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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 4 — Feb. 14, 2011
  • pp: 3063–3076
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Polarization-insensitive subwavelength sharp bends in asymmetric metal/multi-insulator configuration

Yin-Jung Chang and You-Chang Liu  »View Author Affiliations


Optics Express, Vol. 19, Issue 4, pp. 3063-3076 (2011)
http://dx.doi.org/10.1364/OE.19.003063


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Abstract

A new silicon-based sharp waveguide bend in asymmetric metal/multi-insulator configuration is described. TE and TM modes are calculated rigorously electromagnetically from which the general design rules are derived. Numerical simulations show that the respective insertion losses of < 0.085 dB and < 0.229 dB for TE and TM modes can be achieved by introducing a low-index layer between the metal and high-index core. The bending length is determined by the TE mode and has much smaller impacts on the TM that exhibits no resonance-like behavior as does the TE. The combined TE modal and radiation power in the air region is shown to couple back to the Si core through an asymmetric output taper, yielding a high transmission efficiency. Structure-enabled successive photonic-plamsonic mode conversions are shown to increase the TM mode confinement in the high-index core while the plasmonic mode carries up to 42.6% of the input power along the bending section.

© 2011 Optical Society of America

1. Introduction

High-index contrast dielectric waveguides have been in widespread use for many years as they offer a strong mode confinement, dense integration, low propagation loss (if smooth sidewalls are attainable), and the ease of fabrication through mature semiconductor technologies. However, further downscaling waveguiding structures for the realization of optical nanocircuitry is hampered by the natural diffraction limit and strong sub-wavelength field confinement thus becomes crucially important. Nanophotonics using surface plasmon polaritons (SPPs) that can be guided by metallic subwavelength structures beyond diffraction limit is now considered as a promising solution for the implementation of optical nanocircuitry [1

1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

, 2

2. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). [CrossRef]

].

For either long-term developed dielectric- or emerging plasmonics-based photonic devices and circuits, the waveguide bend is one of the most important building blocks and has been attracted continued attention for the last 40 years [3

3. E. A. J. Marcatili, “Bends in optical dielectric waveguides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

5

5. D. R. Mason, D. K. Gramotnev, and K. S. Kim, “Wavelength-dependent transmission through sharp 90° bends in sub-wavelength metallic slot waveguides,” Opt. Express 18, 16139–16145 (2010). [CrossRef] [PubMed]

]. Among various bend designs, air trenches etched into the substrate have been extensively investigated in high- and low-index-contrast material systems [6

6. J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, “Beam-propagation analysis of bent step-index slab waveguides,” Electron. Lett. 26, 822–824 (1990). [CrossRef]

13

13. C. Ma, Q. Zhang, and E. V. Keuren, “Right-angle slot waveguide bends with high bending efficiency,” Opt. Express 16, 14330–14334 (2008). [CrossRef] [PubMed]

]. Corner mirrors formed by deeply-etched reflecting facets, on the other hand, are often found in rib/ridge waveguides [14

14. R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90° waveguide bend structures,” Opt. Express 8, 517–528 (2001). [CrossRef] [PubMed]

16

16. D. Sun, X. Li, D. Wong, Y. Hu, F. Luo, and T. J. Hall, “Modeling and numerical analysis for silicon-on-insulator rib waveguide corners,” J. Lightwave Technol. 27, 4610–4618 (2009). [CrossRef]

]. Alternatively, low-Q resonant cavity [14

14. R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90° waveguide bend structures,” Opt. Express 8, 517–528 (2001). [CrossRef] [PubMed]

, 17

17. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

] and the use of a photonic crystal region as a 90° corner [18

18. G. P. Nordin, S. Kim, J. Cai, and J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Opt. Express 10, 1334–1341 (2002). [PubMed]

] have also been thoroughly studied. In contrast, plasmonics-based waveguide bends using a simple metal-dielectric-metal waveguide [19

19. G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). [CrossRef]

], metal micrograting as Bragg mirrors [20

20. J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, “Surface plasmon routing along right angle bent metal strips,” Appl. Phys. Lett. 87, 221101 (2005). [CrossRef]

], V-groove at 30° in silver with a wedge pillar defect in the corner [21

21. D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186–1188 (2005). [CrossRef] [PubMed]

], dielectric-loaded SPP [22

22. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereus, A. V. Krasavin, and A. V. Zayats, “Bend-and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16, 13585–13592 (2008). [CrossRef] [PubMed]

], and 3-D metallic slot waveguides [5

5. D. R. Mason, D. K. Gramotnev, and K. S. Kim, “Wavelength-dependent transmission through sharp 90° bends in sub-wavelength metallic slot waveguides,” Opt. Express 18, 16139–16145 (2010). [CrossRef] [PubMed]

] have also been reported in the literature.

