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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 24231–24239
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Development of high-density single-mode polymer waveguides with low crosstalk for chip-to-chip optical interconnection

Akio Sugama, Kenichi Kawaguchi, Motoyuki Nishizawa, Hidenobu Muranaka, and Yasuhiko Arakawa  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 24231-24239 (2013)
http://dx.doi.org/10.1364/OE.21.024231


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Abstract

High-density single-mode polymer waveguides were fabricated for chip-to-chip optical interconnection. The waveguides were designed as minimized mode field diameters for the lowest inter-channel crosstalk caused by mode coupling. The optimum relative index difference chosen was 1.2% to ensure compatibility with low crosstalk and wide fabrication tolerances. The 60-mm-length linear waveguides demonstrated a low propagation loss of 0.6 dB/cm and −45 dB crosstalk at 1310 nm. Also, a new crosstalk mechanism for a curved waveguide was revealed.

© 2013 OSA

1. Introduction

Optical waveguides that connect LSIs should have the features of high density, large length, low crosstalk, and easy fabrication. The LSIs have to be mounted on packages, which convert the pin pitches between printed circuit boards (PCBs) and LSI chips. This requires the lengths of the waveguides to at least the same as that of the package. Therefore, dense and long waveguides are required to reduce crosstalk. Moreover, it is desirable that fabrication conditions for optical waveguides are mild, because the waveguides will be formed on various substrates made of plastics, glass, silicon, ceramics, etc.

Polymers have many advantages when used to make optical waveguides. They are easily coated by spin-coating and are cured at mild temperatures. Polymer waveguides can be formed on large areas on various substrates, and they can also be stacked as multilayers [3

3. U. Streppel, P. Dannberg, C. Wachter, A. Brauer, L. Frohlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photoresponsive (inorganic–organic hybrid) polymers,” Opt. Mater. 21(1-3), 475–483 (2003). [CrossRef]

]. Generally, polymer waveguides have been based on actual materials that are not always ideal for chip-to-chip interconnection. In this study, we design the waveguides with no restriction on their refractive indices. Low-crosstalk conditions are searched using mode field diameters (MFD) of the waveguides, and their inter-channel crosstalk are simulated using the beam propagation method (BPM). Then, the characteristics of fabricated parallel waveguides with the linear and S-bend form were found to agree well with the simulation results.

2. Design of high-density waveguides

2.1 Concept of optical interconnection

It is expected that by the year 2018, high-performance LSIs will have several thousand pairs of transmission channels and reception channels because the bandwidth between CPUs and PCBs is expected to increase to over 100 Tbit/s [4

4. R. D. Williams, T. Sze, D. Huang, S. Pannala, and C. Fang, “Server memory roadmap” presented at JEDEC Server Memory Forum Shenzhen, China, 1 Mar. 2012. http://www.jedec.org/sites/default/files/Ricki_Dee_Williams-Final_0.pdf

] and their data rates to 45 Gbit/s [5

5. International Technology Roadmap for Semiconductors, Assembly & Packaging, 2012 Tables, http://www.itrs.net/Links/2012ITRS/2012Tables/AssemblyPkg_2012Tables.xlsx

]. Our proposed interconnect system is shown in Fig. 1
Fig. 1 Concept of high-density optical interconnection.
. For the shortest electric wirings, LSI chips are mounted on electro-optic (E/O) and optic-electro (O/E) conversion interposers. The optical signals are connected to on-board single-mode waveguides by grating couplers, and the waveguides are prolonged to the destinations. As the optical beam diameter increases significantly at the grating coupler, the allowable misalignment between the interposer and on-board waveguides is expected to be almost the same as the VCSEL link.

It is possible for multiple E/O and O/E converters to be integrated in a 2-dimensional layout on the interposer. However, the waveguides should have high density because they are integrated essentially in one dimension, even if they are stacked as multilayers. The interposer is almost the same size as a high-performance LSI, which is 750 mm2 [5

5. International Technology Roadmap for Semiconductors, Assembly & Packaging, 2012 Tables, http://www.itrs.net/Links/2012ITRS/2012Tables/AssemblyPkg_2012Tables.xlsx

].

It is possible to arrange one thousand single-layered waveguides at each edge of the interposer if the pitch of the waveguides can be made to be less than 27 μm. WDM can reduce the waveguide count, but it is necessary to perform absolute wavelength management. At the present time, there is no solution for effective wavelength control.

