Abstract

Light emission is defined by its distribution in energy, momentum, and polarization. Here, we demonstrate a method that resolves these distributions by means of wide-angle energy-momentum spectroscopy. Specifically, we image the back focal plane of a microscope objective through a Wollaston prism to obtain polarized Fourier-space momentum distributions, and disperse these two-dimensional radiation patterns through an imaging spectrograph without an entrance slit. The resulting measurements represent a convolution of individual radiation patterns at adjacent wavelengths, which can be readily deconvolved using any well-defined basis for light emission. As an illustrative example, we use this technique with the multipole basis to quantify the intrinsic emission rates for electric and magnetic dipole transitions in europium-doped yttrium oxide (Eu3+:Y2O3) and chromium-doped magnesium oxide (Cr3+:MgO). Once extracted, these rates allow us to reconstruct the full, polarized, two-dimensional radiation patterns at each wavelength.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Lieb, J. M. Zavislan, and L. Novotny, J. Opt. Soc. Am. B 21, 1210 (2004).
    [CrossRef]
  2. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
    [CrossRef]
  3. T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
    [CrossRef]
  4. R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
    [CrossRef]
  5. W. Zhu, D. Wang, and K. B. Crozier, Nano Lett. 12, 6235 (2012).
    [CrossRef]
  6. D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
    [CrossRef]
  7. A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
    [CrossRef]
  8. I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
    [CrossRef]
  9. S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).
  10. J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
    [CrossRef]
  11. S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
    [CrossRef]
  12. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  13. CVX Research, Inc., “CVX: Matlab software for disciplined convex programming, version 2.0,” http://cvxr.com/cvx (2012).
  14. M. Grant and S. Boyd, in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds., Vol. 371 of Lecture Notes in Control and Information Sciences (Springer, 2008), pp. 95–110.
  15. S. B. Mende, E. S. Claflin, R. L. Rairden, and G. R. Swenson, Appl. Opt. 32, 7095 (1993).
    [CrossRef]
  16. M. Harwit, Hadamard Transform Optics (Academic, 2012).
  17. J. D. Perreault, Opt. Lett. 38, 3874 (2013).
    [CrossRef]

2014 (2)

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

2013 (5)

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
[CrossRef]

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

J. D. Perreault, Opt. Lett. 38, 3874 (2013).
[CrossRef]

2012 (3)

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
[CrossRef]

R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
[CrossRef]

W. Zhu, D. Wang, and K. B. Crozier, Nano Lett. 12, 6235 (2012).
[CrossRef]

2010 (1)

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

2004 (1)

1993 (1)

Best, M. D.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

Boyd, S.

M. Grant and S. Boyd, in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds., Vol. 371 of Lecture Notes in Control and Information Sciences (Springer, 2008), pp. 95–110.

Buckley, S.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Camden, J. P.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

Castro-López, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

Cichos, F.

R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
[CrossRef]

Claflin, E. S.

Crozier, K. B.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

W. Zhu, D. Wang, and K. B. Crozier, Nano Lett. 12, 6235 (2012).
[CrossRef]

Curto, A. G.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

Ghimire, N. J.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Grant, M.

M. Grant and S. Boyd, in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds., Vol. 371 of Lecture Notes in Control and Information Sciences (Springer, 2008), pp. 95–110.

Hancu, I. M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

Harwit, M.

M. Harwit, Hadamard Transform Optics (Academic, 2012).

Hatami, F.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

He, K.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Heerklotz, L.

R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
[CrossRef]

Jones, A. M.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Karaveli, S.

S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
[CrossRef]

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
[CrossRef]

Kortenbruck, N.

R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
[CrossRef]

Kreuzer, M. P.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

Kuttge, M.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

Kymissis, I.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Lieb, M. A.

Majumdar, A.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Mandrus, D. G.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Mende, S. B.

Novotny, L.

M. A. Lieb, J. M. Zavislan, and L. Novotny, J. Opt. Soc. Am. B 21, 1210 (2004).
[CrossRef]

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Perreault, J. D.

Quidant, R.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

Rairden, R. L.

Ross, J. S.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Schiros, T.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Schuller, J. A.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Shan, J.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Swenson, G. R.

Taminiau, T. H.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

van Hulst, N. F.

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

Volpe, G.

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

Vuckovic, J.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Wagner, R.

