Abstract

In this paper, we study the possibility of using lifetime data to estimate the position and orientation of a fluorescent dipole source within a disordered medium. The vector Foldy-Lax equations are employed to calculate the interaction between the fluorescent source and the scatterers that are modeled as point-scatterers. The numerical experiments demonstrate that if good prior knowledge about the positions of the scatterers is available, the position and orientation of the dipole source can be retrieved from its lifetime data with precision. If there is uncertainty about the positions of the scatterers, the dipole source position can be estimated within the same level of uncertainty.

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  1. See K. Suhling, P.W. French, and D. Philipps, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci.4, 13–22 (2005) and references therein.
    [CrossRef]
  2. K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin.1, 693–701 (1970).
    [CrossRef]
  3. R.R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
    [CrossRef]
  4. J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
    [CrossRef] [PubMed]
  5. M. Frimmer, Y. Chen, and A.F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett.107, 123602 (2011).
    [CrossRef] [PubMed]
  6. E.A. Donley and T. Plakhotnik, “Luminescence lifetimes of single molecules in disordered media,” J. Chem. Phys.114, 9993–9997 (2001).
    [CrossRef]
  7. R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
    [CrossRef] [PubMed]
  8. L.S. Froufe-Pérez, R. Carminati, and J.J. Sáenz, “Fluorescence decay rate statistics of a single molecule in a disordered cluster of nanoparticles,” Phys. Rev. A76, 013835 (2007).
    [CrossRef]
  9. M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random media,” Phys. Rev. Lett.105, 013904 (2010).
    [CrossRef] [PubMed]
  10. V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
    [CrossRef]
  11. R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
    [CrossRef] [PubMed]
  12. A. Cazé, R. Pierrat, and R. Carminati, “Near-field interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium,” Phys. Rev. A82, 043823 (2010).
    [CrossRef]
  13. L.S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: The influence of the transition dipole orientation,” Phys. Stat. Sol. (a)205, 1258–1265 (2008).
    [CrossRef]
  14. G. Derveaux, G. Papanicolaou, and C. Tsogka, “Resolution and denoising in near-field imaging,” Inverse Problems22, 1437–1456 (2006).
    [CrossRef]
  15. A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Problems27, 015005 (2011).
    [CrossRef]
  16. N. Irishina, M. Moscoso, and R. Carminati, “Source location from fluorescence lifetime in disordered media,” Optics Letters, 37, 951–953 (2012).
    [CrossRef] [PubMed]
  17. J.M. Wylie and J.E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A30, 1185–1193 (1984).
    [CrossRef]
  18. L.L. Foldy, “The multiple scattering of waves,” Phys. Rev.67, 107–119 (1945).
    [CrossRef]
  19. M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys.23, 287–310 (1951).
    [CrossRef]
  20. S. Koc and W. C. Chew, “Calculation of acoustical scattering from a cluster of scatterers,” J. Acoust. Soc. Am.103, 721–734 (1998).
    [CrossRef]
  21. P. de Vries, D.V. van Coevordden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys.70, 447–466 (1998).
    [CrossRef]
  22. A. Ruszczynski, Nonlinear Optimization (Princeton University Press, Princeton, 2006).
  23. E. R. Hansen, Global Optimization using Interval Analysis (Marcel Dekker, New York, 1992).
  24. R. Horst, P. M. Pardalos, and N. V. Thoai, eds., Introduction to Global Optimization (Kluwer Academic, 2nd ed., 2000).

