Abstract

The modes in a circular metallic waveguide loaded with a high permittivity dielectric rod may possess similar dispersion relations to the modes in the left-handed metamaterial (LHM) waveguide. Therefore such dielectric-loaded metallic waveguide may also support slow light with parameters properly selected. The slow light in the GaAs-rod-loaded metallic waveguide is numerically studied. The results show that the wavelength of slow light varies with the parameters of the waveguide. A linearly tapered waveguide and other realizable simple structures are proposed accordingly to realize the “trapped rainbow” phenomena. Moreover, the practical lossy tapered waveguide is also investigated in the terahertz region. It is shown that the slow light with low loss can be achieved in a realistic GaAs-loaded metallic waveguide.

©2010 Optical Society of America

1. Introduction

Slow light structures have many potential applications such as optical delay lines, nonlinear enhancements, etc [1]. There are many methods/structures with slow light effects including electromagnetically induced transparency [2], directly coupled resonators [3], stimulated Raman scattering [4], photonic crystal [5], surface plasmon polaritons [6] and so on. Recently, several slow light LHM waveguides, which is composed of LHM layer and normal dielectric medium layers, have been proposed [79]. Since the power in LHM layer flows in the opposite direction of that in normal dielectric layers, when they are almost equal, the guided wave will have very low group velocity. K. L. Tsakmakidis et al. went further and proposed a linear slowly tapered waveguide to achieve so-called “trapped rainbow” phenomena [1]. Such structure is able to slow down the light over a broad band at the room temperature and is more valuable in applications. However, the low-lossy uniform bulk of LHM is very difficult to realize now. Besides, The loss and the non-adiabatic tapered structure for a realistic LHM waveguide will severely limit the performance of slow-light propagation [10,11]. Though alternative structures of slow light waveguide based on negative-refractive-index photonic crystal or stack of alternating layer of silver and silica have been proposed [1113], these tapered structures are all difficult to fabricate too.

Actually, LHMs or periodic structures are not necessary to realize opposite power flows in different layers of a waveguide. It has been found in previous work [1417] that such opposite power flows can be obtained in high-permittivity-dielectric-loaded metallic waveguides. Thus, the dielectric-loaded metallic waveguide may also support the slow light propagation, as the LHM waveguide. However, previous papers [1417] mainly focus on the backward waves or the abnormal dispersion relation for the dielectric loaded metallic waveguide.

In this article, we will show that the “trapped rainbow” (broadband slow light) can be obtained in simple and realizable structures based on GaAs-rod-loaded metallic waveguide. We investigate the dispersion relation of the mode in GaAs-rod-loaded circular metallic waveguides in terahertz frequency region. And, the existing conditions for slow light in the GaAs-rod-loaded metallic waveguide of various parameters are analyzed. Then, the realizable tapered waveguide structures are designed accordingly to achieve the “trapped rainbow”. We also show that the slow light with low loss can be realized in a practical GaAs-rod-loaded circular metallic waveguide.

2. Calculation and analysis

The waveguide we consider is shown in the inset of Fig. 1(a) . A metallic cylindrical hollow waveguide (with inner radius of R 0) is coaxially inserted with a GaAs rod (with radius of R 1). The GaAs is chosen for its high permittivity and low loss in terahertz region. The real part of permittivity for GaAs is assumed to be 12.9 [18]. Figure 1(a) shows the dispersion curve of HE11 mode in an ideal lossless waveguide with parameters of R 0 = 2R 1 = 0.4mm in the wavelength range from 1.73mm to 2.51mm. The curve is quite similar to those for LHM waveguides [710,19]. Forward mode, backward mode and complex mode can all exist in the waveguide and are degenerated at the “critical point” [corresponding to the asterisk point in Fig. 1(a)]. It is easy to get that, at the “critical point”, the mode is of zero group velocity (dω/dβ), and near the “critical point”, the forward- and backward- modes all have low group velocities. Thus, such a simple uniform waveguide without LHMs or periodic structures inside can also support slow light propagation.

 

Fig. 1 (a) Dispersion curve for the ideal GaAs-rod-loaded cylindrical metallic waveguide as shown in the inset. For the waveguide, R 0 = 2R 1 = 0.4mm. The permittivity of GaAs is 12.9, and the dielectric between the rod and hollow metallic waveguide is air. The dashed line corresponds to the complex mode. (b) The time average Poynting vector along the waveguide for the forward mode corresponding to circle point A in Fig. 1(a). (c) The time average Poynting vector for the backward mode B.

