- Email: [email protected]
High efficiency fiber coupling to silicon sandwiched slot waveguides
Optics Communications 281 (2008) 5173–5176
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
High efficiency fiber coupling to silicon sandwiched slot waveguides J.V. Galan *, P. Sanchis, J. Blasco, A. Martinez, J. Martí Valencia Nanophotonics Technology Center, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
a r t i c l e
i n f o
Article history: Received 5 May 2008 Received in revised form 8 July 2008 Accepted 8 July 2008
a b s t r a c t The design of a fiber coupler for high efficiency light coupling to silicon sandwiched slot waveguides is reported. The proposed fiber coupler is based on the inverted taper approach. Parameters have been optimized to maximize coupling efficiency for k = 1550 nm and TM polarization. Maximum coupling efficiencies of 93% for a inverted taper length of 150 lm and a inverted taper tip width of 40 nm have been obtained by means of the overlap integral and 3D beam propagation method (BPM) simulations. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction A major goal in current photonic research is to create high performance, highly integrated devices using the most suitable technology so that economies of scale can be obtained. Making use of a CMOS-compatible silicon process is therefore advantageous as it allows us to leverage mature technologies used for microelectronics [1]. Many of the properties that make silicon a good choice for electronic chips are also helpful in optical applications; for example, many silicon-based passive optical devices have been demonstrated [2–4]. However, silicon is a poor material for making modulators or lasers, which are the most fundamental devices in optical communications. Materials which have superior optical properties, such as alloys of Group III and V elements, are used to make the lasers in long-haul telecommunication networks. These materials are regrettably not CMOS compatible, primarily because of mismatched crystal lattice constants with respect to silicon. An emerging alternative to achieve successful silicon optical properties is to attempt to exploit quantum mechanical effects to improve the optical properties of silicon. Following this approach, silicon nanocrystals (Si–nc) has been identified as a promising candidate material for silicon photonics [5–7]. A novel waveguide configuration, known as slot waveguide, has been recently proposed for silicon devices [8–10]. In the slot waveguide, the fundamental mode is highly confined in a very small region (slot region) of a low index material sandwiched between two silicon high index layers. This enables the introduction of active optical materials that can be efficiently exploited for modulation, switching, sensing, and other applications. A very promising active material is silicon nanocrystals (Si–nc) embedded in silica (SiO2). Different slot waveguide configurations have been recently optimized to achieve nonlinear performance in Si–nc/SiO2 based slot waveguides [10]. However, the sandwiched slot waveguide config* Corresponding author. E-mail address: [email protected] (J.V. Galan). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.07.013
uration has the advantage of being easier to fabricate, when compared to the vertical slot waveguide configuration. In this paper, we propose highly efficient coupling between optical fibers and sandwiched slot waveguides based on the inverted taper approach. 2. Optical fiber coupling in sandwiched slot waveguides Optical fiber coupling is a key point in sandwiched slot waveguides. High coupling losses occur due to the high differences in the dimensions of the slot region (rectangular geometry, typically 50 nm thick and 350 nm width) and the fiber (circular geometry, 10 lm core width). Two types of coupling techniques are mainly used for efficient light coupling to silicon photonic integrated circuits: butt-coupling techniques using inverted tapers and surface coupling using grating couplers. Many different configurations of inverted taper [11–13] and grating coupler [14,15], coupling techniques have been recently investigated for efficient coupling between optical fibers and conventional silicon waveguides. Recently, grating couplers for efficient light coupling to sandwiched slot waveguides have also been proposed [16]. However, although around 60% coupling efficiency can be achieved using grating couplers, coupling efficiency can be improved by using inverted tapers. Furthermore, butt-coupling techniques enable the possibility of introducing passive alignment techniques, such as the V-groove structure, and thus a simpler device packaging [11]. Therefore, an inverted taper based coupler has been designed for coupling to sandwiched slot waveguides at a wavelength of k = 1550 nm. 3. Inverted taper approach for sandwiched slot waveguides Fig. 1 shows a schematic of the proposed structure. The coupling structure is based on a sandwiched slot waveguide on top of a silica cladding layer, which is tapered down to create the inverted taper for coupling to the fiber. This geometry allows using commercial SOI (Silicon on Insulator) wafers. A fiber adapted
5174
J.V. Galan et al. / Optics Communications 281 (2008) 5173–5176
Slot waveguide-based inverted taper fiber coupler
w Si-nc/SiO2 based slot waveguide
Fiber adapted waveguide
h Si
(np)
ws air aiz
air
h
nH=3.48 nS
hp
Lt
Si
nH=3.48
wt y
wp SiO2
SiO2
nC=1.46
z x
nC=1.46
Fig. 1. Schematic of the proposed structure for efficient light coupling to sandwiched slot waveguides. A detailed view of the considered layer stack of the sandwiched slot waveguide is also shown.