2012

N. Irishina, M. Moscoso, and R. Carminati, “Source location from fluorescence lifetime in disordered media,” Optics Letters, 37, 951–953 (2012).
[CrossRef] [PubMed]

2011

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

M. Frimmer, Y. Chen, and A.F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett.107, 123602 (2011).
[CrossRef] [PubMed]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Problems27, 015005 (2011).
[CrossRef]

2010

A. Cazé, R. Pierrat, and R. Carminati, “Near-field interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium,” Phys. Rev. A82, 043823 (2010).
[CrossRef]

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random media,” Phys. Rev. Lett.105, 013904 (2010).
[CrossRef] [PubMed]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

2009

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

2008

L.S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: The influence of the transition dipole orientation,” Phys. Stat. Sol. (a)205, 1258–1265 (2008).
[CrossRef]

2007

L.S. Froufe-Pérez, R. Carminati, and J.J. Sáenz, “Fluorescence decay rate statistics of a single molecule in a disordered cluster of nanoparticles,” Phys. Rev. A76, 013835 (2007).
[CrossRef]

2006

G. Derveaux, G. Papanicolaou, and C. Tsogka, “Resolution and denoising in near-field imaging,” Inverse Problems22, 1437–1456 (2006).
[CrossRef]

2005

See K. Suhling, P.W. French, and D. Philipps, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci.4, 13–22 (2005) and references therein.
[CrossRef]

2003

R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
[CrossRef] [PubMed]

2001

E.A. Donley and T. Plakhotnik, “Luminescence lifetimes of single molecules in disordered media,” J. Chem. Phys.114, 9993–9997 (2001).
[CrossRef]

1998

S. Koc and W. C. Chew, “Calculation of acoustical scattering from a cluster of scatterers,” J. Acoust. Soc. Am.103, 721–734 (1998).
[CrossRef]

P. de Vries, D.V. van Coevordden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys.70, 447–466 (1998).
[CrossRef]

1984

J.M. Wylie and J.E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A30, 1185–1193 (1984).
[CrossRef]

1978

R.R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

1970

K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin.1, 693–701 (1970).
[CrossRef]

1951

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys.23, 287–310 (1951).
[CrossRef]

1945

L.L. Foldy, “The multiple scattering of waves,” Phys. Rev.67, 107–119 (1945).
[CrossRef]

Birowosuto, M. D.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random media,” Phys. Rev. Lett.105, 013904 (2010).
[CrossRef] [PubMed]

Bondareff, P.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

Carminati, R.

N. Irishina, M. Moscoso, and R. Carminati, “Source location from fluorescence lifetime in disordered media,” Optics Letters, 37, 951–953 (2012).
[CrossRef] [PubMed]

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

A. Cazé, R. Pierrat, and R. Carminati, “Near-field interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium,” Phys. Rev. A82, 043823 (2010).
[CrossRef]

L.S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: The influence of the transition dipole orientation,” Phys. Stat. Sol. (a)205, 1258–1265 (2008).
[CrossRef]

L.S. Froufe-Pérez, R. Carminati, and J.J. Sáenz, “Fluorescence decay rate statistics of a single molecule in a disordered cluster of nanoparticles,” Phys. Rev. A76, 013835 (2007).
[CrossRef]

Castanié, E.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Cazé, A.

A. Cazé, R. Pierrat, and R. Carminati, “Near-field interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium,” Phys. Rev. A82, 043823 (2010).
[CrossRef]

Chai, A.

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Problems27, 015005 (2011).
[CrossRef]

Chance, R.R.

R.R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Chen, Y.

M. Frimmer, Y. Chen, and A.F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett.107, 123602 (2011).
[CrossRef] [PubMed]

Chew, W. C.

S. Koc and W. C. Chew, “Calculation of acoustical scattering from a cluster of scatterers,” J. Acoust. Soc. Am.103, 721–734 (1998).
[CrossRef]

Colas des Francs, G.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

de Vries, P.

P. de Vries, D.V. van Coevordden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys.70, 447–466 (1998).
[CrossRef]

De Wilde, Y.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Dereux, A.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

Derveaux, G.

G. Derveaux, G. Papanicolaou, and C. Tsogka, “Resolution and denoising in near-field imaging,” Inverse Problems22, 1437–1456 (2006).
[CrossRef]

Donley, E.A.

E.A. Donley and T. Plakhotnik, “Luminescence lifetimes of single molecules in disordered media,” J. Chem. Phys.114, 9993–9997 (2001).
[CrossRef]

Drexhage, K.

K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin.1, 693–701 (1970).
[CrossRef]

Foldy, L.L.

