Abstract

A new integrated-optic coupler was proposed for coupling a guided wave to a free-space wave propagating vertically from the waveguide surface. The coupler consists of a grating coupler in a cavity formed by two distributed Bragg reflectors, and has a small aperture. The cavity was designed to eliminate both transmission and reflection of the incident guided wave, resulting in 100 % radiation by a several-micron aperture. Design consideration was theoretically discussed based on the coupled mode analysis. Predicted performance was simulated and confirmed by the finite difference time domain method.

© 2008 Optical Society of America

1. Introduction

A grating coupler (GC) is an integrated-optic component formed by a refractive index modulation in a thin layer on a waveguide for coupling a guided wave and a free-space wave [1,2] with a surface-coupling scheme. Besides the output or input coupling of the guided wave, GC can simultaneously provide a variety of functions such as focusing [3–7], polarization splitting [8], switching [9], guided-mode selecting [10], etc. A key issue for practical applications is the realization of high coupling efficiency. Blazed gratings [11], parallelogramic gratings [12,13], and combinations with high-reflection substrates [10,14,15] have been discussed and demonstrated to give a one-beam-coupling scheme for the high efficiency. Another concern will be a small coupling aperture. For example, there arises a new important application to the optical-interconnect system-in-packaging for a future ultrahigh- performance signal-processing unit. An integration of GCs of a few hundreds micron coupling length was proposed and reported so far [16–18] for a wavelength-division-multiplexed signal transmission from an array of vertical-cavity surface-emitting laser (VCSELs) to an array of photodetectors. A shorter coupling length enables a narrower channel width since the incident light from VCSEL has circular symmetry. A several-micron coupling length will be able to provide a transmission density of several Tbps/mm. Thus the reduction of the coupling length becomes an important issue.

The effective coupling length Leff of GC is usually given by the reciprocal of a radiation decay factor α. Although larger α gives shorter Leff, α depends on and is therefore limited by the refractive-index modulation depth and the groove depth. Recently, short GCs in semiconductor waveguides have been reported [15,19–21] with use of the large difference in the refractive index between the core material and the air. However, such large index difference is not available in dielectric waveguides. In this paper, we propose a new integrated-optic coupler consisting of one GC and two distributed Bragg reflectors (DBRs), namely a resonance GC (RGC), in order to realize much smaller aperture as well as higher efficiency in comparison to conventional GCs. Theoretical considerations are given on the basis of the coupled mode analysis, and a design example is shown with some simulation results by the finite-difference time-domain (FDTD) method.

2. Configuration and design concept

A basic configuration of the proposed RGC is depicted in Fig. 1. GC of a length LGC is integrated between a front and a rear DBRs with phase-shifting spaces in a single-mode waveguide. We discuss a two-dimensional model without a channel structure in order to avoid nonessential complexity in this paper, and consider a coupling of an incident transverse-electric (TE) guided mode coming from the left-hand side. The incident wave is partially reflected by the front DBR of a length LBF, partially coupled out by GC to radiation waves, and reflected by the rear DBR of a length LBR. The grating period λGC of GC is determined to give vertical radiations by the first order diffraction, causing a reflection to backward propagating guided wave by the second order diffraction. The guided modes and the radiation are illustrated in Fig. 2. The complex field amplitudes of the guided modes propagating forward and backward along z-axis are denoted by A(z) and B(z), respectively. The rear end of GC was chosen as the origin of z. LBR is determined to eliminate A(z) in z > lR + LBR sufficiently. The phase-shifting space lR between GC and the rear DBR is determined so that the wave guided backward from the rear DBR is radiated by GC in phase with the radiation of the forward guided wave. The coupling efficiency of the front DBR and the space lF between GC and the front DBR are chosen so that the transmission of the wave guided backward from GC is canceled by the reflection of A(z) by the front DBR. In other words, B(z) in z < - LGC - lF - LBF is eliminated. Thus the proposed RGC generates neither transmission to z > lR + LBR nor reflection to z < - LGC - lF - LBF, providing 100% radiation even if GC has too small α and LGC to give high efficiency in a usual one-way propagation scheme.

 

Fig. 1. Basic configuration of the proposed resonance grating coupler (RGC).

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Fig. 2. Diagram of the guided modes and the radiation.

