Abstract

Dielectric optical coatings are designed at resonances to reach total absorption, whatever the low value of the imaginary index. The corresponding field enhancement within the stack can be arbitrarily increased with the optimization procedure. Applications concern optical sensors and threshold lasers.

© 2011 Optical Society of America

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References

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  1. H. Iwase, D. Englund, and J. Vučković, “Analysis of the Purcell effect in photonic and plasmonic crystals with losses,” Opt. Express 18, 16546–16560 (2010).
    [CrossRef] [PubMed]
  2. Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect in hyperbolic metamaterials,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QWB2.
  3. J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).
  4. A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).
  5. F. A. Korolev, A. V. Tikhonravov, and A. Y. Klementieva, “Studies on multilayer interference filter with taking into account small absorption in layers,” Vestnik MGU, Series Physics–Astronomy 18, 15–19 (1977) (in Russian).
  6. Y. A. Pirogov and A. V. Tikhonravov, “Interference absorption of wave energy in asymmetric multilayer structures,” Izvestia VUZov, Radioelectronika 21, 15–20 (1978) (in Russian).
  7. Y. A. Pirogov, and A. V. Tikhonravov, “Multilayer interference absorber with arbitrary thickness of working layer,” Vestnik MGU, Series Physics–Astronomy 19, 42–48 (1978) (in Russian).
  8. A. V. Tikhonravov and Y. A. Pirogov, “Multilayer interference absorber with taking into account of losses in non-working layers,” J. Technicheskoi Fiziki 50, 673–679 (1980) (in Russian).
  9. H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
    [CrossRef]
  10. C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” Techniques de l’Ingénieur (2011), Sec. 4, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.
  11. C. Amra and S. Maure, “Mutual coherence and conical pattern of sources optimally excited within multilayer optics,” J. Opt. Soc. Am. A 14, 3114–3124 (1997).
    [CrossRef]
  12. C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” , Techniques de l’Ingénieur (2011), Sec. 5, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

2010 (1)

1997 (1)

1980 (1)

A. V. Tikhonravov and Y. A. Pirogov, “Multilayer interference absorber with taking into account of losses in non-working layers,” J. Technicheskoi Fiziki 50, 673–679 (1980) (in Russian).

1978 (2)

Y. A. Pirogov and A. V. Tikhonravov, “Interference absorption of wave energy in asymmetric multilayer structures,” Izvestia VUZov, Radioelectronika 21, 15–20 (1978) (in Russian).

Y. A. Pirogov, and A. V. Tikhonravov, “Multilayer interference absorber with arbitrary thickness of working layer,” Vestnik MGU, Series Physics–Astronomy 19, 42–48 (1978) (in Russian).

1977 (1)

F. A. Korolev, A. V. Tikhonravov, and A. Y. Klementieva, “Studies on multilayer interference filter with taking into account small absorption in layers,” Vestnik MGU, Series Physics–Astronomy 18, 15–19 (1977) (in Russian).

1976 (1)

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

Amra, C.

C. Amra and S. Maure, “Mutual coherence and conical pattern of sources optimally excited within multilayer optics,” J. Opt. Soc. Am. A 14, 3114–3124 (1997).
[CrossRef]

C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” Techniques de l’Ingénieur (2011), Sec. 4, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” , Techniques de l’Ingénieur (2011), Sec. 5, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

Baskakov, A. N.

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

Benisty, H.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Berger, V.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Englund, D.

Gerard, J.-M.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Grèzes-Besset, C.

C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” , Techniques de l’Ingénieur (2011), Sec. 5, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” Techniques de l’Ingénieur (2011), Sec. 4, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

Iwase, H.

Jacob, Z.

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect in hyperbolic metamaterials,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QWB2.

Klementieva, A. Y.

F. A. Korolev, A. V. Tikhonravov, and A. Y. Klementieva, “Studies on multilayer interference filter with taking into account small absorption in layers,” Vestnik MGU, Series Physics–Astronomy 18, 15–19 (1977) (in Russian).

Kolesnikov, V. S.

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

Korolev, F. A.

F. A. Korolev, A. V. Tikhonravov, and A. Y. Klementieva, “Studies on multilayer interference filter with taking into account small absorption in layers,” Vestnik MGU, Series Physics–Astronomy 18, 15–19 (1977) (in Russian).

Kozar, A. V.

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

Lourtioz, J.-M.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
[CrossRef]

Maure, S.

Maystre, D.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Narimanov, E. E.

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect in hyperbolic metamaterials,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QWB2.