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The time average Poynting vectors of forward mode and backward mode are calculated, and illustrated in Fig. 1(b) and (c), respectively [corresponding to the modes pointed with circles A and B in Fig. 1(a)]. One can see that the power flow in the air gap of the waveguide is negative (the direction of the propagating vector is assumed to be positive) and anti-parallel to the direction of power flow in the rod. The reason is that the normal components of most magnetic fields in the rod are reverse to those in the air gap [17]. And, for the guided mode, the air gap is just like the LHM layer in an LHM waveguide. Therefore, the dispersion relation of the GaAs-rod-loaded metallic waveguide is quite similar to that of LHM waveguides. The mode will be backward (/forward) if its energy mainly flows in the air gap (/GaAs rod), and will have a zero group velocity if the absolute power flow in the air gap exactly equals to that in rod.

The change of the parameters R 1 or R 0 may vary the ratio of power flow in air gap and in the GaAs rod, resulting in the change of the group velocity of the guided wave, as shown in Fig. 2(a) . The group velocity of the guided forward wave decreases as the R 1 of waveguide becomes small. So, for a forward wave propagating along a waveguide of which the rod is slowly tapered, it will slow down and its energy will accumulate. At the “critical point”, the wave will be “trapped” and have the strongest field [12,20,21]. Waves with different wavelength have different waveguide parameters at the “critical point”, as shown in Fig. 2(b) and 2(c). When a broad-band wave propagates along the waveguide of which the dielectric rod or hollow metallic shell is slowly tapered, the different wavelength components of the wave will be partly trapped in different location. Thus, they will be “separated”, and so-called “trapped rainbow” phenomenon is realized.

 

Fig. 2 (a) The group velocities of modes in the GaAs-rod-loaded metallic waveguide with various R 1. The R 0 is 0.4mm and wavelength of modes is 0.214mm. (b) The wavelength, λcp, of mode at the critical point for different R 1 of waveguide. R 0 = 0.4mm. (c) The λcp for different R 0 of waveguide. R 1 = 0.2mm.

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According to Fig. 2(a) and (b), a uniform metallic waveguide of R 0 = 0.4mm with a tapered GaAs rod inserted is designed to obtain the broadband slow light, as shown in Fig. 3(a) . The radii of GaAs rod at two ports are 0.21mm and 0.23mm, respectively. The length of the waveguide is 12mm. The incident wave is coupled into the left port and propagates along to the right, and its polarization is shown in Fig. 3(b). Figure 3(c)-(f) show the finite element method simulation results of the absolute electric field (|E|) distribution for four different wavelengths, i.e. 2.16mm, 2.14mm, 2.12mm and 2.10mm. The four waves are separated due to being accumulated at different positions. The electric fields can be enhanced more if the waveguide has a larger R 1 at the left port and longer length (to ensure that the waveguide is tapered enough slowly).

 

Fig. 3 (a) Schematic diagram of a tapered waveguide with R 0 = 0.4mm, R 1 = 0.23mm, R 2 = 0.21mm and L = 12mm. (b) The electric field distribution of the wave coupled from left port of the waveguide. (c)-(f) the absolute electric field (|E|) distribution at the plane of y = 0 for four different incident waves in the tapered waveguide, respectively. (c) λ = 2.16mm, (d) λ = 2.14mm, (e) λ = 2.12mm, and (f) λ = 2.10mm.

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Besides R 1 and R 0, the wavelength of the “critical point” varies with the permittivity of dielectric rod, as illustrated in Fig. 4 . The wavelength of critical point changes from 2.147mm to 2.17mm when the permittivity of rod increases from 12.6 to 13. The permittivity of GaAs rod can be changed via thermo-optic effect [22]. So, in a tapered waveguide as shown in Fig. 3(a), the wavelength of the “trapped” wave in a particular position can be tuned by changing the temperature. As the temperature of the dielectric rod increases gradually, various wavelength components of the wave will be enhanced one by one. Such a novel structure may have potential applications in sensing or communications. Moreover, the “trapped rainbow” can also be obtained in a uniform structure of the waveguide, if the permittivity of the rod changes gradually along the waveguide (e.g. by placing a heater and a cooler at two ports of waveguide, the temperature gradually changes along the rod). Such waveguide may be easier to realize and more useful than tapered waveguides.