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3. Design consideration based on coupled mode analysis

Two radiation modes are degenerated with respect to the z-propagation constant βν, and the complex amplitude is denoted as aν i(z) with a subscript i = a or s for air or substrate radiation, respectively. Coupled mode equations of two guided modes A(z) and B(z) and the radiation modes aν i(z) in GC can be written [22] as

dA(z)dz=jiavi(z)κvi,A*exp[j{βv(βAKGC)}z]dβv,
dB(z)dz=jiavi(z)κvi,B*exp[j{βv(βB+KGC)}z]dβv,
davi(z)dz=jA(z)κvi,Aexp[j{βv(βAKGC)}z]jB(z)κvi,Bexp[j{βv(βB+KGC)}z](i=aors),

where βA and βB are the propagation constants of A(z) and B(z) along z-direction and should be βB = - βA. KGC is the grating vector size defined by 2π/λGC. Since TE guided mode is considered, coupling coefficients κν i,A and κν i,B are defined by

κvi,A=κvi,B=ε0ω4Evi*(x)ΔεEg(x)dx(i=aors),

where Eν i and Eg are the normalized electric fields of the radiation and guided modes, respectively. ϵ0, ω, and Δϵ are the permittivity in the vacuum, an angular frequency, and the dielectric constant increments representing GC structure, respectively. By substituting aν i(z) in Eqs. (1)–(2) with those calculated from Eq. (3) under an approximation of A(z) ≈ const. and B(z) ≈ const. and executing integrals with respect to βν, we can rewrite the coupled mode equations as

dA(z)dz=αA(z)κGC*B(z)exp(j2ΔGCz),
dB(z)dz=κGCA(z)exp(j2ΔGCz)αB(z).

α, κ□□, and Δ□□ are a radiation decay factor, a guided-mode coupling coefficient, and a phase-mismatching factor, respectively, and are given by

α=π=(κa,A2+κs,A2)=π(κa,B2)+κs,B2)
κGC=π(κa,B*κa,A+κs,B*κs,A),
ΔGC=KGCβA.

A set of boundary conditions of A(0) = 1 and B(0) = rBR gives a solution of A(z) and B(z) expressed by

A(z)={cosh(ζz)sinc(jζz)(rBRκGC+αjΔGC)z}exp(jΔGCz),
B(z)={rBRcosh(ζz)+sinc(jζz)(κGC+rBR[αGC])z}exp(GCz),
ζ=(αGC)2κGC2.

where sinc(x) is a function defied by sin(x)/x. In the phase-matched case of ΔGC = 0, ζ becomes 0 from Eq. (12) because α = κGC is deduced from Eqs. (4), (7) and (8). In this condition, Eqs. (10) and (11) are rewritten as

A(z)=1κGC(1+rBR)z,
B(z)=rBR+κGC(1+rBR)z.

It can be seen from Eq. (3) that the increase of the radiation is proportional to A(z) + B(z). Therefore, rBR should be a positive real number and as large as possible in order to obtain a high-efficiency radiation. rBR is determined by the reflection of the rear DBR and the space lR as discussed in the next paragraph.

Coupled mode equations in both DBRs can be written [22] as

dA(z)dz=BAB(z)exp(j2ΔDBRz),
dB(z)dz=BAA(z)exp(j2ΔDBRz),

where κBA, and ΔDBR are a coupling coefficient, and a phase-mismatching factor, respectively, and are given by

κBA=ε0ω4Eg*(x)ΔεEg(x)dx,
ΔDBR=(KDBR2βA2)=(2KGC2βA2)=ΔGC.

By applying a set of boundary conditions of A(0) = 1 and B(lR + LBR) = 0 to the rear DBR, rBR is expressed by

rBR=B(0)=jexp(j2βAlR)κBAsinh(κBA2ΔDBR2LBR)κBA2ΔDBR2cosh(κBA2ΔDBR2LBR)DBRsinhκBA2ΔDBR2LBR).

In the phase-matched case of ΔDBR = ΔGC =0, Eq. (19) is rewritten as

rBR=jexp(j2βAlR)tanh(κBALBR).

In order to give a large positive real number of rBR as discussed above, κBA LBR should be large and

lR=(i218)ΛGC.  (i: integer)

With respect to the front DBR, A(z) and B(z) at z = - LGC - lF are written as A(- LGC - lF) = A(- LGC) exp(j βA lF) and B(- LGC - lF) = B(- LGC) exp(-j βA lF) with use of A(- LGC) and B(-LGC) given by Eqs. (10) and (11). Therefore, A(- LGC - lF - LBF) and B(- LGC - lF - LBF) are expressed by

A(LGClFLBF)=exp{j(βAlF+ΔDBRLBF)}×{A(LGC)cosh(κBA2ΔDBR2LBF)+jκBAexp(2AlF)B(LGC)ΔDBRA(LGC)κBA2ΔDBR2sinh(κBA2ΔDBR2LBF)),
B(LGClFLBF)=exp{j(βAlF+ΔDBRLBF)}×{B(LGC)cosh(κBA2ΔDBR2LBF)+jκBAexp(2AlF)B(LGC)ΔDBRB(LGC)κBA2ΔDBR2sinh(κBA2ΔDBR2LBF)),

The condition of B(-LGC - lF - LBF) = 0 with ΔDBR = 0 is rewritten from Eq. (23) as

B(LGC)A(LGC)=jexp(2jβAlF)tanh(κBALBF).