waveguide on top of the inverted taper is used to efficiently guide light from the taper to the fiber (see Fig. 1). Fig. 1 also shows the layer stack used for the slot waveguide configuration. The low refractive index (nS) slot layer is sandwiched between two silicon high refractive index (nH) layers. In the sandwiched slot waveguide case, the electric field discontinuity at the interface between the high index contrast silicon waveguides occurs in the vertical direction. Therefore, the highest field confinement is achieved for TM polarization (y-axis direction in Fig. 1). The silicon layers thickness is h, the slot layer thickness is ws, and the slot waveguide width is w, as shown in Fig. 1. Silicon’s refractive index (nH = 3.48) is also indicated in Fig. 1. Furthermore, the slot is made of Si–nc embedded in silica (SiO2) and has a refractive index (nH = 1.6). Finally, the fiber adapted waveguide on top of the inverted taper uses a polymer with a refractive index of np = 1.6, the same refractive index as the Si–nc/SiO2 slot layer. Previously to the coupler design, the sandwiched slot waveguide configuration was analyzed to determine the optimum parameters to achieve maximum field confinement. The optimum waveguide parameters are those that give minimum effective area in the slot region [10]. All analysis was performed at k = 1550 nm and for TM polarization. Optimum performance was obtained for a slot thicknesses of ws = 50 nm, a silicon layer thickness of h = 200 nm and a slot waveguide width of w = 350 nm [10].
g¼
! RR! RR! Re E ðx; yÞdxdy E fib ðx; yÞ Hfib dxdy s
The next optimization parameter has been the inverted taper tip width (wt). The optimum inverted taper tip width, which min100
Power Coupling Efficiency (%)
The main design parameters of the proposed inverted taper coupling structure are the inverted taper length (Lt), the inverted taper tip width (wt), and the dimensions of the fiber adapted waveguide on top or the coupler (wp, hp), as depicted in Fig. 1. Optimization is performed to obtain maximum coupling efficiency. To simplify the design, the dimensions of the fiber adapted waveguide have been chosen to be wp = hp = 3 lm. The mode mismatch between the optical fiber and the fiber adapted waveguide fundamental modes has been evaluated by means of the overlap integral [17]
s
4.1. Inverted taper tip width optimization
90
4. Inverted taper coupling structure design
2 ! R R ! E ðx; yÞ H ðx; yÞdxdy fib
electromagnetic fields of the fiber fundamental mode for TM polarization. The fundamental mode of the fiber adapted waveguide was obtained by using a three dimensional (3D) mode solver based on the beam propagation method (BPM). The fundamental mode of the optical fiber was obtained by means of a Gaussian beam function. Fig. 2 shows the coupling efficiency calculated with Eq. (1). It can be seen that for the considered fiber adapted waveguide dimensions (wp = hp = 3 lm), 98% coupling efficiency may be achieved with a optical fiber with a mode field diameter (MFD) of 2.5 lm. So, the design is aimed to be used with lensed fibers with MFD = 2.5 lm, which are very common for testing silicon devices, and are standard commercially available. It is important to remark that the design can also be optimized for coupling to standard single-mode optical fibers with MFD = 10 lm by changing the fiber adapted waveguide cross-section dimensions.
80 70 60 50 40 30 20
ð1Þ
s
where {E,H} are the TM polarization electromagnetic fields of the fiber adapted waveguide fundamental mode, and {Efib,Hfib} are the
1
2
3
4
5
6
7
8
9
10
Fiber Mode Field Diameter (um) Fig. 2. Coupling efficiency calculations using the overlap integral between fundamental mode profiles of both optical fiber and fiber adapted waveguide as a function of the fiber mode field diameter (MFD). Cross-section dimensions of the fiber adapted waveguide are wp = hp = 3 lm.
