Abstract

The negative-index property of double-negative metamaterials and the effective matching property of single-negative metamaterials are used to achieve ultrathin laser cavities. Open and partially closed cavities are considered. Resonant enhancement of the output fields is demonstrated in both cases with a variety of metamaterial combinations.

© 2006 Optical Society of America

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References

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  1. N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. , Special Issue on Metamaterial Structures, Phenomena, and Applications 53, 1535-1556 (2005).
    [CrossRef]
  2. N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002).
    [CrossRef]
  3. A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: anomalous tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
    [CrossRef]
  4. R. W. Ziolkowski and A. Kipple, "Application of double negative metamaterials to increase the power radiated by electrically small antennas," IEEE Trans. Antennas Propag. 51, 2626-2640 (2003).
    [CrossRef]
  5. R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
    [CrossRef]
  6. R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans. Antennas Propag. (to be published).

2005

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. , Special Issue on Metamaterial Structures, Phenomena, and Applications 53, 1535-1556 (2005).
[CrossRef]

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

2003

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: anomalous tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

R. W. Ziolkowski and A. Kipple, "Application of double negative metamaterials to increase the power radiated by electrically small antennas," IEEE Trans. Antennas Propag. 51, 2626-2640 (2003).
[CrossRef]

2002

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: anomalous tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

Engheta, N.

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. , Special Issue on Metamaterial Structures, Phenomena, and Applications 53, 1535-1556 (2005).
[CrossRef]

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: anomalous tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002).
[CrossRef]

Erentok, A.

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans. Antennas Propag. (to be published).

Kipple, A.

R. W. Ziolkowski and A. Kipple, "Application of double negative metamaterials to increase the power radiated by electrically small antennas," IEEE Trans. Antennas Propag. 51, 2626-2640 (2003).
[CrossRef]

Kipple, A. D.

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. , Special Issue on Metamaterial Structures, Phenomena, and Applications 53, 1535-1556 (2005).
[CrossRef]

R. W. Ziolkowski and A. Kipple, "Application of double negative metamaterials to increase the power radiated by electrically small antennas," IEEE Trans. Antennas Propag. 51, 2626-2640 (2003).
[CrossRef]

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans. Antennas Propag. (to be published).

IEEE Antennas Wireless Propag. Lett.

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002).
[CrossRef]

IEEE Trans. Antennas Propag.

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: anomalous tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

R. W. Ziolkowski and A. Kipple, "Application of double negative metamaterials to increase the power radiated by electrically small antennas," IEEE Trans. Antennas Propag. 51, 2626-2640 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. , Special Issue on Metamaterial Structures, Phenomena, and Applications 53, 1535-1556 (2005).
[CrossRef]

Phys. Rev. E

R. W. Ziolkowski and A. D. Kipple, "Reciprocity between the effects of resonant scattering and enhanced radiated power by electrically small antennas in the presence of nested metamaterial shells," Phys. Rev. E 72, 036602 (2005).
[CrossRef]

Other

R. W. Ziolkowski and A. Erentok, "Metamaterial-based efficient electrically small antennas," IEEE Trans. Antennas Propag. (to be published).

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Figures (17)

Fig. 1
Fig. 1

(Color online) Two-open-slab configuration.

Fig. 2
Fig. 2

(Color online) PEC-backed, open-cavity configuration.

Fig. 3
Fig. 3

(Color online) PMC-backed, open-cavity configuration.

Fig. 4
Fig. 4

(Color online) Closed-cavity configuration.

Fig. 5
Fig. 5

(Color online) Magnitude of the electric field produced by high-impedance ENG–MNG and DPS–DNG slab pairs with a relative wave impedance value η r = 100 in the frequency region of the source.

Fig. 6
Fig. 6

(Color online) Magnitudes of the electric field produced by the high-impedance ENG–MNG and DPS–DNG slab pairs shown in Fig. 5 over an expanded frequency scale.

Fig. 7
Fig. 7

(Color online) Magnitudes of the electric field produced by ENG–MNG slab pairs for different relative wave impedance values.

Fig. 8
Fig. 8

(Color online) Magnitudes of the output electric field produced by an ENG–MNG slab pair for different total thicknesses.