On the other hand, the next equation is obtained from Eqs. (13) and (14).

B(LGC)A(LGC)=rBRκGC(1+rBR)LGC1+κGC(1+rBR)LGC.

Therefore lF and LBF should be given by

lF=(i218)ΛGC,(i:integer)
LBF=1κBAtanh1rBRκGC(1+rBR)LGC1+κGC(1+rBR)LGC.

4. Design example and simulation results

A model structure is depicted in Fig. 3. An operation wavelength of 850 nm is considered. The waveguide consists of 0.65 μm-thick Ge:SiO2 guiding core layer on 1.64 μm-thick SiO2 buffer layer on Si substrate. The refractive indices of the core layer, buffer layer and substrate are 1.54, 1.46 and 3.75, respectively. The refractive index modulation required for GC and DBR is formed by embedded Si-N teeth of 50 nm height and a refractive index of 2.01 in the guiding core layer. The effective refractive index of TE0 mode is 1.516, and the grating periods of GC and DBR are 0.5607 and 0.2804 μm, respectively. α = κ□□ = 8.70 mm-1 and κBA = 140 mm-1 are theoretically predicted. LBR was chosen to be 20 μm, resulting in |rBR | = 0.993 at the wavelength 850 nm. LBF was chosen from Eq. (27) to be 8.55 μm for LGC of 5 μm.

 

Fig. 3. Structure example.

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A calculated example of wavelength dependences of a normalized power transmission PT = (1-|B(0)|2) / |A(- LGC - lF - LBF)|2, a normalized power reflection PR = |B(- LGC - lF - LBF)|2/ |A(- LGC - lF - LBF)|2 and a normalized power radiation into air, namely an output coupling efficiency, Pout = η0 (1- PT - PR) were summarized in Fig. 4. η0 represents a power distribution ratio to the output coupling against all the radiation in GC and is given by |κν a,A|2/ (|κν a,A|2+|κν s,A|2) = |κν a,B|2/ (|κν a,B|2+|κν s,B|2). The SiO2 buffer layer thickness was optimized to maximize η0 by an interference effect [22] caused by a substrate reflection. η0 was calculated to be 0.78 in the current case. An output coupling efficiency as high as η0 is predicted at the coupling wavelength 850 nm with full width at half maximum of 4 nm. The maximum efficiencies are 12 times higher than a value of 0.065 estimated from η0 (1 - 2 αLGC) for GC of the same α and LGC without DBRs.

Wavelength dependences of PT, PR and Pout were simulated by FDTD method, and are summarized in Fig. 5. The simulated dependences were similar to those shown in Fig. 4 except for a couple of points. The most essential difference is in the maximum efficiency. The maximum efficiency was estimated to be lower than the value predicted in Fig. 4 by 0.1. The difference was much smaller for a case of longer LGC such as 10 μm. We think the reason of the difference must be a scattering at the refractive-index boundary of GC. In other words, the smaller the number of the grating teeth, the larger a deformation of the diffraction wavefront from a plane. Even so, the output coupling efficiency is expected to be higher than 0.6.

 

Fig. 4. Wavelength dependences of transmission, reflection and output coupling efficiencies calculated by the coupled mode analysis.

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Fig. 5. Wavelength dependences of transmission, reflection and output coupling efficiencies simulated by FDTD method.

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5. Conclusions

A new integrated-optic coupler named RGC was proposed for coupling a guided wave into a vertically propagating free-space wave. RGC consists of GC located inside a cavity formed by two DBRs. It was designed to eliminate both transmission and reflection of the incident guided wave, resulting in 100% radiation efficiency by a several-micron aperture in a dielectric waveguide. The design consideration was discussed by the coupled mode analysis. A design example using Si substrate was demonstrated with FDTD method, where the output efficiency was predicted almost the same as the power distribution ratio of 0.78, whereas the efficiency can be improved by employing a highly reflective substrate. Experimental work is now under study.

