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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26827–26838
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Design of T-shaped nanophotonic wire waveguide for optical interconnection in H-tree network

H. Kurt, I. H. Giden, and D. S. Citrin  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26827-26838 (2011)
http://dx.doi.org/10.1364/OE.19.026827


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Abstract

Nanophotonic wire waveguides play an important role for the realization of highly dense integrated photonic circuits. The miniaturization of optoelectronic devices and realization of ultra-small integrated circuits strongly demand compact waveguide branches. T-shaped versions of nanophotonic wires are the first stage of both power splitting and optical-interconnection systems based on guided-wave optics; however, the acute transitions at the waveguide junctions typically induce huge bending losses in terms of radiated modes. Both 2D and 3D finite-difference time-domain methods are employed to monitor the efficient light propagation. By introducing appropriate combinations of dielectric posts around the dielectric-waveguide junctions within the 4.096μm× 4.096μm region, we are able to reduce the bending losses dramatically and increase the transmission efficiency from low values of 18% in the absence of the dielectric posts to approximately 49% and 43% in 2D and 3D cases, respectively. These findings may lead to the implementation of such T-junctions in near-future high-density integrated photonics to deliver optical-clock signals via H-tree network.

© 2011 OSA

1. Introduction

Nanophotonic wire waveguide structures play a crucial role for compact photonic integrated circuits (PICs) and are deployed for various applications in the design of optoelectronic devices such as power splitters, ring resonators, optical logic gates, wavelength filters, optical switches, and optical-interconnects in H-tree network [1

1. J. Gamet and G. Pandraud, “Ultralow-loss 1 x 8 splitter based on field matching Y junction,” IEEE Photon. Technol. Lett. 16, 2060–2062 (2004). [CrossRef]

8

8. S. H. Tao, Q. Fang, J. F. Song, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Cascade wide-angle Y-junction 1 x 16 optical power splitter based on silicon wire waveguides on silicon-on-insulator,” Opt. Express 16(26), 21456–21461 (2008). [CrossRef] [PubMed]

]. High-density integrated circuits require the minimization of the dimensions of the photonic devices. In addition, sharp 90° bends are desirable to reduce the overall system size. This strongly militates for the use of dielectric waveguides with high refractive-index contrast. Although standard dielectric waveguides with low-index contrast provide low loss with respect to the transmission efficiency, their deployment requires relatively small bend angles with consequent large bend radii, which is not desirable for high-density PICs [9

9. B. Chen, T. Tang, and H. Chen, “Study on a compact flexible photonic crystal waveguide and its bends,” Opt. Express 17(7), 5033–5038 (2009). [CrossRef] [PubMed]

11

11. B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, “Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals,” Appl. Phys. Lett. 93(18), 181107 (2008). [CrossRef]

].

Increasing the index contrast may help us improve the optical confinement and increase the density of circuits. For single-mode operation, the dimensions of the waveguide should be reduced. Although Refs. 12

12. W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert, B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout, “Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology,” J. Lightwave Technol. 23(1), 401–412 (2005). [CrossRef]

and 13

13. P. Dumon, W. Bogaerts, V. Wiaux, J. Wouters, S. Beckx, J. Van Campenhout, D. Taillaert, B. Luyssaert, P. Bienstman, D. V. Thourhout, and R. Baets, “Low-loss SOI photonic wires and ring resonators fabricated with deep UV lithography,” IEEE Photon. Technol. Lett. 16(5), 1328–1330 (2004). [CrossRef]

have reported the propagation losses for straight photonic wires to be ~0.24 dB/mm, losses become excessive as the bends become sharper, especially for 90° bends [5

5. W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact Wavelength-Selective Functions in Silicon-on-Insulator Photonic Wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006). [CrossRef]

, 14

14. Y. A. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004). [CrossRef] [PubMed]

]. At this stage, it may be helpful to emphasize that the bending losses will be of no consequence when bend radius is adjusted to be high enough. On the other hand, while the bend radius is dramatically decreased to have compact devices, several approaches have been described in the literature to reduce severe bending losses. Corner mirrors, waveguide resonators, air trenches, and topology optimization have been proposed [15

