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Design, optimization and fabrication of an optical mode filter for integrated optics
Optics Express, Vol. 17, Issue 9, pp. 7383-7391 (2009)
http://dx.doi.org/10.1364/OE.17.007383
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– Abstract
1. Introduction
2. Design and optimization
3. Fabrication and results
4. Conclusion and discussion
– References and links
– Abstract
1. Introduction
2. Design and optimization
3. Fabrication and results
4. Conclusion and discussion
– References and links
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Abstract
We present the design, optimization, fabrication and characterization of an optical mode filter, which attenuates the snaking behavior of light caused by a lateral misalignment of the input optical fiber relative to an optical circuit. The mode filter is realized as a bottleneck section inserted in an optical waveguide in front of a branching element. It is designed with Bézier curves. Its effect, which depends on the optical state of polarization, is experimentally demonstrated by investigating the equilibrium of an optical splitter, which is greatly improved however only in TM mode. The measured optical losses induced by the filter are 0.28 dB.
© 2009 Optical Society of America
1. Introduction
The quality of the coupling between an optical fiber and an optical circuit depends in particular on the precision of the alignment. The slightest misalignment will have two main consequences. The first one is additional input losses, which can be reduced by adding an optical taper. Numerous studies have been published on this subject. The second consequence is that the optical beam can snake along the waveguide [1,2], most notably in the case of a lateral misalignment. This can also occur when the optical fiber is tilted relative to the waveguide or when the beam is coming out from a curved section of an optical circuit. This behavior occurs over a certain distance, until the optical beam adapts to the fundamental mode of the waveguide, this mode being in fact a steady-state solution of Maxwell’s equations. In a straight device it will generally pass unnoticed. But it can be a major problem in optical circuits comprising elements such as Y-branches or MMI devices, particularly if there are numerous cascading branching [3,4]. In 1990, Y. Shani published a paper [5] about the characterization of an integrated optic adiabatic polarization splitter whose input waveguide included a narrowed section (5 μm wide instead of 7 μm) in order to remove higher order guided modes which may be excited at the input, but without any details on the performances of this section. Many patents related to optical circuits [6-9] include similar sections, but very few studies have been published in the literature [10,1] and no experimental one to our knowledge. Moreover, optical polarization dependence is never considered.
L. J. Villegas Vicencio, A. V. Khomenko, J. L. Angel Valenzuela, R. Cardoso, D. Salazar, H. Marquez, and H. Porte, “Asymmetry of the output power of a symmetric Y-shaped integrated-optics splitter,” J. Opt. Technol. 69, 54–57 (2002). [CrossRef]
W. Klaus and W. R. Leeb, “Transient fields in the input coupling region of optical single-mode waveguides,” Opt. Express 15, 11808–11826 (2007). [CrossRef] [PubMed]
D. Yap and L. M. Johnson, “Coupling between successive Ti:LiNbO3 waveguide bends and branches,” Appl. Opt. 23, 2991–2998 (1984). [CrossRef] [PubMed]
Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic polarization splitter on silicon,” Appl. Phys. Lett. 56, 120–121 (1990). [CrossRef]
A. Klekamp, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996). [CrossRef]
L. J. Villegas Vicencio, A. V. Khomenko, J. L. Angel Valenzuela, R. Cardoso, D. Salazar, H. Marquez, and H. Porte, “Asymmetry of the output power of a symmetric Y-shaped integrated-optics splitter,” J. Opt. Technol. 69, 54–57 (2002). [CrossRef]
In this paper, we present the design, optimization, fabrication and characterization of a mode filter, which attenuates the snaking behavior due to a lateral misalignment of the input fiber. Our theoretical and experimental study has been carried out in the two polarization states TE and TM. The filter effect is demonstrated both numerically and experimentally by investigating the equilibrium of an optical splitter.