References and links

1. M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, “Grating coupler for efficient excitation of optical guided waves in thin films,” Appl. Phys. Lett. 16, 523–525 (1970). [CrossRef]  

2. H. Kogelnik and T. P. Sosnowski, “Holographic thin film couplers,” Bell Syst. Tech. J. 49, 1602–1608 (1970).

3. A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, “Chirped gratings in integrated optics,” IEEE J. Quantum Electron. QE-13, 296–304 (1977). [CrossRef]  

4. M. Miler and M. Skalsky, “Stigmatically focusing grating coupler,” Electron. Lett. 15, 275–276 (1979). [CrossRef]  

5. D. Heitmann and R. V. Pole, “Two-dimensional focusing holographic grating coupler,” Appl. Phys. Lett. 37, 585–587 (1980). [CrossRef]  

6. S. Ura, T. Suhara, and H. Nishihara, “Linearly focusing grating coupler for integrated-optic parallel data pickup,” Tech. Digest Int’l Sympo. Opt. Memory, pp. 93-94, Kobe, Japan, Sept. 26-28, 1989.

7. S. Ura, T. Endoh, T. Suhara, and H. Nishihara, “Linearly focusing grating couplers for sensing 2- dimensional grating-scale displacement,” Meet. Digest Topical Meet. Int’l Commission Opt., p. 164, Kyoto, Japan, April 4-8, 1994.

8. S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, “Focusing grating couplers for polarization detection,” J. Lightwave Technol. 6, 1028–1033 (1988). [CrossRef]  

9. S. Ura, H. Moriguchi, S. Kido, T. Suhara, and H. Nishihara, “Switching of output coupling in a grating coupler by diffraction transition to the distributed Bragg reflector regime,” Appl. Opt. 38, 2500–2503 (1994). [CrossRef]  

10. K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, “A guided-mode-selective focusing grating coupler,” IEEE Photon. Technol. Lett. 16, 512–514 (2004). [CrossRef]  

11. T. Aoyagi, Y. Aoyagi, and S. Namba, “High-efficiency blazed grating couplers,” Appl. Phys. Lett. 29,303–305 (1976). [CrossRef]  

12. M. Hagberg, N. Eriksson, and A. Larsson, “High efficiency surface emitting lasers using blazed grating outcouplers,” Appl. Phys. Lett. 67, 3685–3687 (1995). [CrossRef]  

13. F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, “Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides,” IEEE Photon. Technol. Lett. 19, 396–398 (2007). [CrossRef]  

14. M. Oh, S. Ura, T. Suhara, and H. Nishihara, “Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide,” J. Lightwave Technolol. 12, 1569–1576 (1994). [CrossRef]  

15. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002). [CrossRef]  

16. S. Ura, “Selective guided mode coupling via bridging mode by integrated gratings for intraboard optical interconnects,” Proc. SPIE 4652, 86–96 (2002). [CrossRef]  

17. J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, “Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects,” Jpn. J. Appl. Phys. 44, 7987–7992 (2005). [CrossRef]  

18. K. Kintaka, J. Nishii, K. Shinoda, and S. Ura, “WDM signal transmission in a thin-film waveguide for optical interconnection,” IEEE Photon. Technol. Lett. 18, 2299–2301 (2006). [CrossRef]  

19. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006). [CrossRef]  

20. G. Roelkens, D. V. Thourhout, and R. Baets, “High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers,” Opt. Lett. 32, 1495–1497 (2007). [CrossRef]   [PubMed]  

21. C. Gunn, “CMOS photonics for high-speed interconnects,” IEEE Micro 26, 58–66 (March-April 2006). [CrossRef]  

22. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989), Chap. 4.