Over the years, the research and developments in sharp waveguide bends have long been restricted exclusively to either dielectric- or plasmonic-based material systems. Because of their ultrasmall footprints, low-Q resonant cavity [17

17. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

] and some corer mirror designs [14

14. R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90° waveguide bend structures,” Opt. Express 8, 517–528 (2001). [CrossRef] [PubMed]

] may be most well-suited for high-density photonic integrations. However, they were investigated strictly for TE polarization and according to our studies [3-nm grid size and a slab mode excitation in two-dimensional (2-D) numerical simulations at λ0 = 1550 nm], the respective TE and TM power transmissions (end-to-end) are < 77% and < 10% for the optimized structure given in [17

17. C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

]. As the high-index-contrast structures can be potentially low-loss, if properly fabricated, while plasmonic-based waveguides are inherently operational beyond the diffraction limit but are lossy in nature, it may be interesting and perhaps of real value to incorporate plasmonic-based structure into the conventional dielectric waveguides in implementing sharp bends for future photonic nanocircuitry.

In this paper, a new polarization-insensitive sharp waveguide bend in metal/multi-insulator configuration is analytically analyzed and numerically investigated through 2-D finite-difference-time-domain (FDTD) simulations. The introduction of the metal in Si-based sharp waveguide bends presents a radical departure from the conventional air trenches and resonant transmission effect reported in the literature. In addition, the insertion of low-index material (e.g. silica) in between the metal and high-index core sustains the low-loss propagation of transverse electric (TE) and transverse magnetic (TM) electromagnetic energy. The design, analysis, optimization, and physical insights behind them are elaborated in detail.

2. Structure Description

Figure 1 depicts the 2-D schematic of the proposed sharp waveguide bend in metal/multi-insulator configuration. It consists of a silica gap region sandwiched by a 100-nm-wide silver strip and a Si waveguide core region. The remaining areas are assumed to be air. The refractive indexes of silica, Si, and silver are 1.46, 3.5, and 0.1441 – j11.2141 at a free-space wavelength λ0 = 1550 nm. The metal/multi-insulator configuration starts with (terminates at) the beginning (end) of the input (output) linearly-tapered section. The propagating (eigen)mode supported by the composite waveguide is asymmetrically excited by a Si waveguide of 450 nm in width followed by a linear input taper of length lin. The Si core width along the linear sections AB¯ and CD¯ is 200 nm. This was chosen such that, in the absence of the silver region, the fundamental TM mode is below cutoff while its TE counterpart is above cutoff at λ0 = 1550 nm.

Fig. 1 Schematic of the proposed sharp waveguide bend in metal/multi-insulator configuration, where δoffset,inx1xin and δoffset,outy2yout.

The existence of plasmonic mode in 3-D metal/multi-insulator configuration with a thickness of 300 nm was first confirmed by 3-D Finite Element Method computations. Its excitation through the linear taper was further numerically demonstrated by 3-D FDTD method (FullWAVETM, RSOFT Design Group). Although being the most memory efficient numerical method, the 3-D FDTD simulation is still computational costly; thus the proposed sharp bend was investigated using 2-D FDTD with a minimum grid size of 3 nm in order for the convergence of numerical results.

3. Dispersion relations of TE and TM eigenmodes

The TE and TM dispersion relations from which the effective mode indexes of guided modes ( Neff=ɛeff) are obtained are the most important equations in describing the guidance characteristics associated with the proposed waveguide. The 2-D schematic (top view) of a general metal/multi-layer structure is depicted in Fig. 2. Each layer is characterized by its thickness hi and relative permittivity ɛi, i = {m, 1, 2,··· ,n}, where the subscript m stands for the metal. For the case presented in Fig. 1, ɛ1, ɛ2, and ɛ3 correspond to the relative permittivities of silica, Si, and air, respectively (ɛ1 = ɛsilica, ɛ2 = ɛSi, ɛ3 = 1.0). For simplicity, both metal (ɛm) and the bottommost dielectric (ɛn) layers are assumed to be semi-infinite in extent.