15. M. Popovic, K. Wada, S. Akiyama, H. A. Haus, and J. Michel, “Air trenches for sharp silica waveguide bends,” J. Lightwave Technol. 20(9), 1762–1772 (2002). [CrossRef]

19

19. J. S. Jensen and O. Sigmund, “Topology optimization of photonic crystal structures: a high-bandwidth low-loss T-junction waveguide,” J. Opt. Soc. Am. B 22(6), 1191–1198 (2005). [CrossRef]

]. In general, the complexity of the proposed solutions and their limited operating bandwidth are issues of concern. Here, we propose a new solution to enhance transmission efficiency of narrow-waveguide T-junctions that can be easily incorporated in H-tree networks. Most of the time, achieving high transmission only within a limited band is not enough and broadband solutions are preferable. We aimed therefore to design bends and branches which provide small bending losses over high bandwidth and occupy small area.

T-junctions are a basic part of a more complicated network configuration such as H-tree circuits that can be used for power distribution and optical-signal clock delivery. An effective design that promotes high power transmission through sharp corners can be systematically duplicated to build larger structures, such as optical interconnects that may contain many branches [20

20. L. Pavesi and G. Guillot, Optical Interconnects: The Silicon Approach (Springer, 2006).

]. Optical clock signals should be distributed to each receiver (photo-detector) with an equal time delay. To achieve that, high-index contrast waveguides with a special layout that resemble an H-tree shape can be used. The potential advantages of optical interconnects over electrical ones include high speed, high bandwidth, and low power consumption. High-speed processors handling large data loads demand the delivery of optical rather than electrical clock signals. Potential drawbacks of electrical interconnects include possible Joule heating that may degrade the attractive features of them such as faster speed and higher density. This argues for high-transmission junctions to minimize requisite optical power levels as well as stray light that may itself contribute to heating. High-efficiency methods that utilize resonant structures, however, may not be robust with respect to wavelength shifts due to any changes occurring in the environment. Such resonant wavelength shifts may occur with the changes in the chip temperature due to the temperature dependence of refractive index of the optical cavities. Hence, our approach is broadband from the start. The waveguide material should be transparent to over the entire range of potential operating wavelengths; consequently, we select Si as a waveguide material.

In this paper, a hybrid structure with a zero bending radius is discussed. The studies reported in Refs. 5

5. W. Bogaerts, P. Dumon, D. V. Thourhout, D. Taillaert, P. Jaenen, J. Wouters, S. Beckx, V. Wiaux, and R. G. Baets, “Compact Wavelength-Selective Functions in Silicon-on-Insulator Photonic Wires,” IEEE J. Sel. Top. Quantum Electron. 12(6), 1394–1401 (2006). [CrossRef]

, 9

9. B. Chen, T. Tang, and H. Chen, “Study on a compact flexible photonic crystal waveguide and its bends,” Opt. Express 17(7), 5033–5038 (2009). [CrossRef] [PubMed]

, 10

10. Y. Zhang and B. Li, “Photonic crystal-based bending waveguides for optical interconnections,” Opt. Express 14(12), 5723–5732 (2006). [CrossRef] [PubMed]

, 11

11. B. Chen, T. Tang, Z. Wang, H. Chen, and Z. Liu, “Flexible optical waveguides based on the omnidirectional reflection of one-dimensional photonic crystals,” Appl. Phys. Lett. 93(18), 181107 (2008). [CrossRef]

and 14

14. Y. A. Vlasov and S. McNab, “Losses in single-mode silicon-on-insulator strip waveguides and bends,” Opt. Express 12(8), 1622–1631 (2004). [CrossRef] [PubMed]

necessitate small bend angles with consequence of large bend radii. The combination of photonic crystals (PC) and photonic wires is proposed in order to cope with the problem of high bend losses. A photonic dielectric wire is surrounded by air and the PC is composed of a square lattice of dielectric rods that are only present in the vicinity of the junctions where excess bend losses would otherwise appear. By means of the photonic band gap (PBG) mechanism [21

21. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996). [CrossRef] [PubMed]

25

25. A. Martinez, J. Garcia, G. Sanchez, and J. Marti, “Planar photonic crystal structure with inherently single-mode waveguides,” J. Opt. Soc. Am. A 20(11), 2131–2136 (2003). [CrossRef] [PubMed]

], the PC behaves as a photonic insulator preventing the light from penetrating into the surrounding region resulting in higher light confinement. After we demonstrate numerically effective signal delivery of T-junction photonic wires both in 2D and 3D, we finally implemented 1 to 4 fanouts in an H-tree configuration in which 1 to 2n fanouts are possible, where n is an integer. We should emphasize that the proposed solution in Ref. 21

21. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996). [CrossRef] [PubMed]

is only for a PC-waveguide structure. However, we here offer a hybrid structure that is composed of a PC and high-index contrast nanowire waveguide. Besides, the PC portion is retained only proximate to the junction itself. The remainder of the structure is Si-waveguide on top of an insulator layer.

The rest of the paper is organized as follows: To address the bend losses in narrow waveguides, we propose optimized waveguide corners designed for H-tree interconnects in Sec. I. Section II describes light transport performance for three cases: standard T-junctions, the same junction surrounded by PC, and the optimized composite version of the structure. Section III outlines 3D investigations of the optimized T-junction. Light transmission in an H-tree network is presented in Sec. IV. We give concluding remarks in Sec. V.

2. Two-dimensional T-junction design and enhanced power transmission

The original T-junction structure is made up of Si (n1=3.45) surrounded by air (nair=1.0) as shown in Fig. 1
Fig. 1 Schematic drawing of the T-junction nanophotonic wire dielectric waveguide is shown. The width and refractive index of the dielectric slab (w) is 0.20a and 3.46, respectively. The equally divided input light pulse is shown in the branches. The arrows indicate the direction of the signal flow.
. The width of the waveguidew, is represented in terms of a constant, a (w=0.20a). The parameter a is defined shortly below. For numerical studies in 2D configurations, a transverse magnetic (TM) guided mode is assumed, in which case the corresponding nonzero electric- and magnetic-field components are Ez, Hx, and Hy respectively. In order to improve the poor power transmission capability of a standard T-junction, some modifications will be made in the area proximate to the junction.

For our 2D analysis of T-junction structures, we first carry out simulations for the propagation of electromagnetic waves by using the 2D finite-difference time-domain (FDTD) method [26

26. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

]. The spectral content of the transmitted power is calculated by taking the ratio of the output power to input power. For the correct normalization of the transmission efficiency, we need to detect both incident and output pulses. The input power is calculated in the absence of sharp corners. Output detector planes are placed outside the engineered area. To eliminate back reflections originating from the ends of the finite computational window, we used perfectly matched layer absorbing boundary conditions [27

27. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

]. In Fig. 2
Fig. 2 The power transmission spectra of three cases are shown. A regular T-junction nanowire dielectric waveguide corresponds to solid-black line. The dashed-green line represents the transmission efficiency of the structure whose schematic drawing is presented in Fig. 4. The T-junction nanowire dielectric waveguide is surrounded by photonic crystal that is composed of dielectric rods with radii, r = 0.20a. The dotted-red line corresponds to the power transmission efficiency spectrum for the case in which r1and r2are adjusted to be 0.18a and 0.26a, respectively. The structure in this case is presented in Fig. 5.
the normalized transmission coefficient for the T-shaped structure is presented with a solid line. As can be seen from the figure, this structure has poor transmission efficiency of around 18%. In the lossless case, that value should correspond to 50% efficiency.