References

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  1. M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
    [CrossRef]
  2. H. Kogelnik and T. P. Sosnowski, "Holographic thin film couplers," Bell Syst. Tech. J. 49, 1602-1608 (1970).
  3. A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
    [CrossRef]
  4. M. Miler and M. Skalsky, "Stigmatically focusing grating coupler," Electron. Lett. 15, 275-276 (1979).
    [CrossRef]
  5. D. Heitmann and R. V. Pole, "Two-dimensional focusing holographic grating coupler," Appl. Phys. Lett. 37, 585-587 (1980).
    [CrossRef]
  6. S. Ura, T. Suhara, and H. Nishihara, "Linearly focusing grating coupler for integrated-optic parallel data pickup," Tech. Digest Int�??l Sympo. Opt. Memory, pp. 93-94, Kobe, Japan, Sept. 26-28, 1989.
  7. S. Ura, T. Endoh, T. Suhara, and H. Nishihara, "Linearly focusing grating couplers for sensing 2-dimensional grating-scale displacement," Meet. Digest Topical Meet. Int�??l Commission Opt., p. 164, Kyoto, Japan, April 4-8, 1994.
  8. S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
    [CrossRef]
  9. S. Ura, H. Moriguchi, S. Kido, T. Suhara, and H. Nishihara, "Switching of output coupling in a grating coupler by diffraction transition to the distributed Bragg reflector regime," Appl. Opt. 38, 2500-2503 (1994).
    [CrossRef]
  10. K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
    [CrossRef]
  11. T. Aoyagi, Y. Aoyagi, and S. Namba, "High-efficiency blazed grating couplers," Appl. Phys. Lett. 29, 303-305 (1976).
    [CrossRef]
  12. M. Hagberg, N. Eriksson, and A. Larsson, "High efficiency surface emitting lasers using blazed grating outcouplers," Appl. Phys. Lett. 67, 3685-3687 (1995).
    [CrossRef]
  13. F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
    [CrossRef]
  14. M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
    [CrossRef]
  15. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
    [CrossRef]
  16. S. Ura, "Selective guided mode coupling via bridging mode by integrated gratings for intraboard optical interconnects," Proc. SPIE 4652, 86-96 (2002).
    [CrossRef]
  17. J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
    [CrossRef]
  18. K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
    [CrossRef]
  19. D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
    [CrossRef]
  20. G. Roelkens, D. V. Thourhout, and R. Baets, "High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers," Opt. Lett. 32, 1495-1497 (2007).
    [CrossRef] [PubMed]
  21. C. Gunn, "CMOS photonics for high-speed interconnects," IEEE Micro 26, 58-66 (March-April 2006).
    [CrossRef]
  22. H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989), Chap. 4.

2007 (2)

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

G. Roelkens, D. V. Thourhout, and R. Baets, "High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers," Opt. Lett. 32, 1495-1497 (2007).
[CrossRef] [PubMed]

2006 (3)

C. Gunn, "CMOS photonics for high-speed interconnects," IEEE Micro 26, 58-66 (March-April 2006).
[CrossRef]

K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
[CrossRef]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

2005 (1)

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

2004 (1)

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

2002 (2)

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

S. Ura, "Selective guided mode coupling via bridging mode by integrated gratings for intraboard optical interconnects," Proc. SPIE 4652, 86-96 (2002).
[CrossRef]

1995 (1)

M. Hagberg, N. Eriksson, and A. Larsson, "High efficiency surface emitting lasers using blazed grating outcouplers," Appl. Phys. Lett. 67, 3685-3687 (1995).
[CrossRef]

1994 (2)

S. Ura, H. Moriguchi, S. Kido, T. Suhara, and H. Nishihara, "Switching of output coupling in a grating coupler by diffraction transition to the distributed Bragg reflector regime," Appl. Opt. 38, 2500-2503 (1994).
[CrossRef]

M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
[CrossRef]

1988 (1)

S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
[CrossRef]

1980 (1)

D. Heitmann and R. V. Pole, "Two-dimensional focusing holographic grating coupler," Appl. Phys. Lett. 37, 585-587 (1980).
[CrossRef]

1979 (1)

M. Miler and M. Skalsky, "Stigmatically focusing grating coupler," Electron. Lett. 15, 275-276 (1979).
[CrossRef]

1977 (1)

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
[CrossRef]

1976 (1)

T. Aoyagi, Y. Aoyagi, and S. Namba, "High-efficiency blazed grating couplers," Appl. Phys. Lett. 29, 303-305 (1976).
[CrossRef]

1970 (2)

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

H. Kogelnik and T. P. Sosnowski, "Holographic thin film couplers," Bell Syst. Tech. J. 49, 1602-1608 (1970).

Aoyagi, T.

T. Aoyagi, Y. Aoyagi, and S. Namba, "High-efficiency blazed grating couplers," Appl. Phys. Lett. 29, 303-305 (1976).
[CrossRef]

Aoyagi, Y.

T. Aoyagi, Y. Aoyagi, and S. Namba, "High-efficiency blazed grating couplers," Appl. Phys. Lett. 29, 303-305 (1976).
[CrossRef]

Ayre, M.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Baets, R.

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

G. Roelkens, D. V. Thourhout, and R. Baets, "High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers," Opt. Lett. 32, 1495-1497 (2007).
[CrossRef] [PubMed]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Bienstman, P.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Bogaerts, W.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Daele, P. V.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Dakss, M. L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Eriksson, N.