The length of the waveguides depends on the LSI package. The package size estimated from the pin count and solder bump pitch in [5

5. International Technology Roadmap for Semiconductors, Assembly & Packaging, 2012 Tables, http://www.itrs.net/Links/2012ITRS/2012Tables/AssemblyPkg_2012Tables.xlsx

] is 40 mm × 40 mm to 50 mm × 50 mm and the corresponding minimum length of the waveguide is about 60 mm.

2.2 Mode field diameter

The main factor affecting the inter-channel crosstalk of single-mode waveguides is the mode coupling between adjacent waveguides [6

6. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguides and directional couplers in GaAs-imbedded and ridged,” Appl. Opt. 13(2), 327–330 (1974). [CrossRef] [PubMed]

,7

7. E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969). [CrossRef]

]. For waveguides having the same pitch, the minimized MFD gives the smallest mode coupling. Hence, we simulate the MFD of the waveguides of the square core. The refractive index of the cladding was fixed at 1.450, and that of the core was calculated from the relative index difference (Δ). The operating wavelength was 1310 nm. Figure 2
Fig. 2 Mode field diameter (MFD) of fundamental mode of square core at 1310 nm. Broken line shows the smaller MFD than surrounding area.
shows the calculated MFD in TE mode using a 3D complex mode solver (FIMMWAVE). The TM mode also had the same results. The broken line shows the valley of MFD which is smaller MFD than the surrounding area. Therefore, we identified six conditions, as indicated by the circles in the Figs., whose core sizes are at intervals of 0.5 μm in Table 1

Table 1. List of Simulated Parameters

table-icon
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.

2.3 Coupling length

The mode coupling theory gives Eqs. (1) and (2), which relate to the mode transfer between two or three parallel waveguides, respectively. z is the propagation length and L is the coupling length required to transfer the optical power completely. κ is the coupling coefficient. As the crosstalk power is very small, both are transformed using the same equation.

P=P0sin2(κz)=P0(κz)2=P0(πz2L)2.
(1)
P=P02sin2(2κz)=P0(κz)2=P0(πz2L)2.
(2)

These formulas are for a single launched waveguide, but the optical interconnection has many launched waveguides. The crosstalk of multichannel waveguides is given in Ref [8

8. S. Tang, R. T. Chen, and M. A. Peskin, “Packing density and interconnection length of a highly parallel optical interconnect using polymer-based, single-mode bus arrays,” Opt. Eng. 33(5), 1581–1586 (1994). [CrossRef]

]. Pcoh and Pinc are for coherent and incoherent light sources, respectively.

Pcoh=4P0(κz1κz)2=4P0(π(z/L)2π(z/L))2.
(3)
Pinc=2P0(κz1κz)2=2P0(π(z/L)2π(z/L))2.
(4)

Figure 3
Fig. 3 Inter-channel crosstalk vs. a ratio of propagation length z to coupling length L calculated from Eqs. (1), (3), and (4).
shows a plot of the crosstalk against the ratio of the propagation length to the coupling length. The target crosstalk value depends on the interconnect system, but a value of −40 dB is sufficient for a wide variety of systems that include telecommunication systems. Then, the target propagation length will be within 0.3% of the coupling length. For a 60-mm-length propagation, the coupling length has to be longer than 20 m.

Then, we calculate the optical power transfer between two parallel waveguides using a 3D beam propagation method (OptiBPM). The propagation length in the simulations was adjusted to the expectable coupling length, but the maximum length was 1 m. The optical power in the adjacent waveguide was fitted to Eq. (1) to solve its coupling length. Our target coupling length was longer than 20 m and its pitch smaller than 27 μm, as shown by the red rectangle in Fig. 4
Fig. 4 Relationship between waveguide pitch and coupling lengthfor a square core at 1310 nm. The red area indicates the target for high-density and low-crosstalk waveguides.
. The simulated conditions except for Δ 0.55% are satisfied by the target.