In Fig. 3
Fig. 3 Steady-state electric field (Ez) distribution of TM mode for the regular T-junction nanowire waveguide when the operating frequency is centered atλ=1.55μm. The red and blue colors represent the maximum and minimum electric-field values, respectively.
, a snap shot of the pulse propagation for the T-junction structure is shown to illustrate the severe power leakage in the junction area. As can be clearly observed, radiated field leaves the waveguide and consequently the resulting bend loss at the junction of the structure is very high. The 18% transmission efficiency in each branch gives rise to 64% radiation loss in total due to the bend loss.

The wavelength of the operating signal is taken to beλ=1.55µm. In that case, the optimal lattice constant isa=512 nm as mentioned previously. The efficient division of the optical pulse into the two branches can be observed in Fig. 6.

3. Three-dimensional analysis of T-junction

While the 2D analysis given above is indicative of performance, a 3D analysis is desirable to obtain more accurate results [29

29. Z. Sheng, D. Dai, and S. He, “Comparative Study of Losses in Ultrasharp Silicon-on-Insulator Nanowire Bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009). [CrossRef]

] and to understand the role of out-of-plane and substrate losses occur. A similar 3D data-extraction procedure as in 2D case is conducted in this section. The optimization steps carried out in 2D are repeated in 3D to finely tune and enhance the transmission efficiency of T-junctions. The schematic drawing of the 3D structure is shown in Fig. 7
Fig. 7 The three-dimensional representation of the T-junction is shown.
. The T-junction photonic wire waveguide is surrounded by dielectric Si rods, with nSi=3.45 and laid upon a SiO2 substrate layer. Above the core region, air is used as cladding. The core region is sandwiched (along the z-direction) by SiO2 from the bottom and air from the top. In addition to that, the corner regions are accompanied by periodic dielectric rods around corner region. The radii of the silicon rods are selected as r=0.23a (117.6 nm). This change was made to obtain optimal results in 3D concerning the transmission efficiency. The height of the waveguide is taken to be h = 3a, which is nearly equal to 1.535 µm. The substrate beneath the Si rods and the wire is composed of silica with refractive indexnSiO2=1.44. The width of the waveguide is 0.20a. The parameters of the structure (waveguide width, radii of rods and slab height) are selected to have large bandwidth for the fundamental guided TM mode. It is known that the slab thickness is usually higher for TM mode than TE mode if one wants to obtain wide bandwidth [30

30. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]

]. Hence, we selected the height of the slab for TM mode according to 3D FDTD analysis that ensures both high transmission for single 90° waveguide bend and single mode operation spanning whole band gap region [25

25. A. Martinez, J. Garcia, G. Sanchez, and J. Marti, “Planar photonic crystal structure with inherently single-mode waveguides,” J. Opt. Soc. Am. A 20(11), 2131–2136 (2003). [CrossRef] [PubMed]

, 28

28. H. Kurt, I. H. Giden, and K. Ustun, “Highly efficient and broadband light transmission in 90° nano-photonic wire waveguide bends,” J. Opt. Soc. Am. B 28(3), 495–501 (2011). [CrossRef]

, 30

30. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]

]. The band-gap guided mode appears in the corner region due to surrounding periodic dielectric rods. The other regions are composed of uniform dielectric wire waveguide. As a result, the confinement mechanism is only due to the total-internal reflection. It can be feasible to fabricate such a waveguide with a high aspect ratio, which corresponds to a value of h/w=(3.00a/0.20a)=15in our study, thanks to the recent advancements in the semiconductor fabrication technology [31

31. G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205 (2011). [CrossRef]

].

