Abstract

The possibility of controlling the spectral position of the zero group-velocity dispersion point of a negative-index material can be exploited by varying the ratio between the electric and the magnetic plasma frequency to obtain dispersion-free propagation in spectral regions otherwise inaccessible using conventional positive-index materials. Our predictions are confirmed by pulse propagation simulations where all the orders of the complex dispersion of the material are taken into account.

© 2005 Optical Society of America

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References

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  1. V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  2. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000), and references therein.
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
    [CrossRef] [PubMed]
  4. C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
    [CrossRef]
  5. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
    [CrossRef] [PubMed]
  6. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
    [CrossRef]
  7. G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
    [CrossRef]
  8. R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004), and references therein.
    [CrossRef]
  9. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  10. The electric field was calculated as follows: E(z,t)=???+?E(0,?)exp(?i?t)[exp(i?z?c)+r(?)exp(?i?z?c)]d? for z<0 and E(z,t)=???+?t(?)E(0,?)exp{i[k?(?)z?i?t]}d? for z>0, where r(?) and t(?) are, respectively, the reflection and transmission coefficient of the air–NIM interface, E(0,?) is the spectral amplitude of the incident pulse, and k?(?) is the complex wave vector of the NIM.
  11. P. St. J. Russell, Science 299, 358 (2003), and references therein.
    [CrossRef] [PubMed]
  12. R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, Opt. Express 12, 1700 (2004), and references therein.
    [CrossRef] [PubMed]

2005 (1)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

2004 (4)

R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004), and references therein.
[CrossRef]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef]

R. Zhang, J. Teipel, X. Zhang, D. Nau, and H. Giessen, Opt. Express 12, 1700 (2004), and references therein.
[CrossRef] [PubMed]

2003 (2)

P. St. J. Russell, Science 299, 358 (2003), and references therein.
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000), and references therein.
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

Bloemer, M. J.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef]

D’Aguanno, G.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Giessen, H.

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Koltenbah, K. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Mattiucci, N.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef]

Nau, D.

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Pendry, J. B.

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000), and references therein.
[CrossRef] [PubMed]

Russell, P. St. J.

P. St. J. Russell, Science 299, 358 (2003), and references therein.
[CrossRef] [PubMed]

Scalora, M.

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Teipel, J.

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Zhang, R.

Zhang, X.

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Ziolkowski, R. W.

R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004), and references therein.
[CrossRef]

Opt. Express (1)

Phys. Rev. E (2)

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. E 71, 046603 (2005).
[CrossRef]

R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004), and references therein.
[CrossRef]

Phys. Rev. Lett. (3)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000), and references therein.
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, K. E. C. Koltenbah, and M. Tanielian, Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

G. D’Aguanno, N. Mattiucci, M. Scalora, and M. J. Bloemer, Phys. Rev. Lett. 93, 213902 (2004).
[CrossRef]

Science (3)

P. St. J. Russell, Science 299, 358 (2003), and references therein.
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

The electric field was calculated as follows: E(z,t)=???+?E(0,?)exp(?i?t)[exp(i?z?c)+r(?)exp(?i?z?c)]d? for z<0 and E(z,t)=???+?t(?)E(0,?)exp{i[k?(?)z?i?t]}d? for z>0, where r(?) and t(?) are, respectively, the reflection and transmission coefficient of the air–NIM interface, E(0,?) is the spectral amplitude of the incident pulse, and k?(?) is the complex wave vector of the NIM.

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Figures (3)

Fig. 1
Fig. 1

(a) Refractive index n versus ω ω pe for different values of the ratio ω pm ω pe : ω pm ω pe = 0.8 (thin solid curve), ω pm ω pe = 1 (dashed curve), ω pm ω pe = 1.2 (thick solid curve). (b) GVD parameter β 2 versus ω ω pe for different values of the ratio ω pm ω pe . Note that the β 2 curves are plotted only in the region around their respective zero GVD points. The arrows indicate the position of the zero GVD points. β 2 is calculated in units of λ pe ( 4 π 2 c 2 ) , where λ pe = 2 π c ω pe .

Fig. 2
Fig. 2

Pulse propagation at different times of an ultrashort, Gaussian, unchirped pulse in a NIM at the zero GVD point for ω pm ω pe = 0.8 . (a) At t 0 = 0 , the pulse is in air directed toward the NIM, and z = 0 is the air–NIM interface. The peak of the square modulus of the incident electric field is normalized to 1. Its FWHM is 5 λ pe . (b) At t 1 = 600 λ pe ( 2 π c ) , the incident pulse has entered the NIM giving rise to a reflected and a transmitted pulse. The FWHM of the transmitted field is 2 λ pe . (c) At t 2 = 1400 λ pe ( 2 π c ) , the transmitted pulse (thick solid curve) has propagated for approximately 50 λ pe in the NIM and its FWHM is 2.67 λ pe . For comparison, the same pulse (dashed curve) at the same time after it has propagated in the same NIM but with the dispersion approximated up to the second order and with the dispersion approximated up to the third order (open circles).

Fig. 3
Fig. 3

Pulse propagation in a NIM at the zero GVD point for ω pm ω pe = 1.2 . (a) Incident pulse at t 0 = 0 . (b) Transmitted and reflected fields at t 1 = 600 λ pe ( 2 π c ) . (c) Transmitted pulse (thick solid curve) at t 2 = 1400 λ pe ( 2 π c ) . For comparison, we also plot the transmitted pulse calculated in Fig. 2(c) (thin solid curve in the present figure) but with its amplitude renormalized to the amplitude of the pulse calculated in this case.

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