2.4 Tolerances of fabrication process

There is a trade-off between Δ and the core size. A low Δ indicates a large core that is easily fabricated, and it requires fine control of the refractive indices. Figure 5
Fig. 5 Changes of MFD due to waveguide parameters, (a) core size and (b) refractive index.
shows that the MFD increases because of the variations in Δ and the core size, whose ranges are possible for the polymer waveguides. Figure 5(a) indicates that the MFD is easily affected by the core size variations when Δ is at least 1.7%. Also, from Fig. 5(b), we see that the MFD is easily increased with variation in the refractive index when Δ is 0.9% or less. Therefore, to ensure good tolerance, we chose the waveguide parameters for which Δ is 1.2% and the core size is 3.0 μm.

3. Fabrication

In general, the polymer waveguides have been fabricated using transparent materials at the operating wavelength. However, we give priority to the refractive indices over transparency. Hence, UV cured epoxy resins with ordered refractive indices (NTT Advanced Technology) were selected to make our waveguides. The UV cured epoxy resins have losses of about 1 dB/cm at 1310 nm. The refractive indices used to fabricate the waveguides were measured by a prism coupler (Metricon model 2010) and are given in Table 2

Table 2. Refractive indices of high-density waveguides

table-icon
View This Table
| View All Tables
.

The waveguides were fabricated by typical processes [9

9. T. Watanabe, M. Hikita, M. Amano, Y. Shuto, and S. Tomaru, “Vertically stacked coupler and serially grafted waveguide: hybrid waveguide structures formed using an electro-optic polymer,” J. Appl. Phys. 83(2), 639–649 (1998). [CrossRef]

]. 10-μm-thick under- and over-cladding layers and a 3-μm-thick core layer were spin coated on a 4 inch glass wafer and cured by UV light. Their thicknesses were adjusted by the rotation speed and duration of the spin-coating. The core pattern was formed by reactive ion etching (RIE) using O2 and CF4 gases. The metal mask used for RIE was made of copper; Cu was dry-etched by argon plasma using a positive photoresist mask exposed i-line stepper. Scanning electron microscope (SEM) images of waveguides with pitches of 10–100 μm are shown in Fig. 6
Fig. 6 SEM images of fabricated high-density polymer waveguides. (a),(b), and (c) are 10 μm pitch, 20 μm pitch, 25 μm pitch, respectively.
.

The exposed area of the i-line stepper was 20 mm × 20 mm. For longer waveguides, we connected the exposing shots with a 100-μm-length overlap. Figure 7
Fig. 7 SEM images of waveguide elongation by connecting exposed i-line stepper.
shows an SEM image of the region. Although each shot is moved by mechanical stages in the stepper using no alignment marks, the shots are connected by very small drifts. The BPM simulation shows that there is very little excess loss within 0.01 dB for reducing the waveguide width by double exposure. However, there was a high incidence of defects of the cores in the region because there was a narrow dose margin for the photoresist, which was not designed to handle two exposures. Then, the correct pattern, which has a 10-μm-width with 1.6 degree tapers, was employed, as shown in Fig. 8
Fig. 8 Compensation pattern at the double-exposure regions. (a) Waveguides whose pitches were less than 30 μm had fan-out structures (b) Wide pitch waveguides were straight patterns at the connections.
.

4. Measurement

4.1 Propagation loss and crosstalk

Optical properties of the fabricated waveguide were measured from 1260 to 1360 nm using a tunable laser (Santec TSL-510). The propagation loss calculated from the 20–40-mm-length waveguides was 0.6 dB/cm at 1310 nm, as shown in Fig. 9
Fig. 9 Propagation losses calculated from 20 to 40 mm length fabricated waveguides at 1260–1360 nm.
, and the average polarization dependent loss (PDL) was 0.06 dB in the measured wavelength range.

Eight parallel waveguides with 10–100 μm pitches were made for the crosstalk measurements. Figure 10(a)
Fig. 10 Adjacent crosstalk of the fabricated waveguides. (a) Effects of waveguide pitches; orange and green lines show Eqs. (1) and (2), respectively. (b) Wavelength properties at 20 μm pitch.
shows the optical power as the crosstalk in the waveguides adjacent to the launched one. The solid lines in the Fig. were shown in Eqs. (1) and (2), and were calculated using their propagation length, with the exception of the correct patterns in Fig. 8(b). Also, their oscillations at a pitch of 10 μm indicate a perfect optical power transition between waveguides. For pitches less than 25 μm, the measured crosstalk agreed well with the calculations. The measurements were carried out for one active waveguide. For the multiactive waveguide in Eq. (3), the crosstalk should be increased by 6 dB. Then, the 20 μm and 25 μm pitches had crosstalk values of −35 dB and −40 dB, respectively.

