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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 13 — Jun. 22, 2009
  • pp: 11066–11076
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Optimized grating coupler with fully etched slots

Bernd Schmid, Alexander Petrov, and Manfred Eich  »View Author Affiliations


Optics Express, Vol. 17, Issue 13, pp. 11066-11076 (2009)
http://dx.doi.org/10.1364/OE.17.011066


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Abstract

A grating coupler with fully etched slots is optimized for fiber coupling into SOI slab waveguides. Such coupler can be produced in one lithography step together with other SOI components. Theoretical maximal coupling efficiency of 49% is demonstrated with a 3dB bandwidth of 35nm. Strong reflection from the fully etched grating was avoided through an antireflection interface. Constructive interference is used to decrease radiation into the substrate and the filling factor is optimized for optimal power coupling into the fiber mode. It was also demonstrated, that the chirped grating approach is inapplicable for fully etched gratings.

© 2009 OSA

1. Introduction

The trend towards high speed and large bandwidth in telecommunication drives the development of ever smaller components and away from electrical towards optical devices. Over decades the technology in silicon microelectronics has grown and enabled to inexpensively fabricate those devices on silicon wafers. Since silicon is transparent at wavelengths typically used in telecommunications (1310 nm and 1550 nm), the silicon-on-insulator (SOI) technology is suitable for photonics and compatible to complementary metal oxide semiconductor (CMOS) technology [1

1. M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]

,2

2. 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]

]. Hence, optical and electrical components can be fabricated on a single chip. Moreover, the high refractive index of silicon results in smaller wavelengths and also strong light confinement within the silicon waveguide (refractive index nsi=3.45) which is situated above an SiO2 buried oxide layer (BOX) with much lower refractive index (nSiO2=1.45).

One of the challenges in nanophotonics and subject of current research is the coupling into and out of these nanoscale devices directly from lasers or from optical fibers which are magnitudes larger in size. A technique that is straight forward and widely used is butt coupling, where the light beam is focused into the silicon waveguide at the edge of a chip. The constraint that light can only be coupled into the nanostructure at the edges, and the high demand on the alignment of the system to focus the beam directly on the facet of such a small waveguide are disadvantageous here. Another technique is the taper coupler for compact mode conversion [3

3. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

,4

4. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002). [CrossRef]

]. Apart from the fact that coupling is also done into or out of a cleaved edge of a chip, exact cleaving alignment is necessary [3

3. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

] or additional waveguide deposition [4

4. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002). [CrossRef]

] is required. A third solution is the grating coupler where periodic perturbations of the waveguide’s refractive index lead to scattering of the propagating light out of the waveguide. The big advantage of such a grating coupler is that one is not limited to couple light at the edges. This enables testing devices anywhere on a chip. Several designs of grating couplers have been published [5

5. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. de 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(7), 949–955 (2002). [CrossRef]

8

8. J. V. Galan, P. Sanchis, J. Blasco, and J. Marti, “Study of High Efficiency Grating Couplers for Silicon-Based Horizontal Slot Waveguides,” IEEE Photon. Technol. Lett. 20(12), 985–987 (2008). [CrossRef]

], where simulated coupling efficiencies of up to 92% and bandwidths in the order of a few tens of nanometers were achieved.

The grating coupling efficiency is dominated by mainly two factors. The light is scattered not only into the air, but a part is also lost to the bottom into the substrate. In addition to that, to achieve high efficiency the light scattered to the top should have a field distribution that matches the fiber mode. To overcome the first issue, grating couplers with gold bottom mirrors [7

7. F. van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007). [CrossRef]

] or multilayer bottom reflectors [5

5. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. de 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(7), 949–955 (2002). [CrossRef]

,6

6. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

] were suggested to avoid radiation into the substrate. However, the process to fabricate such structures is not compatible to CMOS processing technology. Therefore, Roelkens et al. have recently suggested [9

9. G. Roelkens, D. van Thourhout, and R. Baets, “High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay,” Opt. Express 14(24), 11622–11630 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11622. [CrossRef] [PubMed]

,10

10. G. Roelkens, D. Vermeulen, D. van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008). [CrossRef]

] and demonstrated [11

11. G. Roelkens, D. Vermeulen, D. van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008) paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008-IME3