2. Design and optimization
The optical waveguide used in this study (see Fig. 1) is a strip loaded waveguide designed to be monomode at a 1.55-μm wavelength. Its core is a 0.3-μm thick n-i-d InGaAsP quaternary layer whose cut-off wavelength is λg=1.3 μm, covered by a 1.55-μm thick n.i.d InP upper cladding layer. The rib width and height are respectively 4 μm and 1.2 μm. This waveguide was modeled using a semivectorial three dimensional finite differences beam propagation method (3D-FD-BPM). For TE mode, the electric field has the direction of Ox while for TM mode it is in the yOz plane. The optical indexes at λ=1.55 μm used in the modeling are 3.17 for InP and 3.42 for the quaternary layer. The optical beam injected at the input of the waveguide is elliptic: its major axis is three times greater than its minor axis, in order to be very similar to the fundamental mode of the guide.
The mode filter is a bottleneck section placed after the input waveguide of the optical circuit. To define its morphology, we used Bézier curves, a powerful tool first introduced in the automotive industry around 1960 and now present in every CAD or vectorial drawing software [11]. Although allowing drawing complex curves, their mathematical expression is very simple. The upper edge of the filter (Fig. 2(a)) is defined by two joined cubic Bézier curves Q1(t) and Q2(t) expressed by the following parametric polynomials:
where t∈[0,1] is the parameter and the Bi
are points in the plane of the substrate which are called control points. B1
and B4
are the starting point and end point of the first curve, respectively, and B2
and B3
define the tangents at these points and thus the general shape of the curve. B4
, B7
, B5
,B6
have the same roles for the second Bézier curve. In order to limit the number of parameters for optimization, B2
, B3
, B5
,B6
were allowed to be moved only along the propagation axis using the b1
, b2
, b3
and b4
parameters (see Fig. 2(a)). The tangents at the end points of each curve are nonetheless not necessarily horizontal because these four parameters can be zero (Fig. 2(b) and 2(c) for example). The three other dimensions of the search space are the horizontal lengths l1
and l2
of the two Bézier curves, and the half-width n to which the guide is narrowed at the bottleneck. In fact, n can also be negative, leading to a swelling instead of a bottleneck. Figures 2(b), 2(c), 2(d) and 2(e) show some possible morphologies.
Fig. 2. Schematic view of the device with the optimisation parameters (a) and examples of some possible morphologies (b, c, d, e).
Because we planed to optimize the mode filter by using a Genetic Algorithm (GA), based on the algorithm presented in reference [12], we first defined the search space by choosing a reasonable range for each parameter (see Table 1). For example, the length of the filter l1
+l2
was limited to 600 μm for compactness. The bottleneck width was limited downward to 1 μm (n=1.5 μm) for technological reasons. Indeed, a 1 μm width permits a well defined device with low roughness and low losses. It has also the advantage to be possibly fabricated using a carefully optimized photolithography process.
V. Magnin, L. Giraudet, J. Harari, J. Decobert, P. Pagnot, E. Boucherez, and D. Decoster, “Design, optimisation and fabrication of side-illuminated p-i-n photodetectors with high responsivity and high alignment tolerance for 1.3μm and 1.55μm wavelength use,” J. Lightwave Technol. 20, 477–488 (2002). [CrossRef]
Table 1. The seven dimensions search space of the genetic algorithm
| Parameter | b1 | b2 | b3 | b4 | n | l1 | l2 |
|---|---|---|---|---|---|---|---|
| Minimum | 0 μm | 0 μm | 0 μm | 0 μm | -6 μm | 50 μm | 50 μm |
| Maximum | 80 μm | 80 μm | 80 μm | 80 μm | 1.5 μm | 300 μm | 300 μm |
In order to demonstrate experimentally the effect of the mode filter, an optical splitter was added (see Fig. 3). For simplicity reasons, the morphology of its symmetrical branches was also defined using a cubic Bézier curve. Its length is 3200 μm and the two outputs are 80 μm apart. The two branches have a 2-μm width. Only a part of the splitter appears in the 1912x30 μm top views of Fig. 3.
