Polarization independent integrated filter based on a cross-slot waveguide Matthieu Roussey,∗ Petri Stenberg, Arijit Bera, Somnath Paul, Jani Tervo, Markku Kuittinen, and Seppo Honkanen Institute of Photonics, University of Eastern Finland, Yliopistokatu 7, 80101 Joensuu, Finland ∗ [email protected]
Abstract: We investigate an in-line band pass filter, working both for TE and TM polarizations, based on a cross-slot waveguide merged with a Bragg grating and an optical cavity. Different types of cavities (C2 - and C4 -symmetric) are presented in order to optimize the filtering and make the device dependent or independent on the polarization. We show a strong light confinement in an extremely small volume, which offers an advantage for further sensing applications. Moreover, we show how the inclusion of a silicon nanowire in the cavity helps the guiding and increases the amplitude of the resonance. In this study we make use of both the Fourier Modal Method and the Finite Difference Time Domain method to perform the numerical simulations. © 2014 Optical Society of America OCIS codes: (350.4238) Nanophotonics and photonic crystals; (130.3120) Integrated optics devices; (130.5296) Photonic crystal waveguides; (130.5440) Polarization-selective devices; (130.7408) Wavelength filtering devices.
References and links 1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). 2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486– 2489 (1987). 3. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004). 4. S. Noda and T. Baba, Roadmap on Photonic Crystals (Springer, 2003). 5. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photon. 4, 535–544 (2010). 6. J. V. Galan, P. Sanchis, J. Garcia, A. Martinez, J. Blasco, J. M. Martinez, A. Brimont, and J. Marti, “Silicon cross-slot waveguides insensitive to polarization,” in IEEE/LEOS Winter Topicals Meeting Series (2009), pp. 32–33. 7. J. V. Galan, P. Sanchis, J. Garcia, A. Martinez, J. Blasco, J. M. Martinez, A. Brimont, and J. Marti, “Study of asymmetric silicon cross-slot waveguides for polarization diversity schemes,” Appl. Opt. 48, 2693–2696 (2009). 8. A. Khanna, A. S¨ayn¨atjoki, A. Tervonen, and S. Honkanen, “Control of optical mode properties in cross-slot waveguides,” Appl. Opt. 48, 6547–6552 (2009). 9. S. Lin, J. Hu, and K. B. Crozier, “Ultracompact, broadband slot waveguide polarization splitter,” Appl. Phys. Lett. 98, 151101 (2011). 10. X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photon. Technol. Lett. 22, 1324–1326 (2010). 11. B. M. A. Rahman, D. M. H. Leung, N. Kejalakshmy, and L. T. Ip, “Novel silicon cross-slot optical waveguide for polarization diversity applications,” in Advanced Photonics 2013, X. Liu, C. Lu, W. Shieh, J. Cartledge, S. Savory, and C. Xie, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper JT3A.22. 12. P. Stenberg, M. Roussey, P. Ryczkowski, G. Genty, S. Honkanen, and M. Kuittinen, “A merged photonic crystal slot waveguide embedded in ALD-TiO2 ,” Opt. Express 21, 24154–24162 (2013).
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24149
13. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870– 1876 (1996). 14. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). 15. J. P. Hugonin, P. Lalanne, I. Del Villar, and I. R. Matias, “Fourier modal methods for modeling optical dielectric waveguides,” Opt. Quantum Electron. 37, 107–119 (2005). 16. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in siliconnanocrystal waveguides,” Opt. Lett. 37, 2295–2297 (2012). 17. A. Taflove and S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain (Artech House, 2000). 18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995). 19. J. Tervo, I. A. Turunen, and B. Bai, “A general approach to the analysis and description of partially polarized light in rigorous grating theory,” J. Eur. Opt. Soc. Rapid Publ. 3, 08004 (2008). 20. M. C. Lemme, T. Mollenhauer, H. Gottlob, W. Henschel, J. Efavi, C. Welch, and H. Kurz, “Highly selective HBr etch process for fabrication of triple-gate nano-scale SOI-MOSFETs,” Microelectron. Eng. 73–74, 346–350 (2004). 21. R. L. Puurunen, “Surface chemistry of atomic layer deposition: A case study for the trimethylaluminum/water process,” J. Appl. Phys. 97, 121301 (2005). 22. M. Janai, D. D. Allred, D. C. Booth, and B. O. Seraphin, “Optical properties and structure of amorphous silicon films prepared by CVD,” Solar Energy Mat. 1, 11–27 (1979).
1.
Introduction
The size reduction of integrated optical devices is one of the main concerns in nanophotonics. Two major steps in the history of nanophotonics have enabled to satisfy this demand: photonic crystals by Yablonovitch [1] and John [2] in 1987 and slot waveguides by Almeida [3] in 2004. Photonic crystals provide almost an unlimited library of operations on the electromagnetic field [4] and slot waveguides [5] allow to pass through the size limit of classical waveguides by confining light in a few tens of nanometers wide channels. A cross-slot waveguide was introduced in 2009 by Galan et al. [6, 7]. It consists of four rails of a high refractive index material separated by a gap of a low refractive index material of a few tens of nanometers in width. Some attempts of fabrication and experimental demonstration of such a device have already been performed [8] and some applications and characteristics of this structure have been investigated. As examples, one can cite the polarization splitter [9] and the directional coupler [10] but, in general, only a few studies on this topic have been carried out [11]. More generally, this kind of structure can play an important role in integrated optics as a polarization sensitive or insensitive device. In this paper, our contribution concerns the addition of a Bragg grating directly patterned into the cross-slot waveguide, to demonstrate the feasibility of a band pass filter that is independent of polarization. Hence this component is basically a two-dimensional extension of the device proposed by Stenberg et al. in 2013 [12]. The aim of the present work is to study the response of the device and the polarizationdependent behavior of light in the cavity region. Our purpose is to take advantage of such kind of devices when combined with an integrated band pass filter where light is localized in a narrow volume in order to enhance light-matter interaction for further sensing applications. This theoretical work is therefore motivated by two distinct questions: the polarization dependence of the structure and the role of the cavity shape. The first problem is to define a structure, based on a slot waveguide that is able to guide independently both TE and TM polarizations while keeping an extreme confinement of the field in the slot region. We will show that such a property cannot be taken as granted even in the case of a cross-slot waveguide. It raises the second question, which is to observe how the two polarizations interact in a Bragg grating cavity and how the shape of the cavity and the sub-structure we are placing inside may influence the response of the device.
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24150
2.
