Abstract

Based on both analytical dipole model analyses and numerical simulations, we propose a concept of coherent perfect nanoabsorbers (CPNAs) for divergent beams. This concept makes use of the properties of a slab with negative refraction and small losses. The proposed CPNA device would allow focusing radiation in nanoscale regions, and hence could be applied in optical nanodevices for such diverse purposes as reading the results of quantum computation which is based on single photon qubits.

© 2012 OSA

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References

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  1. Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
    [CrossRef] [PubMed]
  2. W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
    [CrossRef] [PubMed]
  3. S. Dutta-Gupta, O. J. F. Martin, S. D. Gupta, and G. S. Agarwal, “Controllable coherent perfect absorption in a composite film,” Opt. Express 20(2), 1330–1336 (2012).
    [CrossRef] [PubMed]
  4. S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
    [CrossRef]
  5. S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83(5), 055804 (2011).
    [CrossRef]
  6. V. Shalaev and W. Cai, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
  7. Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
    [CrossRef]
  8. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  9. J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
    [CrossRef]
  10. V. Klimov, J. Baudon, and M. Ducloy, “Comparative focusing of Maxwell and Dirac fields by negative refraction half-space,” Europhys. Lett. 94(2), 20006 (2011).
    [CrossRef]
  11. V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89(5), 229–232 (2009).
    [CrossRef]
  12. W. C. Chew, Waves and Fields in Inhomogenous Media (IEEE Press Series on Electromagnetic Wave Theory, 1995).
  13. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–681 (1946).
  14. V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31(7), 569–586 (2001).
    [CrossRef]

2012 (1)

2011 (4)

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

V. Klimov, J. Baudon, and M. Ducloy, “Comparative focusing of Maxwell and Dirac fields by negative refraction half-space,” Europhys. Lett. 94(2), 20006 (2011).
[CrossRef]

S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83(5), 055804 (2011).
[CrossRef]

2010 (3)

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[CrossRef]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

2009 (1)

V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89(5), 229–232 (2009).
[CrossRef]

2001 (1)

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31(7), 569–586 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–681 (1946).

Agarwal, G. S.

Baudon, J.

V. Klimov, J. Baudon, and M. Ducloy, “Comparative focusing of Maxwell and Dirac fields by negative refraction half-space,” Europhys. Lett. 94(2), 20006 (2011).
[CrossRef]

Boltasseva, A.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Cao, H.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Chan, C. T.

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

Chong, Y. D.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Dong, J.-W.

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

Ducloy, M.

V. Klimov, J. Baudon, and M. Ducloy, “Comparative focusing of Maxwell and Dirac fields by negative refraction half-space,” Europhys. Lett. 94(2), 20006 (2011).
[CrossRef]

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31(7), 569–586 (2001).
[CrossRef]

Dutta-Gupta, S.

Ge, L.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Gupta, S. D.

Jacob, Z.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Kim, J.-Y.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Klimov, V.

V. Klimov, J. Baudon, and M. Ducloy, “Comparative focusing of Maxwell and Dirac fields by negative refraction half-space,” Europhys. Lett. 94(2), 20006 (2011).
[CrossRef]

V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89(5), 229–232 (2009).
[CrossRef]

Klimov, V. V.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31(7), 569–586 (2001).
[CrossRef]

Lai, Y.

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

Letokhov, V. S.

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31(7), 569–586 (2001).
[CrossRef]

Longhi, S.

S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83(5), 055804 (2011).
[CrossRef]

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[CrossRef]

Martin, O. J. F.

Naik, G. V.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Narimanov, E. E.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Noh, H.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–681 (1946).

Shalaev, V. M.

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Stone, A. D.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

Wan, W.

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Wang, H.-Z.

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

Zheng, H.-H.

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

Appl. Phys. B (1)

Z. Jacob, J.-Y. Kim, G. V. Naik, A. Boltasseva, E. E. Narimanov, and V. M. Shalaev, “Engineering photonic density of states using metamaterials,” Appl. Phys. B 100(1), 215–218 (2010).
[CrossRef]

Europhys. Lett. (1)

V. Klimov, J. Baudon, and M. Ducloy, “Comparative focusing of Maxwell and Dirac fields by negative refraction half-space,” Europhys. Lett. 94(2), 20006 (2011).
[CrossRef]

JETP Lett. (1)

V. Klimov, “Novel approach to a perfect lens,” JETP Lett. 89(5), 229–232 (2009).
[CrossRef]

Opt. Express (1)

Phys. Rev. (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681–681 (1946).

