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Simulation investigation on channel surface plasmon guiding by terahertz wave through subwavelength metal V-groove
ARTICLE IN PRESS Optics & Laser Technology 41 (2009) 535–538
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Simulation investigation on channel surface plasmon guiding by terahertz wave through subwavelength metal V-groove He Xiao-Yong School of Science, Henan University of Technology, Lianhua Road, Zhengzhou, Henan Province 450001, PR China
a r t i c l e in fo
abstract
Article history: Received 30 May 2008 Received in revised form 6 October 2008 Accepted 19 November 2008 Available online 13 January 2009
The waveguide propagation properties of terahertz wave through subwavelength metallic triangular groove channels have been simulationally investigated. The effects of groove depth, groove angle and dielectric filling materials on propagation property have been shown and discussed. The results show that with increasing of groove depth and angle degree the propagation constant of channel surface plasmon polariton mode decreases. The propagation constant of poor conductive metal is larger than that of good conductive metal, which may result from the fact that the former has larger skin depth. In addition, the confinement of CSPP mode could be improved by increasing the refractive index of dielectric filling materials. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Terahertz Surface plasmon Subwavelength
1. Introduction For its unique characters, terahertz (THz, 1 THz ¼ 1012 Hz) technology shows great potential applications in many scientific research and application fields, such as free space communication, environmental sensing and medical imaging [1–3]. Recently, THz technology has made great progress due to the rapid development of radiation sources [4–6] and detector [7], while THz waveguide propagation is also vitally important to the development of THz technology. Therefore, there is a high demand for THz wave components, such as filter, polarizer and attenuator, which have much relationship with surface plasmon polariton (SPP) [8–10]. SPP are quasi-two-dimensional electromagnetic excitations, propagating along a dielectric–metal interface and having the field components decaying exponentially into both neighboring media [11], offering the possibility of realizing subwavelength waveguides. The feature of SPP mode made it very important to the development of integrated optical circuits, which has higher transmitting data speed and operational bandwidth than electronic circuits. There are two main options for the design of metallic plasmon subwavelength waveguide structure, one is groove waveguide, the other is gap plasmon waveguide [12,13]. Those plasmonic waveguide methods have many merits, such as strong subwavelength localization of plasmon, relatively weak dissipation and reasonable propagation distances, and possibility of single-mode operation and nearly 100% transmission through sharp bends. The idea of groove waveguide was firstly proposed
E-mail address: [email protected] 0030-3992/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2008.11.005
by Maradudin, etc. which has been made by cutting channel into planar surface of metal or highly doped semiconductor with negative dielectric constants. This kind of SPP mode could be called as channel surface plasmon polariton (CSPP) [14,15]. which has many merits, such as strongly subwavelength confined modes, relatively low propagation losses, broadband transmission, good compatibility with planar technology and efficient transmission around sharp bends [16,17]. Many theoretically [18,19] and experimentally [15,20] research work have been given to study the waveguide properties of CSPP. But most of research has been carried out in the infrared telecommunication waveband [14,15,21], the waveguide properties of CSPP mode in the THz waveband is relatively little known. The dielectric cladding in the metallic groove also has substantial impact on the propagation property, such as dispersion, dissipation, localization. Therefore, the waveguide properties (the effective index and propagation length) of CSPP mode based on metal triangular groove (V-groove) have been shown. In addition, the effects of dielectric medium filling in the groove has also been given and discussed.