Problem statement a) Plane (P)
Si SiO2
y
z x
Si Si
x,y
first Bragg grating
cavity
output b) slot waveguide
second Bragg grating
10 periods
10 periods
LC
d
z
WR WS
input slot waveguide
D
SiO2
c)
Type I no rail
Type II C2-symmetric (TM)
Type III C2-symmetric (TE)
Type IV C4-symmetric
Type V C4-symmetric
Type VI C4-symmetric cross
y x
Fig. 1. a) 3D sketch of the structure. The structure is made of silicon and the surrounding material is silicon dioxide. b) Top or side view of the structure. We define WS as the slot width, WR the rail width, D the period, F = d/D the fill factor, and LC the cavity length. c) Cross sections (plane P) of the different cavities. Type I: no silicon block in the cavity; type II: horizontal block in the middle of the slot waveguide (C2 ); type III: vertical block (C2 ); type IV: silicon block in the center of the cross-slot waveguide (C4 ); type V: cross silicon block with an aperture in the middle (C4 ); Type VI: cross silicon block (C4 )
.
Our goal is to design a structure in which the electromagnetic field is highly confined and with a transmission spectrum presenting a photonic band gap (PBG) around λ = 1550 nm and a resonance peak in the middle of the PBG. One can then obtain a filter working for both polarizations with an extremely small mode volume. Based on previous works on the subject, it makes sense to assume that a cross-slot waveguide combined with a Bragg grating cavity can be used for such a purpose [10–12]. A scheme of the proposed band-pass filter is presented in Fig. 1. The basis of the structure is a silicon (Si) cross-slot waveguide, which is fully symmetric in xand y-directions. The propagation direction of light is the z-axis. The cross-slot waveguide itself is constituted by four silicon rails separated by a narrow gap. We define WS as the slot width and WR as the rail width. The structure is fully embedded in silicon dioxide (SiO2 , 1.5 μ m × 1.5 μ m in the (xy) plane). Merged to the cross-slot waveguide are two Bragg gratings (BG’s) of 10 #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24151
periods each, separated by a cavity of length LC . The period of the BGs is D = 490 nm, and the fill factor is F = d/D = 50%. The cavity length is set to LC = D. The shape of the cavity is playing the most important role in this study. On one hand, its length affects the position of the resonance. We set it equal to the period of the BG, which leads to a transmission peak in the middle of the PBG. On the other hand, also the polarization sensitivity of the whole device depends on the cavity. By adding a silicon sub-structure in the cavity, one can influence this sensitivity and therefore decide whether the device is dependent or independent on the polarization of the propagating mode. We have selected and investigated six sub-structure types. Their cross sectional geometries, in the plane (P), are presented in Fig. 1(c). The simplest case corresponds to an SiO2 gap between the two BGs (type I). The other types can be classified in two sub-categories with regards to the silicon structure standing inside the cavity. The C2 -symmetric structures (types II and III) present a silicon block in the (xz) plane or in the (yz) plane respectively, i.e., in the horizontal or vertical slot. The C4 -symmetric cavities are identical in the (xz) plane and in the (yz) plane, by a π /2-rotation around the z-axis. The type IV is a silicon block in the middle of the slot having the dimensions of the slot (WS ×WS ). The type V is the complementary of the type IV. It consists of two silicon blocks (horizontal and vertical) and nothing in the middle. The type VI is a Si cross (combination of types IV and V). The C2 -symmetric cavities are expected to be polarization dependent and the C4 -symmetric ones independent. The objective is to verify the behavior of light with the different geometries and to determine which sub-structure presents the highest peak amplitude with the highest field confinement and to observe the response variations with the polarization. 3.
Optimization of the cross-slot waveguide
The cross-slot structure, which is a combination of two orthogonal classical slot waveguides, allows the propagation of a quasi-TE mode (E along the x-axis) confined in the vertical slot and a quasi-TM mode (E along the y-axis) confined in the horizontal slot. The Fourier Modal Method (FMM) [13–15] was used to optimize the parameters of the cross-slot waveguide without the Bragg structure. Note that no particular boundary conditions were used, meaning that the calculated structure is an array of cross-slot waveguides. Since the optimized structure is invariant in the z direction, there is no coupling between the modes of the component. Consequently, it is not necessary to use absorbing layers in FMM to prevent effects from the artificial periodicity, but the artificial periods must be large enough to keep the modes in adjacent periods separated. We also verified the results using another simulation method [Fig. 3]. It is well known that the smaller the slot width, the larger the confinement of the field inside the slot. This parameter depends mainly on the fabrication techniques. In order to reach small feature sizes, we use the electron beam lithography. According to our knowledge regarding e-beam patterning and the work previously done in the reference [12], we set WS = 50 nm. The rail width (WR ) then becomes the single parameter to tailor in order to optimize the field confinement in the slot as well as the effective index of the fundamental slot mode. Figure 2(a) represents the evolution of neff with WR . We note that for small rail cross-sections, neff is low and close to the value of the covering and substrate material (nSiO2 = 1.45). It means that light tends to leak into the surrounding material if WR is too small. This dependence of neff on WR has to be taken into account while tuning WR . This field localization is represented by two factors: the effective area (Aeff ) and the confinement factor (CF) that can be calculated through Eq. (1) [16] and Eq. (2) respectively. They represent the portion of the electromagnetic field in a certain region of the
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24152
2.8
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70 60 50 40 30 20 R
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10 0
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50
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Rail width (WR) [µm]
Fig. 2. a) Effective index neff of the fundamental slot mode in the structure as a function of the rail width WR for one polarization calculated at λ = 1550 nm. b) Wavelength dependence of the confinement factor (CF) in the slot region (blue curves) and in the rails (red curves) for three different rail widths: WR = 180 nm (solid curves), WR = 165 nm (dashed curves), and WR = 150 nm (dotted curves). c) and d) Evolution of the effective area (Aeff ) and the confinement factor respectively, as a function of WR . The black curve with squares represents the ratio between ASeff and AR eff calculated at λ = 1550 nm. The green lines represent the chosen parameters (a, c and d). The green area (b) represents the position of the photonic band gap after inclusion of a photonic crystal in the structure.