R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
[CrossRef]

Wang, D.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

W. Zhu, D. Wang, and K. B. Crozier, Nano Lett. 12, 6235 (2012).
[CrossRef]

Wang, S.

S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
[CrossRef]

Wu, S.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Xiao, G.

S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
[CrossRef]

Xu, X.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Yan, J.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Yang, S.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Yao, W.

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

Zavislan, J. M.

Zhu, W.

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

W. Zhu, D. Wang, and K. B. Crozier, Nano Lett. 12, 6235 (2012).
[CrossRef]

Zia, R.

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
[CrossRef]

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
[CrossRef]

2D Materials (1)

S. Wu, S. Buckley, A. M. Jones, J. S. Ross, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, F. Hatami, J. Vučković, A. Majumdar, and X. Xu, 2D Materials 1, 011001 (2014).

ACS Nano (1)

S. Karaveli, S. Wang, G. Xiao, and R. Zia, ACS Nano 7, 7165 (2013).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Wagner, L. Heerklotz, N. Kortenbruck, and F. Cichos, Appl. Phys. Lett. 101, 081904 (2012).
[CrossRef]

J. Opt. Soc. Am. B (1)

Nano Lett. (3)

I. M. Hancu, A. G. Curto, M. Castro-López, M. Kuttge, and N. F. van Hulst, Nano Lett. 14, 166 (2014).
[CrossRef]

W. Zhu, D. Wang, and K. B. Crozier, Nano Lett. 12, 6235 (2012).
[CrossRef]

D. Wang, W. Zhu, M. D. Best, J. P. Camden, and K. B. Crozier, Nano Lett. 13, 2194 (2013).
[CrossRef]

Nat. Commun. (2)

A. G. Curto, T. H. Taminiau, G. Volpe, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Nat. Commun. 4, 1750 (2013).
[CrossRef]

T. H. Taminiau, S. Karaveli, N. F. van Hulst, and R. Zia, Nat. Commun. 3, 979 (2012).
[CrossRef]

Nat. Nanotechnol. (1)

J. A. Schuller, S. Karaveli, T. Schiros, K. He, S. Yang, I. Kymissis, J. Shan, and R. Zia, Nat. Nanotechnol. 8, 271 (2013).
[CrossRef]

Opt. Lett. (1)

Science (1)

A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, Science 329, 930 (2010).
[CrossRef]

Other (4)

M. Harwit, Hadamard Transform Optics (Academic, 2012).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

CVX Research, Inc., “CVX: Matlab software for disciplined convex programming, version 2.0,” http://cvxr.com/cvx (2012).

M. Grant and S. Boyd, in Recent Advances in Learning and Control, V. Blondel, S. Boyd, and H. Kimura, eds., Vol. 371 of Lecture Notes in Control and Information Sciences (Springer, 2008), pp. 95–110.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

Wide-angle energy-momentum spectroscopy method. Momentum-space emission pattern (a) is separated by a Wollaston prism into orthogonal polarizations (b) and dispersed by a grating into convolved energy-momentum spectra (c).

Fig. 2.
Fig. 2.

Convolution model and decomposition method (shown for simplicity with single polarization). (a) Convolved wide-angle energy-momentum data can be decomposed into a superposition of radiation patterns, where x coefficients describe the contribution of basis functions (e.g., ED and MD) at each wavelength, λi. (b) Schematic representation of mathematical model used for decomposition process highlighting how basis functions and image data are vectorized in A and b to form a matrix equation.

Fig. 3.
Fig. 3.

Wide-angle energy-momentum spectroscopy of Eu3+:Y2O3. (a) Experimental wide-angle data and (b) corresponding theoretical fits obtained using Eq. (1). (c) Experimental polarized 2D radiation patterns using 590±10 and 620±15nm bandpass filters and (d) corresponding 2D radiation patterns extracted from wide-angle fits. White arrows denote polarization.

Fig. 4.
Fig. 4.

Comparison of narrow-slit and wide-angle energy-momentum spectroscopy for (a) Eu3+:Y2O3 and (b) Cr3+:MgO. Extracted ED (red) and MD (blue) normalized emission rates from measurements both with (line) and without (shaded area) a 10μm entrance slit. The inset of (b) highlights the inverted symmetry of ED and MD emission at the ZPL near 700 nm.

Equations (1)

Equations on this page are rendered with MathJax. Learn more.

minimizeAxb+η2+αΔx2subject tox0.

Metrics