Fig. 3. Simulated propagation of light with different lateral shifts (0.2, 0.5 and 1 μm) of the optical input beam. Each top view has been obtained with a 3D-FD-BPM in TM mode. This permits to see the effect of a lateral shift without (on the left) and with modal filter (on the right). The effect of the filter is clearly shown when considering the decrease of the beam snaking amplitude and also the proportions of optical intensity at the splitter outputs in all cases. The last views (g and h) correspond to a reduction of the input waveguide length by 111 μm (half the snaking period). As can be seen in views c, e and g, there is an optical coupling between both branches at the beginning of the splitter.
Figure 3 shows several simulation results illustrating the oscillating phenomenon due to misalignment. The views on the left present the phenomenon without filter and demonstrate that the distribution of optical intensity in the two branches of the splitter depends on the fiber misalignment at the input of the waveguide, and also on the total waveguide length between the input and the splitter separation (compare Figs. 3(c) and 3(g)). With this in mind we have chosen this length to be the same (1110 μm) for the simulation and in practice (within a cleaving error of ± 10 μm). The optimization of the filter has been carried out by using an asymmetry coefficient described later. The right part of Fig. 3 shows the corresponding behavior of the optical circuit including the optimized mode filter. There is a transition zone after the filter where the optical beam is perturbed. Then the oscillation resumes. Its amplitude is far weaker than before the filter and is keeping constant whatever the distance of propagation. The splitter is placed away from the transition zone.
The oscillating phenomenon depends also on the optical polarization as can be seen in Fig. 4, which shows the computed relative powers P1/(P1+P2) and P2/(P1+P2) versus the misalignment in TE and TM mode, with P1 and P2 being the optical powers in the upper and lower branches, respectively.
Fig. 4. Computed relative power of each output port Pi/(P1+P2) of the splitter without mode filter versus the misalignment of the input optical fiber, in TE and TM mode (3D-FD-BPM).
The theoretical approach has been carried out by modeling the filter alone. In order to quantify the oscillations of the optical beam along the straight waveguide, we defined in the BPM an asymmetry coefficient a:
where W(i,j,k) and W(i’,j,k) are the optical intensities at two points (i,j,k) and (i’,j,k) located symmetrically with respect to the vertical symmetry plane of the guide cross-section, i, j, k being the discrete coordinates of the BPM (see Fig. 5). The sum was computed over a volume extending longitudinally over 400 μm just after the mode filter, 3 μm below and above the center of the quaternary layer, and 3 μm on the left of the symmetry plane, in order to take into account each pair of points only once. The 400 μm value was chosen to embed approximately two oscillations of the optical beam.
This asymmetry coefficient is null for a perfectly symmetric optical beam and increases with its asymmetry. It can therefore be used as a measure of the oscillations at the output of the mode filter. During the optimization process, a was systematically computed for a 0.5-μm horizontal misalignment of the input optical beam.
Fig. 5. Cross-section of the guide and the optical beam (gray ellipse). The points (i,j,k) and (i’,j,k) are located symmetrically with respect to the vertical symmetry plane (dashed line). The dotted rectangle is a section of the volume used to compute the asymmetry coefficient.
The fitness function f to optimize is equal to minus a, in order to be maximum (f=0) when there is no oscillation in the guide. This function was optimized using a 3D-FD-BPM coupled to the genetic algorithm, which was parallelized because the 3D-FD-BPM is much more time-consuming than a two dimensional one. GA are naturally parallelizable because they work by evolving a population of independent devices [13]. We used a client-server architecture: a server PC manages a list of devices to evaluate and each client PC picks a device in this list, evaluates it by 3D-FD-BPM, writes its results on the server, then picks another device on the list, and so on. The server applies the classical GA operators (selection, mutations and crossover) and proposes to clients the new generation to evaluate. The optimizations were carried out using thirty standard PCs from the network of the Polytech’Lille engineering school. The program was compiled using the GNU Fortran compiler under a GNU/Linux operating system.