Fig. 2 Schematic of a general metal/multi-insulator waveguiding structure.

The general dispersion relation can be obtained conveniently based upon the transmission-line network approach incorporated with the transverse resonance condition
Zup+Zdn=0,
(1)
where Zup and Zdn denote the input impedance seen looking upward and downward from the reference plane, respectively. The characteristic impedance Z0,i of the transmission line associated with the i-th layer is given by
Zi={ωμ0/κiTEmodeκi/(ωɛ0ɛi)TMmode,
(2)
in which ω is the angular frequency, μ0 the free-space permeability, ɛ0 the free-space permittivity, and κi=(2π/λ0)ɛiɛeff is the complex propagation constant of the transmission line associated with the i-th layer. Notice that κi is in the direction transverse to the layer interface, or equivalently, to the direction of propagation.

The input impedance seen looking downward from the reference plane can be calculated successively, starting from the bottommost, semi-infinite region, with the following general equation
Zin,i=Zi(1+Γi,i+1ej2κihi1Γi,i+1ej2κihi),
(3)
where hi is the thickness of the i-th layer (specifically, h1 = wgap and h2 = wSi in the present case) and Γi,i+1 denotes the reflection coefficient at the i-(i + 1) interface
Γi,i+1=Zin,i+1ZiZin,i+1+Zi
(4)
with Zin,i+1 being the input impedance seen looking toward the (i + 1)-th layer from below the i-(i + 1) layer interface. It is worth mentioning that the input impedance seen looking toward the bottommost layer is equal to its characteristic impedance, provided that layer is assumed semi-infinite in extent.

Equations (9) and (10) can then be numerically solved for the complex effective refractive index Neff using the complex Newton’s method [23

23. Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, “Attenuation in waveguides on FR-4 boards due to periodic substrate undulations,” Appl. Opt. 46, 2234–2243 (2007). [CrossRef] [PubMed]

]. The effective mode index will be used in section 4 in developing the design rules for the proposed sharp bend.

4. Design and optimization

A systematic approach, starting with the input linearly-tapered section, was taken in the design and optimization of the proposed sharp bend. In this approach, the entire structure was divided into several building blocks, each of which was successively optimized. The design, optimization, and their physical reasonings are described below.

4.1. Input linearly-tapered section

The input taper is described by the taper length lin and the lateral offset δoffset,in defined as δoffset,in = x1xin, which is the x-position difference between the center line of the linear section and that of the input waveguide (Fig. 1). Figure 3 shows the isometric plots of the transmission (coefficient) as a function of lin and δoffset,in for both mode types. For the TE mode, the silver-silica boundary effectively resembles a reflection plane with a minimal field penetration. Accordingly, TE behaviors along the linear and linearly-tapered sections would be very similar to that along an asymmetric, single-layer slab waveguide. Hence, as is seen in Fig. 3(a), for all lin values under consideration, their respective transmissions are only slightly skewed toward negative δoffset,in and are nearly identical at δoffset,in = −10 nm, which is close to the zero-offset point. The highest TE transmission falls within δoffset,in = [10, 35]nm for lin ≤ 900 nm.

Fig. 3 Transmission coefficient of (a) TE and (b) TM modes with varying input taper length lin and input lateral offset δoffset,inx1xin (Fig. 1). The highest transmissions for TE and TM modes are 88.24% and 96.36% at (lin,δoffset,in) = (700, 30) and (lin,δoffset,in) = (900, 5) nm, respectively.

A positive δoffset,in is required for the TM mode to compensate for a shorter lin in order to maintain > 90% TM transmission at the end of input taper. However, its functionality becomes minimum for lin ≥ 800 nm for both mode types. Further investigations show that, for lin > 700 nm, the TM power channeled in the silica gap varies merely within 2.79% over the span of δoffset,in (not shown in the figure). This indicates that the phase matching condition is fulfilled and is hardly altered with varying lin if lin is sufficiently large. The parameters lin and δin are thus chosen to be 700 nm and 45 nm, respectively, for maintaining transmissions of 88.18% and 96.09% for the respective TE and TM modes at a position 300 nm away from the taper end. It should be emphasized that, physically, δoffset,in is intended to adjust the equi-phase front associated with the y-directed complex Poynting vector so that it is nearly in parallel to that along the liner metal/multi-insulator waveguide section for minimizing the mode mismatch. This can be also perceived in Fig. 4.