structure compare to the total field. Region Aeff
+∞ Region −∞ Pz (x, y)dxdy
=a
CFRegion =
Region Pz (x, y)dxdy
aRegion Region
Aeff
× 100,
,
(1)
(2)
where Pz is the z-component of the Poynting vector. The Region, of surface aRegion , can be either the slot part (S) or the four silicon rails (R). For both, we define an effective area (ASeff and AReff ) and a confinement factor (CFS and CFR ), with a surface aS = WS2 and aR = 4WR2 for the slot region and the rails respectively. Since one of the requirements of the device is to strongly confine the electromagnetic field into the slot region, the ideal structure parameters correspond to a maximized CFS (or minimized ASeff ) compared to CFR and AReff . The device is intended to work around λ = 1550 nm and should hence be optimized for this wavelength. Figure 2(b) shows the wavelength dependence of CFS and CFR for three values of WR . One remark is that for thinner rails the confinement factor is higher in the slot than in the rails over a broader wavelength range. Nevertheless, with regards to the effective index and to #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24153
the wavelength for which CFS is maximum, we excluded the low values of WR . This choice is confirmed by Fig. 2(c) and (d) showing the rail width dependence of the effective area and the confinement factor. The highest confinement factor and the lowest effective area are obtained for WR = 180 nm, which corresponds to neff = 1.843. The effective area is ASeff = 0.359 μ m2 and the confinement factor CFS = 33%. These values are in the same range as those calculated for classical slot waveguides. One can remark that the percentage of light in the silicon rails is still high (CFSi = 35%) and to reduce this value the rail width has to be decreased (CFR 12% for WR = 120 nm). In this case, the confinement factor of the slot waveguide decreases too much and the waveguide will no more be optimized for good guiding of light. As already mentioned, reducing the rail width will lead to a decrease of the effective index and thus eventually to leaking of light in the substrate. The rail width is then fixed to WR = 180 nm. Note that these optimizations have been made considering the TE-mode only for the wavelength λ = 1550 nm. One can remark that CFR + CFR < 100%, which is due to a part of the field leaking into the surrounding material, as can be seen in Fig. 3.
1500
FDTD 500
1000
x-direction [nm]
TM polarization
0 0
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1000
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1500
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x-direction [nm]
1500
b)
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1000
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1500
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y-direction [nm]
1500
FDTD 500
1000
x-direction [nm]
1500
Unpolarized light f)
1000
500
0 0
FMM 500
1000
x-direction [nm]
1500
Fig. 3. Distributions of the z-component of the Poynting vector in a cross section plane of a cross-slot waveguide. Comparison between the calculation using the Finite Difference Time Domain (FDTD) (a, c, and e) method and the Fourier Modal Method (FMM) (b, d, and f) for the TM (a and d), TE (b and e) and unpolarized light (c and f) cases. The cross section of the structure is highlighted with blue lines.
Fig. 3 presents the field distribution in the (xy) plane calculated with the FMM and the Finite Difference Time Domain method (FDTD) [17] for comparison for the TE and TM mode and for an unpolarized illuminating light. Considering the whole study, it is important at this point to determine whether the two calculation methods are in good agreement, which is indeed the case. FMM is an efficient and fast method used here for the modal study and waveguide optimization while FDTD is more convenient for the design and the spectral investigation of the nanostructure itself. From the field distributions [Fig. 3], one can see, as expected, that this perfectly symmetric structure presents no difference between the two polarizations. If most of the field is concentrated in the slot region between the silicon rails, a remarkable part of the field is confined in the central part. The shape of the cavity plays a critical role in the structure. It affects the mode propagation and may determine whether the structure is dependent or independent on the polarization. #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24154
Remark that the case corresponding to the unpolarized light is one representation coming from the superposition in intensity of the two linear polarizations which is possible since they do not correlate. In this case, the incident light is assumed unpolarized (see, for example, [18]). Due to the symmetry of the structure, such light is coupled to uncorrelated TE and TM modes with equal weights. Further information about such a technique can be found, e.g., in [19]. 4.
Merging a photonic crystal cavity to a cross-slot waveguide
The proposed structure is designed to present a photonic band gap (PBG) between λ = 1420 nm and λ = 1580 nm and a transmission peak in the middle of the PBG, centered around λ = 1500 nm. Figure 4 shows the transmission spectrum of the photonic crystal without a cavity together with the z-component of the Poynting vector at the output of the photonic crystal at three particular wavelengths. One can see, as predicted by the results in Fig. 2, that the field is guided mostly in the silicon rails for the shortest wavelength and is mainly confined in the slot for the longest wavelengths. At λ = 1500 nm, the field is also well localized in the slot, which is the intended result.
Normalized transmission
l=1250 nm
l=1800 nm
l=1500 nm
1 0.8 0.6 0.4 0.2 0 1300
1400
1500
Wavelength [nm]
1600
1700
1800
Fig. 4. Transmission spectrum (calculation made for the TE polarization) of the structure without a cavity. The three insets are the distribution of the z-component of the Poynting vector at the output of the photonic crystal at the wavelengths λ = 1250 nm, λ = 1500 nm, and λ = 1800 nm.
Figure 5 presents the transmission spectra through the structure for the different cavity types. In order to observe only the evolution of the resonance peak with the sub-structure shape, the plotted transmission curves are normalized by the spectrum through the structure without a cavity (transmission spectrum presented in Fig. 4). This figure has to be explained with regards to Fig. 6, representing the z-component of the Poynting vector distributions in the plane (P) [Fig. 1(a)], which is centered in the cavity. The calculations were performed at the resonant wavelength. In order to simplify the discussion, we split the cavities into two groups: C4 -symmetric (Fig. 5(a), type I, IV, V, and VI) and C2 -symmetric (Fig. 5(b), type II and III) cavities. The results obtained with the cavity type I show that the field is well confined in the structure and the spectrum presents a weak peak. One can remark from Fig. 6 that the field is spread out of the cavity, which explains the low amplitude of the peak. #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24155
120
Transmission [arb. u.]
100
80
60
a)
C4-symmetric cavities: Type I TE Type I TM Type IV TE Type IV TM Type V TE Type V TM Type VI TE Type VI TM
40
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40
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Fig. 5. Transmission spectra through the device for the different cavity types and polarizations (TE: solid lines; TM: circles) normalized by the transmission spectrum of the photonic band gap structure without a cavity. a) C4 -symmetric cavity types I (blue curves), IV (green curves), V (red curves) and VI (black curves). Type I and IV are almost superimposed. In all cases, responses for TE and TM are identical. b) C2 -symmetric cavity types II (blue curves) and III (red curves). Responses for TE and TM are reversed for the type II and III.
The spectrum of the type IV does not present major variations, which proves that the electromagnetic field is still mostly confined between the silicon rails and not in the central slot region. This is confirmed by the results of the cavity type V. In this case the transmission amplitude is much higher compared to the other cases, and from the Poynting vector distribution in Fig. 6, one can see that the field is much more concentrated in the middle of the cavity and there is less leakage to the silicon dioxide surrounding the structure. This can be explained by the fact that the silicon blocks of the cavity create a slot waveguide for the cavity mode. In this case, both polarizations are guided mostly in the 50 nm×50 nm central slot. In the case of the cavity type VI, the amplitude of the peak is again increased and one can observe a strong localization of the field around the center of the cross in the middle of the cavity. This is due to the fact that the sub-structure acts as a nanowire allowing a continuity of the guidance of the field along the cavity. This effect is already partially observable for the type IV, where the field distribution presents an enhancement around the cavity sub-structure. When considering an unpolarized illumination, one can observe that the field intensity is invariant around the axis of the structure (z-axis). For types V and VI, there is almost no difference between the three polarization cases. This allows us to conclude that the structure acts as a band pass filter independent on the polarization. This is not the case for the the other types, which proves that a C4 -symmetric structure is not necessary polarization independent. #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24156
TM Polarization
0
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y [µm]
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Fig. 6. Distribution of the z-component of the Poynting vector, at the resonant wavelength, in the plane P (center of the cavity, figure 1a) for the six cavity types and for TE and TM polarized and unpolarized light. The contour of the Silicon sub-structures standing in the cavity is superimposed to the pictures.
