Abstract

A realization of a reflectionless power splitter is proposed by use of a metamaterial junction. To design the junction, the electromagnetic wave transmission in multiple connected leads is investigated theoretically and numerically. A closed analytical form is derived for the scattering matrix of any geometry of the interconnected leads. We show that the use of a junction made of ϵ-near-zero (ENZ) material allows production of perfect transmission. This can be achieved by reducing the area of the ENZ junction (squeezing effect) and by tuning the widths of the output leads with respect to the input lead. It is also shown that the same effect is obtained without squeezed junction by using a match impedance zero index material (MIZIM junction).

© 2013 Optical Society of America

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References

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  1. J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
    [CrossRef]
  2. R. W. Ziolkowski, Phys. Rev. E 70, 046608 (2004).
    [CrossRef]
  3. A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).
  4. J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
    [CrossRef]
  5. M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
    [CrossRef]
  6. V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
    [CrossRef]
  7. Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
    [CrossRef]
  8. R. Fleury and A. Alu, “Extraordinary sound transmission through density-near-zero ultranarrow channels,” arXiv:1210.8056 (2012).

2012

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

2011

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

2010

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

2007

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).

2006

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

2004

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

2003

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Alu, A.

R. Fleury and A. Alu, “Extraordinary sound transmission through density-near-zero ultranarrow channels,” arXiv:1210.8056 (2012).

Alù, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).

Chan, C. T.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Chen, H.

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

Chen, L.

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Engheta, N.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Fleury, R.

R. Fleury and A. Alu, “Extraordinary sound transmission through density-near-zero ultranarrow channels,” arXiv:1210.8056 (2012).

Gao, L.

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

Halterman, K.

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Lai, Y.

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

Li, J.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Luo, J.

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

Nguyen, V. C.

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Salandrino, A.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).

Sheng, P.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Silveirinha, M.

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

Silveirinha, M. G.

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).

Xu, P.

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

Xu, Y.

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

Zhou, L.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

Ziolkowski, R. W.

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

Appl. Phys. Lett.

Y. Xu and H. Chen, Appl. Phys. Lett. 98, 113501 (2011).
[CrossRef]

Phys. Rev. B

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, Phys. Rev. B 75, 155410 (2007).

Phys. Rev. E

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

Phys. Rev. Lett.

J. Li, L. Zhou, C. T. Chan, and P. Sheng, Phys. Rev. Lett. 90, 083901 (2003).
[CrossRef]

M. Silveirinha and N. Engheta, Phys. Rev. Lett. 97, 157403 (2006).
[CrossRef]

V. C. Nguyen, L. Chen, and K. Halterman, Phys. Rev. Lett. 105, 233908 (2010).
[CrossRef]

Plasmonics

J. Luo, P. Xu, L. Gao, Y. Lai, and H. Chen, Plasmonics 7, 353 (2012).
[CrossRef]

Other

R. Fleury and A. Alu, “Extraordinary sound transmission through density-near-zero ultranarrow channels,” arXiv:1210.8056 (2012).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Geometry of the leads connected to a ZIM junction. (b) Geometry of the power splitter with N outlets.

Fig. 2.
Fig. 2.

Real part of the magnetic field H(x,y) for a three output power splitter. (a) The junction is made of a MIZIM with ϵ=μ=0.001 and a junction area Ah02. (b) Same geometry as in (a) with a nonmagnetic ENZ material; μ=1 and ϵ=0.001. (c) ENZ junction with a squeezed junction A0.1h02. (d) Removing the ENZ material in the squeezing geometry μ=ϵ=1. All fields have been calculated at frequency f=0.8GHz (kh0=1.6π).

Fig. 3.
Fig. 3.

(a) Reflection coefficient in energy R at the inlet lead as a function of the normalized frequency kh0/(2π) in the squeezed geometry for three different junctions. (b) Corresponding transmission coefficients |Tn| at the three output leads [as indicated in Fig. 2(c)]: n=1, solid line; n=2, in dashed–dotted lines; and n=3, dotted line.

Equations (5)

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

(1ϵH)+k2μH=0.
A1ϵHQ+Ak2μHQ+m=0NLm1ϵmnH(m)Q=0.
Snm=2Zmhmj=0NZjhjikμAδnm,
{r=1+ikμA/h0n=1Nhn/h01ikμA/h0+n=1Nhn/h0,tn=1r,
t=2n=1Nhn/h01ikμA/h0+n=1Nhn/h0,

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