5175
J.V. Galan et al. / Optics Communications 281 (2008) 5173–5176
coupling efficiency between the fundamental modes of the structures depicted in Fig. 3. For TM polarization, it is obtained that coupling efficiency gets lower than 95% if the inverted taper is wider than 40 nm. So, in agreement with results shown in Fig. 4a, it can be concluded that the optimum taper tip width will be wt = 40 nm.
imizes the mode mismatch for TM polarization, has been designed by means of the overlap integral between the fundamental mode of the fiber adapted waveguide and the inverted taper tip waveguide, assuming an infinitely long waveguide having the same cross-section as the taper tip. The design process is depicted in Fig. 3 for infinitely waveguides along the z-axis, according to axis definition in Fig. 3. However, the effective index of the guided mode at the taper tip interface was also first calculated as a function of the taper tip with and for different slot thicknesses. The obtained results are shown in Fig. 4a. The effective index increases with the taper tip width for the three considered slot thicknesses owing to the higher confinement in the slot waveguide. However, the effective index remains almost equal to the effective index of the fiber adapted waveguide (wt = 0 case), when taper tip is less than 40 nm wide, so that the lower mode mismatching is achieved at the taper tip interface. As a result, and taking into account that nonlinear effects in the slot region are higher for lower slot thicknesses, a slot thickness of ws = 50 nm has been chosen. Furthermore, an inverted taper tip width of wt = 40 nm seems also to be optimum as the effective index does not significantly change compared to the refractive index of the fiber adapted waveguide so the highest mode matching will be achieved at the taper tip interface. Mode mismatching at the taper tip interface has been calculated by means of the overlap integral. Fig. 4b shows the power
4.2. Inverted taper length optimization The optimum inverted taper length has been designed by means of 3D-BPM simulations using the optimum taper tip width (wt = 40 nm), which was previously obtained, and the polymer fiber adapted waveguide dimensions (wp = hp = 3 lm). Fig. 5a shows the field distribution in a 150 lm long inverted taper obtained by means of a 3D-BPM simulation. To obtain coupling efficiency, the structure is excited at z = 0 by the fiber adapted waveguide fundamental mode and a 1550 nm wavelength and for TM polarization, according to axis definition in Fig. 3. The power coupled at the 350 nm wide slot waveguide is then measured to evaluate coupling efficiency. Fig. 5b shows the coupling efficiency as a function of the inverted taper length. It can be observed that coupling efficiency increases as the inverted taper gets longer due to the lower mode mismatching. Furthermore, if the inverted taper is longer that
350nm
Inverted t aper tip interface air
air ai air n p =1.6 n p =1.6
3µm
Lt
3µm
y n C=1.46
wt
3µm
3µm SiO 2
wt
SiO 2
n p =1.6
3µm
3µm
n C=1.46
SiO2
n C=1.46
TM polarization fundamental modes overla p i ntegral
z x
Fig. 3. Schematic of the design process to find the optimum inverted taper tip
1.7
ws=50nm
1.68
ws=100nm
1.66
ws=150nm
b
1.64 1.62 1.6 1.58 1.56
0
20
40
60
80
Inverted taper tip width (nm)
100
100
Power Coupling Efficiency (%)
Effective index
a
90 80 70 60 50 40 30 20 10 0
0
20
40
60
80
100
120
Inverted taper tip width (nm)
Fig. 4. (a) Effective index as a function of the taper tip width (wt) for different slot thicknesses (ws) and (b) coupling efficiency as a function of the inverted taper tip width, for a slot thickness of ws = 50 nm.
5176
J.V. Galan et al. / Optics Communications 281 (2008) 5173–5176
a
b Power Coupling Efficiency (%)
Z (µm)
100
80
60
40
20
0 0
50
100
150
200
Inverted taper length (μm)
Fig. 5. (a) Field distribution in a 150 lm long sandwiched slot waveguide based inverted taper obtained by means of 3D-BPM simulations abd (b) coupling efficiency as a function of the inverted taper length.