 

Fig. 4 The wavelength at the critical point varies with permittivity of dielectric rod of the waveguide (R 0 = 2R 1 = 0.4mm).

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Although the metal is nearly perfect conductor in low frequency of terahertz region, the loss of GaAs is much larger than that in infrared and is not negligible for the propagation of slow light. So, for the practical waveguide operating in THz range, we only consider the loss of GaAs, and the complex permittivity of GaAs is assumed to be 12.9 + 0.02i [18]. Figure 5(a) shows the guided modes vary with R 1 at the fixed wavelength of λ = 2.14mm. In a lossy waveguide, the modes at the “critical point” do not degenerate, but instead split into a forward mode and a backward one. Therefore the mode with zero group velocity at the “critical point” cannot be obtained. However, the guided wave near the “critical point” is still with low group velocity and low loss, the field of the wave can be enhanced much at corresponding location in the tapered waveguide as well [20,21]. Figure 5(b) shows the |E| distribution for the wave of λ = 2.14mm propagating in a lossy tapered waveguide with the same structure as in Fig. 3(a). It can be seen that the wave will still be enhanced in a realistic lossy slow light waveguide, though the maximum field is a bit lower than that in an ideal waveguide [as shown in Fig. 3(e)]. If the dielectric rod is replaced with a gain medium, such as terahertz quantum cascade lasers [23], the loss of the wave can be compensated or the wave even can be amplified [13].

 

Fig. 5 (a) The propagation constants of modes as R 1 of lossy and lossless waveguide varies. The wavelength of the guided mode equals to 2.14mm. For both waveguides, R 0 = 0.4mm. The black and gray solid curves correspond to the lossy case, and the green thick lines and red dotted lines correspond to the lossless case. (b) The |E| distribution at plane of y = 0 for incident wave of λ = 2.14mm in the lossy waveguide as shown in Fig. 3(a).

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3. Conclusion

In summary, a simple GaAs-rod-loaded metallic waveguide with uniform or non-uniform structure for slow light operation was proposed and analyzed. It was shown that the so-called “trapped rainbow” can be realized in a tapered waveguide or a uniform waveguide with the permittivity of rod properly modulated. We also analyzed the practical lossy tapered waveguide in terahertz region. The results show that the slow light with low loss can still be obtained in a realistic waveguide. Besides, it is worth noting that the dielectric rod can be get by a similar method to fabricate the semiconductor core optical fiber [24], and that the waveguides we proposed can be simplified by replacing half of the structure with a metal plane, due to the symmetric modes in the circular waveguide [17]. And our other numerical analyses show that slow light can also be obtained in such semicircular GaAs-rod-loaded waveguides. This kind of waveguides can be fabricated more easily, since the dielectric rod in the waveguide is sustained by the metal plane.

Acknowledgments

This work is partly supported by the Zhejiang Provincial Natural Science Foundation of China (Y1091001), the National Natural Science Foundation of China (60977066), and grant Y200702848 from the Zhejiang Provincial Education Office of China.

References and links

1. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007). [CrossRef]   [PubMed]  

2. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001). [CrossRef]   [PubMed]  

3. A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003). [CrossRef]  

4. K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78(6), 703–705 (2001). [CrossRef]  

5. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005). [CrossRef]   [PubMed]  

6. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008). [CrossRef]   [PubMed]  

7. J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wirel. Compon. Lett. 16(2), 96–98 (2006). [CrossRef]  

8. K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006). [CrossRef]  

9. Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008). [CrossRef]  

10. A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008). [CrossRef]  

11. T. Jiang, J. Zhao, and Y. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17(1), 170–177 (2009). [CrossRef]   [PubMed]  

12. J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express 16(15), 11077–11082 (2008). [CrossRef]   [PubMed]  

13. T. Jiang, Q. Zhang, and Y. Feng, “Compensating loss with gain in slow-light propagation along slab waveguide with anisotropic metamaterial cladding,” Opt. Lett. 34(24), 3869–3871 (2009). [CrossRef]   [PubMed]  

14. P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Control 15, 325–330 (1963). [CrossRef]  

15. G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975). [CrossRef]  

16. M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004). [CrossRef]   [PubMed]  

17. A. Salandrino and D. N. Christodoulides, “Negative index Clarricoats-Waldron waveguides for terahertz and far infrared applications,” Opt. Express 18(4), 3626–3631 (2010). [CrossRef]   [PubMed]  

18. G. Grüner, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, Berlin, 1998), Chap. 3.

19. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003). [CrossRef]   [PubMed]  

20. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008). [CrossRef]  

21. J. He, Centre for THz Research, China Jiliang University, Hangzhou 310018, China, and Z. Hong et al. are preparing a manuscript to be called “Backward coupling of modes in a left-handed metamaterial tapered waveguide.”

22. Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009). [CrossRef]   [PubMed]  

23. N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009). [CrossRef]  

24. J. Ballato, T. Hawkins, P. Foy, C. McMillen, L. Burka, J. Reppert, R. Podila, A. M. Rao, and R. R. Rice, “Binary III-V semiconductor core optical fiber,” Opt. Express 18(5), 4972–4979 (2010). [CrossRef]   [PubMed]  

References

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  1. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
    [Crossref] [PubMed]
  2. M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
    [Crossref] [PubMed]
  3. A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003).
    [Crossref]
  4. K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78(6), 703–705 (2001).
    [Crossref]
  5. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
    [Crossref] [PubMed]
  6. Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
    [Crossref] [PubMed]
  7. J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wirel. Compon. Lett. 16(2), 96–98 (2006).
    [Crossref]
  8. K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
    [Crossref]
  9. Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
    [Crossref]
  10. A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008).
    [Crossref]
  11. T. Jiang, J. Zhao, and Y. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17(1), 170–177 (2009).
    [Crossref] [PubMed]
  12. J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express 16(15), 11077–11082 (2008).
    [Crossref] [PubMed]
  13. T. Jiang, Q. Zhang, and Y. Feng, “Compensating loss with gain in slow-light propagation along slab waveguide with anisotropic metamaterial cladding,” Opt. Lett. 34(24), 3869–3871 (2009).
    [Crossref] [PubMed]
  14. P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Control 15, 325–330 (1963).
    [Crossref]
  15. G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
    [Crossref]
  16. M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
    [Crossref] [PubMed]
  17. A. Salandrino and D. N. Christodoulides, “Negative index Clarricoats-Waldron waveguides for terahertz and far infrared applications,” Opt. Express 18(4), 3626–3631 (2010).
    [Crossref] [PubMed]
  18. G. Grüner, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, Berlin, 1998), Chap. 3.
  19. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003).
    [Crossref] [PubMed]
  20. K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008).
    [Crossref]
  21. J. He, Centre for THz Research, China Jiliang University, Hangzhou 310018, China, and Z. Hong et al. are preparing a manuscript to be called “Backward coupling of modes in a left-handed metamaterial tapered waveguide.”
  22. Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009).
    [Crossref] [PubMed]
  23. N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
    [Crossref]
  24. J. Ballato, T. Hawkins, P. Foy, C. McMillen, L. Burka, J. Reppert, R. Podila, A. M. Rao, and R. R. Rice, “Binary III-V semiconductor core optical fiber,” Opt. Express 18(5), 4972–4979 (2010).
    [Crossref] [PubMed]

2010 (2)

2009 (4)

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009).
[Crossref] [PubMed]

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

T. Jiang, J. Zhao, and Y. Feng, “Stopping light by an air waveguide with anisotropic metamaterial cladding,” Opt. Express 17(1), 170–177 (2009).
[Crossref] [PubMed]

T. Jiang, Q. Zhang, and Y. Feng, “Compensating loss with gain in slow-light propagation along slab waveguide with anisotropic metamaterial cladding,” Opt. Lett. 34(24), 3869–3871 (2009).
[Crossref] [PubMed]

2008 (5)

J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express 16(15), 11077–11082 (2008).
[Crossref] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[Crossref] [PubMed]

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008).
[Crossref]

2007 (1)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

2006 (2)

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wirel. Compon. Lett. 16(2), 96–98 (2006).
[Crossref]

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

2005 (1)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

2004 (1)

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

2003 (2)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003).
[Crossref] [PubMed]

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003).
[Crossref]

2001 (2)

K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78(6), 703–705 (2001).
[Crossref]

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

1975 (1)

G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
[Crossref]

1963 (1)

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Control 15, 325–330 (1963).
[Crossref]

Aryal, D. P.