Table 2. The optimized device
| Parameter | b 1 | b 2 | b 3 | b 4 | n | l 1 | l 2 |
|---|---|---|---|---|---|---|---|
| Optimized device | 80 μm | 51.9 μm | 72.6 μm | 61.1 μm | 1.50 μm | 228 μm | 296 μm |
Several optimization sessions yielded various devices. Best ones were of bottleneck type (n>0), the case n<0 corresponding to devices with a wide multimode guiding section which has no filtering effect. Despite many optimizations, we did not succeed to design a filter improving the TE mode behavior. The best results were obtained with devices optimized for TM mode. The parameters of the most interesting device are presented Table 2. Its length is 524 μm and its smallest width is 1 μm, the minimum value allowed in the search space. The modeling results for this device are those of Figs. 3(c) and 3(d): without mode filter, one branch of the splitter is guiding 66% of light. With the filter the same branch is guiding 46% of light. The computed ratio of the asymmetry coefficients without and with mode filter is 10.5, which means that the oscillations are effectively dampened by the filter, as is clearly visible in Fig. 3.
3. Fabrication and results
Special care has been taken during the fabrication of the device, in order to minimize optical losses and to avoid perturbations in the light propagation. Moreover, the masks were drawn with the aim to ease later device characterization: firstly, cleaving marks have been placed in order to obtain a length of 1110 μm (± 10 μm) between the cleaved facet and the splitter separation. Secondly, each mask included three adjacent objects, namely a straight waveguide, an optical circuit with splitter, and an optical circuit with splitter and filter. The resulting devices allowed a convenient adjustment of the input and output fiber during testing, by using the straight waveguide first and later comparing and investigating precisely the behavior of the two other circuits. Additionally, because of the complexity of the filter shapes, the drawing of the masks (see Fig. 6) was automated. The 3D-FD-BPM simulation program generated a BASIC script which was interpreted by the WaveMaker LAYOUT software [14]. The Bézier curves were approximated by a great number of segments, each segment being one micron long.
WaveMaker LAYOUT, Barnard Microsystems Limited, http://www.barnardmicrosystems.com/
Fig. 6. Mask layout of the optimized mode filter. The beginning of the optical splitter is also shown. The vertical scale is strongly dilated to enhance clarity. The total length between the waveguide input and the splitter separation is 1110 μm. The cleaving marks are located 180 μm before the filter input.
The epitaxial structure was grown using MBE (molecular beam epitaxy) on an InP substrate. It was constituted of a 1.3 μm n.i.d (non intentionally doped) InP buffer layer, a 0.3 μm n-i-d InGaAsP with a bandgap wavelength λ=1.3 μm, as core of the waveguide, and a 1.55-μm thick n.i.d InP upper cladding layer. A 200-nm thick SiO2 film deposited by plasma enhanced vapour deposition (PECVD) at 300°C chamber temperature in a Plasma 80 Plus reactor, was used as an etching mask of the waveguide. The pattern was defined by a conventional negative tone electron beam resist (SAL-601). Several trials were needed to determine the best conditions to obtain the shape and resolution adapted to the aspect ratio of the filter. The wafer was baked at 200°C for 10 min to remove any residual water.
Hexamethyldisilizane was spun onto the wafer under these conditions: 3000 rpm, 1000 rpm2 acceleration, during 20 s. Then Microposit SAL-601 was spun onto the wafer. The thickness deposited is around 570 nm under these parameters: 2000 rpm, 1000 rpm2 acceleration, during 15 s. The wafer was pre-baked in a hot plate at 105°C for 3 min. The lithography step was performed using a Leica EBPG 5000+ e-beam writer. Following exposure, the samples were baked in a hot plate at 105°C for 5 min and the resist was developed in Microposit MF-322 (Shipley) for 3 min and rinsed in running DI water. After e-beam lithography, a O2 plasma treatment was performed in order to eliminate the residual resist around the pattern. During the plasma treatment, the resist thickness is reduced by less than 5%. The SiO2 masking layer was patterned by using a 23 sccm CHF3 flow rate and a 23 sccm CF4 flow rate with 180 W power and 0.05 mT pressure during 4 min.