Phys. Rev. A (2)

S. Longhi, “PT-symmetric laser absorber,” Phys. Rev. A 82(3), 031801 (2010).
[CrossRef]

S. Longhi, “Coherent perfect absorption in a homogeneously broadened two-level medium,” Phys. Rev. A 83(5), 055804 (2011).
[CrossRef]

Phys. Rev. B (1)

J.-W. Dong, H.-H. Zheng, Y. Lai, H.-Z. Wang, and C. T. Chan, “Metamaterial slab as a lens, a cloak or an intermediate,” Phys. Rev. B 83(11), 115124 (2011).
[CrossRef]

Phys. Rev. Lett. (2)

Y. D. Chong, L. Ge, H. Cao, and A. D. Stone, “Coherent perfect absorbers: time-reversed lasers,” Phys. Rev. Lett. 105(5), 053901 (2010).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Quantum Electron. (1)

V. V. Klimov, M. Ducloy, and V. S. Letokhov, “Spontaneous emission of an atom in the presence of nanobodies,” Quantum Electron. 31(7), 569–586 (2001).
[CrossRef]

Science (1)

W. Wan, Y. D. Chong, L. Ge, H. Noh, A. D. Stone, and H. Cao, “Time-reversed lasing and interferometric control of absorption,” Science 331(6019), 889–892 (2011).
[CrossRef] [PubMed]

Other (2)

W. C. Chew, Waves and Fields in Inhomogenous Media (IEEE Press Series on Electromagnetic Wave Theory, 1995).

V. Shalaev and W. Cai, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of a plane wave coherent perfect absorber.

Fig. 2
Fig. 2

Schematic diagram of a coherent perfect nanoabsorber for the divergent beams. All the energy from the 2 point sources is absorbed by the nanoparticle (red circle), placed inside the negative refraction slab.

Fig. 3
Fig. 3

Energy flows from the left and right sources to the sink in the middle of the slab without losses with ε2 = −1, µ2 = −1 (light blue rectangle) placed in vacuum with ε1 = 1, µ1 = 1 [according to solution (2)] .

Fig. 4
Fig. 4

The power radiated by the source (Wrad, dashed line) and the power absorbed by the nanoparticle (Wabs, solid line) relative to the power radiated by one source (W0) in free space, as a function of the relative amplitude of the dipole moment of the nanoparticle ξ= p abs / p 0 . It is assumed that the slab is made of a metamaterial with ε2 = -1 + i0.03, µ2 = -1 + i0.03, λ = 3 μm, d = 500 nm, l = 250 nm.

Fig. 5
Fig. 5

Plot of energy flow lines in a coherent perfect nanoabsorber, illustrating that almost all streamlines outgoing from the sources (denoted by the red stars) to the slab are converged to the nanoparticle (denoted by the blue circle). Parameters of the simulation are ε2 = −1 + 0.03i, µ2 = -1 + 0.03i, d = 500 nm for the slab; εc = 1.3 + 0.4i, µc = 1, R = 50 nm for the cylinder; and λ = 3 μm, l = 250 nm for the sources.

Fig. 6
Fig. 6

Electric field intensity distribution (logarithmic scale) in the coherent perfect nanoabsorber. Simulation parameters are d = 500nm, l = 250nm, λ = 3μm, ε 2 = μ 2 =1+0.03i , R = 50nm, εc = 1 + 0.21i, μc = 1.

Fig. 7
Fig. 7

Power absorbed by the nanocylinder (Wabs) normalized to the power of one source in free space (W0) as a function of both the real and imaginary parts of the cylinder permittivity. Other parameters are the same as in Fig. 6

Fig. 8
Fig. 8

Radiated and absorbed powers normalized to the power of one source in free space as a function of the imaginary part of the cylinder permittivity (a) and also of the dipole moment of the cylinder ξ= p cyl / p 0 (b). Simulation parameters are R = 50 nm, d = 500 nm, l = 250 nm, λ = 3μm, ε 2 = μ 2 =1+0.03i , εc = 1 + i ε , μc = 1.

Fig. 9
Fig. 9

Schematic diagram of a single-side coherent perfect nanoabsorber. A perfect electric conductor (PEC) [perfect magnetic conductor (PMC)] mirror should be used for the electrically [ magnetically] polarized source.