Pagnoux, D.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Pirogov, Y. A.

A. V. Tikhonravov and Y. A. Pirogov, “Multilayer interference absorber with taking into account of losses in non-working layers,” J. Technicheskoi Fiziki 50, 673–679 (1980) (in Russian).

Y. A. Pirogov, and A. V. Tikhonravov, “Multilayer interference absorber with arbitrary thickness of working layer,” Vestnik MGU, Series Physics–Astronomy 19, 42–48 (1978) (in Russian).

Y. A. Pirogov and A. V. Tikhonravov, “Interference absorption of wave energy in asymmetric multilayer structures,” Izvestia VUZov, Radioelectronika 21, 15–20 (1978) (in Russian).

Pirogov, Yu. A.

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

Smolyaninov, I.

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect in hyperbolic metamaterials,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QWB2.

Tchelnokov, A.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

Tikhonravov, A. V.

A. V. Tikhonravov and Y. A. Pirogov, “Multilayer interference absorber with taking into account of losses in non-working layers,” J. Technicheskoi Fiziki 50, 673–679 (1980) (in Russian).

Y. A. Pirogov, and A. V. Tikhonravov, “Multilayer interference absorber with arbitrary thickness of working layer,” Vestnik MGU, Series Physics–Astronomy 19, 42–48 (1978) (in Russian).

Y. A. Pirogov and A. V. Tikhonravov, “Interference absorption of wave energy in asymmetric multilayer structures,” Izvestia VUZov, Radioelectronika 21, 15–20 (1978) (in Russian).

F. A. Korolev, A. V. Tikhonravov, and A. Y. Klementieva, “Studies on multilayer interference filter with taking into account small absorption in layers,” Vestnik MGU, Series Physics–Astronomy 18, 15–19 (1977) (in Russian).

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

Vuckovic, J.

Izvestia VUZov, Radioelectronika (1)

Y. A. Pirogov and A. V. Tikhonravov, “Interference absorption of wave energy in asymmetric multilayer structures,” Izvestia VUZov, Radioelectronika 21, 15–20 (1978) (in Russian).

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

J. Tech. Fis. Lett. (1)

A. N. Baskakov, A. V. Kozar, V. S. Kolesnikov, Yu. A. Pirogov, and A. V. Tikhonravov, “Resonanse effect of full interfence absorption in thin layers with small extinction coefficient,” J. Tech. Fis. Lett. 2, 91–93 (1976) (in Russian).

J. Technicheskoi Fiziki (1)

A. V. Tikhonravov and Y. A. Pirogov, “Multilayer interference absorber with taking into account of losses in non-working layers,” J. Technicheskoi Fiziki 50, 673–679 (1980) (in Russian).

Opt. Express (1)

Vestnik MGU, Series Physics–Astronomy (2)

F. A. Korolev, A. V. Tikhonravov, and A. Y. Klementieva, “Studies on multilayer interference filter with taking into account small absorption in layers,” Vestnik MGU, Series Physics–Astronomy 18, 15–19 (1977) (in Russian).

Y. A. Pirogov, and A. V. Tikhonravov, “Multilayer interference absorber with arbitrary thickness of working layer,” Vestnik MGU, Series Physics–Astronomy 19, 42–48 (1978) (in Russian).

Other (5)

H. A. Macleod, Thin-Film Optical Filters, 3rd ed. (Institute of Physics, 2001).
[CrossRef]

C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” Techniques de l’Ingénieur (2011), Sec. 4, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

Z. Jacob, I. Smolyaninov, and E. E. Narimanov, “Broadband Purcell effect in hyperbolic metamaterials,” in Quantum Electronics and Laser Science Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2010), paper QWB2.

J.-M. Lourtioz, H. Benisty, V. Berger, D. Pagnoux, J.-M. Gerard, D. Maystre, and A. Tchelnokov, Photonic Crystals: Towards Nanoscale Photonic Devices, 2nd ed. (Springer, 2008).

C. Amra and C. Grèzes-Besset, “Couches minces optiques et filtrage interférentiel,” , Techniques de l’Ingénieur (2011), Sec. 5, http://www.techniques-ingenieur.fr/base-documentaire/sciences-fondamentales-th8/physique-chimie-ti053/couches-minces-optiques-et-filtrage-interferentiel-af3348/.

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Figures (11)

Fig. 1
Fig. 1

Definition of an optical coating.