] structures where the Bloch modes that propagate in the grating were modified such that a better directionality is achieved. They have done this by deposition of an additional silicon-layer before etching. This makes the process better compatible to CMOS processing technology. Better directionality can also be achieved through slanted gratings in the cladding material [12

12. B. Wang, J. Jiang, and G. Nordin, “Compact slanted grating couplers,” Opt. Express 12(15), 3313–3326 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-15-3313. [CrossRef] [PubMed]

]. Grating couplers that lead to a better modematch with the fiber mode have also been designed. Nonuniform perturbation of the refractive index is required [6

6. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

]. Even better mode match can be achieved in long nonuniform gratings coupled through free space optics [13

13. L. Vivien, D. Pascal, S. Lardenois, D. MarTis-Morini, E. Cassan, F. Grillot, S. Laval, J. M. Fedeli, and L. El Melhaoui, “Light injection in SOI microwaveguides using high-efficiency grating couplers,” J. Lightwave Technol. 24(10), 3810–3815 (2006). [CrossRef]

].

All grating couplers proposed so far are achieved by shallow or slanted etching of slots into the waveguide or cladding. Such gratings have the advantage that coupling from the waveguide into the grating occurs with little reflection and the etched slots radiate efficiently. However, a significant drawback, for instance, of such shallow etched gratings is the additional lithography step. In this paper the design of a grating-fiber coupler with fully etched slots is proposed. All structures on the wafer can be fabricated in just one step because the second lithography step for shallow etching is not necessary. This grating would offer a fast and economic experimental solution for the coupling problem. Due to the fully etched slots, the periodic perturbation of the index contrast is very strong, which makes coupling into the grating from the slab waveguides more difficult to achieve. We have therefore developed an anti-reflection interface section that enhances coupling in order to reach a coupling efficiency comparable to shallow etched gratings.

2. Design approach

2.1 Geometrical structure

Figure 1
Fig. 1 Schematic representation of the grating coupler. Light is transmitted from the TE mode of the slab waveguide on the left into the grating and the slots scatter the light into the fiber positioned at angle ϕ. In this figure the wave is scattered at a negative angle which appears in counterclockwise direction with respect to the grating normal.
depicts the grating to fiber coupler and its geometrical parameters. The height of the silicon slab waveguide is h=220    nm. It is surrounded by air on top of it and by a BOX layer with thickness d. A silicon substrate below the BOX caters for mechanical stability. The period of the grating is a, w is the air slot width (w/a is the filling factor). N is the number of slots in the grating and defines the overall coupler length L=Na. The grating’s lateral mode width is chosen to fit the fiber mode width, what is achieved with waveguide lateral width wg=12    μm [6

6. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

]. For coupling reasons, the widths of the first and the last slot are given by wc=w/2 as discussed later. ϕ is the angle of the fiber towards the grating normal and, thus, the angle of the beam that is incident on or scattered from the grating.

Full wave simulations using CST Microwave Studio [14

14. Available at, www.cst.com.

], based on the finite integration technique (FIT) [15

15. T. Weiland, “Time domain electromagnetic field computation with finite difference methods,” Int. J. Numer. Model. 9(4), 295–319 (1996). [CrossRef]

,16

16. M. Clemens, and T. Weiland, “Discrete electromagnetism with the finite integration technique,” in Geometric Methods for Computational Electromagnetics, PIER. 32, F. L. Teixeira, J. A. Kong, eds., (EMW Publishing, 2001) 65–87.

], are carried out to evaluate the field radiated from the grating. The simulation volume corresponds to the one depicted in Fig. 1. The two dimensional (2D) simulations presented here assume the waveguide extension in x direction to be infinite. In 3D case the coupling efficiency is determined by the overlap integral of the scattered field and fiber mode profiles. This overlap integral can be split into two orthogonal contributions. The contribution from integrating along x-direction can be derived from a single 3D calculation. For coupling into a single mode fiber with a mode field diameter of 10µm this calculation yields an optimum waveguide width wg=12    μm and a coupling efficiency contribution of 97%. The contribution from the direction orthogonal to x is obtained from the 2D calculation as described further.