The etching conditions of InP in CH4/H2 plasma have been optimized in order to get a ridge with small sidewall roughness. The optimum parameters were 20 sccm CH4 and 80 sccm H2 plasma at 150 W and 30 mT, leading to a 0.015 μm/min etching rate. Figure 7 shows a scanning electron microscopy (SEM) photograph of the central part of the mode filter.
Fig. 9. Measured relative power of each output port Pi/(P1+P2) versus the misalignment of the input optical fiber, with and without filter, in TM mode.
After fabrication, the device was characterized using the experimental setup presented in Fig. 8. Light coming from an EXFO 2600 tunable laser source through a Lefevre polarization controller is injected in the optical circuit using a 4-μm focusing lensed fiber from Yenista Optics. The delivered circular output beam differs from the elliptic beam used in the simulation. At each output of the splitter, light is detected using the same type of fiber and a HP 8153A lightwave multimeter. The optical fibers and the optical circuit are all mounted on calibrated piezoelectric micropositioners. The input fiber must first be precisely aligned in order to get the same power at the output of the branches of the splitter. The output powers of each branch P1 and P2 are then measured versus the input optical fiber lateral misalignment. The fiber to fiber losses in central position (50% of the light out of each branch of the splitter) are measured for each circuit. The filter losses are found by comparing two adjacent circuits, one with filter, the other without.
Concerning now the results, we observed a strong polarization dependence of the improvement caused by the filter. In TE mode the snaking behavior of the input optical beam is not corrected. As shown in Fig. 4, the consequences of lateral misalignment without filter are lower in TE than in TM. Our characterization in TE mode of the different mode filters we have fabricated makes appear a behavior close to the theoretical predictions of the Fig. 4 (some percents higher), but no improvement. On the other hand, there is a strong improvement in TM mode as shown in Fig. 9, which presents the measured relative powers P1/(P1+P2) and P2/(P1+P2) versus the optical fiber misalignment, with and without the mode filter, in TM mode. In both cases, if the input optical fiber is perfectly aligned, each branch of the splitter carries the same optical power. Without filter, a slight fiber misalignment induces a strong asymmetry: for a 0.5 μm misalignment, 25% of light is guided in the first branch and 75% in the second one, which is even worse than the simulation results. With the filter, the same misalignment induces a far lower asymmetry: 53% in one branch and 47% in the other one. The small improvement of the filter behavior for a misalignment of 1 μm is probably due to a measurement error. These measurement results clearly demonstrate the filter effect. And beyond numbers, the operator felt it was far easier and faster to manually align the fiber in front of the optical circuit comprising a mode filter, and its effect appears clearly when observing the two splitter outputs with an infrared video camera. In TE mode, the distribution in the two branches is 61% and 39% for a 0.5 μm misalignment.
The optical losses induced by the mode filter were measured to be 0.28 dB, quite close to the 0.21 dB obtained using the BPM. The filter behavior showed no dependence on wavelength in the 1.54 μm – 1.6 μm range.