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24157
For all the C4 -symmetric sub-structures, the transmission spectra are absolutely identical while varying the polarization of the illumination. Only the field distribution changes in certain cases. The C2 -symmetric cavity type II corresponds to the type III by a rotation of 90◦ . From the spectra in Fig. 5(b), one can see that for one polarization the peak amplitude is weak, and high for the other. This means that in one case the cavity acts like type I and in the other case like type VI. This can be seen from the Poynting vector distributions, where the field is either highly confined in the center of the structure and well guided (thanks to the combination of the slot waveguide and the nanowire) or less localized and leaking into the surrounding material. One can remark on the importance of the inclusion of a silicon nanowire in the cavity. The electromagnetic field is guided around the thin block instead of leaking into the substrate due to the divergent mode coming out from the cross-slot waveguide. Nevertheless, the term nanowire is misleading since the silicon block should then be far smaller than the wavelength in both transverse directions, which is not the case for all cavity types. However one can observe the nanowire effect for the polarization that is orthogonal to the shortest dimension of the silicon block. In the case of the type VI, the field is located in the very near vicinity of the center of the Si-cross in the cavity which makes it ideal for sensing applications, for example. Moreover it prevents the field to be spread out from the structure like in the case of type I. In the case of the cavity type V, we observe a two-dimensional slot waveguide effect. It allows the concentration of the field inside the extremely tiny two-dimensional slot in the middle of the structure. This case is not directly usable for sensing since there is no opening, but the structure may find some applications, e.g., in telecommunications, allowing the doubling of the transfer of information while maintaining a highly integrated device. We point out that the overlap between the polarizations has been neglected since the minor component of the field is at least one order of magnitude lower in amplitude than the major component. We have shown the behavior of the different cavity types, with the different polarizations. The main area of applications of these devices is sensing. From the mechanism point of view, the performance may change drastically from one structure to another. In the case of type V, for example, the field is enclosed inside the structure and only the overlap between the field guided inside the two dimensional slot waveguide and an external analyte is possible. If we consider the case of infiltration of the analyte by a capillary force directly inside the slot waveguide itself, ultra-high sensitivity is possible. However, this kind of nano-fluidistics may be beyond the reach with today’s fabrication methods. The advantage of the cross-slot waveguide is to guide the two polarizations with the possibility of having the same transmission response when the refractive indices of the structure are identical in x and y. In this case, the structure is the type VI. If there is a mismatch between x and y, the structure will act as the type II or III. If we consider the type II, with an open vertical slot filled with an analyte, the response in transmission of the structure will vary between the one of the type II and type VI depending on the refractive index variation of the analyte. This allows then to follow the refractive index variation in real time, and to make an easy monitoring of this variation by measuring the difference of amplitudes of the two resonant peaks corresponding to the two polarizations, without any interferometric system or any additional alignment devices. 5.
Possible fabrication procedure
The fabrication of the structures described is challenging for several reasons that we will detail in this section. The structures should be fabricated layer by layer, mixing fabrication methods and materials, as well as a patterning technique such as the e-beam lithography and Atomic Layer Deposition (ALD). The first challenge is the nanostructure itself. The required feature sizes are of a great impor-
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24158
tance for the confinement of light in the device and the response signal depends drastically on the parameters such as the period and the fill factor of the Bragg cavity. Nevertheless, we have shown in a previous work [12] that structures with this small features can be fabricated with a good control of the dimensions. The second issue is the perfect symmetry, which is mandatory to obtain a perfectly polarization independent device. Using CVD deposited amorphous silicon, one can facilitate the deposition of the top rails [20]. The silicon dioxide spacers and the cladding silicon dioxide layers can be deposited by ALD [21]. This technique offers us the advantage of an accurate thickness control as well as conformal coating enabling complete filling of the structure even in the smallest details. Moreover, it allows the deposition of thin films of material which will not be chemically affected by the RIE processes, which can be used as etch-stop layer [22]. 6.
Conclusion
By combining silicon slot waveguides, photonic crystal cavities, and nanowire waveguides, we achieved the theoretical demonstration of a band pass filter, independent of the polarization and having an extremely small size. Moreover, we have taken advantage of both FMM and FDTD methods to determine the optimized parameters of the structure and calculate its transmission spectrum. The principal interest of the studied structure is its versatility in terms of applications. The structure is independent of the polarization, giving an opportunity to double the capacity in telecommunication devices via polarization multiplexing, by using just a single structure. It also means that this invariance in polarization can be broken in order to use the device as a sensor. Indeed, a slight modification of the refractive index due to the addition of a gas or a liquid around the structure will break the symmetry. Then it becomes possible, for example, to monitor the properties of the analyte by following the fluctuation of the field at both polarizations. Finally we have shown that in certain cases (cavity type V), one can guide both polarizations in a two-dimensional 50 nm-wide slot waveguide. Acknowledgments This research is supported by the Finnish Funding Agency for Technology and Innovation (TEKES) through the EAKR projects ALD-nano-medi and Nanobio (grants 70011/12 and 70005/14) and the Academy of Finland (grants 272155 and 250968).
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24159
Abstract: We investigate an in-line band pass filter, working both for TE and TM polarizations, based on a cross-slot waveguide merged with a Bragg grating and an optical cavity. Different types of cavities (C2 - and C4 -symmetric) are presented in order to optimize the filtering and make the device dependent or independent on the polarization. We show a strong light confinement in an extremely small volume, which offers an advantage for further sensing applications. Moreover, we show how the inclusion of a silicon nanowire in the cavity helps the guiding and increases the amplitude of the resonance. In this study we make use of both the Fourier Modal Method and the Finite Difference Time Domain method to perform the numerical simulations. © 2014 Optical Society of America OCIS codes: (350.4238) Nanophotonics and photonic crystals; (130.3120) Integrated optics devices; (130.5296) Photonic crystal waveguides; (130.5440) Polarization-selective devices; (130.7408) Wavelength filtering devices.
