigh fixed at 2.3 while #al is varied and (b) #al fixed at 10 while nhigh is varied. In both cases λ D = λ D u max. For the Bragg structures, higher UCQY values at much lower irradiances are achievable. The maximum for each design is marked with a large dot.
Fig. 9
Fig. 9 UCQY (left) and relative UCPL (right) as a function of nhigh and #al for λ D = λ D u max. The black contour lines indicate 99% (solid line) and 95% (dashed line) of the maximum in each plot. The rows show different irradiance scenarios of I = 30 W/m2, 1000 W/m2, and 10000 W/m2 (1 W/cm2).

Equations (21)

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u ( x ) = 1 2 ε ( x ) | E ( x ) | 2 .
u rel ( x ˜ ) = u brg ( x ˜ ) u ref ( x ˜ ) ,
u ¯ rel = u brg ( x ˜ ) d x ˜ u ref ( x ˜ ) d x ˜ .
d d + δ d ,
k = k a 2 π , ω = ω a n 2 π c 0 ,
LDOS ( x , ω ) = b k K b , ω | E b , k ( x ) | 2 2 π k y   with K b , ω = { k j   | ω ω b , k j   ω + Δ ω } ,
| E b , k ( x ) | 2 = 2 u b , k ( x ) ε ( x ) .
DOS 3 D ( ω ) = 4 π n 3 Δ k 2 ω 2 .
LDOS ref ( ω ) = ω ω + Δ ω DOS 3 D ( ω ) d ω = 4 π n 3 Δ ω Δ k 2 ( ω 2 + ω Δ ω + Δ ω 2 3 )
LDOS rel ( x , ω ) = LDOS brg ( x , ω ) LDOS ref ( ω ) .
LDOS ¯ rel ( ω ) = LDOS brg ( x ˜ , ω ) d x ˜ LDOS ref ( ω ) d x ˜ .
ω f i = n low + n high 4 n low n high λ D λ f i .
n ˙ = [ M GSA + M ESA + M STE + M SPE + M MPR ] n + v ETU ( n ) + v CR ( n ) ,
W f i = π 2 c 0 3 ω f i 3 g f g i u ( x , ω f i ) A f i u ( x , ω f i ) ,
M GSG M GSA u rel ( x , ω f i ) , M ESA M ESA u rel ( x , ω f i ) , M STE M STE u rel ( x , ω f i ) .
P f i = 2 π | f | H int | i | 2 LDOS ( x , ω f i ) L D O S ( x , ω f i ) ,
A f i A f i LDOS rel ( x , ω f i ) .
PL f i = A f i ( x ) N i ( x ) d x
UCPL = PL 31 .
UCQY = UCPL N 1 M GSA , 12 + N 2 M ESA , 24 + N 4 M ESA , 46 .
UCPL rel = UCPL brg UCPL ref .

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