Abstract

We demonstrate a wavelength-dependent spatial lateral beam shift of a reflective Gaussian beam on the surface of multilayer thin-film coatings. Numerical analysis of the behavior of a Gaussian-form light beam incident on the surface of the coatings is performed. The theoretical analysis is for a two-dimensional light sheet. The spatial lateral beam dispersion can be determined rigorously from the numerical wave field in the region of the incident medium. The coatings present a spatial dispersion effect much larger than in previous reports. The thin-film coatings can act not only as positive spatial dispersion devices but in a proper case, also as negative spatial dispersion devices. As such, the devices produce a wavelength-dependent negative lateral shift of the reflective beam.

© 2007 Optical Society of America

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  1. M. Gerken and D. A. B. Miller, "Multilayer thin-film structures with high spatial dispersion," Appl. Opt. 42, 1330-1345 (2003).
    [CrossRef] [PubMed]
  2. T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
    [CrossRef]
  3. K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
    [CrossRef]
  4. L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
    [CrossRef]
  5. T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
    [CrossRef]
  6. D. Felbacq, B. Guizal, and F. Zolla, "Ultra-refraction phenomena in Bragg mirrors," J. Opt. A, Pure Appl. Opt. 2, L30-L32 (2000).
    [CrossRef]
  7. H. Kosaka, T. Kwawashima, and A. Tomita, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
    [CrossRef]
  8. T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
    [CrossRef]
  9. H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
    [CrossRef]
  10. M. Gerken and D. A. B. Miller, "Wavelength demultiplexer using the spatial dispersion of multilayer thin-film structures," IEEE Photon. Technol. Lett. 15, 1097-1099 (2003).
    [CrossRef]
  11. N. Matuschek, F. X. Kärtner, and U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998).
    [CrossRef]
  12. B. Gralak, G. Tayeb, and S. Enoch, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
    [CrossRef]
  13. J. P. Barton, "Electromagnetic field for a focused light sheet incident on a plane surface," J. Opt. Soc. Am. A 22, 978-983 (2005).
    [CrossRef]
  14. J. Kong, B. Wu, and Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
    [CrossRef]
  15. J. Kong, B. Wu, and Y. Zhang, "Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability," Appl. Phys. Lett. 80, 2084-2086 (2002).
    [CrossRef]
  16. M. Gerken and D. A. B. Miller, "Multilayer thin-film stacks with steplike spatial beam shifting," J. Lightwave Technol. 22, 612-618 (2004).
    [CrossRef]
  17. D. Felbacq and A. Moreau, "Direct evidence of negative refraction at media with negative ϵ and μ," J. Opt. A, Pure Appl. Opt. 5, L9-L11 (2003).
    [CrossRef]
  18. A. Alú and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2571 (2003).
    [CrossRef]

2005

2004

2003

M. Gerken and D. A. B. Miller, "Wavelength demultiplexer using the spatial dispersion of multilayer thin-film structures," IEEE Photon. Technol. Lett. 15, 1097-1099 (2003).
[CrossRef]

M. Gerken and D. A. B. Miller, "Multilayer thin-film structures with high spatial dispersion," Appl. Opt. 42, 1330-1345 (2003).
[CrossRef] [PubMed]

D. Felbacq and A. Moreau, "Direct evidence of negative refraction at media with negative ϵ and μ," J. Opt. A, Pure Appl. Opt. 5, L9-L11 (2003).
[CrossRef]

A. Alú and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2571 (2003).
[CrossRef]

2002

J. Kong, B. Wu, and Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

J. Kong, B. Wu, and Y. Zhang, "Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability," Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

2000

D. Felbacq, B. Guizal, and F. Zolla, "Ultra-refraction phenomena in Bragg mirrors," J. Opt. A, Pure Appl. Opt. 2, L30-L32 (2000).
[CrossRef]

B. Gralak, G. Tayeb, and S. Enoch, "Anomalous refractive properties of photonic crystals," J. Opt. Soc. Am. A 17, 1012-1020 (2000).
[CrossRef]

1999

1998

N. Matuschek, F. X. Kärtner, and U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998).
[CrossRef]

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Alú, A.

A. Alú and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2571 (2003).
[CrossRef]

Baba, T.

T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
[CrossRef]

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

Barton, J. P.

Chung, K. B.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

Engheta, N.

A. Alú and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2571 (2003).
[CrossRef]

Enoch, S.

Felbacq, D.