References and links 1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). 2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486– 2489 (1987). 3. V. R. Almeida, Q. Xu, C. A. Barrios, and M. Lipson, “Guiding and confining light in void nanostructure,” Opt. Lett. 29, 1209–1211 (2004). 4. S. Noda and T. Baba, Roadmap on Photonic Crystals (Springer, 2003). 5. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photon. 4, 535–544 (2010). 6. J. V. Galan, P. Sanchis, J. Garcia, A. Martinez, J. Blasco, J. M. Martinez, A. Brimont, and J. Marti, “Silicon cross-slot waveguides insensitive to polarization,” in IEEE/LEOS Winter Topicals Meeting Series (2009), pp. 32–33. 7. J. V. Galan, P. Sanchis, J. Garcia, A. Martinez, J. Blasco, J. M. Martinez, A. Brimont, and J. Marti, “Study of asymmetric silicon cross-slot waveguides for polarization diversity schemes,” Appl. Opt. 48, 2693–2696 (2009). 8. A. Khanna, A. S¨ayn¨atjoki, A. Tervonen, and S. Honkanen, “Control of optical mode properties in cross-slot waveguides,” Appl. Opt. 48, 6547–6552 (2009). 9. S. Lin, J. Hu, and K. B. Crozier, “Ultracompact, broadband slot waveguide polarization splitter,” Appl. Phys. Lett. 98, 151101 (2011). 10. X. Tu, S. S. N. Ang, A. B. Chew, J. Teng, and T. Mei, “An ultracompact directional coupler based on GaAs cross-slot waveguide,” IEEE Photon. Technol. Lett. 22, 1324–1326 (2010). 11. B. M. A. Rahman, D. M. H. Leung, N. Kejalakshmy, and L. T. Ip, “Novel silicon cross-slot optical waveguide for polarization diversity applications,” in Advanced Photonics 2013, X. Liu, C. Lu, W. Shieh, J. Cartledge, S. Savory, and C. Xie, eds., OSA Technical Digest (online) (Optical Society of America, 2013), paper JT3A.22. 12. P. Stenberg, M. Roussey, P. Ryczkowski, G. Genty, S. Honkanen, and M. Kuittinen, “A merged photonic crystal slot waveguide embedded in ALD-TiO2 ,” Opt. Express 21, 24154–24162 (2013).
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24149
13. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870– 1876 (1996). 14. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767 (1997). 15. J. P. Hugonin, P. Lalanne, I. Del Villar, and I. R. Matias, “Fourier modal methods for modeling optical dielectric waveguides,” Opt. Quantum Electron. 37, 107–119 (2005). 16. I. D. Rukhlenko, M. Premaratne, and G. P. Agrawal, “Effective mode area and its optimization in siliconnanocrystal waveguides,” Opt. Lett. 37, 2295–2297 (2012). 17. A. Taflove and S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain (Artech House, 2000). 18. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995). 19. J. Tervo, I. A. Turunen, and B. Bai, “A general approach to the analysis and description of partially polarized light in rigorous grating theory,” J. Eur. Opt. Soc. Rapid Publ. 3, 08004 (2008). 20. M. C. Lemme, T. Mollenhauer, H. Gottlob, W. Henschel, J. Efavi, C. Welch, and H. Kurz, “Highly selective HBr etch process for fabrication of triple-gate nano-scale SOI-MOSFETs,” Microelectron. Eng. 73–74, 346–350 (2004). 21. R. L. Puurunen, “Surface chemistry of atomic layer deposition: A case study for the trimethylaluminum/water process,” J. Appl. Phys. 97, 121301 (2005). 22. M. Janai, D. D. Allred, D. C. Booth, and B. O. Seraphin, “Optical properties and structure of amorphous silicon films prepared by CVD,” Solar Energy Mat. 1, 11–27 (1979).
1.
Introduction
The size reduction of integrated optical devices is one of the main concerns in nanophotonics. Two major steps in the history of nanophotonics have enabled to satisfy this demand: photonic crystals by Yablonovitch [1] and John [2] in 1987 and slot waveguides by Almeida [3] in 2004. Photonic crystals provide almost an unlimited library of operations on the electromagnetic field [4] and slot waveguides [5] allow to pass through the size limit of classical waveguides by confining light in a few tens of nanometers wide channels. A cross-slot waveguide was introduced in 2009 by Galan et al. [6, 7]. It consists of four rails of a high refractive index material separated by a gap of a low refractive index material of a few tens of nanometers in width. Some attempts of fabrication and experimental demonstration of such a device have already been performed [8] and some applications and characteristics of this structure have been investigated. As examples, one can cite the polarization splitter [9] and the directional coupler [10] but, in general, only a few studies on this topic have been carried out [11]. More generally, this kind of structure can play an important role in integrated optics as a polarization sensitive or insensitive device. In this paper, our contribution concerns the addition of a Bragg grating directly patterned into the cross-slot waveguide, to demonstrate the feasibility of a band pass filter that is independent of polarization. Hence this component is basically a two-dimensional extension of the device proposed by Stenberg et al. in 2013 [12]. The aim of the present work is to study the response of the device and the polarizationdependent behavior of light in the cavity region. Our purpose is to take advantage of such kind of devices when combined with an integrated band pass filter where light is localized in a narrow volume in order to enhance light-matter interaction for further sensing applications. This theoretical work is therefore motivated by two distinct questions: the polarization dependence of the structure and the role of the cavity shape. The first problem is to define a structure, based on a slot waveguide that is able to guide independently both TE and TM polarizations while keeping an extreme confinement of the field in the slot region. We will show that such a property cannot be taken as granted even in the case of a cross-slot waveguide. It raises the second question, which is to observe how the two polarizations interact in a Bragg grating cavity and how the shape of the cavity and the sub-structure we are placing inside may influence the response of the device.
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24150
2.
Problem statement a) Plane (P)
Si SiO2
y
z x
Si Si
x,y
first Bragg grating
cavity
output b) slot waveguide
second Bragg grating
10 periods
10 periods
LC
d
z
WR WS
input slot waveguide
D
SiO2
c)
Type I no rail
Type II C2-symmetric (TM)
Type III C2-symmetric (TE)
Type IV C4-symmetric
Type V C4-symmetric
Type VI C4-symmetric cross
y x
Fig. 1. a) 3D sketch of the structure. The structure is made of silicon and the surrounding material is silicon dioxide. b) Top or side view of the structure. We define WS as the slot width, WR the rail width, D the period, F = d/D the fill factor, and LC the cavity length. c) Cross sections (plane P) of the different cavities. Type I: no silicon block in the cavity; type II: horizontal block in the middle of the slot waveguide (C2 ); type III: vertical block (C2 ); type IV: silicon block in the center of the cross-slot waveguide (C4 ); type V: cross silicon block with an aperture in the middle (C4 ); Type VI: cross silicon block (C4 )
.