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

Ballato, J.

Barbieri, S.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Bartoli, F. J.

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009).
[Crossref] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[Crossref] [PubMed]

Birtles, A. B.

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Control 15, 325–330 (1963).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Burka, L.

Christodoulides, D. N.

Clarricoats, P. J. B.

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Control 15, 325–330 (1963).
[Crossref]

Davies, A. G.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Dhillon, S. S.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Dignam, M. M.

A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008).
[Crossref]

Ding, Y. J.

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009).
[Crossref] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[Crossref] [PubMed]

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Feng, Y.

Fink, Y.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

Foy, P.

Fu, Z.

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[Crossref] [PubMed]

Gan, Q.

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009).
[Crossref] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[Crossref] [PubMed]

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Hawkins, T.

He, J.

J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express 16(15), 11077–11082 (2008).
[Crossref] [PubMed]

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wirel. Compon. Lett. 16(2), 96–98 (2006).
[Crossref]

He, S.

J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express 16(15), 11077–11082 (2008).
[Crossref] [PubMed]

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wirel. Compon. Lett. 16(2), 96–98 (2006).
[Crossref]

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

Hong, Z.

Huang, Y. J.

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

Hughes, S.

A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008).
[Crossref]

Ibanescu, M.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

Imamoglu, A.

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

Jamois, C.

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

Jiang, T.

Jin, Y.

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

Jukam, N.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Khanna, S. P.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003).
[Crossref] [PubMed]

Klaedtke, A.

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Lawandy, N. M.

K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78(6), 703–705 (2001).
[Crossref]

Lee, K.

K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78(6), 703–705 (2001).
[Crossref]

Linfield, E. H.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Lu, W. T.

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

Lukin, M. D.

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

Luo, C.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

Madeo, J.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Manquest, C.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Martinelli, M.

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003).
[Crossref]

McMillen, C.

Melloni, A.

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003).
[Crossref]

Morichetti, F.

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003).
[Crossref]

Oustinov, D.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Podila, R.

Rao, A. M.

Reppert, J.

Reza, A.

A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008).
[Crossref]

Rice, R. R.

Roundy, D.

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

Salandrino, A.

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003).
[Crossref] [PubMed]

Sirtori, C.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Sridhar, S.

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003).
[Crossref] [PubMed]

Tignon, J.

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

Tsandoulas, G. N.

G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
[Crossref]

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Zhang, Q.

Zhao, J.

Appl. Phys. Lett. (2)

K. Lee and N. M. Lawandy, “Optically induced pulse delay in a solid-state Raman amplifier,” Appl. Phys. Lett. 78(6), 703–705 (2001).
[Crossref]

K. L. Tsakmakidis, A. Klaedtke, D. P. Aryal, C. Jamois, and O. Hess, “Single-mode operation in the slow-light regime using oscillatory waves in generalized left-handed heterostructures,” Appl. Phys. Lett. 89(20), 201103 (2006).
[Crossref]

IEEE Microw. Wirel. Compon. Lett. (1)

J. He and S. He, “Slow propagation of electromagnetic waves in a dielectric slab waveguide with a left-handed material substrate,” IEEE Microw. Wirel. Compon. Lett. 16(2), 96–98 (2006).
[Crossref]

IEEE Trans. Microw. Theory Tech. (1)

G. N. Tsandoulas, “Propagation in Dielectric-Lined Square Waveguides,” IEEE Trans. Microw. Theory Tech. 23(5), 406–410 (1975).
[Crossref]

J. Electron Control (1)

P. J. B. Clarricoats and A. B. Birtles, “Circular Waveguide Backward-wave Experiments,” J. Electron Control 15, 325–330 (1963).
[Crossref]

Nat. Photonics (1)

N. Jukam, S. S. Dhillon, D. Oustinov, J. Madeo, C. Manquest, S. Barbieri, C. Sirtori, S. P. Khanna, E. H. Linfield, A. G. Davies, and J. Tignon, “Terahertz amplifier based on gain switching in a quantum cascade laser,” Nat. Photonics 3(12), 715–719 (2009).
[Crossref]

Nature (4)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Can light be stopped in realistic metamaterials? Reply,” Nature 455, E11–E12 (2008).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “‘Trapped rainbow’ storage of light in metamaterials,” Nature 450(7168), 397–401 (2007).
[Crossref] [PubMed]