2. Model and simulation method For an individual metal surface, the SPP propagation constant b could be written as
b ¼ ð2p=lÞ½m d =ðm þ d Þ0:5 ,
(1)
where k0 ¼ 2p=l is the wavevector of incident light, l is the wavelength, and d and m are the dielectric constant of filling dielectrics in the groove and metal, respectively. For the case of
ARTICLE IN PRESS 536
H. Xiao-Yong / Optics & Laser Technology 41 (2009) 535–538
two close metal surfaces with the gap width of w (filled with the dielectric in the space), the SPP associated with individual metal surfaces become coupled and the dispersion relation for propagation constant b could be expressed as [22]
2 a2 ð1 a3 þ 3 a1 Þ , tanhða2 wÞ ¼ 1 3 a22 þ 22 a1 a3
(2)
a2j ¼ b2 k20 j ;
(3)
j ¼ 1; 2; 3,
where 2 is the permittivity of dielectric filling materials, 1 and 3 are the permittivity of metal and w is the width between those two different metals. b is the propagation constant of fundamental mode, which can be written as b ¼ br þ ibi . The propagation constant have been acquired by numerically solving above equations, not liking the results of many published paper based on analytic equations. The sketch for V-groove structure has been given in the inset of Fig. 1(a), y is the angle of the groove, d is the groove depth. The character of V-groove structure is that its width decreases with the increases of groove depth. At the position of groove depth is d, the according groove width w could be expressed as w ¼ 2d tanðy=2Þ.
(4)
By using the effective index method (EIM) approximation, the waveguide properties of metal V-groove could be acquired. The main attractive character of EIM method is that the feature of 2D (channel) waveguides could be acquired by combining the results of one-dimensional (1D) waveguide configurations [23].
Fig. 1. The effective indexes of CSPP modes and their propagation lengths as a function of groove depth for different metals. The inset shows the groove configuration. The incident radiation frequency is 1.0 THz, the groove angle is 30 .
The permittivity of metal in THz waveband could be written as [24] !
ðoÞ ¼ 1
o2p ot o2p , þ o2 þ o2t oðo2 þ o2t Þ
(5)
where op and ot are the plasma frequency and damping frequency, respectively. The effective index neff and propagation length L are related with the real part and imaginary part of SPP mode, which could be expressed as neff ¼ ReðbÞ=k0 ,
(6)
L ¼ ½2 ImðbÞ1 .
(7)
The penetration depth of SPP mode in the air is related to the effective index and could be written as dm ¼
c0
1 pffiffiffiffiffiffi ,
o Imð m Þ
da ¼ ðl=2pÞðn2eff 1Þ0:5 .
(8) (9)
3. Results and discussion Fig. 1 shows that the effective index and propagation length of CSPP mode change with groove depth for different metals, the radiation frequency is 1.0 THz, the groove angle is 30 . The effective index and propagation length could be acquired by numerically solving Eq. (2). It could be found that with the increases of groove depth, the effective index decreases and the propagation length increases, i.e. the propagation constant decreases as groove depth increases. Since the effective index determines the CSPP mode confinement, it seems that the mode could be better confined in narrow groove, though it is difficult to fabricate sharp V-groove. The reason maybe is as follows. With the decreases of groove depth (i.e. the width of groove also increases as well), there are more electromagnetic field penetrating into metal, the scattering cross section and ohmic loss increases, leading to propagation constant increasing. This is according with the experimental results in Ref. [25]. In addition, it could also be found from Fig. 1 that the propagation property of CSPP is also affected by the properties of different kinds of metal. Good conductive metal (Cu and Ag) has smaller effective index and larger propagation length than poor conductive metal (Fe and Pb). The reason maybe is that at THz waveband the skin depth of metal is large, which result in the fact that the electromagnetic properties of metal play an important role in determining the property of CSPP mode. The surface impedance and the internal inductance is largely changed by the electric field and current that penetrate into the metal. The permittivity of good conductive metal is larger than poor conductive metal. The SPP mode penetration into metal (i.e. skin depth) is inversely proportional to the dielectric constant of metal, which could be found in Eq. (8). The skin depth of Cu is smaller than that of Pb. E.g. at 1 THz the permittivity of Cu and Pb are 5:49 105 þ 1:20 106 i and 1:32 103 þ 6:49 104 i, respectively, their skin depth are 310 and 1648 nm, respectively. The larger skin depth of Pb means the larger interaction section of THz wave with metal, leading to the propagation constant increasing, which is according with the suggestion that the SPP confinement could be improved by decreasing the SPP mode spatial extent into dielectric and increasing the portion of SPP power absorbed by metal [25]. Fig. 2 shows the effective index and propagation length of SPP mode versus groove angle y for different metals, the radiation frequency is 1.0 THz, the groove depth is 100 mm. With the increases of groove angle degree, the propagation constant of
ARTICLE IN PRESS H. Xiao-Yong / Optics & Laser Technology 41 (2009) 535–538
537
Fig. 2. The effective indexes of CSPP modes and their propagation lengths as a function of groove angles for different metals. The incident radiation frequency is 1.0 THz, the groove depth is 100 mm.