150 lm, coupling efficiency gets constant with the taper length, and 95% coupling efficiency is achieved. As maximum coupling efficiency is achieved for a 150 lm longer inverted taper, a taper length of Lt = 150 lm has been chosen. The obtained coupling efficiency is in a very good agreement with the results shown in Fig. 4b which were calculated using the overlap integral. It is also important to point out that the structure analyzed in the simulations is excited by the fiber adapted waveguide fundamental mode, so the coupling efficiency results are shown in Fig. 5b for a taper length of Lt = 150 lm is only due to the mode mismatching at the taper tip interface. Therefore, as mode mismatching at the fiber interface is not considered in the simulation results depicted in Fig. 5b, the total coupling efficiency will be the product of the coupling efficiency obtained in Fig. 5b and the coupling efficiency previously obtained in Fig. 2 at the fiber interface. The final result is a 93% total coupling efficiency for TM polarization and k = 1550 nm. 5. Conclusions In this paper, we report a highly efficient fiber coupler for light coupling between optical fiber and Si–nc/SiO2 based sandwiched slot waveguides. Parameters have been optimized to achieve maximum coupling efficiency for TM polarization and k = 1550 nm by means of 3D-BPM simulations and overlap integral calculations. According to simulation results, maximum 93% coupling efficiency is achieved for an inverted taper of 150 lm length and 40 nm tip width, when coupling from a lensed fiber with MFD = 2.5 lm, and taking into account a polymer fiber adapted waveguide of 3 lm 3 lm cross-section dimensions.
Acknowledgments Authors acknowledge financial support by EC under project 017158-PHOLOGIC and Spanish MEC and EU-FEDER under contact TEC2005-07830 SILPHONICS. It is also acknowledged the support of Generalitat Valencia under project reference 20070775 EFIDIS. References [1] R. Soref, IEEE J. Quantum Electron. 12 (2006) 1678. [2] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, H. Morita, IEEE J. Quantum Electron. 11 (2005) 232. [3] B. Jalali, S. Fathpour, IEEE J. Lightwave Technol. 24 (2006) 4600. [4] N. Izhakty, M.T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, M.J. Paniccia, IEEE J. Quantum Electron. 12 (2006) 1688. [5] D. Kovalev, H. Heckler, G. Polisski, J. Diener, F. Koch, Opt. Mater. 17 (2001) 35. [6] L. Pavesi, L.D. Negro, C. Mazzoleni, G. Franzo, F. Priolo, Nature 408 (2000) 440. [7] L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franz‘o, F. Priolo, Appl. Phys. Lett. 82 (2003) 4636. [8] V.R. Almeida, Q. Xu, C.A. Barrios, M. Lipson, Opt. Lett. 29 (2004) 1209. [9] T. Baehr-Jones, M. Hochberg, C. Walker, A. Scherer, Appl. Phys. Lett. 86 (2005) 81. [10] P. Sanchis, J. Blasco, A. Martinez, J. Marti, IEEE J. Lightwave Technol. 25 (2007) 1298. [11] J.V. Galan, P. Sanchis, G. Sanchez, J. Marti, Opt. Express 15 (2007) 7058. [12] V.R. Almeida, R.R. Panepucci, M. Lipson, Opt. Lett. 28 (2003) 1302. [13] G.Y. Liu, J.Z. Yu, Appl. Opt. 46 (2007) 7858. [14] G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, R. Baets, Photon. Technol. Lett. 17 (2005) 2613. [15] L. Vivien, D. Pascal, S. Lardenois, D. Marris-Morini, E. Cassan, F. Grillot, S. Laval, J.-M. Fédéli, L. El Melhaoui, IEEE J. Ligthwave. Technol. 24 (2006) 3810. [16] J.V. Galan, P. Sanchis, J. Blasco, J. Marti, IEEE Photon. Technol. Lett. 20 (2008) 985. [17] G. Roelkens, D.V. Thourhout, R. Baets, Opt. Lett. 32 (2007) 1495.