Fig. 4 Phase plots of the y-directed complex Poynting vector along the input taper followed by the linear section of length l1 for (a) TE and (b) TM excitations.

4.2. Linear metal/multi-insulator section

The functionality of linear metal/multi-insulator sections (l1 and l2) before and after the bending section is to ensure the equi-phase front associated with the y-directed complex Poynting vector Py is phase-matched (“well-aligned”) across each boundary and is (nearly) perpendicular to the y axis, as shown in Fig. 4. The phase mismatch across each interface along the taper section is clearly seen for the TM mode owing to the phase mismatch associated with the x-directed electric field. On the contrary, the TE phase front is always continuous across the boundaries and is perpendicular to the y axis right after the input taper end. Compared to the TE case, the TM mode requires approximately another 225 nm for its phase front to become well-aligned. Thus both l1 and l2 were set to 364 nm, which is approximately one half the TM guided wavelength.

4.3. Waveguide bending section

With a fixed silica gap width, the geometry of the bending section is completely described by its length lbend and width wbend and may be fully characterized by the bending efficiency η defined as
η=T|bendT|straight,
(17)
where T|bend and T|straight denote the power transmissions associated with the bend and its straight counterpart of identical length, respectively. Specifically, the straight counterpart refers to a structure having exactly the same input waveguide and input taper section, and a straight, 200-nm-wide linear section with its length identical to the total length measured along the joint boundary EGHJ¯. The bending efficiency thus defined would reveal the reflection and excess loss on top of the propagation loss introduced by the proposed sharp bend.

The dependency of the bending efficiency on wbend and lbend is illustrated in Fig. 5. Simulations were conducted with varying bending length at a 10-nm step for differing bending widths. Curves shown in Fig. 5 were obtained through curve fitting of the discrete data. To provide an insight into this figure, it may be necessary to express the physical dimensions in terms of the guided wavelength. Using the dispersion relations, Eqs. (9) and (10), the effective refractive indexes (Neff) of the fundamental mode for wbend ranging from 290 nm to 350 nm and their corresponding guided wavelengths at λ0 = 1550 nm were obtained (Table 1). Notice that with the increase in wbend, the imaginary part of the effective index (Im [Neff]) decreases and the real part (Re [Neff]) increases as more electromagnetic energy is confined within the Si core region. These results are shown to be significant in understanding the transmission behaviors discussed below.

Fig. 5 Bending efficiency as a function of the bending length for differing bending widths from 290 nm to 350 nm for (a) TE and (b) TM modes. The Ez field component in the case of (wbend, lbend) = (350, 250) nm is shown as an inset in (a).

Table 1. Effective refractive index Neff and the corresponding guided wavelength λg at the operating wavelength of 1550 nm for differing bending widths wbend. wbend and λg are in units of nm

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For the TE mode, transmission valleys exist for wbend ≥ 310nm owing to the resonance-like field behavior. The z-component of the electric field Ez is shown as an inset in Fig. 5(a) for (wbend, lbend) = (350,250) nm as a representative case. It exhibits a standing-wave-like pattern between the beginning of the input waveguide and the end of the bending section. However, as the forward- and backward-propagating fields do not form a perfect standing wave, the field amplitude is nonzero at those node-like positions, yielding a nonzero transmission through the bend. On the other hand, the bending efficiency is larger than 90% for lbend ≥ 0.85λg,TE, if wbend ≥ 310 nm, which is one-fifth of the operating wavelength.

For the TM mode, an allowable range of lbend between which the bending efficiency is above 95% is observed. For a fixed lbend value, the bending efficiency is progressively increased as the bending width increases. This may be physically interpreted from the effective length standpoint where, with a larger wbend value, a longer effective bending length in terms of the guided wavelength (lbend/λg) is seen by the guided mode. In addition, the highest bending efficiency associated with each case in Fig. 5(b) occurs when lbend ≈ 0.85λg,TM. However, the bending efficiency stays above 90% for lbend > 0.40λg,TM if wbend is larger than 0.2λ0. It is apparent that, when wbend ≥ 330 nm, the bending efficiency is larger than unity for certain ranges of lbend. Further investigations into the time-average Poynting vectors along the Si-air boundaries reveal that this is determined by the combined net power flow across the boundaries AB¯, BC¯, and CD¯ [24

24. Y.-J. Chang and Y.-C. Liu, “A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry,” IEEE Photon. Technol. Lett.23, 121–123 (2011). [CrossRef]

]. In general, with the increase in wbend, a net power density is coupled across the joint boundary ABCD¯ into the Si core. The arguments also applies to those TE cases having larger-than-unity bending efficiencies shown in Fig. 5(a).