M. D. Lukin and A. Imamoğlu, “Controlling photons using electromagnetically induced transparency,” Nature 413(6853), 273–276 (2001).
[Crossref] [PubMed]

A. Reza, M. M. Dignam, and S. Hughes, “Can light be stopped in realistic metamaterials?” Nature 455(7216), E10–E11 (2008).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Opt. Photon. News (1)

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14(11), 44–48 (2003).
[Crossref]

Phys. Rev. A (1)

Y. J. Huang, W. T. Lu, and S. Sridhar, “Nanowire waveguide made from extremely anisotropic metamaterials,” Phys. Rev. A 77(6), 063836 (2008).
[Crossref]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(5 Pt 2), 057602 (2003).
[Crossref] [PubMed]

Phys. Rev. Lett. (4)

Q. Gan, Y. J. Ding, and F. J. Bartoli, ““Rainbow” trapping and releasing at telecommunication wavelengths,” Phys. Rev. Lett. 102(5), 056801 (2009).
[Crossref] [PubMed]

M. Ibanescu, S. G. Johnson, D. Roundy, C. Luo, Y. Fink, and J. D. Joannopoulos, “Anomalous dispersion relations by symmetry breaking in axially uniform waveguides,” Phys. Rev. Lett. 92(6), 063903 (2004).
[Crossref] [PubMed]

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in photonic crystal waveguides,” Phys. Rev. Lett. 94(7), 073903 (2005).
[Crossref] [PubMed]

Q. Gan, Z. Fu, Y. J. Ding, and F. J. Bartoli, “Ultrawide-bandwidth slow-light system based on THz plasmonic graded metallic grating structures,” Phys. Rev. Lett. 100(25), 256803 (2008).
[Crossref] [PubMed]

Other (2)

G. Grüner, Millimeter and Submillimeter Wave Spectroscopy of Solids (Springer, Berlin, 1998), Chap. 3.

J. He, Centre for THz Research, China Jiliang University, Hangzhou 310018, China, and Z. Hong et al. are preparing a manuscript to be called “Backward coupling of modes in a left-handed metamaterial tapered waveguide.”

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Figures (5)

Fig. 1
Fig. 1 (a) Dispersion curve for the ideal GaAs-rod-loaded cylindrical metallic waveguide as shown in the inset. For the waveguide, R 0 = 2R 1 = 0.4mm. The permittivity of GaAs is 12.9, and the dielectric between the rod and hollow metallic waveguide is air. The dashed line corresponds to the complex mode. (b) The time average Poynting vector along the waveguide for the forward mode corresponding to circle point A in Fig. 1(a). (c) The time average Poynting vector for the backward mode B.
Fig. 2
Fig. 2 (a) The group velocities of modes in the GaAs-rod-loaded metallic waveguide with various R 1. The R 0 is 0.4mm and wavelength of modes is 0.214mm. (b) The wavelength, λcp , of mode at the critical point for different R 1 of waveguide. R 0 = 0.4mm. (c) The λcp for different R 0 of waveguide. R 1 = 0.2mm.
Fig. 3
Fig. 3 (a) Schematic diagram of a tapered waveguide with R 0 = 0.4mm, R 1 = 0.23mm, R 2 = 0.21mm and L = 12mm. (b) The electric field distribution of the wave coupled from left port of the waveguide. (c)-(f) the absolute electric field (|E|) distribution at the plane of y = 0 for four different incident waves in the tapered waveguide, respectively. (c) λ = 2.16mm, (d) λ = 2.14mm, (e) λ = 2.12mm, and (f) λ = 2.10mm.
Fig. 4
Fig. 4 The wavelength at the critical point varies with permittivity of dielectric rod of the waveguide (R 0 = 2R 1 = 0.4mm).
Fig. 5
Fig. 5 (a) The propagation constants of modes as R 1 of lossy and lossless waveguide varies. The wavelength of the guided mode equals to 2.14mm. For both waveguides, R 0 = 0.4mm. The black and gray solid curves correspond to the lossy case, and the green thick lines and red dotted lines correspond to the lossless case. (b) The |E| distribution at plane of y = 0 for incident wave of λ = 2.14mm in the lossy waveguide as shown in Fig. 3(a).

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