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
High efficiency fiber coupling to silicon sandwiched slot waveguides J.V. Galan *, P. Sanchis, J. Blasco, A. Martinez, J. Martí Valencia Nanophotonics Technology Center, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
a r t i c l e
i n f o
Article history: Received 5 May 2008 Received in revised form 8 July 2008 Accepted 8 July 2008
a b s t r a c t The design of a fiber coupler for high efficiency light coupling to silicon sandwiched slot waveguides is reported. The proposed fiber coupler is based on the inverted taper approach. Parameters have been optimized to maximize coupling efficiency for k = 1550 nm and TM polarization. Maximum coupling efficiencies of 93% for a inverted taper length of 150 lm and a inverted taper tip width of 40 nm have been obtained by means of the overlap integral and 3D beam propagation method (BPM) simulations. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction A major goal in current photonic research is to create high performance, highly integrated devices using the most suitable technology so that economies of scale can be obtained. Making use of a CMOS-compatible silicon process is therefore advantageous as it allows us to leverage mature technologies used for microelectronics [1]. Many of the properties that make silicon a good choice for electronic chips are also helpful in optical applications; for example, many silicon-based passive optical devices have been demonstrated [2–4]. However, silicon is a poor material for making modulators or lasers, which are the most fundamental devices in optical communications. Materials which have superior optical properties, such as alloys of Group III and V elements, are used to make the lasers in long-haul telecommunication networks. These materials are regrettably not CMOS compatible, primarily because of mismatched crystal lattice constants with respect to silicon. An emerging alternative to achieve successful silicon optical properties is to attempt to exploit quantum mechanical effects to improve the optical properties of silicon. Following this approach, silicon nanocrystals (Si–nc) has been identified as a promising candidate material for silicon photonics [5–7]. A novel waveguide configuration, known as slot waveguide, has been recently proposed for silicon devices [8–10]. In the slot waveguide, the fundamental mode is highly confined in a very small region (slot region) of a low index material sandwiched between two silicon high index layers. This enables the introduction of active optical materials that can be efficiently exploited for modulation, switching, sensing, and other applications. A very promising active material is silicon nanocrystals (Si–nc) embedded in silica (SiO2). Different slot waveguide configurations have been recently optimized to achieve nonlinear performance in Si–nc/SiO2 based slot waveguides [10]. However, the sandwiched slot waveguide config* Corresponding author. E-mail address: [email protected] (J.V. Galan). 0030-4018/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2008.07.013
uration has the advantage of being easier to fabricate, when compared to the vertical slot waveguide configuration. In this paper, we propose highly efficient coupling between optical fibers and sandwiched slot waveguides based on the inverted taper approach. 2. Optical fiber coupling in sandwiched slot waveguides Optical fiber coupling is a key point in sandwiched slot waveguides. High coupling losses occur due to the high differences in the dimensions of the slot region (rectangular geometry, typically 50 nm thick and 350 nm width) and the fiber (circular geometry, 10 lm core width). Two types of coupling techniques are mainly used for efficient light coupling to silicon photonic integrated circuits: butt-coupling techniques using inverted tapers and surface coupling using grating couplers. Many different configurations of inverted taper [11–13] and grating coupler [14,15], coupling techniques have been recently investigated for efficient coupling between optical fibers and conventional silicon waveguides. Recently, grating couplers for efficient light coupling to sandwiched slot waveguides have also been proposed [16]. However, although around 60% coupling efficiency can be achieved using grating couplers, coupling efficiency can be improved by using inverted tapers. Furthermore, butt-coupling techniques enable the possibility of introducing passive alignment techniques, such as the V-groove structure, and thus a simpler device packaging [11]. Therefore, an inverted taper based coupler has been designed for coupling to sandwiched slot waveguides at a wavelength of k = 1550 nm. 3. Inverted taper approach for sandwiched slot waveguides Fig. 1 shows a schematic of the proposed structure. The coupling structure is based on a sandwiched slot waveguide on top of a silica cladding layer, which is tapered down to create the inverted taper for coupling to the fiber. This geometry allows using commercial SOI (Silicon on Insulator) wafers. A fiber adapted
5174
J.V. Galan et al. / Optics Communications 281 (2008) 5173–5176
Slot waveguide-based inverted taper fiber coupler
w Si-nc/SiO2 based slot waveguide
Fiber adapted waveguide
h Si
(np)
ws air aiz
air
h
nH=3.48 nS
hp
Lt
Si
nH=3.48
wt y
wp SiO2
SiO2
nC=1.46
z x
nC=1.46
Fig. 1. Schematic of the proposed structure for efficient light coupling to sandwiched slot waveguides. A detailed view of the considered layer stack of the sandwiched slot waveguide is also shown.