L.L. Foldy, “The multiple scattering of waves,” Phys. Rev.67, 107–119 (1945).
[CrossRef]

French, P.W.

See K. Suhling, P.W. French, and D. Philipps, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci.4, 13–22 (2005) and references therein.
[CrossRef]

Frimmer, M.

M. Frimmer, Y. Chen, and A.F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett.107, 123602 (2011).
[CrossRef] [PubMed]

Froufe-Pérez, L.S.

L.S. Froufe-Pérez and R. Carminati, “Lifetime fluctuations of a single emitter in a disordered nanoscopic system: The influence of the transition dipole orientation,” Phys. Stat. Sol. (a)205, 1258–1265 (2008).
[CrossRef]

L.S. Froufe-Pérez, R. Carminati, and J.J. Sáenz, “Fluorescence decay rate statistics of a single molecule in a disordered cluster of nanoparticles,” Phys. Rev. A76, 013835 (2007).
[CrossRef]

Habert, B.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

Hansen, E. R.

E. R. Hansen, Global Optimization using Interval Analysis (Marcel Dekker, New York, 1992).

Heinis, D.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

Hoogenboom, J.P.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

Irishina, N.

N. Irishina, M. Moscoso, and R. Carminati, “Source location from fluorescence lifetime in disordered media,” Optics Letters, 37, 951–953 (2012).
[CrossRef] [PubMed]

Koc, S.

S. Koc and W. C. Chew, “Calculation of acoustical scattering from a cluster of scatterers,” J. Acoust. Soc. Am.103, 721–734 (1998).
[CrossRef]

Koenderink, A.F.

M. Frimmer, Y. Chen, and A.F. Koenderink, “Scanning emitter lifetime imaging microscopy for spontaneous emission control,” Phys. Rev. Lett.107, 123602 (2011).
[CrossRef] [PubMed]

Krachmalnicoff, V.

V. Krachmalnicoff, E. Castanié, Y. De Wilde, and R. Carminati, “Fluctuations of the local density of states probe localized surface plasmons on disordered metal films,” Phys. Rev. Lett.105, 183901 (2010).
[CrossRef]

Kuipers, L.

R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
[CrossRef] [PubMed]

Lagendijk, A.

P. de Vries, D.V. van Coevordden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys.70, 447–466 (1998).
[CrossRef]

Lax, M.

M. Lax, “Multiple scattering of waves,” Rev. Mod. Phys.23, 287–310 (1951).
[CrossRef]

Legay, G.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

Moscoso, M.

N. Irishina, M. Moscoso, and R. Carminati, “Source location from fluorescence lifetime in disordered media,” Optics Letters, 37, 951–953 (2012).
[CrossRef] [PubMed]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Problems27, 015005 (2011).
[CrossRef]

Mosk, A. P.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random media,” Phys. Rev. Lett.105, 013904 (2010).
[CrossRef] [PubMed]

Papanicolaou, G.

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Problems27, 015005 (2011).
[CrossRef]

G. Derveaux, G. Papanicolaou, and C. Tsogka, “Resolution and denoising in near-field imaging,” Inverse Problems22, 1437–1456 (2006).
[CrossRef]

Philipps, D.

See K. Suhling, P.W. French, and D. Philipps, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci.4, 13–22 (2005) and references therein.
[CrossRef]

Pierrat, R.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

A. Cazé, R. Pierrat, and R. Carminati, “Near-field interactions and nonuniversality in speckle patterns produced by a point source in a disordered medium,” Phys. Rev. A82, 043823 (2010).
[CrossRef]

Plakhotnik, T.

E.A. Donley and T. Plakhotnik, “Luminescence lifetimes of single molecules in disordered media,” J. Chem. Phys.114, 9993–9997 (2001).
[CrossRef]

Prock, A.

R.R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Ruszczynski, A.

A. Ruszczynski, Nonlinear Optimization (Princeton University Press, Princeton, 2006).

Sáenz, J.J.