D. Felbacq and A. Moreau, "Direct evidence of negative refraction at media with negative ϵ and μ," J. Opt. A, Pure Appl. Opt. 5, L9-L11 (2003).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, "Ultra-refraction phenomena in Bragg mirrors," J. Opt. A, Pure Appl. Opt. 2, L30-L32 (2000).
[CrossRef]

Gerken, M.

Gralak, B.

Guizal, B.

D. Felbacq, B. Guizal, and F. Zolla, "Ultra-refraction phenomena in Bragg mirrors," J. Opt. A, Pure Appl. Opt. 2, L30-L32 (2000).
[CrossRef]

Hong, S. W.

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

Karle, T.

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Kärtner, F. X.

N. Matuschek, F. X. Kärtner, and U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Keller, U.

N. Matuschek, F. X. Kärtner, and U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998).
[CrossRef]

Kong, J.

J. Kong, B. Wu, and Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

J. Kong, B. Wu, and Y. Zhang, "Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability," Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kwawashima, and A. Tomita, "Superprism phenomena in photonic crystals: toward microscale lightwave circuits," J. Lightwave Technol. 17, 2032-2038 (1999).
[CrossRef]

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Krauss, T. F.

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Kwawashima, T.

Matsumoto, T.

T. Matsumoto and T. Baba, "Photonic crystal k-vector superprism," J. Lightwave Technol. 22, 917-922 (2004).
[CrossRef]

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

Matuschek, N.

N. Matuschek, F. X. Kärtner, and U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998).
[CrossRef]

Mazilu, M.

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Miller, D. A. B.

Moreau, A.

D. Felbacq and A. Moreau, "Direct evidence of negative refraction at media with negative ϵ and μ," J. Opt. A, Pure Appl. Opt. 5, L9-L11 (2003).
[CrossRef]

Nakamura, M.

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

Notomi, M.

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Sato, T.

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tamamura, T.

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tayeb, G.

Tomita, A.

Wu, B.

J. Kong, B. Wu, and Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

J. Kong, B. Wu, and Y. Zhang, "Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability," Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

Wu, L. J.

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

Zhang, Y.

J. Kong, B. Wu, and Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

J. Kong, B. Wu, and Y. Zhang, "Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability," Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

Zolla, F.

D. Felbacq, B. Guizal, and F. Zolla, "Ultra-refraction phenomena in Bragg mirrors," J. Opt. A, Pure Appl. Opt. 2, L30-L32 (2000).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

T. Baba and T. Matsumoto, "Resolution of photonic crystal superprism," Appl. Phys. Lett. 81, 2325-2327 (2002).
[CrossRef]

K. B. Chung and S. W. Hong, "Wavelength demultiplexers based on the superprism phenomena in photonic crystals," Appl. Phys. Lett. 81, 1549-1551 (2002).
[CrossRef]

J. Kong, B. Wu, and Y. Zhang, "Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability," Appl. Phys. Lett. 80, 2084-2086 (2002).
[CrossRef]

IEEE J. Quantum Electron.

L. J. Wu, M. Mazilu, T. Karle, and T. F. Krauss, "Superprism phenomena in planar photonic crystals," IEEE J. Quantum Electron. 38, 915-918 (2002).
[CrossRef]

T. Baba and M. Nakamura, "Photonic crystal light deflection devices using the superprism effect," IEEE J. Quantum Electron. 38, 909-914 (2002).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

N. Matuschek, F. X. Kärtner, and U. Keller, "Theory of double-chirped mirrors," IEEE J. Sel. Top. Quantum Electron. 4, 197-208 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

M. Gerken and D. A. B. Miller, "Wavelength demultiplexer using the spatial dispersion of multilayer thin-film structures," IEEE Photon. Technol. Lett. 15, 1097-1099 (2003).
[CrossRef]

IEEE Trans. Antennas Propag.

A. Alú and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2571 (2003).
[CrossRef]

J. Lightwave Technol.

J. Opt. A, Pure Appl. Opt.

D. Felbacq and A. Moreau, "Direct evidence of negative refraction at media with negative ϵ and μ," J. Opt. A, Pure Appl. Opt. 5, L9-L11 (2003).
[CrossRef]

D. Felbacq, B. Guizal, and F. Zolla, "Ultra-refraction phenomena in Bragg mirrors," J. Opt. A, Pure Appl. Opt. 2, L30-L32 (2000).
[CrossRef]

J. Opt. Soc. Am. A

Microwave Opt. Technol. Lett.

J. Kong, B. Wu, and Y. Zhang, "A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability," Microwave Opt. Technol. Lett. 33, 136-139 (2002).
[CrossRef]

Phys. Rev. B

H. Kosaka, T. Kawashima, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Configuration of a Gaussian beam incident on a multilayer thin-film structure.