Fig. 3. The effective indexes of CSPP modes and their propagation lengths as a function of groove angles for different filling materials, their dielectric constant are 1.0, 2.0, 4.0, 6.0, 8.0, 10.0, the radiation frequency is 1.0 THz, the groove depth is 100 mm, the groove angle is 30 .
CSPP mode decreases, which has been shown in Fig. 2. The reason maybe is that on condition that the groove depth is fixed as groove angle increases the groove width increases, resulting in the electromagnetic field penetrating into the metal decreasing, i.e. scattering cross section and ohmic loss decreasing. In addition, it should be noted that the propagation length in THz waveband is much larger than that of CSPP mode in visible light waveband. The reason may come from the difference of dielectric constant for metal in THz waveband and visible light waveband. The character of dielectric constant for metal in visible light waveband is the imaginary part could be omitted compared with that of real part, e.g. the dielectric constant of Ag at 0:6328 mm is 9:8949 þ 1:0458i. While the dielectric constant of metal in THz waveband is very larger and the imaginary part is comparable to that of the real part, e.g. the dielectric constant of Ag at 1 THz is 1:12 105 þ 7:22 105 i. Therefore, the larger dielectric constant of metal in THz waveband results in the smaller propagation constant of CSPP mode and larger propagation length. Fig. 3 shows that the effects of dielectric filling materials on the propagation properties of CSPP mode, the radiation frequency is 1.0 THz, the depth is 100 mm, the groove angle is 30 , the metal materials is Cu. The difference of effective index between neff and nd (the refractive index of filling materials) has been given in Fig. 3(a), the propagation length is also shown in Fig. 3(b). It could be found that with the increasing of dielectric permittivity the effective index increases and propagation length decreases. The reason maybe is that as the dielectric constant of groove filling materials increases the contrast of dielectric constant between dielectric cladding materials and metal decreases, resulting in
the penetration depth of THz wave into metal increasing. Therefore, there are more THz wave penetration into metal at high dielectric filling materials, leading to the propagation constant increases.
4. Conclusions The waveguide propagation properties of CSPP mode through metal V-groove at THz waveband have been simulated. The effects of groove depth, groove angle and dielectric filling materials on propagation constants have been given and discussed. The results show that as groove depth and angle degree increase the effective index decreases and propagation length increases. Good conductive metal has smaller effective index and larger propagation length than poor conductive metal due to the former has smaller skin depth. In addition, the effective index increases and the propagation length decreases with the increases of groove dielectric filling materials. References [1] Lee M, Wanke MC. Searching for a solid-state terahertz technology. Science 2007;316(5821):64–5. [2] Yu HY, Lee SC, Kim DC, Zhang C, Harrison P. Optical losses in dielectric apertured terahertz VCSEL. Opt Laser Technol 2004;36(7):575–80. [3] Ferguson B, Zhang XC. Materials for terahertz science and technology. Nat Mater 2002;1(1):26–33. [4] Ko¨hler R, Tredicucci A, Beltram F, Beere HE, Linfield EH, Davies AG, et al. Terahertz semiconductor heterostructure laser. Nature 2002;417(6685): 156–9.