Our goal is to design a structure in which the electromagnetic field is highly confined and with a transmission spectrum presenting a photonic band gap (PBG) around λ = 1550 nm and a resonance peak in the middle of the PBG. One can then obtain a filter working for both polarizations with an extremely small mode volume. Based on previous works on the subject, it makes sense to assume that a cross-slot waveguide combined with a Bragg grating cavity can be used for such a purpose [10–12]. A scheme of the proposed band-pass filter is presented in Fig. 1. The basis of the structure is a silicon (Si) cross-slot waveguide, which is fully symmetric in xand y-directions. The propagation direction of light is the z-axis. The cross-slot waveguide itself is constituted by four silicon rails separated by a narrow gap. We define WS as the slot width and WR as the rail width. The structure is fully embedded in silicon dioxide (SiO2 , 1.5 μ m × 1.5 μ m in the (xy) plane). Merged to the cross-slot waveguide are two Bragg gratings (BG’s) of 10 #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24151
periods each, separated by a cavity of length LC . The period of the BGs is D = 490 nm, and the fill factor is F = d/D = 50%. The cavity length is set to LC = D. The shape of the cavity is playing the most important role in this study. On one hand, its length affects the position of the resonance. We set it equal to the period of the BG, which leads to a transmission peak in the middle of the PBG. On the other hand, also the polarization sensitivity of the whole device depends on the cavity. By adding a silicon sub-structure in the cavity, one can influence this sensitivity and therefore decide whether the device is dependent or independent on the polarization of the propagating mode. We have selected and investigated six sub-structure types. Their cross sectional geometries, in the plane (P), are presented in Fig. 1(c). The simplest case corresponds to an SiO2 gap between the two BGs (type I). The other types can be classified in two sub-categories with regards to the silicon structure standing inside the cavity. The C2 -symmetric structures (types II and III) present a silicon block in the (xz) plane or in the (yz) plane respectively, i.e., in the horizontal or vertical slot. The C4 -symmetric cavities are identical in the (xz) plane and in the (yz) plane, by a π /2-rotation around the z-axis. The type IV is a silicon block in the middle of the slot having the dimensions of the slot (WS ×WS ). The type V is the complementary of the type IV. It consists of two silicon blocks (horizontal and vertical) and nothing in the middle. The type VI is a Si cross (combination of types IV and V). The C2 -symmetric cavities are expected to be polarization dependent and the C4 -symmetric ones independent. The objective is to verify the behavior of light with the different geometries and to determine which sub-structure presents the highest peak amplitude with the highest field confinement and to observe the response variations with the polarization. 3.
Optimization of the cross-slot waveguide
The cross-slot structure, which is a combination of two orthogonal classical slot waveguides, allows the propagation of a quasi-TE mode (E along the x-axis) confined in the vertical slot and a quasi-TM mode (E along the y-axis) confined in the horizontal slot. The Fourier Modal Method (FMM) [13–15] was used to optimize the parameters of the cross-slot waveguide without the Bragg structure. Note that no particular boundary conditions were used, meaning that the calculated structure is an array of cross-slot waveguides. Since the optimized structure is invariant in the z direction, there is no coupling between the modes of the component. Consequently, it is not necessary to use absorbing layers in FMM to prevent effects from the artificial periodicity, but the artificial periods must be large enough to keep the modes in adjacent periods separated. We also verified the results using another simulation method [Fig. 3]. It is well known that the smaller the slot width, the larger the confinement of the field inside the slot. This parameter depends mainly on the fabrication techniques. In order to reach small feature sizes, we use the electron beam lithography. According to our knowledge regarding e-beam patterning and the work previously done in the reference [12], we set WS = 50 nm. The rail width (WR ) then becomes the single parameter to tailor in order to optimize the field confinement in the slot as well as the effective index of the fundamental slot mode. Figure 2(a) represents the evolution of neff with WR . We note that for small rail cross-sections, neff is low and close to the value of the covering and substrate material (nSiO2 = 1.45). It means that light tends to leak into the surrounding material if WR is too small. This dependence of neff on WR has to be taken into account while tuning WR . This field localization is represented by two factors: the effective area (Aeff ) and the confinement factor (CF) that can be calculated through Eq. (1) [16] and Eq. (2) respectively. They represent the portion of the electromagnetic field in a certain region of the
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24152
2.8
Confinement factor (CF) [%]
a)
Effective index (neff)
2.6 2.4 2.2 2 1.8 1.6 1.4 0.12 0.14 0.16 0.18 0.2
70
40 30 20 10
1
Rail width (WR) [µm]
c)
in the Si rails (Aeff) S in the slot (Aeff) S R ratio (Aeff/Aeff)
Confinement factor (CF) [%]
Effective area (Aeff) [µm2]
1.1
R
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.12 0.14 0.16 0.18 0.2
80
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
2
Wavelength (l) [µm]
d)
70 60 50 40 30 20 R
in the Si rails (CF ) S in the slot (CF )
10 0
0.22 0.24 0.26 0.28 0.3
R
in the Si rails (CF ) S in the slot (CF )
50
0
0.22 0.24 0.26 0.28 0.3
b)
60
Rail width (WR) [µm]
0.12 0.14 0.16 0.18 0.2
0.22 0.24 0.26 0.28 0.3
Rail width (WR) [µm]
Fig. 2. a) Effective index neff of the fundamental slot mode in the structure as a function of the rail width WR for one polarization calculated at λ = 1550 nm. b) Wavelength dependence of the confinement factor (CF) in the slot region (blue curves) and in the rails (red curves) for three different rail widths: WR = 180 nm (solid curves), WR = 165 nm (dashed curves), and WR = 150 nm (dotted curves). c) and d) Evolution of the effective area (Aeff ) and the confinement factor respectively, as a function of WR . The black curve with squares represents the ratio between ASeff and AR eff calculated at λ = 1550 nm. The green lines represent the chosen parameters (a, c and d). The green area (b) represents the position of the photonic band gap after inclusion of a photonic crystal in the structure.