The transmission efficiency in 3D configuration was calculated and the result is presented in the solid-blue line in Fig. 8
Fig. 8 The power transmission efficiency spectrum for the optimized 3D structure is shown with a solid-blue line. The dashed-red line indicates the efficiency curve obtained by 2D FDTD method.
. As compared to 2D analysis, the transmission efficiency drops 4-5% near the central region of the spectrum, which is actually due to the out-of-plane loss. The finding dictates that the leading loss mechanism in 3D is, again, due to bend loss. For high-index contrast dielectric waveguides, the out-of-plane and substrate to leakage losses are not a major concern as we see from the 3D FDTD results. This is mainly because of the fact that the index contrast between core and cladding/substrate is high enough for the total internal reflection to give strong vertical field confinement. 4-5% efficiency drop corresponds to a power level change that occurs when 3D analysis is performed instead of 2D one. The out-of-plane and leakage to substrate losses are only considered in 3D. As a result, the comparison between 4 and 5% additional loss due to out-of-plane and leakage to substrate losses versus 64% bending loss shows the fact that the main loss contribution in these structures arises because of the sharp corners. It is again important to mention that we excluded insertionand propagation losses in the current work. On the other hand, we should emphasize the importance of the scattering losses that may occur due to sidewall roughness. It will be very crucial to determine the overall performance of fabricated systems; however, we do not address such loss being outside the scope of the present work. The other critical aspect of deployed systems is the input and output coupling. The size mismatch between various waveguides necessitates the implementation of spot-size converters. Novel solutions achieving efficient couplers were proposed in the literature [32

32. H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007). [CrossRef]

, 33

33. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009). [CrossRef]

].

4. 1x4 optical pulse distribution in H-tree network

This section outlines a prototype for optical signal distribution in an H-tree optical waveguide network. It’s well-known that optical clock signal distribution for routing timing signals to all parts of a chip with the same propagation delays plays a key role to reduce skew of clocking in VLSI design [20

20. L. Pavesi and G. Guillot, Optical Interconnects: The Silicon Approach (Springer, 2006).

, 34

34. T. Fukazawa, A. Sakai, and T. Baba, “H-tree-type optical clock signal distribution circuit using a Si photonic wire waveguide,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1461–L1463 (2002). [CrossRef]

]. Therefore, the use of H-tree interconnections is inevitable for high-density photonic integrated circuits. Below, we demonstrate numerically transmission of light to 4 fanouts. By duplicating the optimized T-junction in a systematic manner, we obtain an H-tree configuration that is represented in Fig. 9
Fig. 9 The schematic presentation of the 1x4 optical signal distribution in H-tree network.
. This topology ensures the delivery of the input signal to output ports at equal propagation delays. The parameters of the structure are kept the same as before. The source is placed in the input waveguide. The output signals are detected at the end of each branch.

The calculated transmission efficiency of the 1x4 branches is around 23%, as can be seen in Fig. 10
Fig. 10 The transmission efficiency of 1x4 optical signal distribution in H-tree network.
. We observed narrowing in the bandwidth despite the high transmission. Such an observation can be explained as follows: Even though we do not directly incorporate a cavity configuration at the junction, surrounding the waveguide by the dielectric rods gives rise to a very low-Q cavity (Q<10) type of configuration. Each additional T-junction included in the structure contributes to the enhancement of Q associated with the junctions. As a result, the slightly larger Q diminishes the overall bandwidth of the nanowire waveguide.

In order to demonstrate the high transmission capability of the designed branches in the H-tree network configuration, we prepared a snap shot of the pulse propagation down the waveguide and also provided a movie (Media 1). The effective power distribution is apparent in Fig. 11
Fig. 11 The steady-state e-field distribution of the input signal in H-tree network is shown. T1 and T2 correspond to transmitted powers at the junctions (Media 1).
. Each time the input pulse is divided equally, the color of the electric field in the respective waveguide branch fades. Even though we have achieved 4 fanouts in the H-tree in Fig. 11, the idea is easily generalize to 2n fanouts, with n an integer.