M. Hagberg, N. Eriksson, and A. Larsson, "High efficiency surface emitting lasers using blazed grating outcouplers," Appl. Phys. Lett. 67, 3685-3687 (1995).
[CrossRef]

Gunn, C.

C. Gunn, "CMOS photonics for high-speed interconnects," IEEE Micro 26, 58-66 (March-April 2006).
[CrossRef]

Hagberg, M.

M. Hagberg, N. Eriksson, and A. Larsson, "High efficiency surface emitting lasers using blazed grating outcouplers," Appl. Phys. Lett. 67, 3685-3687 (1995).
[CrossRef]

Heidrich, P. F.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Heitmann, D.

D. Heitmann and R. V. Pole, "Two-dimensional focusing holographic grating coupler," Appl. Phys. Lett. 37, 585-587 (1980).
[CrossRef]

Imaoka, Y.

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

Katzir, A.

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
[CrossRef]

Kido, S.

Kintaka, K.

K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
[CrossRef]

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

Kogelnik, H.

H. Kogelnik and T. P. Sosnowski, "Holographic thin film couplers," Bell Syst. Tech. J. 49, 1602-1608 (1970).

Kotlyar, M. V.

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

Krauss, T. F.

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Kuhn, L.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Laere, F. V.

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Larsson, A.

M. Hagberg, N. Eriksson, and A. Larsson, "High efficiency surface emitting lasers using blazed grating outcouplers," Appl. Phys. Lett. 67, 3685-3687 (1995).
[CrossRef]

Livanos, A. C.

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
[CrossRef]

Mesel, K. D.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Miler, M.

M. Miler and M. Skalsky, "Stigmatically focusing grating coupler," Electron. Lett. 15, 275-276 (1979).
[CrossRef]

Moerman, I.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Moriguchi, H.

Namba, S.

T. Aoyagi, Y. Aoyagi, and S. Namba, "High-efficiency blazed grating couplers," Appl. Phys. Lett. 29, 303-305 (1976).
[CrossRef]

Nishihara, H.

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

S. Ura, H. Moriguchi, S. Kido, T. Suhara, and H. Nishihara, "Switching of output coupling in a grating coupler by diffraction transition to the distributed Bragg reflector regime," Appl. Opt. 38, 2500-2503 (1994).
[CrossRef]

M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
[CrossRef]

Nishii, J.

K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

Oh, M.

M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
[CrossRef]

Ohmori, J.

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

Pole, R. V.

D. Heitmann and R. V. Pole, "Two-dimensional focusing holographic grating coupler," Appl. Phys. Lett. 37, 585-587 (1980).
[CrossRef]

Roelkens, G.

Satoh, R.

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

Scott, B. A.

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

Shellan, J. B.

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
[CrossRef]

Shinoda, K.

K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
[CrossRef]

Skalsky, M.

M. Miler and M. Skalsky, "Stigmatically focusing grating coupler," Electron. Lett. 15, 275-276 (1979).
[CrossRef]

Sosnowski, T. P.

H. Kogelnik and T. P. Sosnowski, "Holographic thin film couplers," Bell Syst. Tech. J. 49, 1602-1608 (1970).

Suhara, T.

S. Ura, H. Moriguchi, S. Kido, T. Suhara, and H. Nishihara, "Switching of output coupling in a grating coupler by diffraction transition to the distributed Bragg reflector regime," Appl. Opt. 38, 2500-2503 (1994).
[CrossRef]

M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
[CrossRef]

Sunagawa, H.

S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
[CrossRef]

Taillaert, D.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Taillarert, D.

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

Thorhout, D. V.

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

Thourhout, D. V.

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

G. Roelkens, D. V. Thourhout, and R. Baets, "High efficiency grating coupler between silicon-on-insulator waveguides and perfectly vertical optical fibers," Opt. Lett. 32, 1495-1497 (2007).
[CrossRef] [PubMed]

Ura, S.

K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
[CrossRef]

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

S. Ura, "Selective guided mode coupling via bridging mode by integrated gratings for intraboard optical interconnects," Proc. SPIE 4652, 86-96 (2002).
[CrossRef]

M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
[CrossRef]

S. Ura, H. Moriguchi, S. Kido, T. Suhara, and H. Nishihara, "Switching of output coupling in a grating coupler by diffraction transition to the distributed Bragg reflector regime," Appl. Opt. 38, 2500-2503 (1994).
[CrossRef]

S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
[CrossRef]

Verstuyft, S.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

Yariv, A.