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[5] Lu¨ JT, Cao JC. Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers. Appl Phys Lett 2006;89(21):211115. [6] Williams BS, Callebaut H, Kumar S, Hu Q, Reno JL. 3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation. Appl Phys Lett 2003;82(7):1015–7. [7] Cao JC. Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Phys Rev Lett 2003;91(23):237401. [8] Ebbesen TW, Lezec HJ, Ghaemi HF, Thio T, Wolff PA. Extraordinary optical transmission through sub-wavelength hole arrays. Nature 1998;391(6668): 667–9. [9] Barnes WL, Dereux A, Ebbesen TW. Surface plasmon subwavelength optics. Nature 2003;391(6950):824–30. [10] Boltasseva A, Volkov VS, Nielsen RB, Moreno E, Rodrigo SG, Bozhevolnyi SI. Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths. Opt Express 2008;16(8):5252–60. [11] Raether H. Surface plasmons. Berlin: Springer; 1988. [12] Vernon KC, Gramontnev DK, Pile DFP. Channel plasmon-polariton modes in Vgrooves filled with dielectric. J Appl Phys 2008;103(03):034304. [13] Bozhevolnyi SI, Jung J. Scaling for gap plasmon based waveguides. Opt Express 2008;16(4):2676–84. [14] Bozhevolnyi SI, Volkov VS, Devaux E, Ebbesen TW. Channel plasmon-polariton guiding by subwavelength metal groove. Phys Rev Lett 2005;95(04):046802. [15] Bozhevolnyi SI, Volkov VS, Devaux E, Laluet JY, Ebbesen TW. Channel plasmon subwavelength waveguide components including interferometers and ring resonators. Nature 2006;440(7083):508–11.
[16] Bozhevolnyi SI, Volkov VS, Devaux E, Laluet JY, Ebbesen TW. Channelling surface plasmons. Appl Phys A 2007;89(2):225–31. [17] Holmgaard T, Chen Z, Bozhevolnyi SI, Markey L, Dereux A, Krasavin AV, et al. Bend- and splitting loss of dielectric-loaded surface plasmon-polariton waveguidess. Opt Express 2008;16(18):13585–92. [18] Moreno E, Garcia-Vidal FJ, Rodrigo SG, Moreno LM, Bozhevolnyi SI. Channel plasmon-polaritons: modal shape, dispersion, and losses. Opt Lett 2006;31(23):3447–9. [19] Ogawa T, Pile DFP, Okamoto H, Fukui M, Gramotney DK. Numerical and experimental investigation of wedge tip radius effect on wedge plasmons. J Appl Phys 2008;104:033102. [20] Arbel D, Orenstein M. Plasmonic modes in W-shaped metal-coated silicon grooves. Opt Express 2008;16(5):3114–9. [21] Volkov VS, Bozhevolnyi SI, Devaux E, Ebbesen TW. Compact gradual bends for channel plasmon polaritons. Opt Express 2006;14(10): 4494–503. [22] Yang F, Sambles JR, Bradberry GW. Phys Rev B 1991;44(11):5855–72. [23] Hocker GB, Burns WK. Mode dispersion in diffused channel waveguides by the effective index method. Appl Opt 1977;16(1):113–8. [24] Ordal MA, Bell RJ, Alexander RW, Long LL, Querry MR. Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W. Appl Opt 1985;24(24):4449–93. [25] Isaac TH, Rivas JG, Sambles JR, Barnes WL, Hendry E. Surface plasmon mediated transmission of subwavelength slits at THz frequencies. Phys Rev B 2008;77(11):113411.