L.S. Froufe-Pérez, R. Carminati, and J.J. Sáenz, “Fluorescence decay rate statistics of a single molecule in a disordered cluster of nanoparticles,” Phys. Rev. A76, 013835 (2007).
[CrossRef]

Sanchez-Mosteiro, G.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

Sapienza, R.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

Silbey, R.

R.R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Sipe, J.E.

J.M. Wylie and J.E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A30, 1185–1193 (1984).
[CrossRef]

Skipetrov, S. E.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random media,” Phys. Rev. Lett.105, 013904 (2010).
[CrossRef] [PubMed]

Suhling, See K.

See K. Suhling, P.W. French, and D. Philipps, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci.4, 13–22 (2005) and references therein.
[CrossRef]

Tomczak, N.

R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
[CrossRef] [PubMed]

Tsogka, C.

G. Derveaux, G. Papanicolaou, and C. Tsogka, “Resolution and denoising in near-field imaging,” Inverse Problems22, 1437–1456 (2006).
[CrossRef]

Vallée, R.A.L.

R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
[CrossRef] [PubMed]

van Coevordden, D.V.

P. de Vries, D.V. van Coevordden, and A. Lagendijk, “Point scatterers for classical waves,” Rev. Mod. Phys.70, 447–466 (1998).
[CrossRef]

van Hulst, N. F.

R. Sapienza, P. Bondareff, R. Pierrat, B. Habert, R. Carminati, and N. F. van Hulst, “Long-Tail statistics of the Purcell factor in disordered media driven by near-field interactions,” Phys. Rev. Lett.106, 163902 (2011).
[CrossRef] [PubMed]

van Hulst, N.F.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
[CrossRef] [PubMed]

Vancso, G.J.

R.A.L. Vallée, N. Tomczak, L. Kuipers, G.J. Vancso, and N.F. van Hulst, “Single molecule lifetime fluctuations reveal segmental dynamics in polymers,”Phys. Rev. Lett.91, 038301 (2003).
[CrossRef] [PubMed]

Vos, W. L.

M. D. Birowosuto, S. E. Skipetrov, W. L. Vos, and A. P. Mosk, “Observation of spatial fluctuations of the local density of states in random media,” Phys. Rev. Lett.105, 013904 (2010).
[CrossRef] [PubMed]

Wylie, J.M.

J.M. Wylie and J.E. Sipe, “Quantum electrodynamics near an interface,” Phys. Rev. A30, 1185–1193 (1984).
[CrossRef]

Adv. Chem. Phys.

R.R. Chance, A. Prock, and R. Silbey, “Molecular fluorescence and energy transfer near interfaces,” Adv. Chem. Phys.37, 1–65 (1978).
[CrossRef]

Inverse Problems

G. Derveaux, G. Papanicolaou, and C. Tsogka, “Resolution and denoising in near-field imaging,” Inverse Problems22, 1437–1456 (2006).
[CrossRef]

A. Chai, M. Moscoso, and G. Papanicolaou, “Array imaging using intensity-only measurements,” Inverse Problems27, 015005 (2011).
[CrossRef]

J. Acoust. Soc. Am.

S. Koc and W. C. Chew, “Calculation of acoustical scattering from a cluster of scatterers,” J. Acoust. Soc. Am.103, 721–734 (1998).
[CrossRef]

J. Chem. Phys.

E.A. Donley and T. Plakhotnik, “Luminescence lifetimes of single molecules in disordered media,” J. Chem. Phys.114, 9993–9997 (2001).
[CrossRef]

J. Lumin.

K. Drexhage, “Influence of a dielectric interface on fluorescence decay time,” J. Lumin.1, 693–701 (1970).
[CrossRef]

Nano Lett.

J.P. Hoogenboom, G. Sanchez-Mosteiro, G. Colas des Francs, D. Heinis, G. Legay, A. Dereux, and N.F. van Hulst, “The single molecule probe: nanoscale vectorial mapping of photonic mode density in a metal nanocavity,” Nano Lett.9, 1189–1195 (2009).
[CrossRef] [PubMed]

Optics Letters

N. Irishina, M. Moscoso, and R. Carminati, “Source location from fluorescence lifetime in disordered media,” Optics Letters, 37, 951–953 (2012).
[CrossRef] [PubMed]

Photochem. Photobiol. Sci.