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (4)

M. L. Dakss, L. Kuhn, P. F. Heidrich, and B. A. Scott, "Grating coupler for efficient excitation of optical guided waves in thin films," Appl. Phys. Lett. 16, 523-525 (1970).
[CrossRef]

D. Heitmann and R. V. Pole, "Two-dimensional focusing holographic grating coupler," Appl. Phys. Lett. 37, 585-587 (1980).
[CrossRef]

T. Aoyagi, Y. Aoyagi, and S. Namba, "High-efficiency blazed grating couplers," Appl. Phys. Lett. 29, 303-305 (1976).
[CrossRef]

M. Hagberg, N. Eriksson, and A. Larsson, "High efficiency surface emitting lasers using blazed grating outcouplers," Appl. Phys. Lett. 67, 3685-3687 (1995).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik and T. P. Sosnowski, "Holographic thin film couplers," Bell Syst. Tech. J. 49, 1602-1608 (1970).

Electron. Lett. (1)

M. Miler and M. Skalsky, "Stigmatically focusing grating coupler," Electron. Lett. 15, 275-276 (1979).
[CrossRef]

IEEE J. Quantum Electron. (2)

A. Katzir, A. C. Livanos, J. B. Shellan, and A. Yariv, "Chirped gratings in integrated optics," IEEE J. Quantum Electron. QE-13, 296-304 (1977).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. V. Daele, I. Moerman, S. Verstuyft, K. D. Mesel, and R. Baets, "An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers," IEEE J. Quantum Electron. 38, 949-955 (2002).
[CrossRef]

IEEE Micro (1)

C. Gunn, "CMOS photonics for high-speed interconnects," IEEE Micro 26, 58-66 (March-April 2006).
[CrossRef]

IEEE Photon. Technol. Lett. (3)

K. Kintaka, J. Nishii. K. Shinoda, and S. Ura, "WDM signal transmission in a thin-film waveguide for optical interconnection," IEEE Photon. Technol. Lett. 18, 2299-2301 (2006).
[CrossRef]

F. V. Laere, M. V. Kotlyar, D. Taillarert, D. V. Thourhout, T. F. Krauss, and R. Baets, "Compact slanted grating couplers between optical fiber and InP-InGaAsP waveguides," IEEE Photon. Technol. Lett. 19, 396-398 (2007).
[CrossRef]

K. Kintaka, J. Nishii, Y. Imaoka, J. Ohmori, S. Ura, R. Satoh, and H. Nishihara, "A guided-mode-selective focusing grating coupler," IEEE Photon. Technol. Lett. 16, 512-514 (2004).
[CrossRef]

J. Lightwave Technol. (1)

S. Ura, H. Sunagawa, T. Suhara, and H. Nishihara, "Focusing grating couplers for polarization detection," J. Lightwave Technol. 6, 1028-1033 (1988).
[CrossRef]

J. Lightwave Technolol. (1)

M. Oh, S. Ura, T. Suhara, and H. Nishihara, "Integrated-optic focal-spot intensity modulator using electrooptic polymer waveguide," J. Lightwave Technolol. 12, 1569-1576 (1994).
[CrossRef]

Jpn. J. Appl. Phys. (2)

D. Taillaert, F. V. Laere, M. Ayre, W. Bogaerts, D. V. Thorhout, P. Bienstman, and R. Baets, "Grating couplers for coupling between optical fibers and nanophotonic waveguides," Jpn. J. Appl. Phys. 45, 6071-6077 (2006).
[CrossRef]

J. Ohmori, Y. Imaoka, S. Ura, K. Kintaka, R. Satoh, and H. Nishihara, "Integrated-optic add/drop multiplexing of free-space waves for intra-board chip-to-chi optical interconnects," Jpn. J. Appl. Phys. 44, 7987-7992 (2005).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

S. Ura, "Selective guided mode coupling via bridging mode by integrated gratings for intraboard optical interconnects," Proc. SPIE 4652, 86-96 (2002).
[CrossRef]

Other (3)

S. Ura, T. Suhara, and H. Nishihara, "Linearly focusing grating coupler for integrated-optic parallel data pickup," Tech. Digest Int�??l Sympo. Opt. Memory, pp. 93-94, Kobe, Japan, Sept. 26-28, 1989.

S. Ura, T. Endoh, T. Suhara, and H. Nishihara, "Linearly focusing grating couplers for sensing 2-dimensional grating-scale displacement," Meet. Digest Topical Meet. Int�??l Commission Opt., p. 164, Kyoto, Japan, April 4-8, 1994.