waveguide on top of the inverted taper is used to efficiently guide light from the taper to the fiber (see Fig. 1). Fig. 1 also shows the layer stack used for the slot waveguide configuration. The low refractive index (nS) slot layer is sandwiched between two silicon high refractive index (nH) layers. In the sandwiched slot waveguide case, the electric field discontinuity at the interface between the high index contrast silicon waveguides occurs in the vertical direction. Therefore, the highest field confinement is achieved for TM polarization (y-axis direction in Fig. 1). The silicon layers thickness is h, the slot layer thickness is ws, and the slot waveguide width is w, as shown in Fig. 1. Silicon’s refractive index (nH = 3.48) is also indicated in Fig. 1. Furthermore, the slot is made of Si–nc embedded in silica (SiO2) and has a refractive index (nH = 1.6). Finally, the fiber adapted waveguide on top of the inverted taper uses a polymer with a refractive index of np = 1.6, the same refractive index as the Si–nc/SiO2 slot layer. Previously to the coupler design, the sandwiched slot waveguide configuration was analyzed to determine the optimum parameters to achieve maximum field confinement. The optimum waveguide parameters are those that give minimum effective area in the slot region [10]. All analysis was performed at k = 1550 nm and for TM polarization. Optimum performance was obtained for a slot thicknesses of ws = 50 nm, a silicon layer thickness of h = 200 nm and a slot waveguide width of w = 350 nm [10].
g¼
! RR! RR! Re E ðx; yÞdxdy E fib ðx; yÞ Hfib dxdy s
The next optimization parameter has been the inverted taper tip width (wt). The optimum inverted taper tip width, which min100
Power Coupling Efficiency (%)
The main design parameters of the proposed inverted taper coupling structure are the inverted taper length (Lt), the inverted taper tip width (wt), and the dimensions of the fiber adapted waveguide on top or the coupler (wp, hp), as depicted in Fig. 1. Optimization is performed to obtain maximum coupling efficiency. To simplify the design, the dimensions of the fiber adapted waveguide have been chosen to be wp = hp = 3 lm. The mode mismatch between the optical fiber and the fiber adapted waveguide fundamental modes has been evaluated by means of the overlap integral [17]
s
4.1. Inverted taper tip width optimization
90
4. Inverted taper coupling structure design
2 ! R R ! E ðx; yÞ H ðx; yÞdxdy fib
electromagnetic fields of the fiber fundamental mode for TM polarization. The fundamental mode of the fiber adapted waveguide was obtained by using a three dimensional (3D) mode solver based on the beam propagation method (BPM). The fundamental mode of the optical fiber was obtained by means of a Gaussian beam function. Fig. 2 shows the coupling efficiency calculated with Eq. (1). It can be seen that for the considered fiber adapted waveguide dimensions (wp = hp = 3 lm), 98% coupling efficiency may be achieved with a optical fiber with a mode field diameter (MFD) of 2.5 lm. So, the design is aimed to be used with lensed fibers with MFD = 2.5 lm, which are very common for testing silicon devices, and are standard commercially available. It is important to remark that the design can also be optimized for coupling to standard single-mode optical fibers with MFD = 10 lm by changing the fiber adapted waveguide cross-section dimensions.
80 70 60 50 40 30 20
ð1Þ
s
where {E,H} are the TM polarization electromagnetic fields of the fiber adapted waveguide fundamental mode, and {Efib,Hfib} are the
1
2
3
4
5
6
7
8
9
10
Fiber Mode Field Diameter (um) Fig. 2. Coupling efficiency calculations using the overlap integral between fundamental mode profiles of both optical fiber and fiber adapted waveguide as a function of the fiber mode field diameter (MFD). Cross-section dimensions of the fiber adapted waveguide are wp = hp = 3 lm.