Equations (22)

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j 1,x =iω p 0 δ( x )δ( z+l ), j 2,x =iω p 0 δ( x )δ( z+l2d ); j 3,x =+iω p 0 δ( x )δ( zl )
H 0,y = k 0 π p 0 z H 0 ( 1 ) ( k 0 x 2 + ( z+l ) 2 ),z<0 H 0,y = k 0 π p 0 z H 0 ( 1 ) ( k 0 x 2 + ( zl ) 2 ),0<z<d H 0,y = k 0 π p 0 z H 0 ( 1 ) ( k 0 x 2 + ( z2d+l ) 2 ),z>d
rotH=i k 0 εE.
W abs =+ ω 2 Im p 0 E ( r abs )= ω 2 k 0 2 | p 0 | 2 π 2 .
W rad = ω 2 Im p 0 E ( r 1 )= ω 2 k 0 2 | p 0 | 2 π 2 .
j 1,x =iω p 0 δ( x )δ( z+l ), j 2,x =iω p 0 δ( x )δ( z+l2d ); j 3,x =iω p abs δ( x )δ( zl )
W abs =+ ω 2 Im p abs E ( r abs ).
E( r abs )= E ( abs ),0 ( r abs )+ E ( abs ),R ( r abs )+ E ( 1 ) ( r abs )+ E ( 2 ) ( r abs )
E( r )= G ( r, r 0 ) p 0 ; G ( r, r 0 )= G ( 0 ) ( r, r 0 )+ G ( R ) ( r, r 0 ),
W abs = ω 2 Im p abs * ( G xx ( abs )0 p abs + G xx ( abs )R p abs + G xx ( 1 ) p 0 + G xx ( 2 ) p 0 )
H 0,y = k 0 π p abs z H 0 ( 1 ) ( k 2 x 2 + ( zl ) 2 ) E 0,x = iπ p abs ε 2 2 z 2 H 0 ( 1 ) ( k 2 x 2 + ( zl ) 2 )= G xx (abs)0 p abs
G xx ( abs )0 = iπ ε 2 2 z 2 H 0 ( 1 ) ( k 2 | zl | ) | z=l
H 0 ( 1 ) ( k 2 x 2 + ( z ) 2 )= 1 π + dq e iqx e i k z,2 | z | k z,2 .
G xx,abs 0 = i ε 2 1/R 1/R dq k 0 2 ε 2 μ 2 q 2
j x =iω p 0 δ( x )δ( z+l )
H 0,y =i k 0 p 0 + dqsign( z+l ) e iqx+i k z,1 | z+l | .
H y =i k 0 p + dq e iqx [ sign( z+l ) e i k z,1 | z+l | +A( q ) e i k z,1 z ] ,z<0 H y =i k 0 p + dq e iqx [ B( q ) e i k z,2 z +C( q ) e i k z,2 z ] ,0<z<d H y =i k 0 p + dq e iqx [ D( q ) e i k z,1 z ] ,z>d
G xx ( 1 ) ( r abs )= G xx ( 2 ) ( r abs )=2i dq k z,1 k z,2 e id/2( k z,1 + k z,2 ) ( k z,1 ε 2 + k z,2 )+( k z,1 ε 2 k z,2 ) e i k z,2 d ( k z,1 ε 2 k z,2 ) 2 e 2i k 2z d ( k z,1 ε 2 + k z,2 ) 2 G xx abs( R ) ( r abs )=2i dq k z,2 ε 2 e i k zz,2 d ( k z,1 2 ε 2 2 k z,2 2 )+ ( k z,1 ε 2 k z,22 ) 2 e i k z,2 d ( k z,1 ε 2 k z,2 ) 2 e 2i k z,2 d ( k z,1 ε 2 + k z,2 ) 2 .
W rad = ω 2 Im p 0 E ( r 1 )
E( r 1 )=( E ( 1 )0 ( r 1 )+ E ( 1 )R ( r 1 )+ E ( 2 ) ( r 1 )+ E ( abs ) ( r 1 ) )
W rad =+ ω 2 Im p 0 ( G xx ( 1 )0 ( r 1 ) p 0 + G xx ( 1 )R ( r 1 ) p 0 + G xx ( 2 ) ( r 1 ) p 0 + G xx ( absorber ) ( r 1 ) p abs )
j 1,x =iω p 0 δ( x )δ( z+l ), j 2,x =iω p 0 δ( x )δ( z+l2d )

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