We summarize the best values of the transmission efficiencies achieved in the present work. It provides us a concise way to judge the performance of the proposed idea. The difference between the values of transmission efficiencies in 2D and 3D configurations corresponds to out-of-plane and leakage to substrate losses. (43x2)% efficiency represents 3D result. The 14% loss includes bending, out-of-plane and leakage to substrate losses for one-junction. On the other hand, (23x4)% efficiency represents the findings of 2D analysis. The 8% loss is due to the 1x4 H-tree network configuration. As a result, loss per junction is 4%. The difference between the 2D and 3D results is 10% that encloses out-of-plane and leakage to substrate losses for one-junction, under the assumption that the bending losses in 2D and 3D structures are equal. When there is no manipulation made to the corner region, the loss per junction is 64%. That means we report a sixteen times improvement in terms of bending loss reduction (64% loss reduces down to 4%).

The flow of the input power at each junction can be monitored as shown in Fig. 11. If we define the power split at first junction as T1 then at the second junction, the wave splits again. This efficiency is defined as T2. There exists a relationship between T1 and T2 asT2=(T1)2. When the value of T1 is taken asT1=48.6%, as reported in Sec. 2 then T2 turns out to be(0.486)2=23.61%. This number is very close to 23% efficiency value as reported in Sec. 4. We have 0.12 dB bending loss for 1x2 T-junction and 0.377 dB bending loss for 1x4 H-tree network case according to 2D study. On the other hand, 3D analysis gives us a loss value of 0.49 dB that includes other loss mechanisms in addition to bending loss. Ref. 8

8. S. H. Tao, Q. Fang, J. F. Song, M. B. Yu, G. Q. Lo, and D. L. Kwong, “Cascade wide-angle Y-junction 1 x 16 optical power splitter based on silicon wire waveguides on silicon-on-insulator,” Opt. Express 16(26), 21456–21461 (2008). [CrossRef] [PubMed]

experimentally reported 0.15 dB and 2.41 dB excess losses for 1x2 and 1x16 splitter cases, respectively that excluded insertion and propagation losses.

5. Conclusion

The low transmission through T-junctions made of high-index contrast narrow waveguides associated with bend losses is addressed and a novel solution is proposed. Transmission efficiencies extending up to 43% (ideal case corresponds to 50%) are predicted based on a 3D FDTD analysis. Sharp corners appearing along the waveguide branches were optimized for low-loss and uniform light propagation with a balanced propagation delay. Taking advantage of the optimized T-junction, we have shown efficient distribution of an input pulse in a 1x4 H-tree network configuration. The proposed solution in the present study may contribute to the widespread usage of photonic integrated circuits based on high-index Si nanophotonic wires.

Acknowledgments

I.H.G and H.K. gratefully acknowledge the financial support of the Scientific and Technological Research Council of Turkey (TUBITAK), Project numbers 108T717 and 110T306. H.K. also acknowledges support from the Turkish Academy of Sciences Distinguished Young Scientist Award (TUBA-GEBIP). D.S.C. acknowledges the support of the National Science Foundation under grant ECCS 0925713.

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L. Pavesi and G. Guillot, Optical Interconnects: The Silicon Approach (Springer, 2006).

21.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides,” Phys. Rev. Lett. 77(18), 3787–3790 (1996). [CrossRef] [PubMed]

22.

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys. 73(9), 096501–096557 (2010). [CrossRef]

23.

H. Kurt and D. S. Citrin, “Photonic-crystal heterostructure waveguides,” IEEE J. Quantum Electron. 43(1), 78–84 (2007). [CrossRef]

24.

H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express 13(25), 10316–10326 (2005). [CrossRef] [PubMed]

25.

A. Martinez, J. Garcia, G. Sanchez, and J. Marti, “Planar photonic crystal structure with inherently single-mode waveguides,” J. Opt. Soc. Am. A 20(11), 2131–2136 (2003). [CrossRef] [PubMed]

26.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).

27.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114(2), 185–200 (1994). [CrossRef]

28.

H. Kurt, I. H. Giden, and K. Ustun, “Highly efficient and broadband light transmission in 90° nano-photonic wire waveguide bends,” J. Opt. Soc. Am. B 28(3), 495–501 (2011). [CrossRef]

29.