The waveguide had very small structural losses, such as scattering loss, because the propagation losses were the same level as the material properties. It was then realized that mode coupling was the dominant factor affecting the crosstalk. However, waveguides with wider pitches had a fixed background of −45 dB. Generally, the polymer resins are light scattering compared with silica waveguide. It is difficult to reduce background to extremely low level. Figure 10(b) shows the wavelength dependency of the crosstalk at a 20 μm pitch. There was a tendency for longer wavelengths to have a larger crosstalk. However, the fabricated waveguides were demonstrated satisfactory performance because their average crosstalk was less than −37 dB for the entire range of measured wavelengths.

4.2 Bend loss and crosstalk

Figure 11
Fig. 11 SEM image of 45 degree + 45 degree S-bend waveguides with radiuses of 1 mm.
shows fabricated 45 degree + 45 degree S-bend waveguides with 25 μm and 50μm pitches. Their losses and crosstalk are shown in Figs. 12
Fig. 12 Bending loss of the fabricated waveguides at 1310 nm. The simulated curve was found using the measured refractive indices.
and 13
Fig. 13 (a) Measured and BPM simulated bending crosstalk for the fabricated waveguides at the 25μm pitch at 1310 nm. (b) Coupling into the waveguides for external beam using ray-tracing technique.
, respectively. The bending losses obtained in measurements showed good agreement with those obtained by BPM simulation using the measured refractive indices in Table 2.

The measured crosstalk at the 25 μm pitch was asymmetric irrespective of whether the waveguide was on the left or right side of the launched one. The BPM simulation was performed on the refractive index profile using conformal mapping [10

10. D. Cai, C. Chen, C. Lee, and T. Wang, “Study of coupling length of concentrically curved waveguides,” IEEE Photon. J. 4(1), 80–85 (2012). [CrossRef]

], and its results also indicated the same tendency. This crosstalk is explained by the ray-tracing technique, and not the mode coupling theory in Fig. 13(b), and it was expressed for both conditions. First, the incident beam is in the direction close to the tangent line of the curved waveguide. Second, the beam is propagated directly into the linear waveguide. Usually, the incident beam cannot be coupled to the propagation mode because of the mismatch of angle θ2, but the second condition compensates for the angle θ3. This is the case for conditions involving limited beam angles. However, a high-density optical interconnection has to be made for the waveguides with very low losses, such as bending losses, scattering losses, and coupling losses, because the background level will easily increase to a large level leading to a small loss by each waveguide. Also, the background may be coupled with the waveguides.

5. Conclusion

We propose low-crosstalk single-mode waveguides for high-density optical interconnections. An optimum waveguide was designed without restricting the values of refractive indices. We defined a 1.2% relative index difference and 3.0 μm × 3.0 μm core to ensure compatibility with low crosstalk and wide fabrication tolerances. This result will be realized using low loss polymer materials which are adjusted their refractive indices. Because the range of the refractive indices of reported low loss materials [11

11. S. Takenobu and Y. Morizawa, “Long spiral optical waveguides using ultra low loss perfluorinated polymer for optical interconnect” in Optical Fiber Communication Conference, Technical Digest (CD)) (Optical Society of America, 2009), paper JThA24. [CrossRef]

,12

12. S. Takenobu, “Low loss heat resistant fluorinated polymer optical waveguides for optical interconnects” in Optical Fiber Communication Conference, Technical Digest (CD)) (Optical Society of America, 2010), paper OMV3. [CrossRef]

] can be covered the optimum conditions of the waveguide. The low-loss waveguides were used to demonstrate low-crosstalk propagations. The 20-μm-pitch and 60-mm-length waveguides had low crosstalk values of under −40 dB at 1310 nm. Then, we achieved a high-density (50 wire/cm) optical interconnection.

A curved waveguide can have structural crosstalk. It is essential to design the waveguides without bending losses. However, high-density waveguides are prone to higher background from causes other than the bending losses. Therefore, we have to pay enough attention to design and fabricate waveguides with minimum loss.

Acknowledgments

This work was supported by Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

References and links

1.