4.4. Output linearly-tapered section

The output linearly-tapered section is equally important as the input one whenever the plasmonic-to-photonic mode conversion is necessary in the photonic nanocircuitry. It is therefore described and optimized in a similar manner as is the input taper. The output lateral offset defined as δoffset,outy2yout is, like the input lateral offset, meant to reshape the equi-phase front associated with the x-directed complex Poynting vector that would normally require a longer taper length lout to “stabilize”. This is necessary since for both TE and TM modes the metal/multi-insulator structure is asymmetric with respect to the direction of propagation as opposed to the symmetric output Si waveguide. Thus the output taper serves as a transition for minimizing mode mismatch due to structure variations. The optimum values for lout and δoffset,in were found to be 660 nm and −85 nm, respectively.

5. Results and discussions

Figure 6 shows the time-average power flow for the optimized structure for TE and TM polarization. The normalized end-to-end transmission to that of a straight, 450-nm-wide Si waveguide of identical length is 98.07% for TE and 94.87% for TM, corresponding to the respective insertion losses of < 0.085 dB and < 0.229 dB introduced by the entire metal/multi-insulator structure. Also, it is worth mentioning that the insertion loss associated with the optimized bend design without the silver region is found to be > 0.65 dB for TE and > 1.61 dB for TM. This indicates that the metal/multi-insulator configuration can indeed significantly improve the transmission efficiency, in particular for the TM mode.

Fig. 6 Time average power flow of the optimized sharp waveguide bend for (a) TE and (b) TM modes with structure parameters wgap = 80, lin = 700, δoffset,in = 45, l1 = l2 = 364, wbend = 330, lbend = 450, lout = 660, and δoffset,out = −85. All figures are in units of nm.

The general design rules for the waveguide bend, in particular for the following five parameters {wgap, l1, wbend, lbend, l2} were derived from the 1550-nm case and are given in Table 2. They were subsequently tested on the bend design at λ0 = 1310 nm and produced immediate result of > 90% end-to-end transmission for both mode types without further optimization. Note that wbend expressed in terms of the free-space wavelength uniquely determines lbend through the calculation of TE effective mode index.

Table 2. General design rules for the proposed waveguide bend

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As is shown in Fig. 6(b), time-average power varies within the Si core and silica gap in the direction of propagation, suggesting power interchange exists between these two regions. The investigation of power interchange (or photonic-plasmonic mode conversion in the case presented) is therefore necessary in gaining physical insight into the waveguiding structures of this kind. However, before further investigations could be made on the sharp waveguide bend, it is helpful and perhaps equally important to first understand the mode conversions associated with its straight counterpart.

Fig. 7 Power interchange of a straight silver-silica-Si waveguide for (a) TE and (b) TM modes with input/output tapers identical to those used in the optimized waveguide bend.

The coupling of TE radiation modes into the output taper may seem, at the first glance, to disagree with the conventional description of the radiation modes in that their ray paths would transmit through at least one core-cladding interface of an asymmetric waveguide with the propagation angles smaller than the critical angle for that interface [25

25. D. L. Lee, Electromagnetic Principles of Integrated Optics (John Wiley & Sons, Inc., 1986).

]. However, when both critical angles for the two core-cladding interfaces are exceeded, the ray associated with the radiation mode can be totally internally reflected at both interfaces and the guidance condition is satisfied. In the present case, since the structure is asymmetric and the radiation modes are incident from the lower-index region, it can be shown that if the total internal reflection (TIR) condition is satisfied at the silica-Si interface, then the TIR condition at the Si-air interface will also be satisfied. To have the TIR take place at the silica-Si interface, the following condition must be satisfied for the angle ϕ between the normals to the two sides of the output taper
ϕθc,12sin1(n0n2),
(18)
where θc,12 denotes the critical angle for the silica-Si interface and n2 and n0 are the refractive indexes of the Si and air, respectively. In the optimized output taper, ϕ = 21.37° which is larger than the minimum required value of 8.05° imposed by Eq. (18) and thus fulfill the condition described above.