We approach the design of the grating coupler as if we consider coupling from the grating to the fiber. That is, in the simulation we excite the slab waveguide with the fundamental TE-mode that is coupled into the grating, whose slots should radiate a field into free space that is coupled into the fiber. Due to reciprocity, the results would be the same as if a wave is coupled from the fiber to the grating. The design approach is explained in more detail in the following sections.

2.2 Scattering angle

Each slot of the grating approximately radiates a spherical wave. All the single waves superpose and shape the radiated field. For a specific wavelength λ the distance between two radiating slots a determines towards which direction the single spherical waves interfere constructively and, thus, along which angle ϕ the phase front propagates. If ϕ is too large, due to the mechanical constraints, the fiber core will be relatively far away from the grating and the beam divergence will limit the coupling efficiency. If, on the other hand, ϕ is too small, the beam coming from the fiber would be strongly reflected from the grating back into the fiber or vice versa. For our coupler it is chosen ϕ=10° at the operating free space wavelength λ0=1550    nm or in terms of frequency f0=c/λ0=193.4    THz. The positive angle is defined in the clock wise direction. The negative angle indicates that the scattered wave propagates in the opposite direction to the excitation mode. To achieve ϕ, the corresponding a, which is constant relative to the guided wavelength, can be determined. Hence, a will vary with the slot width w because the effective refractive index of the grating is a function of w.

2.3 Coupling efficiency

Three factors determine the overall efficiency of the coupler. We are designing the coupler by optimizing those factors step by step.

First of all, there is the radiation efficiency η1 of the grating which indicates how much of the energy in the slab waveguide is scattered by the slots. It is dependent on two factors. The better the slab mode can be coupled into the grating, and the less energy is transmitted through the grating, the more energy is being scattered. Thus, we define

η1=PscatteredPtotal=1RT,
(1)

where R is the reflection coefficient of the grating back into the slab waveguide and T is the transmission coefficient through the grating. That part which is neither reflected nor transmitted is scattered by the slots.

A second efficiency η2 indicates what part of this scattered energy is radiated into the direction of the fiber. Initially the grating radiates about 50% of the energy into the air, whereas the other 50% are radiated downward into the BOX. At the lower BOX-silicon-interface, a part of the power is transmitted into the substrate and a part of it is reflected. The reflected part propagates upward again through the BOX toward the air and interferes with the wave that is radiated upward by the grating directly. The interference should be constructive to maximize the scattered power radiated upward into the air. This leads to the definition

η2=PairPScattered,
(2)

which is the ratio of the power radiated to the air and the power scattered by the grating. Since d defines the distance that the wave propagates in the BOX, η2 can be maximized by finding the optimum BOX thickness dopt for constructive interference of the two partial waves at the waveguide-air-interface [7

7. F. van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007). [CrossRef]

,17

17. T. Suhara and H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22(6), 845–867 (1986). [CrossRef]

,18

18. R. M. Emmons and D. G. Hall, “Buried-oxide silicon-on-insulator structures. II. Waveguide gratingcouplers,” IEEE J. Quantum Electron. 28(1), 164–175 (1992). [CrossRef]

].

We now have defined what amount of the total power is scattered in the direction to the fiber by η1 and η2. In order to obtain the total coupling efficiency, we need to know how much energy is coupled into the fundamental mode of the fiber. This partial efficiency is η3, which is given by the following equations:

η3=η3aη3bη3c,
(3)
η3a=|(E¯fiber(z')E¯grating(z'))2dz'E¯2fiber(z')dz'E¯2grating(z')dz'|,
(4)
η3b=0.97,
(5)
η3c=4β1β2(β1+β2)2=0.9663,
(6)

The enumerator of η3a is the overlap integral of the E-field distributions squared of the scattered wave and the fundamental fiber mode along the coordinate z', which is parallel to the fiber input interface. This is normalized by the powers of the two waves. The scattered electric field was evaluated close to the grating. This is justified as the fiber core will be positioned much closer than the Rayleigh length of the scattered beam. η3b is the same efficiency as η3a but evaluated for an integration direction perpendicular to the yz-plane. It depends on the lateral width of the grating, which was determined from a 3D simulation as wg=12μm, in accordance with Ref [6

6. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

]. η3c in the Eq. (6) is the Fresnel transmission of a normally incident electromagnetic wave, where β1 and β2 are the phase constants of the wave in air and in the fiber medium, respectively. Hence, η3 is higher if the scattered field resembles the fiber mode more closely.