Contents lists available at ScienceDirect
Optics & Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Simulation investigation on channel surface plasmon guiding by terahertz wave through subwavelength metal V-groove He Xiao-Yong School of Science, Henan University of Technology, Lianhua Road, Zhengzhou, Henan Province 450001, PR China
a r t i c l e in fo
abstract
Article history: Received 30 May 2008 Received in revised form 6 October 2008 Accepted 19 November 2008 Available online 13 January 2009
The waveguide propagation properties of terahertz wave through subwavelength metallic triangular groove channels have been simulationally investigated. The effects of groove depth, groove angle and dielectric filling materials on propagation property have been shown and discussed. The results show that with increasing of groove depth and angle degree the propagation constant of channel surface plasmon polariton mode decreases. The propagation constant of poor conductive metal is larger than that of good conductive metal, which may result from the fact that the former has larger skin depth. In addition, the confinement of CSPP mode could be improved by increasing the refractive index of dielectric filling materials. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Terahertz Surface plasmon Subwavelength
1. Introduction For its unique characters, terahertz (THz, 1 THz ¼ 1012 Hz) technology shows great potential applications in many scientific research and application fields, such as free space communication, environmental sensing and medical imaging [1–3]. Recently, THz technology has made great progress due to the rapid development of radiation sources [4–6] and detector [7], while THz waveguide propagation is also vitally important to the development of THz technology. Therefore, there is a high demand for THz wave components, such as filter, polarizer and attenuator, which have much relationship with surface plasmon polariton (SPP) [8–10]. SPP are quasi-two-dimensional electromagnetic excitations, propagating along a dielectric–metal interface and having the field components decaying exponentially into both neighboring media [11], offering the possibility of realizing subwavelength waveguides. The feature of SPP mode made it very important to the development of integrated optical circuits, which has higher transmitting data speed and operational bandwidth than electronic circuits. There are two main options for the design of metallic plasmon subwavelength waveguide structure, one is groove waveguide, the other is gap plasmon waveguide [12,13]. Those plasmonic waveguide methods have many merits, such as strong subwavelength localization of plasmon, relatively weak dissipation and reasonable propagation distances, and possibility of single-mode operation and nearly 100% transmission through sharp bends. The idea of groove waveguide was firstly proposed
E-mail address: [email protected] 0030-3992/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.optlastec.2008.11.005
by Maradudin, etc. which has been made by cutting channel into planar surface of metal or highly doped semiconductor with negative dielectric constants. This kind of SPP mode could be called as channel surface plasmon polariton (CSPP) [14,15]. which has many merits, such as strongly subwavelength confined modes, relatively low propagation losses, broadband transmission, good compatibility with planar technology and efficient transmission around sharp bends [16,17]. Many theoretically [18,19] and experimentally [15,20] research work have been given to study the waveguide properties of CSPP. But most of research has been carried out in the infrared telecommunication waveband [14,15,21], the waveguide properties of CSPP mode in the THz waveband is relatively little known. The dielectric cladding in the metallic groove also has substantial impact on the propagation property, such as dispersion, dissipation, localization. Therefore, the waveguide properties (the effective index and propagation length) of CSPP mode based on metal triangular groove (V-groove) have been shown. In addition, the effects of dielectric medium filling in the groove has also been given and discussed.
2. Model and simulation method For an individual metal surface, the SPP propagation constant b could be written as
b ¼ ð2p=lÞ½m d =ðm þ d Þ0:5 ,
(1)
where k0 ¼ 2p=l is the wavevector of incident light, l is the wavelength, and d and m are the dielectric constant of filling dielectrics in the groove and metal, respectively. For the case of
ARTICLE IN PRESS 536
H. Xiao-Yong / Optics & Laser Technology 41 (2009) 535–538
two close metal surfaces with the gap width of w (filled with the dielectric in the space), the SPP associated with individual metal surfaces become coupled and the dispersion relation for propagation constant b could be expressed as [22]
2 a2 ð1 a3 þ 3 a1 Þ , tanhða2 wÞ ¼ 1 3 a22 þ 22 a1 a3
(2)
a2j ¼ b2 k20 j ;
(3)
j ¼ 1; 2; 3,
where 2 is the permittivity of dielectric filling materials, 1 and 3 are the permittivity of metal and w is the width between those two different metals. b is the propagation constant of fundamental mode, which can be written as b ¼ br þ ibi . The propagation constant have been acquired by numerically solving above equations, not liking the results of many published paper based on analytic equations. The sketch for V-groove structure has been given in the inset of Fig. 1(a), y is the angle of the groove, d is the groove depth. The character of V-groove structure is that its width decreases with the increases of groove depth. At the position of groove depth is d, the according groove width w could be expressed as w ¼ 2d tanðy=2Þ.
(4)
By using the effective index method (EIM) approximation, the waveguide properties of metal V-groove could be acquired. The main attractive character of EIM method is that the feature of 2D (channel) waveguides could be acquired by combining the results of one-dimensional (1D) waveguide configurations [23].
Fig. 1. The effective indexes of CSPP modes and their propagation lengths as a function of groove depth for different metals. The inset shows the groove configuration. The incident radiation frequency is 1.0 THz, the groove angle is 30 .
The permittivity of metal in THz waveband could be written as [24] !