In the presence of the bending section, a forced change in the power transfer between PSi and Psilica is found to occur at each waveguide discontinuity for TE and TM modes (Fig. 8). The propagation distance is defined in the same manner as that in Fig. 7. In the TE case, the PSi curve remains almost the same as that in the straight case before point F [shown in the inset of Fig. 8(a)] and gradually increases until 70 nm after point G. Further, the 9.34% increase in PSi from BF to B′–G cuts and the corresponding 3.14% decrease in Psilica from FF′ to GG′ cuts indicate the coupling of “air” modes back to the Si core. Between B′ – G and C′–H cuts, the bending section is transversely uniform, consequently the variation in PSi is negligibly small (1.87%). However, the largest difference in Psilica from G′ to H′ in Fig. 8(a) is 3.56%. Further investigations show that the increase in Psilica is mainly supplied by the radiation from the air region as the TIR at Si-silica interface is not attainable. Similar arguments are also applicable to sections beyond C′–H and HH′ cuts as the structure is symmetric from AE′ to DJ′ cuts with respect to the middle of the bending section.

Fig. 8 Power interchange of the optimized sharp waveguide bend for (a) TE and (b) TM modes.

6. Summary

Acknowledgments

This research was supported in part by Grant NSC-99-2221-E-008-057 from the National Science Council and in part by Grant 99-EC-17-A-07-S1-001 from the Ministry of Economic Affairs, R.O.C. (Taiwan).

References and links

1.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]

2.

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4, 83–91 (2010). [CrossRef]

3.

E. A. J. Marcatili, “Bends in optical dielectric waveguides,” Bell Syst. Tech. J. 48, 2103–2132 (1969).

4.

I. C. Goyal, R. L. Gallawa, and A. K. Ghatak, “Bent planar waveguides and whispering gallery modes: A new method of analysis,” J. Lightwave Technol. 8, 768–774 (1990). [CrossRef]

5.

D. R. Mason, D. K. Gramotnev, and K. S. Kim, “Wavelength-dependent transmission through sharp 90° bends in sub-wavelength metallic slot waveguides,” Opt. Express 18, 16139–16145 (2010). [CrossRef] [PubMed]

6.

J. Yamauchi, S. Kikuchi, T. Hirooka, and H. Nakano, “Beam-propagation analysis of bent step-index slab waveguides,” Electron. Lett. 26, 822–824 (1990). [CrossRef]

7.

L. H. Spiekman, Y. S. Oei, E. G. Metaal, F. H. Groen, P. Demeester, and M. K. Smit, “Ultrasmall waveguide bends: The corner mirrors of the future?” Proc. Inst. Elect. Eng.–Optoelectronics 142, 61–65 (1995). [CrossRef]

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M. Popovič, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, “Air trenches for sharp silica waveguide bends,” J. Lightwave Technol. 16, 1762–1772 (2008).

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L. Li, G. P. Nordin, J. M. English, and J. Jiang, “Small-area bends and beamsplitters for low-index-contrast waveguides,” Opt. Express 11, 282–290 (2003). [CrossRef] [PubMed]

12.

Y. Qian, S. Kim, J. Song, G. P. Nordin, and J. Jiang, “Compact and low loss silicon-on-insulator rib waveguide 90° bend,” Opt. Express 14, 6020–6028 (2006). [CrossRef] [PubMed]

13.

C. Ma, Q. Zhang, and E. V. Keuren, “Right-angle slot waveguide bends with high bending efficiency,” Opt. Express 16, 14330–14334 (2008). [CrossRef] [PubMed]

14.

R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, “A study of high-index-contrast 90° waveguide bend structures,” Opt. Express 8, 517–528 (2001). [CrossRef] [PubMed]

15.

R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood Jr., “Ultracompact coner-mirrors and T-branches in silicon-on-insulator,” IEEE Photon. Technol. Lett.14, 65–67 (2002). [CrossRef]

16.

D. Sun, X. Li, D. Wong, Y. Hu, F. Luo, and T. J. Hall, “Modeling and numerical analysis for silicon-on-insulator rib waveguide corners,” J. Lightwave Technol. 27, 4610–4618 (2009). [CrossRef]

17.

C. Manolatou, S. G. Johnson, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, “High-density integrated optics,” J. Lightwave Technol. 17, 1682–1692 (1999). [CrossRef]

18.

G. P. Nordin, S. Kim, J. Cai, and J. Jiang, “Hybrid integration of conventional waveguide and photonic crystal structures,” Opt. Express 10, 1334–1341 (2002). [PubMed]

19.