The overall coupling efficiency of the grating-fiber-configuration is given by the product of the three efficiencies defined.

η=η1η2η3.
(7)

The presented coupling efficiency is valid for the ideal structure with a perfectly aligned optical system. A disorder introduced by the manufacturing process may lead to additional losses. However, for the typical deviations of 5 nm [19

19. D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004). [CrossRef] [PubMed]

] the disorder induced losses are expected to be low taking into account the very short length of the grating.

2.4 Chirped grating

For a uniform grating, where all slots have the same width, the power in the grating decreases exponentially by P(z)=P0exp(2γz). Thus the scattered power has also an exponentially decaying spatial distribution. This results in an inherent mismatch of the radiated field and the fiber mode, such that the maximum achievable η3a is about 80% for a uniform grating [6

6. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

]. γ is the loss factor of the grating per length and is constant over z due to constant w. A more Gaussian like profile for the radiated field can be achieved if the loss factor is designed to be z-dependent. Thus, w should vary with z such that the power that is lost in the grating per length matches the fiber mode. Hence,

dPdz=2γ(z)P(z), and dPdz=ρEfiber2(z),
(8)

with

ρ=PScattered0LEfiber2(z)dz.
(9)

From this follows the z dependent loss factor to achieve a Gaussian profile for the radiated field

γ(z)=12ρEfiber,n2(z)P(z).
(10)

Since a is a function of w, the correct chirp of the grating can be determined with the help of the a-dependence of γ by

γi=ai1aiγ(x)dxai=γ(ai),
(11)

where ai is the corresponding grating period to the ith slot, with a0=0. The width of the ith slot can then be determined, since a and w are directly related.

3. Simulation results and discussion

3.1 Radiation efficiency

There is strong reflection close to the band gap for modes above and below band gap, as shown in Fig. 2(b) with a grey line. That is, the group velocity of the Bloch modes is relatively small and coupling is more difficult to achieve than for gratings with shallow etched slots. However, coupling from a slab mode into a Bloch mode can be optimized for a narrow range of frequencies if the coupling interface to the grating coupler is properly adjusted. We choose to couple from the silicon slab directly into the xy symmetry plane of the 1D-Bragg stack. That is why at the input there is effectively half of the slot present (see Fig. 1). In Fig. 2(b) the reflected intensity is plotted with a black line for a grating with such an antireflection interface at the input and output. We can observe resonant coupling into the mode below the band edge and strong reflection above the band edge. Therefore, we define the radiation angle to be ϕ=10°.

The resonant coupling to the mode below the band gap can be explained through Bloch mode consideration. The Bloch modes can be described as a sum of forward and backward propagating plane waves in every layer of the Stack. The 1D transfer matrix simulations show that in the mode below the band gap these forward and backward propagating waves interfere in anti-phase at the center planes of dielectric and air layers. At the same time the coupling from silicon into air leads to a strong reflection at the interface, which is in phase to the incident field. Thus the backward propagating plane wave of the Bloch mode and the reflection at the silicon-air interface can compensate each other when their amplitudes become equal. On the other hand in the mode above the band gap the forward and backward propagating waves interfere in phase at the symmetry planes. To compensate the reflection the coupling from air into silicon should be considered, which is not possible in a slab waveguide configuration.

Having defined the direction of radiation and given the parameters in section 2.1, everything is known to find the function a(w). It is depicted in Fig. 3
Fig. 3 Grating period as a function of slot width, given ϕ = −10° at λ0. In the range depicted, a should be increased by approximately 1 nm for a change of w by 2 nm to maintain radiation in constant angle ϕ.
. Thus increasing slot width should be compensated by the increasing lattice constant to achieve the same scattering angle.

We have then investigated the dependence of η1 on w. Therefore, different uniform gratings with N=20 have been simulated and Fig. 4
Fig. 4 Radiation efficiency as a function of slot width monotonously increases and reaches saturation after 400 nm.
shows the behavior of η1 over w at the operating wavelength λ0. It is observed, that the radiation efficiency is larger for gratings with wider slots and it saturates at about w>400    nm. The transmission through a grating falls since a wider slot is a stronger radiator and for the same number N of slots, more power is radiated and less is transmitted through the grating. The result also confirms that coupling from the slab waveguide into the grating is not degraded for stronger gratings.