Fig. 2
Fig. 2

(a) Case where the incident medium is air ( n 0 index). Total reflection cannot occur because the incident spatial frequency is limited by n 0 . The abscissa is the normalized spatial frequency: ν * = ( λ / 2 π ) σ . (b) Case of a high-index superstrate ( n 0 index). Total reflection occurs at spatial pulsations greater than k s . Resonances may occur in the range [ n s , max ( n i ) ]. The abscissa is the normalized spatial frequency: ν * = ( λ / 2 π ) σ .

Fig. 3
Fig. 3

(a) S-polarized resonances within a six-layer stack of design glass/H/5L/2H/6L/2H/6L/air, with Ta 2 O 5 and S i O 2 as low- and high-index materials ( n H = 2.3 and n L = 1.49 ). The design wavelength is 633 nm , while the illumination wavelength is 514.5 nm . The imaginary indices are put to 10 4 in the high index material. At each resonance, the field enhancement is responsible for high absorption and, consequently, for a loss of reflection. (b) Field enhancement within the design of Fig. 3a. The overintensity exceeds four decades.

Fig. 4
Fig. 4

Stack deposited on a high-index prism (the superstrate). The substrate is air ( n s index).

Fig. 5
Fig. 5

Location of admittance Y versus the total stack thickness. The initial value ň s lies on the imaginary axis, while the final value n 0 cos θ 0 is real.

Fig. 6
Fig. 6

Σ is a surface within the stack that is limited by altitudes z 1 and z 2 .

Fig. 7
Fig. 7

Absorption versus incidence angle for three different stacks of 9, 11, and 19 layers (see text). The stacks are calculated with an imaginary index of 10 3 , 1.5 × 10 4 , and 7 × 10 7 , respectively.

Fig. 8
Fig. 8

Absorption versus imaginary index for three different stacks of 9, 11, and 19 layers (see text). The stacks are calculated with an imaginary index of 10 3 , 1.5 × 10 4 , and 7 × 10 7 , respectively. Total absorption is reached for the right value of the imaginary index.

Fig. 9
Fig. 9

Overintensity for the nine-layer stack ( n = 10 3 ). The design structure is glass / ( HL ) 4 / 2.122 H / air .

Fig. 10
Fig. 10

Overintensity for the 11 layer stack ( n = 1.5 × 10 4 ). The design structure is glass / ( HL ) 4 / 4.122 H / air .

Fig. 11
Fig. 11

Overintensity for the 19 layer stack ( n = 7 × 10 7 ). The design structure is glass / ( HL ) 4 / 4.122 H / air .

Equations (23)

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σ = k 0 sin θ 0 = 2 π ν < k 0
α i ( σ ) = ( k i 2 σ 2 ) 0.5 ,
α i ( σ ) = k i cos θ I .
σ < k i σ = k i sin θ I .
ň i ( σ ) = n i α i ( σ ) / k i for TE polarization and ň i ( σ ) = n i k i / α i ( σ ) for TM polarization,
ň i = n i cos θ i for TE and ň i = n i / cos θ i for TM .
δ i ( σ ) = α i ( σ ) e i .
δ i ( σ ) = ( 2 π / λ ) n i e i cos θ I .
Y p = ň p + 1 = ň s ,
Y i 1 = ( j ň i sin δ i + Y i cos δ i ) / ( cos δ i j Y i sin δ i / ň i )
R = ( ň 0 Y 0 ) / ( ň 0 + Y 0 ) .
Φ T = Real ( ň S ) | E s + | 2 ,
σ < k s α s is real ň S is real Φ T 0 ,
σ > k s α s is purely imaginary ň S is purely imaginary Φ T = 0.
A ( σ ) = ( ω / 2 ) z ε | E 2 ( σ , z ) | d z .
R = ( ň 0 Y 0 ) / ( ň 0 + Y 0 ) = 1 A = 0 Y 0 ( ň s ) = ň 0 ,
0 < Y p 1 < Y p 3 < < Y 0 .
e i = e i ( σ m , n H , n B ) ,
Φ ( Σ ) = Real ( Y 2 ) | E 2 ( z 2 ) | + Real ( Y 1 ) | E 2 ( z 1 ) | ,
Φ ( Σ ) = Real ( Y 2 ) | E 2 ( z 2 ) | .
A ( n ) = 1 = Real ( ň 0 ) | E 2 ( z 0 , n ) | ,
lim n 0 [ Real ( ň 0 ) | E 2 ( z 0 , n ) | ] = 1.
A / ε ( σ , 0 ) = ( ω / 2 ) z | E 2 ( σ , 0 , z ) | d z .

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