Fig. 9
Fig. 9

(Color online) Magnitudes of the output electric field produced by the high-relative-impedance ENG–MNG and DPS–ENG slab pairs for the PEC-backed, partially reflecting mirror configuration.

Fig. 10
Fig. 10

(Color online) Magnitudes of the output electric field produced by the unity-relative-impedance ENG–MNG and DPS–ENG slab pairs for the PEC-backed, partially reflecting mirror configuration.

Fig. 11
Fig. 11

(Color online) Magnitudes of the output electric field produced by the low-relative-impedance ENG–MNG and DPS–ENG slab pairs for the PEC-backed, partially reflecting mirror configuration.

Fig. 12
Fig. 12

(Color online) Magnitudes of the output electric field produced by several PEC-backed, partially reflecting mirror, high-relative-impedance-slab DPS–DNG pairs when the mirror reflection coefficient is varied.

Fig. 13
Fig. 13

(Color online) Magnitudes of the output electric field produced by several PEC-backed, partially reflecting mirror, unity-relative-impedance-slab DPS–DNG pair cases when the mirror reflection coefficient is varied.

Fig. 14
Fig. 14

(Color online) Magnitudes of the output electric field produced by several PEC-backed, partially reflecting mirror, high-relative-impedance-slab DPS–DNG pairs when the total cavity thickness is varied.

Fig. 15
Fig. 15

(Color online) Magnitudes of the output electric field produced by several PEC-backed, partially reflecting mirror, high-relative-impedance-slab DNG–DPS pairs when the permittivity in the DPS slab and its thickness are varied.

Fig. 16
Fig. 16

(Color online) Magnitudes of the output electric field produced by the PEC-backed, partially reflecting mirror, zero-DPS pair and DPS-zero pairs.

Fig. 17
Fig. 17

(Color online) Magnitudes of the output electric field produced by the PEC-backed, partially reflecting mirror, zero-DPS pair when the total thickness of the cavity is varied.

Equations (50)