5175
J.V. Galan et al. / Optics Communications 281 (2008) 5173–5176
coupling efficiency between the fundamental modes of the structures depicted in Fig. 3. For TM polarization, it is obtained that coupling efficiency gets lower than 95% if the inverted taper is wider than 40 nm. So, in agreement with results shown in Fig. 4a, it can be concluded that the optimum taper tip width will be wt = 40 nm.
imizes the mode mismatch for TM polarization, has been designed by means of the overlap integral between the fundamental mode of the fiber adapted waveguide and the inverted taper tip waveguide, assuming an infinitely long waveguide having the same cross-section as the taper tip. The design process is depicted in Fig. 3 for infinitely waveguides along the z-axis, according to axis definition in Fig. 3. However, the effective index of the guided mode at the taper tip interface was also first calculated as a function of the taper tip with and for different slot thicknesses. The obtained results are shown in Fig. 4a. The effective index increases with the taper tip width for the three considered slot thicknesses owing to the higher confinement in the slot waveguide. However, the effective index remains almost equal to the effective index of the fiber adapted waveguide (wt = 0 case), when taper tip is less than 40 nm wide, so that the lower mode mismatching is achieved at the taper tip interface. As a result, and taking into account that nonlinear effects in the slot region are higher for lower slot thicknesses, a slot thickness of ws = 50 nm has been chosen. Furthermore, an inverted taper tip width of wt = 40 nm seems also to be optimum as the effective index does not significantly change compared to the refractive index of the fiber adapted waveguide so the highest mode matching will be achieved at the taper tip interface. Mode mismatching at the taper tip interface has been calculated by means of the overlap integral. Fig. 4b shows the power
4.2. Inverted taper length optimization The optimum inverted taper length has been designed by means of 3D-BPM simulations using the optimum taper tip width (wt = 40 nm), which was previously obtained, and the polymer fiber adapted waveguide dimensions (wp = hp = 3 lm). Fig. 5a shows the field distribution in a 150 lm long inverted taper obtained by means of a 3D-BPM simulation. To obtain coupling efficiency, the structure is excited at z = 0 by the fiber adapted waveguide fundamental mode and a 1550 nm wavelength and for TM polarization, according to axis definition in Fig. 3. The power coupled at the 350 nm wide slot waveguide is then measured to evaluate coupling efficiency. Fig. 5b shows the coupling efficiency as a function of the inverted taper length. It can be observed that coupling efficiency increases as the inverted taper gets longer due to the lower mode mismatching. Furthermore, if the inverted taper is longer that
350nm
Inverted t aper tip interface air
air ai air n p =1.6 n p =1.6
3µm
Lt
3µm
y n C=1.46
wt
3µm
3µm SiO 2
wt
SiO 2
n p =1.6
3µm
3µm
n C=1.46
SiO2
n C=1.46
TM polarization fundamental modes overla p i ntegral
z x
Fig. 3. Schematic of the design process to find the optimum inverted taper tip
1.7
ws=50nm
1.68
ws=100nm
1.66
ws=150nm
b
1.64 1.62 1.6 1.58 1.56
0
20
40
60
80
Inverted taper tip width (nm)
100
100
Power Coupling Efficiency (%)
Effective index
a
90 80 70 60 50 40 30 20 10 0
0
20
40
60
80
100
120
Inverted taper tip width (nm)
Fig. 4. (a) Effective index as a function of the taper tip width (wt) for different slot thicknesses (ws) and (b) coupling efficiency as a function of the inverted taper tip width, for a slot thickness of ws = 50 nm.
5176
J.V. Galan et al. / Optics Communications 281 (2008) 5173–5176
a
b Power Coupling Efficiency (%)
Z (µm)
100
80
60
40
20
0 0
50
100
150
200
Inverted taper length (μm)
Fig. 5. (a) Field distribution in a 150 lm long sandwiched slot waveguide based inverted taper obtained by means of 3D-BPM simulations abd (b) coupling efficiency as a function of the inverted taper length.