3.2 BOX width optimization

Now, the BOX width is determined that maximizes the power radiated to the top and minimizes the power radiated into the substrate. The η2 dependence on d for a fixed radiation angle ϕ is depicted in Fig. 5
Fig. 5 η2 as function of BOX thickness.
. The maximum achievable value for η2 with our structure is η2,max=73% and its minimum value is η2,min=36%. It is a periodic function of BOX thickness with a periodicity that is consistent with the expected value Δd=(λ0cosϕ)/(2nBOX)=0.53    μm.

3.3 Mode matching in uniform gratings

Having obtained the results so far, we know how we can optimize the grating such that maximum power is scattered to the fiber. Now, η3a is calculated for different uniform gratings with N=20, dopt and ϕ=10°. The result is plotted in Fig. 6(a)
Fig. 6 (a) η3a(w) is almost a constant function of slot width with slightly decreasing values at large slot widths. (b) η1(w)*η3a(w) has a flat maximum. A smaller slot width leads to less radiation efficiency because more power is transmitted through the grating and a larger slot width leads to a narrower radiation such that the mode match efficiency is less.
. The slot width w does not have a very strong effect on the mode match. The scattering profile is a section of an exponentially decaying function on length of L=20a. It can be shown that the coupling integral does not vary much until the decay length becomes much smaller than the grating length what is observed at slot widths of more than 400nm. This is due to the fact that for wider slots, the radiated power is more and more concentrated in a region that is smaller than the width of the Gaussian beam of the fiber.

Both, η3a(w) and η1(w) are functions of w. That is, an optimum slot width wopt can be found where the product η1(w)η3(w) is maximized, this function is shown in Fig. 6(b). η2, η3b and η3c stay unaffected, they are independent of w. Due to the flat maximum we chose for our coupler the smallest slot width wopt=350nm at the maximum, because a smaller slot width results in wider bandwidth due to the steeper dispersion curve. The overall coupling efficiency at λ0 is maximized to η=η1η2η3=49%. The efficiencies over wavelength are visualized in Fig. 7
Fig. 7 Coupling efficiencies over wavelength for grating with w = 350 nm.
.

The coupling efficiency is maximal at the wavelength 1.55 µm and decreasing at shorter and longer wavelengths. η3 is the factor that mainly limits the bandwidth. Due to the flat dispersion curve the radiation angle is relatively strongly dependent on the wavelength and a slightly different radiation angle would lead to strong mismatch of the radiated field and the fiber mode. All data of the designed grating is given in the following table:

Table 1. Optimized grating parameters for wavelength 1.55µm.

table-icon
View This Table

As we can see from Fig. 7, η1 is relatively high. η2 is already maximized for this structure and cannot be optimized further. Figure 8
Fig. 8 Field distribution of the field radiated by the designed uniform grating (red) and of the fundamental mode with 10.4 μm beam diameter (black).
visualizes the radiated field of the uniform grating along its phasefront and the field distribution of the fundamental fiber mode. We can see that the two fields have a certain expected mismatch.

3.4 Chirped grating

There is room to increase η3 theoretically by a chirped grating as described in section 2.4. Figure 9(a)
Fig. 9 (a) Theoretical γ(z) along the grating to achieve a scattered field with a Gaussian distribution. (b) Scattering coefficient γ(w) calculated from simulations, shown with points, and approximated with a square dependence on slot width, shown with a line.
depicts the loss factor γ(z), determined by Eq. (9), to achieve a Gaussian distribution of the radiated field at 97% of the scattered power. Through the function γ(w), which is depicted in Fig. 9(b), and Eq. (11) the discrete slot widths can be computed.

Simulations have shown that chirped gratings with fully etched slots and the restriction that it is coupled directly to the fiber are not more effective than their uniform counterparts. One reason is the strong discretization of the gradual function. We can see in Fig. 10(a)
Fig. 10 (a) η1 as a function of frequency for a chirped grating. Resonances close to the band edge are observed. (b) Radiated field distribution, the overlap integral shows an 80% match with the Gaussian profile of the fiber.
that η1 is quite low in comparison to uniform grating presented in Fig. 7 and shows resonances at frequencies close to the band edge. This indicates that coupling into these chirped gratings is not as efficient as for uniform gratings with antireflection interface. The gradual change in the slot width is not accepted by the wave as an adiabatic coupling. Reflections lead to distortion of the scattered profile and the overlap integral results only in η3a80% which is no essential improvement.