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J s ( x , y , z ) = I 0 δ ( z ) x ̂ .
E ω x , 3 ( x , y , z ) = A e j k 3 ( z d 2 ) ,
H ω y , 3 ( x , y , z ) = A η 3 e j k 3 ( z d 2 ) ;
E ω x , 2 ( x , y , z ) = B e j k 2 z + C e + j k 2 z ,
H ω y , 2 ( x , y , z ) = B η 2 e j k 2 z C η 2 e + j k 2 z ;
E ω x , 1 ( x , y , z ) = D e + j k 1 z + E e j k 1 z ,
H ω y , 1 ( x , y , z ) = D η 1 e + j k 1 z + E η 1 e j k 1 z ;
E ω x , 4 ( x , y , z ) = F e + j k 4 ( z + d 1 ) ,
H ω y , 4 ( x , y , z ) = F η 4 e + j k 4 ( z + d 1 ) .
A = η 1 η 2 I 0 Z total ( T 32 e j k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 + R 41 e j 2 k 1 d 1 1 R 41 e j 2 k 1 d 1 ) ,
B = η 1 η 2 I 0 Z total ( 1 1 R 32 e j 2 k 2 d 2 ) ( 1 + R 41 e j 2 k 1 d 1 1 R 41 e j 2 k 1 d 1 ) ,
C = η 1 η 2 I 0 Z total ( R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 + R 41 e j 2 k 1 d 1 1 R 41 e j 2 k 1 d 1 ) ,
D = η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 1 R 41 e j 2 k 1 d 1 ) ,
E = η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( R 41 e j 2 k 1 d 1 1 R 41 e j 2 k 1 d 1 ) ,
F = η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( T 41 e j k 1 d 1 1 R 41 e j 2 k 1 d 1 ) ,
Z total = η 2 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 + η 1 1 + R 41 e j 2 k 1 d 1 1 R 41 e j 2 k 1 d 1 = Z i n , 32 + Z i n , 41 .
R 41 = η 4 η 1 η 4 + η 1 ,
T 41 = 2 η 4 η 4 + η 1 ;
R 32 = η 3 η 2 η 3 + η 2 ,
T 32 = 2 η 3 η 3 + η 2 .
A = η 1 η 2 I 0 Z total ( T 32 e j k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) ,
B = η 1 η 2 I 0 Z total ( 1 1 R 32 e j 2 k 2 d 2 ) ( 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) ,
C = η 1 η 2 I 0 Z total ( R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) ,
D = η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 1 + e j 2 k 1 d 1 ) ,
E = + η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) ,
Z total = η 2 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 + η 1 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 = Z i n , 32 + Z i n , P E C .
Z total = η 2 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 + η 1 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 = η 1 + R 32 e j ψ 1 R 32 e j ψ η 1 e j ψ 1 + e j ψ ,
Z total = η 2 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 + η 1 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 = η 1 + R 32 e + j ψ 1 R 32 e + j ψ + η 1 e j ψ 1 + e j ψ = η 1 + R 32 e + j ψ 1 R 32 e + j ψ η 1 e + j ψ 1 + e + j ψ ,
A = η 1 η 2 I 0 Z total ( T 32 e j k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 + e j 2 k 1 d 1 1 e j 2 k 1 d 1 ) ,
B = η 1 η 2 I 0 Z total ( 1 1 R 32 e j 2 k 2 d 2 ) ( 1 + e j 2 k 1 d 1 1 e j 2 k 1 d 1 ) ,
C = η 1 η 2 I 0 Z total ( R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 + e j 2 k 1 d 1 1 e j 2 k 1 d 1 ) ,
D = η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( 1 1 e j 2 k 1 d 1 ) ,
E = η 1 η 2 I 0 Z total ( 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 ) ( e j 2 k 1 d 1 1 e j 2 k 1 d 1 ) ,
Z total = η 2 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 + η 1 1 + e j 2 k 1 d 1 1 e j 2 k 1 d 1 = Z i n , 32 + Z i n , P M C .
Z total = η 2 1 + R 32 e j 2 k 2 d 2 1 R 32 e j 2 k 2 d 2 + η 1 1 + e j 2 k 1 d 1 1 e j 2 k 1 d 1 = η 1 + R 32 e j ψ 1 R 32 e j ψ η 1 + e j ψ 1 e j ψ ,
R M = ξ e j δ ,
E ω x , 3 ( x , y , z ) = A e j k 3 ( z d 2 ) ,
H ω y , 3 ( x , y , z ) = A η 3 e j k 3 ( z d 2 ) ;
E ω x , 2 ( x , y , z ) = B e j k 2 ( z d 2 ) + B R M e + j k 2 ( z d 2 ) ,
H ω y , 2 ( x , y , z ) = B η 2 e j k 2 ( z d 2 ) B R M η 2 e + j k 2 ( z d 2 ) ;
E ω x , 1 ( x , y , z ) = C e + j k 1 z + D e j k 1 z ,
H ω y , 1 ( x , y , z ) = C η 1 e + j k 1 z + D η 1 e j k 1 z .
A = η 1 η 2 I 0 Z total [ ( 1 + R M ) e j k 2 d 2 1 R M e j 2 k 2 d 2 ] ( 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) ,
B = η 1 η 2 I 0 Z total [ e j k 2 d 2 1 R M e j 2 k 2 d 2 ] ( 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) ,
C = η 1 η 2 I 0 Z total [ 1 + R M e j k 2 d 2 1 R M e j 2 k 2 d 2 ] ( 1 1 + e j 2 k 1 d 1 ) ,
D = + η 1 η 2 I 0 Z total [ 1 + R M e j k 2 d 2 1 R M e j 2 k 2 d 2 ] ( e j 2 k 1 d 1 1 + e j 2 k 1 d 1 ) .
Z total = η 2 1 + R M e j 2 k 2 d 2 1 R M e j 2 k 2 d 2 + η 1 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 = Z i n , mirror + Z i n , P E C .
Z total η 2 1 e j 2 k 2 d 2 1 + e j 2 k 2 d 2 + η 1 1 e j 2 k 1 d 1 1 + e j 2 k 1 d 1 .
ε r ( ω ) = 1 ω p e 2 ω ( ω j Γ e ) ,
μ r ( ω ) = 1 ω p m 2 ω ( ω j Γ m ) ,

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