structure compare to the total field. Region Aeff
+∞ Region −∞ Pz (x, y)dxdy
=a
CFRegion =
Region Pz (x, y)dxdy
aRegion Region
Aeff
× 100,
,
(1)
(2)
where Pz is the z-component of the Poynting vector. The Region, of surface aRegion , can be either the slot part (S) or the four silicon rails (R). For both, we define an effective area (ASeff and AReff ) and a confinement factor (CFS and CFR ), with a surface aS = WS2 and aR = 4WR2 for the slot region and the rails respectively. Since one of the requirements of the device is to strongly confine the electromagnetic field into the slot region, the ideal structure parameters correspond to a maximized CFS (or minimized ASeff ) compared to CFR and AReff . The device is intended to work around λ = 1550 nm and should hence be optimized for this wavelength. Figure 2(b) shows the wavelength dependence of CFS and CFR for three values of WR . One remark is that for thinner rails the confinement factor is higher in the slot than in the rails over a broader wavelength range. Nevertheless, with regards to the effective index and to #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24153
the wavelength for which CFS is maximum, we excluded the low values of WR . This choice is confirmed by Fig. 2(c) and (d) showing the rail width dependence of the effective area and the confinement factor. The highest confinement factor and the lowest effective area are obtained for WR = 180 nm, which corresponds to neff = 1.843. The effective area is ASeff = 0.359 μ m2 and the confinement factor CFS = 33%. These values are in the same range as those calculated for classical slot waveguides. One can remark that the percentage of light in the silicon rails is still high (CFSi = 35%) and to reduce this value the rail width has to be decreased (CFR 12% for WR = 120 nm). In this case, the confinement factor of the slot waveguide decreases too much and the waveguide will no more be optimized for good guiding of light. As already mentioned, reducing the rail width will lead to a decrease of the effective index and thus eventually to leaking of light in the substrate. The rail width is then fixed to WR = 180 nm. Note that these optimizations have been made considering the TE-mode only for the wavelength λ = 1550 nm. One can remark that CFR + CFR < 100%, which is due to a part of the field leaking into the surrounding material, as can be seen in Fig. 3.
1500
FDTD 500
1000
x-direction [nm]
TM polarization
0 0
FMM 500
1000
x-direction [nm]
1500
FDTD 500
1000
x-direction [nm]
1500
b)
500
500
0 0
1500
1000
1000
TE polarization 1000
500
0 0
FMM 500
1000
x-direction [nm]
1500
500
1500
d)
Unpolarized light e)
1000
0 0
1500
y-direction [nm]
500
1500
c) y-direction [nm]
y-direction [nm]
TE polarization
1000
0 0
y-direction [nm]
1500
TM polarization a)
y-direction [nm]
y-direction [nm]
1500
FDTD 500
1000
x-direction [nm]
1500
Unpolarized light f)
1000
500
0 0
FMM 500
1000
x-direction [nm]
1500
Fig. 3. Distributions of the z-component of the Poynting vector in a cross section plane of a cross-slot waveguide. Comparison between the calculation using the Finite Difference Time Domain (FDTD) (a, c, and e) method and the Fourier Modal Method (FMM) (b, d, and f) for the TM (a and d), TE (b and e) and unpolarized light (c and f) cases. The cross section of the structure is highlighted with blue lines.
Fig. 3 presents the field distribution in the (xy) plane calculated with the FMM and the Finite Difference Time Domain method (FDTD) [17] for comparison for the TE and TM mode and for an unpolarized illuminating light. Considering the whole study, it is important at this point to determine whether the two calculation methods are in good agreement, which is indeed the case. FMM is an efficient and fast method used here for the modal study and waveguide optimization while FDTD is more convenient for the design and the spectral investigation of the nanostructure itself. From the field distributions [Fig. 3], one can see, as expected, that this perfectly symmetric structure presents no difference between the two polarizations. If most of the field is concentrated in the slot region between the silicon rails, a remarkable part of the field is confined in the central part. The shape of the cavity plays a critical role in the structure. It affects the mode propagation and may determine whether the structure is dependent or independent on the polarization. #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24154
Remark that the case corresponding to the unpolarized light is one representation coming from the superposition in intensity of the two linear polarizations which is possible since they do not correlate. In this case, the incident light is assumed unpolarized (see, for example, [18]). Due to the symmetry of the structure, such light is coupled to uncorrelated TE and TM modes with equal weights. Further information about such a technique can be found, e.g., in [19]. 4.
Merging a photonic crystal cavity to a cross-slot waveguide
The proposed structure is designed to present a photonic band gap (PBG) between λ = 1420 nm and λ = 1580 nm and a transmission peak in the middle of the PBG, centered around λ = 1500 nm. Figure 4 shows the transmission spectrum of the photonic crystal without a cavity together with the z-component of the Poynting vector at the output of the photonic crystal at three particular wavelengths. One can see, as predicted by the results in Fig. 2, that the field is guided mostly in the silicon rails for the shortest wavelength and is mainly confined in the slot for the longest wavelengths. At λ = 1500 nm, the field is also well localized in the slot, which is the intended result.
Normalized transmission
l=1250 nm
l=1800 nm
l=1500 nm
1 0.8 0.6 0.4 0.2 0 1300
1400
1500
Wavelength [nm]
1600
1700
1800
Fig. 4. Transmission spectrum (calculation made for the TE polarization) of the structure without a cavity. The three insets are the distribution of the z-component of the Poynting vector at the output of the photonic crystal at the wavelengths λ = 1250 nm, λ = 1500 nm, and λ = 1800 nm.
Figure 5 presents the transmission spectra through the structure for the different cavity types. In order to observe only the evolution of the resonance peak with the sub-structure shape, the plotted transmission curves are normalized by the spectrum through the structure without a cavity (transmission spectrum presented in Fig. 4). This figure has to be explained with regards to Fig. 6, representing the z-component of the Poynting vector distributions in the plane (P) [Fig. 1(a)], which is centered in the cavity. The calculations were performed at the resonant wavelength. In order to simplify the discussion, we split the cavities into two groups: C4 -symmetric (Fig. 5(a), type I, IV, V, and VI) and C2 -symmetric (Fig. 5(b), type II and III) cavities. The results obtained with the cavity type I show that the field is well confined in the structure and the spectrum presents a weak peak. One can remark from Fig. 6 that the field is spread out of the cavity, which explains the low amplitude of the peak. #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24155
120
Transmission [arb. u.]
100
80
60
a)
C4-symmetric cavities: Type I TE Type I TM Type IV TE Type IV TM Type V TE Type V TM Type VI TE Type VI TM
40
20
0 1400
1420
1440
1460
1480
1500
1520
1540
1560
1580
1600
Wavelength [nm]
Transmission [arb. u.]
80
60
b)
C2-symmetric cavities: Type II TE Type II TM Type III TE Type III TM
40
20
0 1400
1420
1440
1460
1480
1500
1520
1540
1560
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Fig. 5. Transmission spectra through the device for the different cavity types and polarizations (TE: solid lines; TM: circles) normalized by the transmission spectrum of the photonic band gap structure without a cavity. a) C4 -symmetric cavity types I (blue curves), IV (green curves), V (red curves) and VI (black curves). Type I and IV are almost superimposed. In all cases, responses for TE and TM are identical. b) C2 -symmetric cavity types II (blue curves) and III (red curves). Responses for TE and TM are reversed for the type II and III.