4. Conclusion and discussion
We designed an optical mode filter using Bézier curves. The complete optical circuit was composed of an InGaAsP/InP strip loaded waveguide (4 μm wide, monomode at 1.55 μm wavelength), the filter and an optical splitter. The modeling and optimization were carried out using a 3D-FD-BPM and a parallel genetic algorithm, running on a computer cluster. TE and TM polarization states were investigated but we only found structures improving the TM behavior. The optimized mode filter is 524 μm long and is 1 μm wide at the bottleneck. The fabrication involved e-beam lithography. For the TM mode, the optical characterization showed a strong enhancement of the symmetry of the optical splitter. The optical losses induced by the mode filter are only 0.28 dB. They are caused mainly by the filtering of higher order modes but also by the roughness of the waveguide sidewalls. Because the roughness has not been introduced in our model, a comparison between experimental and BPM results (0.21 dB) permits to conclude that the impact of roughness is small in our case. Concerning TE mode, more investigations are needed in order to find how a similar device could be designed. Some interesting possibilities have not yet been introduced in the optimization: a longer filter or a different position of the filter relative to the input cleaved facet and to the splitter. Another question is the possibility to act efficiently on TE and TM modes with one and the same device.
Acknowledgments
Work achieved with the financial support of the European Union, the French Government and the Regional Council. The authors would also like to thank Thales Airborne Systems for its support, M. Muller and C. Legrand from IEMN for their contribution to the technological process and the Polytech’Lille engineering school for the use of its computing power.
References and links
L. J. Villegas Vicencio, A. V. Khomenko, J. L. Angel Valenzuela, R. Cardoso, D. Salazar, H. Marquez, and H. Porte, “Asymmetry of the output power of a symmetric Y-shaped integrated-optics splitter,” J. Opt. Technol. 69, 54–57 (2002). [CrossRef] | |
W. Klaus and W. R. Leeb, “Transient fields in the input coupling region of optical single-mode waveguides,” Opt. Express 15, 11808–11826 (2007). [CrossRef] [PubMed] | |
D. Yap and L. M. Johnson, “Coupling between successive Ti:LiNbO3 waveguide bends and branches,” Appl. Opt. 23, 2991–2998 (1984). [CrossRef] [PubMed] | |
H. G. Kim, “Y-branched optical waveguide and multi-stage optical power splitter using the same,” Samsung Electronics Co., European Patent No. EP 1 279 974 A3 (filed Apr. 4, 2002). | |
Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, “Integrated optic adiabatic polarization splitter on silicon,” Appl. Phys. Lett. 56, 120–121 (1990). [CrossRef] | |
A. Klekamp, “Optical branching element,” Sel Alcatel AG, European Patent No. EP 0 737 872 A3 (filed Apr. 13, 1995). | |
K. Kashihara, “Arrayed waveguide grating multiplexer with tapered waveguides,” Furukawa Electric Co., European Patent No. EP 1 113 297 (filed 2000). | |
O. Osaka-shi, “Y-branching optical circuit,” Nippon Sheet Glass Co., European Patent No. EP 0 484 878 B1(filed Nov. 5, 1991). | |
H. G. Kim, “Optical power splitter having a stabilizing waveguide,” Samsung Electronics Co., United States Patent No. US 6,961,497 B2(filed Nov. 25, 2002). | |
A. Klekamp, P. Kersten, and W. Rehm, “An improved single-mode Y-branch design for cascaded 1:2 splitters,” J. Lightwave Technol. 14, 2684–2686 (1996). [CrossRef] | |
G. Farin, “Shape representation,” in Wiley Encyclopedia of Electrical and Electronics Engineering, vol. 19, J.G. Webster, ed. (John Wiley & Sons, Inc., New York, 1999). | |
