February 1, 2014 / Vol. 39, No. 3 / OPTICS LETTERS
697
Dihedron dielectric loaded surface plasmon athermal polarization converter K. Hassan, F. Leroy, G. Colas-des-Francs, and J.-C. Weeber* LICB, UMR 6303 CNRS-Université de Bourgogne, 9 Av. A. Savary, BP 47870, F-21078 DIJON Cedex, France *Corresponding author: jcweeber@u‑bourgogne.fr Received October 11, 2013; revised December 23, 2013; accepted December 23, 2013; posted December 23, 2013 (Doc. ID 199300); published January 30, 2014 We investigate numerically a novel plasmonic polarization converter relying on the excitation of a so-called dihedron dielectric loaded plasmon polariton. The dihedron dielectric loaded waveguide consists of a dielectric ridge implemented at the inner corner of a metal-coated dielectric step. For a dielectric ridge with a square cross section, the plasmon polariton modes supported by each side of the metallized step hybridize to create supermodes with crossed polarizations. We show that the two supermodes can be operated in a dual-mode interferometer configuration to perform an efficient (24 dB) TE–TM/TM–TE polarization conversion over typical distances below 30 μm at telecommunications wavelengths. In addition, on the basis of the thermo-optical properties of our device, we find that the dihedron plasmonic polarization converter is temperature insensitive. © 2014 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (130.3120) Integrated optics devices; (130.5460) Polymer waveguides; (230.5440) Polarization-selective devices. http://dx.doi.org/10.1364/OL.39.000697
Plasmonic components for integrated optics at telecommunication wavelengths have been extensively investigated recently [1]. Among many configurations, the so-called dielectric loaded surface plasmon polariton waveguides (DLSPPWs) [2] composed of a dielectric ridge deposited onto a metal film (or strip) are considered promising for applications where integration into a silicon-on-insulator (SOI) circuitry is needed [3] and/or for the design of thermo-optical components [4,5]. For example, DLSPPW thermo-optical routers have been implemented for true high-bit rate data traffic [6]. Singlemode DLSPPWs can only be operated with TM polarized light (dominant electric field component perpendicular to the metal film) because of the plasmonic nature of their fundamental mode. For datacom applications where polarization independence is highly desirable, the use of plasmonic devices imposes the development of a polarization diversity scheme [7]. Polarization diversity schemes have already been demonstrated with silicon photonics and rely on polarization separators and polarization converters. A polarization separator can be as simple as a directional coupler [8,9], whereas the polarization converter is usually more difficult to implement. Many different types of polarization converters have been reported in the literature [10–13], including highly compact hybrid silicon plasmonic converters [14–16]. In this work, we investigate numerically an original design of a compact, low-loss DLSPPW-based polarization converter. More importantly, and beyond the intrinsic performance of the converter, we investigate the thermooptical properties of our configuration. We show that the performance of our converter is only marginally impacted by a temperature change of several tenths of degrees, making our design appealing for integration into a fluctuating temperature environment, such as a thermooptical reconfiguration plateform. A schematic view of the plasmonic polarization converter we consider is shown in Fig. 1. A metallic dihedron is created by coating with gold the vertical and horizontal sides of a dielectric step. A dielectric ridge is then formed at the inner corner of the dihedron. This 0146-9592/14/030697-04$15.00/0
ridge has two adjacent sides in contact with the metal. In this Letter, this configuration will be denoted as a dihedron DLSPPW. From a practical point of view, such a structure could be obtained by a deep etching process followed by a metal evaporation under a tilted angle and a subsequent dielectric ridge fabrication using lithography and dry etching. We investigate the optical and thermo-optical properties of the dihedron DLSPPW by means of 2D and 3D finite element method (FEM) software [17]. Knowing the basic properties of standard DLSPPWs [2], one can anticipate that in the presence of a vertical wall of sufficient height (in the range of 2 μm at telecom wavelengths [18]), a plasmonic mode will be supported by the vertical metal–polymer interface. We investigate the interplay of this vertical plasmonic mode with the horizontal one by performing a 2D FEM analysis of the computational situation depicted in Fig. 2(a). The dihedron DLSPPW is composed of a polymer ridge (n 1.535) with a cross section wg × hg . In this Letter, we consider polymer ridges with a fixed width wg 800 nm supporting a single plasmon mode along the horizontal direction for heights hg around wg . In addition, we use optically thick metal films with a thickness of t 100 nm, roughly 10 times the skin depth of gold (nAu 0.55 i11.5 [19]) at λ0 1.55 μm in such a way that the dielectric step supporting the vertical film can be safely disregarded as long as plasmon modes confined at the inner metal interfaces are of interest. Figure 2(b) shows the dispersion of the real effective index of the two
Fig. 1. Schematic view of the dihedron DLSPPW. © 2014 Optical Society of America
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OPTICS LETTERS / Vol. 39, No. 3 / February 1, 2014
Fig. 2. (a) Schematic view of the 2D dihedron DLSPPW investigated numerically. (b) For wg 800 nm, real effective index of the vertical and horizontal DLSPPW mode as a function of hg . (c) Electric field modulus distribution for the horizontal mode when hg 900 nm. (d) Electric field modulus distribution for the vertical mode when hg 900 nm. (e) and (f) For hg wg 800 nm, electric field modulus distribution for the two supermodes. Solid arrows, supermode transverse polarization.