150 lm, coupling efficiency gets constant with the taper length, and 95% coupling efficiency is achieved. As maximum coupling efficiency is achieved for a 150 lm longer inverted taper, a taper length of Lt = 150 lm has been chosen. The obtained coupling efficiency is in a very good agreement with the results shown in Fig. 4b which were calculated using the overlap integral. It is also important to point out that the structure analyzed in the simulations is excited by the fiber adapted waveguide fundamental mode, so the coupling efficiency results are shown in Fig. 5b for a taper length of Lt = 150 lm is only due to the mode mismatching at the taper tip interface. Therefore, as mode mismatching at the fiber interface is not considered in the simulation results depicted in Fig. 5b, the total coupling efficiency will be the product of the coupling efficiency obtained in Fig. 5b and the coupling efficiency previously obtained in Fig. 2 at the fiber interface. The final result is a 93% total coupling efficiency for TM polarization and k = 1550 nm. 5. Conclusions In this paper, we report a highly efficient fiber coupler for light coupling between optical fiber and Si–nc/SiO2 based sandwiched slot waveguides. Parameters have been optimized to achieve maximum coupling efficiency for TM polarization and k = 1550 nm by means of 3D-BPM simulations and overlap integral calculations. According to simulation results, maximum 93% coupling efficiency is achieved for an inverted taper of 150 lm length and 40 nm tip width, when coupling from a lensed fiber with MFD = 2.5 lm, and taking into account a polymer fiber adapted waveguide of 3 lm 3 lm cross-section dimensions.
Acknowledgments Authors acknowledge financial support by EC under project 017158-PHOLOGIC and Spanish MEC and EU-FEDER under contact TEC2005-07830 SILPHONICS. It is also acknowledged the support of Generalitat Valencia under project reference 20070775 EFIDIS. References [1] R. Soref, IEEE J. Quantum Electron. 12 (2006) 1678. [2] T. Tsuchizawa, K. Yamada, H. Fukuda, T. Watanabe, J. Takahashi, M. Takahashi, T. Shoji, E. Tamechika, S. Itabashi, H. Morita, IEEE J. Quantum Electron. 11 (2005) 232. [3] B. Jalali, S. Fathpour, IEEE J. Lightwave Technol. 24 (2006) 4600. [4] N. Izhakty, M.T. Morse, S. Koehl, O. Cohen, D. Rubin, A. Barkai, G. Sarid, R. Cohen, M.J. Paniccia, IEEE J. Quantum Electron. 12 (2006) 1688. [5] D. Kovalev, H. Heckler, G. Polisski, J. Diener, F. Koch, Opt. Mater. 17 (2001) 35. [6] L. Pavesi, L.D. Negro, C. Mazzoleni, G. Franzo, F. Priolo, Nature 408 (2000) 440. [7] L. Dal Negro, M. Cazzanelli, L. Pavesi, S. Ossicini, D. Pacifici, G. Franz‘o, F. Priolo, Appl. Phys. Lett. 82 (2003) 4636. [8] V.R. Almeida, Q. Xu, C.A. Barrios, M. Lipson, Opt. Lett. 29 (2004) 1209. [9] T. Baehr-Jones, M. Hochberg, C. Walker, A. Scherer, Appl. Phys. Lett. 86 (2005) 81. [10] P. Sanchis, J. Blasco, A. Martinez, J. Marti, IEEE J. Lightwave Technol. 25 (2007) 1298. [11] J.V. Galan, P. Sanchis, G. Sanchez, J. Marti, Opt. Express 15 (2007) 7058. [12] V.R. Almeida, R.R. Panepucci, M. Lipson, Opt. Lett. 28 (2003) 1302. [13] G.Y. Liu, J.Z. Yu, Appl. Opt. 46 (2007) 7858. [14] G. Roelkens, P. Dumon, W. Bogaerts, D. Van Thourhout, R. Baets, Photon. Technol. Lett. 17 (2005) 2613. [15] L. Vivien, D. Pascal, S. Lardenois, D. Marris-Morini, E. Cassan, F. Grillot, S. Laval, J.-M. Fédéli, L. El Melhaoui, IEEE J. Ligthwave. Technol. 24 (2006) 3810. [16] J.V. Galan, P. Sanchis, J. Blasco, J. Marti, IEEE Photon. Technol. Lett. 20 (2008) 985. [17] G. Roelkens, D.V. Thourhout, R. Baets, Opt. Lett. 32 (2007) 1495.