V. Magnin, L. Giraudet, J. Harari, J. Decobert, P. Pagnot, E. Boucherez, and D. Decoster, “Design, optimisation and fabrication of side-illuminated p-i-n photodetectors with high responsivity and high alignment tolerance for 1.3μm and 1.55μm wavelength use,” J. Lightwave Technol. 20, 477–488 (2002). [CrossRef] | |
M. Nowostawski and R. Poli, “Parallel genetic algorithm taxonomy,” in 1999 Third International Conference on Knowledge-Based Intelligent Information Engineering Systems, L.C. Jain, ed. (Academic, Adelaide, South Australia, 1999), pp. 88–92. | |
WaveMaker LAYOUT, Barnard Microsystems Limited, http://www.barnardmicrosystems.com/ |
OCIS Codes
(130.3120) Integrated optics : Integrated optics devices
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.1360) Optical devices : Beam splitters
(250.5300) Optoelectronics : Photonic integrated circuits
ToC Category:
Integrated Optics
History
Original Manuscript: June 18, 2008
Revised Manuscript: July 20, 2008
Manuscript Accepted: September 21, 2008
Published: April 21, 2009
Citation
Vincent Magnin, Malek Zegaoui, Joseph Harari, Marc Franςois, and Didier Decoster, "Design, optimization and fabrication of an
optical mode filter for integrated optics," Opt. Express 17, 7383-7391 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-9-7383
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References
- Q1. L. J. Villegas Vicencio, A. V. Khomenko, J. L. Angel Valenzuela, R. Cardoso, D. Salazar, H. Marquez, and H. Porte, "Asymmetry of the output power of a symmetric Y-shaped integrated-optics splitter," J. Opt. Technol. 69, 54-57 (2002). [CrossRef]
- W. Klaus and W. R. Leeb, "Transient fields in the input coupling region of optical single-mode waveguides," Opt. Express 15,11808-11826 (2007). [CrossRef] [PubMed]
- D. Yap and L. M. Johnson, "Coupling between successive Ti:LiNbO3 waveguide bends and branches," Appl. Opt. 23, 2991-2998 (1984). [CrossRef] [PubMed]
- H. G. Kim, "Y-branched optical waveguide and multi-stage optical power splitter using the same," Samsung Electronics Co., European Patent No. EP 1 279 974 A3 (filed Apr. 4, 2002).
- Y. Shani, C. H. Henry, R. C. Kistler, R. F. Kazarinov, and K. J. Orlowsky, "Integrated optic adiabatic polarization splitter on silicon," Appl. Phys. Lett. 56,120-121 (1990). [CrossRef]
- A. Klekamp, "Optical branching element," Sel Alcatel AG, European Patent No. EP 0 737 872 A3 (filed Apr. 13, 1995).
- K. Kashihara, "Arrayed waveguide grating multiplexer with tapered waveguides," Furukawa Electric Co., European Patent No. EP 1 113 297 (filed 2000).
- O. Osaka-shi, "Y-branching optical circuit," Nippon Sheet Glass Co., European Patent No. EP 0 484 878 B1 (filed Nov. 5, 1991).
- H. G. Kim, "Optical power splitter having a stabilizing waveguide," Samsung Electronics Co., United States Patent No. US 6,961,497 B2 (filed Nov. 25, 2002).
- A. Klekamp, P. Kersten, and W. Rehm, "An improved single-mode Y-branch design for cascaded 1:2 splitters," J. Lightwave Technol. 14, 2684-2686 (1996). [CrossRef]
- G. Farin, "Shape representation," in Wiley Encyclopedia of Electrical and Electronics Engineering, J. G. Webster, ed. (John Wiley & Sons, Inc., New York, 1999), vol. 19, .
- V. Magnin, L. Giraudet, J. Harari, J. Decobert, P. Pagnot, E. Boucherez, and D. Decoster, "Design, optimisation and fabrication of side-illuminated p-i-n photodetectors with high responsivity and high alignment tolerance for 1.3µm and 1.55µm wavelength use," J. Lightwave Technol. 20, 477-488 (2002). [CrossRef]
- M. Nowostawski and R. Poli, "Parallel genetic algorithm taxonomy," in 1999 Third International Conference on Knowledge-Based Intelligent Information Engineering Systems, L. C. Jain, ed., (Academic, Adelaide, South Australia, 1999), pp. 88-92.
- WaveMaker LAYOUT, Barnard Microsystems Limited, http://www.barnardmicrosystems.com/
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