4. Conclusion

We have presented the design of a grating-to-fiber coupler that can be fabricated with fully etched slots. Resonant coupling into the dielectric mode of the grating is achieved by choosing an antireflection interface of the photonic crystal and operating below the second bandgap with negative scattering angle. A total maximum coupling efficiency of η=49% is theoretically achieved, which is comparable to the efficiency of shallow etch gratings. The 3dB bandwidth of 35nm is approximately two times smaller in comparison to shallow etched grating, which is unavoidable due to the flat mode close to the band edge of the fully etched structures. However, this does not pose a particular problem as the grating coupler is intended to be designed specifically for a device application at a fixed wavelength and narrow bandwidth.

Additional loss occurs mainly to radiation into the substrate and mismatch of the radiated field and the Gaussian beam of the fiber. The radiation in the substrate was reduced by optimization of the BOX width. The mode mismatch loss we have tried to improve with a nonuniform slot width along the grating. However, even though we have a gradually changing taper at the input, the coupling into a chirped grating is more difficult than into uniform gating with antireflection interface and thus the fiber coupling efficiency is not improved in comparison to a uniform grating.

Acknowledgements

This research is supported by the German Research Foundation (DFG). The authors acknowledge the support from CST, Darmstadt, Germany with their Microwave Studio software.

References and links

1.

M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]

2.

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]

3.

V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]

4.

T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002). [CrossRef]

5.

D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. de 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(7), 949–955 (2002). [CrossRef]

6.

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]

7.

F. van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007). [CrossRef]

8.

J. V. Galan, P. Sanchis, J. Blasco, and J. Marti, “Study of High Efficiency Grating Couplers for Silicon-Based Horizontal Slot Waveguides,” IEEE Photon. Technol. Lett. 20(12), 985–987 (2008). [CrossRef]

9.

G. Roelkens, D. van Thourhout, and R. Baets, “High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay,” Opt. Express 14(24), 11622–11630 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11622. [CrossRef] [PubMed]

10.

G. Roelkens, D. Vermeulen, D. van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008). [CrossRef]

11.

G. Roelkens, D. Vermeulen, D. van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008) paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008-IME3

12.

B. Wang, J. Jiang, and G. Nordin, “Compact slanted grating couplers,” Opt. Express 12(15), 3313–3326 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-15-3313. [CrossRef] [PubMed]

13.

L. Vivien, D. Pascal, S. Lardenois, D. MarTis-Morini, E. Cassan, F. Grillot, S. Laval, J. M. Fedeli, and L. El Melhaoui, “Light injection in SOI microwaveguides using high-efficiency grating couplers,” J. Lightwave Technol. 24(10), 3810–3815 (2006). [CrossRef]

14.

Available at, www.cst.com.

15.

T. Weiland, “Time domain electromagnetic field computation with finite difference methods,” Int. J. Numer. Model. 9(4), 295–319 (1996). [CrossRef]

16.

M. Clemens, and T. Weiland, “Discrete electromagnetism with the finite integration technique,” in Geometric Methods for Computational Electromagnetics, PIER. 32, F. L. Teixeira, J. A. Kong, eds., (EMW Publishing, 2001) 65–87.

17.

T. Suhara and H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22(6), 845–867 (1986). [CrossRef]

18.

R. M. Emmons and D. G. Hall, “Buried-oxide silicon-on-insulator structures. II. Waveguide gratingcouplers,” IEEE J. Quantum Electron. 28(1), 164–175 (1992). [CrossRef]

19.