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Figures (8)

Fig. 1
Fig. 1

Top row: Different fluorophore positions and orientations (r0, θ) within the same realization of a disordered medium. The fluorophore’s orientations are indicated with an arrow. Bottom row: Frequency dependence of the decay rates Γ(r0, θ, ω) of the fluorophores shown in the top row.

Fig. 2
Fig. 2

Reconstructions of the source positions in the same disordered medium as in Fig. 1. We consider a 1 × 1μm2 DOI (black square), and noiseless data from 3 frequencies. The scattering strength regimes are from left to right : (kls)−1 = 0.18 − 0.23, (kls)−1 = 0.09 − 0.11, and (kls)−1 = 0.01 − 0.02. The dipole source positions are shown by stars. The orientations are θ0 = 0 rad (top row) and θ0 = π/2 rad (bottom rows). The estimates of the source positions are shown by circles, and their orientations by arrows.

Fig. 3
Fig. 3

Same as Fig. 2 but with data corrupted by noise. The noise levels (from left to right) are: 1%, 3% and 8%. The estimates of the source positions are shown by circles, and their orientations by arrows. The scattering strength regime is (kls)−1 = 0.18 − 0.23.

Fig. 4
Fig. 4

Reconstructions of the positions and orientations of dipole sources for different realizations of a disordered medium. We use data from 3 frequencies corrupted with 1% of additive noise. The scattering strength regime is (kls)−1 = 0.18 − 0.23.

Fig. 5
Fig. 5

Reconstructions of the same dipole sources as in Fig. 4, but with an uncertainty on the scatterers positions of ±λ/8. We use data from 3 frequencies corrupted by 1% of noise. The scattering strength is (kls)−1 = 0.18 − 0.23.

Fig. 6
Fig. 6

Same as Fig. 5, but using data from 9 frequencies. There is a ±λ/8 uncertainty on the scatterers positions and the data is corrupted with 1% of additive noise.

Fig. 7
Fig. 7

Left panel: Reconstructions of a dipole source (shown by star) using 3 (circle) and 9 (diamond) frequencies. Middle and right panels: Residuals along the x and y axes, respectively. Dashed-dotted lines correspond to 3 frequencies, solid lines correspond to 9 frequencies. The data is corrupted with 1% of gaussian noise, and there is an uncertainty of ±λ/8 on the scatterers positions. The scattering strength is (kls)−1 = 0.18 − 0.23.

Fig. 8
Fig. 8

Reconstructions of the same dipole sources as in Figs. 4 and 5, but using data from 9 frequencies (with 1% noise) and an uncertain on the scatterers positions of ±λ/4.

Equations (7)

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Γ ( r 0 , u , ω ) Γ 0 Γ 0 = 2 μ 0 ω 2 | p eg | 2 h ¯ Γ 0 Im [ u G s ( r 0 , r 0 , ω ) u ] .
E s ( r ; r 0 , u , ω ) = k 2 j G 0 ( r , r j , ω ) α ( ω ) E exc ( r j ; r 0 , u , ω ) ,
E exc ( r j ; r 0 , u , ω ) = E inc ( r j ; r 0 , u , ω ) + k 2 m j M G 0 ( r j , r m , ω ) α ( ω ) E exc ( r m ; r 0 , u , ω ) .
G 0 ( r r , ω ) = i 4 ( I r ^ r ^ ) H 0 ( 1 ) ( k 0 R ) + i 4 { ( 2 r ^ r ^ I ) H 1 ( 1 ) ( k 0 R ) k 0 R } .
α ( ω ) = ( 4 γ / k 2 ) 1 ω ω 0 + i γ / 2 ,
Γ ( r 0 , θ , ω i ) = d ( ω i ) i = 1 , 2 , .
R ( r 0 , θ ) = i = 1 N ω | Γ ( r 0 , θ , ω i ) d ( ω i ) | 2 ,

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