A. Alduino, L. Liao, R. Jones, M. Morse, B. Kim, W. Lo, J. Basak, B. Koch, H. Liu, H. Rong, M. Sysak, C. Krause, R. Saba, D. Lazar, L. Horwitz, R. Bar, S. Litski, A. Liu, K. Sullivan, O. Dosunmu, N. Na, T. Yin, F. Haubensack, I. Hsieh, J. Heck, R. Beatty, H. Park, J. Bovington, S. Lee, H. Nguyen, H. Au, K. Nguyen, P. Merani, M. Hakami, and M. Paniccia, “Demonstration of a high speed 4-channel integrated silicon photonics WDM link with hybrid silicon lasers” in Integrated Photonics Research, Silicon and Nanophotonics, Technical Digest (online)) (Optical Society of America, 2010), paper PDIWI5.

2.

Y. Urino, T. Shimizu, M. Okano, N. Hatori, M. Ishizaka, T. Yamamoto, T. Baba, T. Akagawa, S. Akiyama, T. Usuki, D. Okamoto, M. Miura, M. Noguchi, J. Fujikata, D. Shimura, H. Okayama, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, E. Saito, T. Nakamura, and Y. Arakawa, “First demonstration of high density optical interconnects integrated with lasers, optical modulators and photodetectors on a single silicon substrate” in European Conference and Exposition on Optical Communications, Technical Digest (CD) (Optical Society of America, 2011), paper We.9.LeSaleve.4. [CrossRef]

3.

U. Streppel, P. Dannberg, C. Wachter, A. Brauer, L. Frohlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photoresponsive (inorganic–organic hybrid) polymers,” Opt. Mater. 21(1-3), 475–483 (2003). [CrossRef]

4.

R. D. Williams, T. Sze, D. Huang, S. Pannala, and C. Fang, “Server memory roadmap” presented at JEDEC Server Memory Forum Shenzhen, China, 1 Mar. 2012. http://www.jedec.org/sites/default/files/Ricki_Dee_Williams-Final_0.pdf

5.

International Technology Roadmap for Semiconductors, Assembly & Packaging, 2012 Tables, http://www.itrs.net/Links/2012ITRS/2012Tables/AssemblyPkg_2012Tables.xlsx

6.

S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguides and directional couplers in GaAs-imbedded and ridged,” Appl. Opt. 13(2), 327–330 (1974). [CrossRef] [PubMed]

7.

E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J. 48(7), 2071–2102 (1969). [CrossRef]

8.

S. Tang, R. T. Chen, and M. A. Peskin, “Packing density and interconnection length of a highly parallel optical interconnect using polymer-based, single-mode bus arrays,” Opt. Eng. 33(5), 1581–1586 (1994). [CrossRef]

9.

T. Watanabe, M. Hikita, M. Amano, Y. Shuto, and S. Tomaru, “Vertically stacked coupler and serially grafted waveguide: hybrid waveguide structures formed using an electro-optic polymer,” J. Appl. Phys. 83(2), 639–649 (1998). [CrossRef]

10.

D. Cai, C. Chen, C. Lee, and T. Wang, “Study of coupling length of concentrically curved waveguides,” IEEE Photon. J. 4(1), 80–85 (2012). [CrossRef]

11.

S. Takenobu and Y. Morizawa, “Long spiral optical waveguides using ultra low loss perfluorinated polymer for optical interconnect” in Optical Fiber Communication Conference, Technical Digest (CD)) (Optical Society of America, 2009), paper JThA24. [CrossRef]

12.

S. Takenobu, “Low loss heat resistant fluorinated polymer optical waveguides for optical interconnects” in Optical Fiber Communication Conference, Technical Digest (CD)) (Optical Society of America, 2010), paper OMV3. [CrossRef]

OCIS Codes
(200.4650) Optics in computing : Optical interconnects
(130.5460) Integrated optics : Polymer waveguides

ToC Category:
Integrated Optics

History
Original Manuscript: April 30, 2013
Revised Manuscript: August 20, 2013
Manuscript Accepted: August 20, 2013
Published: October 3, 2013

Citation
Akio Sugama, Kenichi Kawaguchi, Motoyuki Nishizawa, Hidenobu Muranaka, and Yasuhiko Arakawa, "Development of high-density single-mode polymer waveguides with low crosstalk for chip-to-chip optical interconnection," Opt. Express 21, 24231-24239 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-24231