D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004). [CrossRef] [PubMed]

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(130.0250) Integrated optics : Optoelectronics
(130.3120) Integrated optics : Integrated optics devices

ToC Category:
Integrated Optics

History
Original Manuscript: March 2, 2009
Revised Manuscript: May 8, 2009
Manuscript Accepted: June 9, 2009
Published: June 18, 2009

Citation
Bernd Schmid, Alexander Petrov, and Manfred Eich, "Optimized grating coupler with fully etched slots," Opt. Express 17, 11066-11076 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-13-11066


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References

  1. M. Lipson, “Guiding, modulating, and emitting light on silicon-challenges and opportunities,” J. Lightwave Technol. 23(12), 4222–4238 (2005). [CrossRef]
  2. 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]
  3. V. R. Almeida, R. R. Panepucci, and M. Lipson, “Nanotaper for compact mode conversion,” Opt. Lett. 28(15), 1302–1304 (2003). [CrossRef] [PubMed]
  4. T. Shoji, T. Tsuchizawa, T. Watanabe, K. Yamada, and H. Morita, “Low loss mode size converter from 0.3 mu m square Si wire waveguides to singlemode fibres,” Electron. Lett. 38(25), 1669–1670 (2002). [CrossRef]
  5. D. Taillaert, W. Bogaerts, P. Bienstman, T. F. Krauss, P. van Daele, I. Moerman, S. Verstuyft, K. de 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(7), 949–955 (2002). [CrossRef]
  6. D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004). [CrossRef] [PubMed]
  7. F. van Laere, G. Roelkens, M. Ayre, J. Schrauwen, D. Taillaert, D. van Thourhout, T. E. Krauss, and R. Baets, “Compact and highly efficient grating couplers between optical fiber and nanophotonic waveguides,” J. Lightwave Technol. 25(1), 151–156 (2007). [CrossRef]
  8. J. V. Galan, P. Sanchis, J. Blasco, and J. Marti, “Study of High Efficiency Grating Couplers for Silicon-Based Horizontal Slot Waveguides,” IEEE Photon. Technol. Lett. 20(12), 985–987 (2008). [CrossRef]
  9. G. Roelkens, D. van Thourhout, and R. Baets, “High efficiency Silicon-on-Insulator grating coupler based on a poly-Silicon overlay,” Opt. Express 14(24), 11622–11630 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-24-11622 . [CrossRef] [PubMed]
  10. G. Roelkens, D. Vermeulen, D. van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fédéli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008). [CrossRef]
  11. G. Roelkens, D. Vermeulen, D. van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J. M. Fedeli, “High efficiency SOI fiber-to-waveguide grating couplers fabricated using CMOS technology,” in Integrated Photonics and Nanophotonics Research and Applications, (Optical Society of America, 2008) paper IME3, http://www.opticsinfobase.org/abstract.cfm?URI=IPNRA-2008-IME3
  12. B. Wang, J. Jiang, and G. Nordin, “Compact slanted grating couplers,” Opt. Express 12(15), 3313–3326 (2004), http://www.opticsinfobase.org/abstract.cfm?URI=oe-12-15-3313 . [CrossRef] [PubMed]
  13. L. Vivien, D. Pascal, S. Lardenois, D. MarTis-Morini, E. Cassan, F. Grillot, S. Laval, J. M. Fedeli, and L. El Melhaoui, “Light injection in SOI microwaveguides using high-efficiency grating couplers,” J. Lightwave Technol. 24(10), 3810–3815 (2006). [CrossRef]
  14. Available at, www.cst.com .
  15. T. Weiland, “Time domain electromagnetic field computation with finite difference methods,” Int. J. Numer. Model. 9(4), 295–319 (1996). [CrossRef]
  16. M. Clemens, and T. Weiland, “Discrete electromagnetism with the finite integration technique,” in Geometric Methods for Computational Electromagnetics, PIER. 32, F. L. Teixeira, J. A. Kong, eds., (EMW Publishing, 2001) 65–87.
  17. T. Suhara and H. Nishihara, “Integrated optics components and devices using periodic structures,” IEEE J. Quantum Electron. 22(6), 845–867 (1986). [CrossRef]
  18. R. M. Emmons and D. G. Hall, “Buried-oxide silicon-on-insulator structures. II. Waveguide gratingcouplers,” IEEE J. Quantum Electron. 28(1), 164–175 (1992). [CrossRef]
  19. D. Gerace and L. C. Andreani, “Disorder-induced losses in photonic crystal waveguides with line defects,” Opt. Lett. 29(16), 1897–1899 (2004). [CrossRef] [PubMed]

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