ðoÞ ¼ 1
o2p ot o2p , þ o2 þ o2t oðo2 þ o2t Þ
(5)
where op and ot are the plasma frequency and damping frequency, respectively. The effective index neff and propagation length L are related with the real part and imaginary part of SPP mode, which could be expressed as neff ¼ ReðbÞ=k0 ,
(6)
L ¼ ½2 ImðbÞ1 .
(7)
The penetration depth of SPP mode in the air is related to the effective index and could be written as dm ¼
c0
1 pffiffiffiffiffiffi ,
o Imð m Þ
da ¼ ðl=2pÞðn2eff 1Þ0:5 .
(8) (9)
3. Results and discussion Fig. 1 shows that the effective index and propagation length of CSPP mode change with groove depth for different metals, the radiation frequency is 1.0 THz, the groove angle is 30 . The effective index and propagation length could be acquired by numerically solving Eq. (2). It could be found that with the increases of groove depth, the effective index decreases and the propagation length increases, i.e. the propagation constant decreases as groove depth increases. Since the effective index determines the CSPP mode confinement, it seems that the mode could be better confined in narrow groove, though it is difficult to fabricate sharp V-groove. The reason maybe is as follows. With the decreases of groove depth (i.e. the width of groove also increases as well), there are more electromagnetic field penetrating into metal, the scattering cross section and ohmic loss increases, leading to propagation constant increasing. This is according with the experimental results in Ref. [25]. In addition, it could also be found from Fig. 1 that the propagation property of CSPP is also affected by the properties of different kinds of metal. Good conductive metal (Cu and Ag) has smaller effective index and larger propagation length than poor conductive metal (Fe and Pb). The reason maybe is that at THz waveband the skin depth of metal is large, which result in the fact that the electromagnetic properties of metal play an important role in determining the property of CSPP mode. The surface impedance and the internal inductance is largely changed by the electric field and current that penetrate into the metal. The permittivity of good conductive metal is larger than poor conductive metal. The SPP mode penetration into metal (i.e. skin depth) is inversely proportional to the dielectric constant of metal, which could be found in Eq. (8). The skin depth of Cu is smaller than that of Pb. E.g. at 1 THz the permittivity of Cu and Pb are 5:49 105 þ 1:20 106 i and 1:32 103 þ 6:49 104 i, respectively, their skin depth are 310 and 1648 nm, respectively. The larger skin depth of Pb means the larger interaction section of THz wave with metal, leading to the propagation constant increasing, which is according with the suggestion that the SPP confinement could be improved by decreasing the SPP mode spatial extent into dielectric and increasing the portion of SPP power absorbed by metal [25]. Fig. 2 shows the effective index and propagation length of SPP mode versus groove angle y for different metals, the radiation frequency is 1.0 THz, the groove depth is 100 mm. With the increases of groove angle degree, the propagation constant of
ARTICLE IN PRESS H. Xiao-Yong / Optics & Laser Technology 41 (2009) 535–538
537
Fig. 2. The effective indexes of CSPP modes and their propagation lengths as a function of groove angles for different metals. The incident radiation frequency is 1.0 THz, the groove depth is 100 mm.
Fig. 3. The effective indexes of CSPP modes and their propagation lengths as a function of groove angles for different filling materials, their dielectric constant are 1.0, 2.0, 4.0, 6.0, 8.0, 10.0, the radiation frequency is 1.0 THz, the groove depth is 100 mm, the groove angle is 30 .