Z. Sheng, D. Dai, and S. He, “Comparative Study of Losses in Ultrasharp Silicon-on-Insulator Nanowire Bends,” IEEE J. Sel. Top. Quantum Electron. 15(5), 1406–1412 (2009). [CrossRef]

30.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60(8), 5751–5758 (1999). [CrossRef]

31.

G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B 29(2), 021205 (2011). [CrossRef]

32.

H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett. 19(19), 1532–1534 (2007). [CrossRef]

33.

O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys. 105(10), 103708 (2009). [CrossRef]

34.

T. Fukazawa, A. Sakai, and T. Baba, “H-tree-type optical clock signal distribution circuit using a Si photonic wire waveguide,” Jpn. J. Appl. Phys. 41(Part 2, No. 12B), L1461–L1463 (2002). [CrossRef]

OCIS Codes
(130.2790) Integrated optics : Guided waves
(130.3120) Integrated optics : Integrated optics devices
(200.4650) Optics in computing : Optical interconnects
(250.5300) Optoelectronics : Photonic integrated circuits
(130.5296) Integrated optics : Photonic crystal waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: September 6, 2011
Revised Manuscript: November 18, 2011
Manuscript Accepted: December 1, 2011
Published: December 15, 2011

Citation
H. Kurt, I. H. Giden, and D. S. Citrin, "Design of T-shaped nanophotonic wire waveguide for optical interconnection in H-tree network," Opt. Express 19, 26827-26838 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26827


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  21. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High Transmission through Sharp Bends in Photonic Crystal Waveguides,” Phys. Rev. Lett.77(18), 3787–3790 (1996). [CrossRef] [PubMed]
  22. M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Prog. Phys.73(9), 096501–096557 (2010). [CrossRef]
  23. H. Kurt and D. S. Citrin, “Photonic-crystal heterostructure waveguides,” IEEE J. Quantum Electron.43(1), 78–84 (2007). [CrossRef]
  24. H. Kurt and D. S. Citrin, “Annular photonic crystals,” Opt. Express13(25), 10316–10326 (2005). [CrossRef] [PubMed]
  25. A. Martinez, J. Garcia, G. Sanchez, and J. Marti, “Planar photonic crystal structure with inherently single-mode waveguides,” J. Opt. Soc. Am. A20(11), 2131–2136 (2003). [CrossRef] [PubMed]
  26. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2005).
  27. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys.114(2), 185–200 (1994). [CrossRef]
  28. H. Kurt, I. H. Giden, and K. Ustun, “Highly efficient and broadband light transmission in 90° nano-photonic wire waveguide bends,” J. Opt. Soc. Am. B28(3), 495–501 (2011). [CrossRef]
  29. Z. Sheng, D. Dai, and S. He, “Comparative Study of Losses in Ultrasharp Silicon-on-Insulator Nanowire Bends,” IEEE J. Sel. Top. Quantum Electron.15(5), 1406–1412 (2009). [CrossRef]
  30. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B60(8), 5751–5758 (1999). [CrossRef]
  31. G. Si, A. J. Danner, S. Lang Teo, E. J. Teo, J. Teng, and A. A. Bettiol, “Photonic crystal structures with ultrahigh aspect ratio in lithium niobate fabricated by focused ion beam milling,” J. Vac. Sci. Technol. B29(2), 021205 (2011). [CrossRef]
  32. H. Kurt and D. S. Citrin, “A novel optical coupler design with graded-index photonic crystals,” IEEE Photon. Technol. Lett.19(19), 1532–1534 (2007). [CrossRef]
  33. O. Cakmak, E. Colak, H. Caglayan, H. Kurt, and E. Ozbay, “High efficiency of graded index photonic crystal as an input coupler,” J. Appl. Phys.105(10), 103708 (2009). [CrossRef]
  34. T. Fukazawa, A. Sakai, and T. Baba, “H-tree-type optical clock signal distribution circuit using a Si photonic wire waveguide,” Jpn. J. Appl. Phys.41(Part 2, No. 12B), L1461–L1463 (2002). [CrossRef]

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