The spectrum of the type IV does not present major variations, which proves that the electromagnetic field is still mostly confined between the silicon rails and not in the central slot region. This is confirmed by the results of the cavity type V. In this case the transmission amplitude is much higher compared to the other cases, and from the Poynting vector distribution in Fig. 6, one can see that the field is much more concentrated in the middle of the cavity and there is less leakage to the silicon dioxide surrounding the structure. This can be explained by the fact that the silicon blocks of the cavity create a slot waveguide for the cavity mode. In this case, both polarizations are guided mostly in the 50 nm×50 nm central slot. In the case of the cavity type VI, the amplitude of the peak is again increased and one can observe a strong localization of the field around the center of the cross in the middle of the cavity. This is due to the fact that the sub-structure acts as a nanowire allowing a continuity of the guidance of the field along the cavity. This effect is already partially observable for the type IV, where the field distribution presents an enhancement around the cavity sub-structure. When considering an unpolarized illumination, one can observe that the field intensity is invariant around the axis of the structure (z-axis). For types V and VI, there is almost no difference between the three polarization cases. This allows us to conclude that the structure acts as a band pass filter independent on the polarization. This is not the case for the the other types, which proves that a C4 -symmetric structure is not necessary polarization independent. #217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24156
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Fig. 6. Distribution of the z-component of the Poynting vector, at the resonant wavelength, in the plane P (center of the cavity, figure 1a) for the six cavity types and for TE and TM polarized and unpolarized light. The contour of the Silicon sub-structures standing in the cavity is superimposed to the pictures.
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24157
For all the C4 -symmetric sub-structures, the transmission spectra are absolutely identical while varying the polarization of the illumination. Only the field distribution changes in certain cases. The C2 -symmetric cavity type II corresponds to the type III by a rotation of 90◦ . From the spectra in Fig. 5(b), one can see that for one polarization the peak amplitude is weak, and high for the other. This means that in one case the cavity acts like type I and in the other case like type VI. This can be seen from the Poynting vector distributions, where the field is either highly confined in the center of the structure and well guided (thanks to the combination of the slot waveguide and the nanowire) or less localized and leaking into the surrounding material. One can remark on the importance of the inclusion of a silicon nanowire in the cavity. The electromagnetic field is guided around the thin block instead of leaking into the substrate due to the divergent mode coming out from the cross-slot waveguide. Nevertheless, the term nanowire is misleading since the silicon block should then be far smaller than the wavelength in both transverse directions, which is not the case for all cavity types. However one can observe the nanowire effect for the polarization that is orthogonal to the shortest dimension of the silicon block. In the case of the type VI, the field is located in the very near vicinity of the center of the Si-cross in the cavity which makes it ideal for sensing applications, for example. Moreover it prevents the field to be spread out from the structure like in the case of type I. In the case of the cavity type V, we observe a two-dimensional slot waveguide effect. It allows the concentration of the field inside the extremely tiny two-dimensional slot in the middle of the structure. This case is not directly usable for sensing since there is no opening, but the structure may find some applications, e.g., in telecommunications, allowing the doubling of the transfer of information while maintaining a highly integrated device. We point out that the overlap between the polarizations has been neglected since the minor component of the field is at least one order of magnitude lower in amplitude than the major component. We have shown the behavior of the different cavity types, with the different polarizations. The main area of applications of these devices is sensing. From the mechanism point of view, the performance may change drastically from one structure to another. In the case of type V, for example, the field is enclosed inside the structure and only the overlap between the field guided inside the two dimensional slot waveguide and an external analyte is possible. If we consider the case of infiltration of the analyte by a capillary force directly inside the slot waveguide itself, ultra-high sensitivity is possible. However, this kind of nano-fluidistics may be beyond the reach with today’s fabrication methods. The advantage of the cross-slot waveguide is to guide the two polarizations with the possibility of having the same transmission response when the refractive indices of the structure are identical in x and y. In this case, the structure is the type VI. If there is a mismatch between x and y, the structure will act as the type II or III. If we consider the type II, with an open vertical slot filled with an analyte, the response in transmission of the structure will vary between the one of the type II and type VI depending on the refractive index variation of the analyte. This allows then to follow the refractive index variation in real time, and to make an easy monitoring of this variation by measuring the difference of amplitudes of the two resonant peaks corresponding to the two polarizations, without any interferometric system or any additional alignment devices. 5.
Possible fabrication procedure
The fabrication of the structures described is challenging for several reasons that we will detail in this section. The structures should be fabricated layer by layer, mixing fabrication methods and materials, as well as a patterning technique such as the e-beam lithography and Atomic Layer Deposition (ALD). The first challenge is the nanostructure itself. The required feature sizes are of a great impor-
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24158
tance for the confinement of light in the device and the response signal depends drastically on the parameters such as the period and the fill factor of the Bragg cavity. Nevertheless, we have shown in a previous work [12] that structures with this small features can be fabricated with a good control of the dimensions. The second issue is the perfect symmetry, which is mandatory to obtain a perfectly polarization independent device. Using CVD deposited amorphous silicon, one can facilitate the deposition of the top rails [20]. The silicon dioxide spacers and the cladding silicon dioxide layers can be deposited by ALD [21]. This technique offers us the advantage of an accurate thickness control as well as conformal coating enabling complete filling of the structure even in the smallest details. Moreover, it allows the deposition of thin films of material which will not be chemically affected by the RIE processes, which can be used as etch-stop layer [22]. 6.
Conclusion
By combining silicon slot waveguides, photonic crystal cavities, and nanowire waveguides, we achieved the theoretical demonstration of a band pass filter, independent of the polarization and having an extremely small size. Moreover, we have taken advantage of both FMM and FDTD methods to determine the optimized parameters of the structure and calculate its transmission spectrum. The principal interest of the studied structure is its versatility in terms of applications. The structure is independent of the polarization, giving an opportunity to double the capacity in telecommunication devices via polarization multiplexing, by using just a single structure. It also means that this invariance in polarization can be broken in order to use the device as a sensor. Indeed, a slight modification of the refractive index due to the addition of a gas or a liquid around the structure will break the symmetry. Then it becomes possible, for example, to monitor the properties of the analyte by following the fluctuation of the field at both polarizations. Finally we have shown that in certain cases (cavity type V), one can guide both polarizations in a two-dimensional 50 nm-wide slot waveguide. Acknowledgments This research is supported by the Finnish Funding Agency for Technology and Innovation (TEKES) through the EAKR projects ALD-nano-medi and Nanobio (grants 70011/12 and 70005/14) and the Academy of Finland (grants 272155 and 250968).
#217323 - $15.00 USD Received 18 Jul 2014; revised 2 Sep 2014; accepted 2 Sep 2014; published 25 Sep 2014 (C) 2014 OSA 6 October 2014 | Vol. 22, No. 20 | DOI:10.1364/OE.22.024149 | OPTICS EXPRESS 24159