CSPP mode decreases, which has been shown in Fig. 2. The reason maybe is that on condition that the groove depth is fixed as groove angle increases the groove width increases, resulting in the electromagnetic field penetrating into the metal decreasing, i.e. scattering cross section and ohmic loss decreasing. In addition, it should be noted that the propagation length in THz waveband is much larger than that of CSPP mode in visible light waveband. The reason may come from the difference of dielectric constant for metal in THz waveband and visible light waveband. The character of dielectric constant for metal in visible light waveband is the imaginary part could be omitted compared with that of real part, e.g. the dielectric constant of Ag at 0:6328 mm is 9:8949 þ 1:0458i. While the dielectric constant of metal in THz waveband is very larger and the imaginary part is comparable to that of the real part, e.g. the dielectric constant of Ag at 1 THz is 1:12 105 þ 7:22 105 i. Therefore, the larger dielectric constant of metal in THz waveband results in the smaller propagation constant of CSPP mode and larger propagation length. Fig. 3 shows that the effects of dielectric filling materials on the propagation properties of CSPP mode, the radiation frequency is 1.0 THz, the depth is 100 mm, the groove angle is 30 , the metal materials is Cu. The difference of effective index between neff and nd (the refractive index of filling materials) has been given in Fig. 3(a), the propagation length is also shown in Fig. 3(b). It could be found that with the increasing of dielectric permittivity the effective index increases and propagation length decreases. The reason maybe is that as the dielectric constant of groove filling materials increases the contrast of dielectric constant between dielectric cladding materials and metal decreases, resulting in
the penetration depth of THz wave into metal increasing. Therefore, there are more THz wave penetration into metal at high dielectric filling materials, leading to the propagation constant increases.
4. Conclusions The waveguide propagation properties of CSPP mode through metal V-groove at THz waveband have been simulated. The effects of groove depth, groove angle and dielectric filling materials on propagation constants have been given and discussed. The results show that as groove depth and angle degree increase the effective index decreases and propagation length increases. Good conductive metal has smaller effective index and larger propagation length than poor conductive metal due to the former has smaller skin depth. In addition, the effective index increases and the propagation length decreases with the increases of groove dielectric filling materials. References [1] Lee M, Wanke MC. Searching for a solid-state terahertz technology. Science 2007;316(5821):64–5. [2] Yu HY, Lee SC, Kim DC, Zhang C, Harrison P. Optical losses in dielectric apertured terahertz VCSEL. Opt Laser Technol 2004;36(7):575–80. [3] Ferguson B, Zhang XC. Materials for terahertz science and technology. Nat Mater 2002;1(1):26–33. [4] Ko¨hler R, Tredicucci A, Beltram F, Beere HE, Linfield EH, Davies AG, et al. Terahertz semiconductor heterostructure laser. Nature 2002;417(6685): 156–9.
ARTICLE IN PRESS 538
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[5] Lu¨ JT, Cao JC. Coulomb scattering in the Monte Carlo simulation of terahertz quantum-cascade lasers. Appl Phys Lett 2006;89(21):211115. [6] Williams BS, Callebaut H, Kumar S, Hu Q, Reno JL. 3.4-THz quantum cascade laser based on longitudinal-optical-phonon scattering for depopulation. Appl Phys Lett 2003;82(7):1015–7. [7] Cao JC. Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Phys Rev Lett 2003;91(23):237401. [8] Ebbesen TW, Lezec HJ, Ghaemi HF, Thio T, Wolff PA. Extraordinary optical transmission through sub-wavelength hole arrays. Nature 1998;391(6668): 667–9. [9] Barnes WL, Dereux A, Ebbesen TW. Surface plasmon subwavelength optics. Nature 2003;391(6950):824–30. [10] Boltasseva A, Volkov VS, Nielsen RB, Moreno E, Rodrigo SG, Bozhevolnyi SI. Triangular metal wedges for subwavelength plasmon-polariton guiding at telecom wavelengths. Opt Express 2008;16(8):5252–60. [11] Raether H. Surface plasmons. Berlin: Springer; 1988. [12] Vernon KC, Gramontnev DK, Pile DFP. Channel plasmon-polariton modes in Vgrooves filled with dielectric. J Appl Phys 2008;103(03):034304. [13] Bozhevolnyi SI, Jung J. Scaling for gap plasmon based waveguides. Opt Express 2008;16(4):2676–84. [14] Bozhevolnyi SI, Volkov VS, Devaux E, Ebbesen TW. Channel plasmon-polariton guiding by subwavelength metal groove. Phys Rev Lett 2005;95(04):046802. [15] Bozhevolnyi SI, Volkov VS, Devaux E, Laluet JY, Ebbesen TW. Channel plasmon subwavelength waveguide components including interferometers and ring resonators. Nature 2006;440(7083):508–11.
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