G. Veronis and S. Fan, “Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides,” Appl. Phys. Lett. 87, 131102 (2005). [CrossRef]

20.

J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, “Surface plasmon routing along right angle bent metal strips,” Appl. Phys. Lett. 87, 221101 (2005). [CrossRef]

21.

D. F. P. Pile and D. K. Gramotnev, “Plasmonic subwavelength waveguides: next to zero losses at sharp bends,” Opt. Lett. 30, 1186–1188 (2005). [CrossRef] [PubMed]

22.

T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereus, A. V. Krasavin, and A. V. Zayats, “Bend-and splitting loss of dielectric-loaded surface plasmon-polariton waveguides,” Opt. Express 16, 13585–13592 (2008). [CrossRef] [PubMed]

23.

Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, “Attenuation in waveguides on FR-4 boards due to periodic substrate undulations,” Appl. Opt. 46, 2234–2243 (2007). [CrossRef] [PubMed]

24.

Y.-J. Chang and Y.-C. Liu, “A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry,” IEEE Photon. Technol. Lett.23, 121–123 (2011). [CrossRef]

25.

D. L. Lee, Electromagnetic Principles of Integrated Optics (John Wiley & Sons, Inc., 1986).

OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(230.7370) Optical devices : Waveguides
(240.6680) Optics at surfaces : Surface plasmons
(250.5403) Optoelectronics : Plasmonics

ToC Category:
Integrated Optics

History
Original Manuscript: December 7, 2010
Revised Manuscript: January 27, 2011
Manuscript Accepted: January 27, 2011
Published: February 2, 2011

Citation
Yin-Jung Chang and You-Chang Liu, "Polarization-insensitive subwavelength sharp bends in asymmetric metal/multi-insulator configuration," Opt. Express 19, 3063-3076 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-4-3063


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References

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  13. C. Ma, Q. Zhang, and E. V. Keuren, "Right-angle slot waveguide bends with high bending efficiency," Opt. Express 16, 14330-14334 (2008). [CrossRef] [PubMed]
  14. R. Espinola, R. Ahmad, F. Pizzuto, M. Steel, and R. Osgood, "A study of high-index-contrast 90◦ waveguide bend structures," Opt. Express 8, 517-528 (2001). [CrossRef] [PubMed]
  15. R. U. Ahmad, F. Pizzuto, G. S. Camarda, R. L. Espinola, H. Rao, and R. M. Osgood, Jr., "Ultracompact cone mirrors and T-branches in silicon-on-insulator," IEEE Photon. Technol. Lett. 14, 65-67 (2002). [CrossRef]
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  18. G. P. Nordin, S. Kim, J. Cai, and J. Jiang, "Hybrid integration of conventional waveguide and photonic crystal structures," Opt. Express 10, 1334-1341 (2002). [PubMed]
  19. G. Veronis, and S. Fan, "Bends and splitters in metal-dielectric-metal subwavelength plasmonic waveguides," Appl. Phys. Lett. 87, 131102 (2005). [CrossRef]
  20. J.-C. Weeber, M. U. Gonzalez, A.-L. Baudrion, and A. Dereux, "Surface plasmon routing along right angle bent metal strips," Appl. Phys. Lett. 87, 221101 (2005). [CrossRef]
  21. D. F. P. Pile, and D. K. Gramotnev, "Plasmonic subwavelength waveguides: next to zero losses at sharp bends," Opt. Lett. 30, 1186-1188 (2005). [CrossRef] [PubMed]
  22. T. Holmgaard, Z. Chen, S. I. Bozhevolnyi, L. Markey, A. Dereus, A. V. Krasavin, and A. V. Zayats, "Bend-and splitting loss of dielectric-loaded surface plasmon-polariton waveguides," Opt. Express 16, 13585-13592 (2008). [CrossRef] [PubMed]
  23. Y.-J. Chang, T. K. Gaylord, and G.-K. Chang, "Attenuation in waveguides on FR-4 boards due to periodic substrate undulations," Appl. Opt. 46, 2234-2243 (2007). [CrossRef] [PubMed]
  24. Y.-J. Chang, and Y.-C. Liu, "A plasmonic-mode-assisted sharp waveguide bend for silicon optical nanocircuitry," IEEE Photon. Technol. Lett. 23, 121-123 (2011). [CrossRef]
  25. D. L. Lee, Electromagnetic Principles of Integrated Optics (John Wiley & Sons, Inc., 1986).

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