H. Nishihara, M. Haruna, and T. Suhara, Optical Integrated Circuits (McGraw-Hill, 1989), Chap. 4.

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Figures (5)

Fig. 1.
Fig. 1.

Basic configuration of the proposed resonance grating coupler (RGC).

Fig. 2.
Fig. 2.

Diagram of the guided modes and the radiation.

Fig. 3.
Fig. 3.

Structure example.

Fig. 4.
Fig. 4.

Wavelength dependences of transmission, reflection and output coupling efficiencies calculated by the coupled mode analysis.

Fig. 5.
Fig. 5.

Wavelength dependences of transmission, reflection and output coupling efficiencies simulated by FDTD method.

Equations (27)

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dA ( z ) dz = j i a vi ( z ) κ vi , A * exp [ j { β v ( β A K GC ) } z ] d β v ,
dB ( z ) dz = j i a vi ( z ) κ vi , B * exp [ j { β v ( β B + K GC ) } z ] d β v ,
da vi ( z ) dz = jA ( z ) κ vi , A exp [ j { β v ( β A K GC ) } z ] jB ( z ) κ vi , B exp [ j { β v ( β B + K GC ) } z ] ( i = a or s ) ,
κ vi , A = κ vi , B = ε 0 ω 4 E vi * ( x ) Δ εE g ( x ) dx ( i = a or s ) ,
dA ( z ) dz = αA ( z ) κ GC * B ( z ) exp ( j 2 Δ GC z ) ,
dB ( z ) dz = κ GC A ( z ) exp ( j 2 Δ GC z ) αB ( z ) .
α = π = ( κ a , A 2 + κ s , A 2 ) = π ( κ a , B 2 ) + κ s , B 2 )
κ GC = π ( κ a , B * κ a , A + κ s , B * κ s , A ) ,
Δ GC = K GC β A .
A ( z ) = { cosh ( ζ z ) sin c ( j ζ z ) ( r BR κ GC + α j Δ GC ) z } exp ( j Δ GC z ) ,
B ( z ) = { r BR cosh ( ζ z ) + sin c ( j ζ z ) ( κ GC + r BR [ α GC ] ) z } exp ( GC z ) ,
ζ = ( α GC ) 2 κ GC 2 .
A ( z ) = 1 κ GC ( 1 + r BR ) z ,
B ( z ) = r BR + κ GC ( 1 + r BR ) z .
dA ( z ) dz = BA B ( z ) exp ( j 2 Δ DBR z ) ,
dB ( z ) dz = BA A ( z ) exp ( j 2 Δ DBR z ) ,
κ BA = ε 0 ω 4 E g * ( x ) Δ εE g ( x ) dx ,
Δ DBR = ( K DBR 2 β A 2 ) = ( 2 K GC 2 β A 2 ) = Δ GC .
r BR = B ( 0 ) = j exp ( j 2 β A l R ) κ BA sinh ( κ BA 2 Δ DBR 2 L BR ) κ BA 2 Δ DBR 2 cosh ( κ BA 2 Δ DBR 2 L BR ) DBR sinh κ BA 2 Δ DBR 2 L BR ) .
r BR = j exp ( j 2 β A l R ) tanh ( κ BA L BR ) .
l R = ( i 2 1 8 ) Λ GC .    ( i : integer)
A ( L GC l F L BF ) = exp { j ( β A l F + Δ DBR L BF ) } × { A ( L GC ) cosh ( κ BA 2 Δ DBR 2 L BF ) + j κ BA exp ( 2 A l F ) B ( L GC ) Δ DBR A ( L GC ) κ BA 2 Δ DBR 2 sinh ( κ BA 2 Δ DBR 2 L BF ) ) ,
B ( L GC l F L BF ) = exp { j ( β A l F + Δ DBR L BF ) } × { B ( L GC ) cosh ( κ BA 2 Δ DBR 2 L BF ) + j κ BA exp ( 2 A l F ) B ( L GC ) Δ DBR B ( L GC ) κ BA 2 Δ DBR 2 sinh ( κ BA 2 Δ DBR 2 L BF ) ) ,
B ( L GC ) A ( L GC ) = j exp ( 2 j β A l F ) tanh ( κ BA L BF ) .
B ( L GC ) A ( L GC ) = r BR κ GC ( 1 + r BR ) L GC 1 + κ GC ( 1 + r BR ) L GC .
l F = ( i 2 1 8 ) Λ GC , ( i : integer )
L BF = 1 κ BA tanh 1 r BR κ GC ( 1 + r BR ) L GC 1 + κ GC ( 1 + r BR ) L GC .

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