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References

  1. A. Alduino, L. Liao, R. Jones, M. Morse, B. Kim, W. Lo, J. Basak, B. Koch, H. Liu, H. Rong, M. Sysak, C. Krause, R. Saba, D. Lazar, L. Horwitz, R. Bar, S. Litski, A. Liu, K. Sullivan, O. Dosunmu, N. Na, T. Yin, F. Haubensack, I. Hsieh, J. Heck, R. Beatty, H. Park, J. Bovington, S. Lee, H. Nguyen, H. Au, K. Nguyen, P. Merani, M. Hakami, and M. Paniccia, “Demonstration of a high speed 4-channel integrated silicon photonics WDM link with hybrid silicon lasers” in Integrated Photonics Research, Silicon and Nanophotonics, Technical Digest (online)) (Optical Society of America, 2010), paper PDIWI5.
  2. Y. Urino, T. Shimizu, M. Okano, N. Hatori, M. Ishizaka, T. Yamamoto, T. Baba, T. Akagawa, S. Akiyama, T. Usuki, D. Okamoto, M. Miura, M. Noguchi, J. Fujikata, D. Shimura, H. Okayama, T. Tsuchizawa, T. Watanabe, K. Yamada, S. Itabashi, E. Saito, T. Nakamura, and Y. Arakawa, “First demonstration of high density optical interconnects integrated with lasers, optical modulators and photodetectors on a single silicon substrate” in European Conference and Exposition on Optical Communications, Technical Digest (CD) (Optical Society of America, 2011), paper We.9.LeSaleve.4. [CrossRef]
  3. U. Streppel, P. Dannberg, C. Wachter, A. Brauer, L. Frohlich, R. Houbertz, and M. Popall, “New wafer-scale fabrication method for stacked optical waveguide interconnects and 3D micro-optic structures using photoresponsive (inorganic–organic hybrid) polymers,” Opt. Mater.21(1-3), 475–483 (2003). [CrossRef]
  4. R. D. Williams, T. Sze, D. Huang, S. Pannala, and C. Fang, “Server memory roadmap” presented at JEDEC Server Memory Forum Shenzhen, China, 1 Mar. 2012. http://www.jedec.org/sites/default/files/Ricki_Dee_Williams-Final_0.pdf
  5. International Technology Roadmap for Semiconductors, Assembly & Packaging, 2012 Tables, http://www.itrs.net/Links/2012ITRS/2012Tables/AssemblyPkg_2012Tables.xlsx
  6. S. Somekh, E. Garmire, A. Yariv, H. L. Garvin, and R. G. Hunsperger, “Channel optical waveguides and directional couplers in GaAs-imbedded and ridged,” Appl. Opt.13(2), 327–330 (1974). [CrossRef] [PubMed]
  7. E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” Bell Syst. Tech. J.48(7), 2071–2102 (1969). [CrossRef]
  8. S. Tang, R. T. Chen, and M. A. Peskin, “Packing density and interconnection length of a highly parallel optical interconnect using polymer-based, single-mode bus arrays,” Opt. Eng.33(5), 1581–1586 (1994). [CrossRef]
  9. T. Watanabe, M. Hikita, M. Amano, Y. Shuto, and S. Tomaru, “Vertically stacked coupler and serially grafted waveguide: hybrid waveguide structures formed using an electro-optic polymer,” J. Appl. Phys.83(2), 639–649 (1998). [CrossRef]
  10. D. Cai, C. Chen, C. Lee, and T. Wang, “Study of coupling length of concentrically curved waveguides,” IEEE Photon. J.4(1), 80–85 (2012). [CrossRef]
  11. S. Takenobu and Y. Morizawa, “Long spiral optical waveguides using ultra low loss perfluorinated polymer for optical interconnect” in Optical Fiber Communication Conference, Technical Digest (CD)) (Optical Society of America, 2009), paper JThA24. [CrossRef]
  12. S. Takenobu, “Low loss heat resistant fluorinated polymer optical waveguides for optical interconnects” in Optical Fiber Communication Conference, Technical Digest (CD)) (Optical Society of America, 2010), paper OMV3. [CrossRef]

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