Fig. 2
Fig. 2

Time-averaged power density on the X Z plane in the incident medium when the wavelength is equal to (a) 747.57 nm and (b) 745 nm for a 30.263° incidence.

Fig. 3
Fig. 3

Comparison of time-averaged power density along X at Z = 0 for a 30.263° incidence of a Gaussian beam with different wavelengths on the multilayer structure.

Fig. 4
Fig. 4

Reflection GD and reflectance as a function of wavelength for 30.263° incidence.

Fig. 5
Fig. 5

Theoretically expected shift with wavelength calculated by our method with the different diameter beams and Gerken’s method.

Fig. 6
Fig. 6

Reflection GD and reflectance of this multilayer thin-film structure as a function of wavelength.

Fig. 7
Fig. 7

Time-averaged power density in the incident medium. (a) Wavelength = 747.565 nm , (b) wavelength = 747.3 nm .

Fig. 8
Fig. 8

Theoretically expected negative shift as a function of wavelength.

Fig. 9
Fig. 9

Comparison of the time-averaged power density along X at the first interface for a 50° incidence of a Gaussian beam on the multilayer structure.

Tables (1)

Tables Icon

Table 1 Composition of the 23-Layer Coating Discussed in Sections 3, 4

Equations (19)

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E i y = d k x exp [ i ( k x x + k z z ) ] Ψ ( k x ) ,
Ψ ( k x ) = g 2 π 1 2 exp { [ g 2 ( k x k i x ) 2 4 ] }
E l y = d k x [ A l exp ( i k l z z ) + B l exp ( i k l z z ) ] exp ( i k x x ) Ψ ( k x ) ,
H l x = d k x k l z ω μ l [ A l exp ( i k l z z ) B l exp ( i k l z z ) ] exp ( i k x x ) Ψ ( k x ) ,
H l z = d k x k x ω μ l [ A l exp ( i k l z z ) + B l exp ( i k l z z ) ] exp ( i k x x ) Ψ ( k x ) .
[ A l B l ] = M l ( l + 1 ) [ A l + 1 B l + 1 ] ,
M l ( l + 1 ) = 1 2 [ ( 1 + p l ( l + 1 ) ) exp [ i ( k l z k ( l + 1 ) z ) d l ] ( 1 p l ( l + 1 ) ) exp [ i ( k l z + k ( l + 1 ) z ) d l ] ( 1 p l ( l + 1 ) ) exp [ i ( k l z + k ( l + 1 ) z ) d l ] ( 1 + p l ( l + 1 ) ) exp [ i ( k l z k ( l + 1 ) z ) d l ] ] ,
p l ( l + 1 ) = ε l k ( l + 1 ) z ε ( l + 1 ) k l z .
[ A 0 1 ] = M 0 t [ 0 B t ] ,
M 0 t = M 01 M n ( n 1 ) M n t
S ¯ l = 1 2 { [ Re ( E l y H l z * ) ] 2 + [ Re ( E l y H l x * ) ] 2 } 1 2 ,
β 1 = β 0 + Δ β ,
β 2 = β 0 Δ β ,
E i y ( x , t ) = E 1 i y ( x , t ) + E 2 i y ( x , t ) = exp ( i ω t ) { exp [ i ( β 1 x ) ] + exp [ i ( β 2 x ) ] } = 2 cos ( Δ β x ) exp [ i ( β 0 x ω t ) ] .
δ 1 = δ 0 + δ 0 β Δ β ,
δ 2 = δ 0 δ 0 β Δ β ,
E r y ( x , t ) = E 1 r y ( x , t ) + E 2 r y ( x , t ) = exp ( i ω t ) { exp ( i δ 1 ) exp [ i ( β 1 x ) ] + exp ( i δ 2 ) exp [ i ( β 2 x ) ] } = 2 cos [ Δ β ( x + δ 0 β ) ] exp { i [ ( β 0 x + δ 0 ) ω t ] } .
Δ x = δ 0 β = δ 0 ω ω β = τ ν g x .
ν g x β c 2 ω i { d i [ n i 2 ( β c ω ) 2 ] 1 2 } i { n i 2 d i [ n i 2 ( β c ω ) 2 ] 1 2 } = n 0 c sin θ 0 i { d i [ n i 2 ( n 0 sin θ 0 ) 2 ] 1 2 } i { n i 2 d i [ n i 2 ( n 0 sin θ 0 ) 2 ] 1 2 } .

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