modes supported by the dihedron DLSPPW (wg 800 nm) when the waveguide height hg is varied. For hg < wg (or hg > wg ) the larger effective index mode is confined along the horizontal (or vertical) metal–polymer interface. The dominant electric field component of these modes is perpendicular to the metal–polymer interface on which the mode is peaked. As shown by the field intensity distributions displayed in Figs. 2(c) and 2(d), the two modes are repelled away from the inner corner of the dihedron owing to the boundary condition for their dominant electric field component at the tangential metal wall. Thus the effective index of each dihedron mode is lower as compared to the modes of a standard (single metal interface) DLSPPW of the same cross section. In this way, a dihedron waveguide with a given cross section can be single mode along one given metal interface, whereas the corresponding single interface DLSPPW would be multimode for the same polymer ridge cross
section. For the dielectric ridge nearly symmetric (hg ≃ wg ), the polarization of the eigenmodes departs from the quasi-TE or quasi-TM and becomes more hybrid with significant components of the electric field perpendicular to both metallic walls. When the dielectric ridge is made symmetric (hg wg ), the dispersion curves feature an anticrossing due to the hybridization of the DLSPPW modes supported by the horizontal and vertical interfaces. The resulting supermodes feature either in-phase or out-of-phase transverse electric field E x and E z components leading to a polarization respectively aligned with the symmetry axis of the dihedron [noted 45° in Fig. 2(e)] or perpendicular to that axis [noted 135° in Fig. 2(f)]. These two supermodes are the basic ingredients of the dual-mode interferometer plasmonic polarization converter we investigate in this work. For the symmetric dihedron DLSPPW, the two supermodes feature a very similar field intensity distribution with slightly different field confinement within the polymer and accordingly different real effective indices 45 such that Δneff n135 eff − neff 1.332 − 1.304 0.028. The damping distance given by LSPP λo ∕4πn0eff where n0eff is the effective index imaginary part is found to be around 41 μm (or 36 μm) for the 135° (or 45°) polarization. From this modal analysis, we conclude that if excited simultaneously, the interference of the two supermodes should create a beating pattern along the symmetric dihedron DLSPPW with a half-beating length of LHB λ0 ∕2Δneff 27.7 μm. Figure 3(a) shows the full 3D FEM modeling of the propagation along a 30 μm long symmetric dihedron DLSPPW when a quasi-TM polarized mode of a standard DLSPPW is used as an input field. As expected from the 2D eigenmode analysis, we observe a beating with a length of 29.8 μm leading to an efficient polarization conversion at the output of the 30 μm long dihedron DLSPPW. The polarization conversion efficiency is quantitatively evaluated by computing the extinction ratio (ER) defined by [10] ERTM→TE 10 log10
out P TM ; P out TE
(1)
out where P out TE and P TM are the flux through the output cross section of the finite-length device of the time average Poynting vector associated with the dominant electric field component E x (or E z ) for TE (or TM) polarization.
Fig. 3. Dihedron DLSPPW quasi-TM to quasi-TE polarization conversion obtained by 3D FEM calculation. (a) Input and electric field map distribution. (b) Electric field distribution along the device. (c) Output electric field map distribution.
February 1, 2014 / Vol. 39, No. 3 / OPTICS LETTERS Table 1. Polarization Converter Performance and Comparison to Previous Numerical (n.) and/or Experimental (e.) Worksa Dihedron Ref. [11] Ref. [12] Ref. [13] Ref. [15,16] n./e. n. e. e. n./e. Material Au/Poly. L (μm)
697
Dihedron dielectric loaded surface plasmon athermal polarization converter K. Hassan, F. Leroy, G. Colas-des-Francs, and J.-C. Weeber* LICB, UMR 6303 CNRS-Université de Bourgogne, 9 Av. A. Savary, BP 47870, F-21078 DIJON Cedex, France *Corresponding author: jcweeber@u‑bourgogne.fr Received October 11, 2013; revised December 23, 2013; accepted December 23, 2013; posted December 23, 2013 (Doc. ID 199300); published January 30, 2014 We investigate numerically a novel plasmonic polarization converter relying on the excitation of a so-called dihedron dielectric loaded plasmon polariton. The dihedron dielectric loaded waveguide consists of a dielectric ridge implemented at the inner corner of a metal-coated dielectric step. For a dielectric ridge with a square cross section, the plasmon polariton modes supported by each side of the metallized step hybridize to create supermodes with crossed polarizations. We show that the two supermodes can be operated in a dual-mode interferometer configuration to perform an efficient (24 dB) TE–TM/TM–TE polarization conversion over typical distances below 30 μm at telecommunications wavelengths. In addition, on the basis of the thermo-optical properties of our device, we find that the dihedron plasmonic polarization converter is temperature insensitive. © 2014 Optical Society of America OCIS codes: (240.6680) Surface plasmons; (130.3120) Integrated optics devices; (130.5460) Polymer waveguides; (230.5440) Polarization-selective devices. http://dx.doi.org/10.1364/OL.39.000697
Plasmonic components for integrated optics at telecommunication wavelengths have been extensively investigated recently [1]. Among many configurations, the so-called dielectric loaded surface plasmon polariton waveguides (DLSPPWs) [2] composed of a dielectric ridge deposited onto a metal film (or strip) are considered promising for applications where integration into a silicon-on-insulator (SOI) circuitry is needed [3] and/or for the design of thermo-optical components [4,5]. For example, DLSPPW thermo-optical routers have been implemented for true high-bit rate data traffic [6]. Singlemode DLSPPWs can only be operated with TM polarized light (dominant electric field component perpendicular to the metal film) because of the plasmonic nature of their fundamental mode. For datacom applications where polarization independence is highly desirable, the use of plasmonic devices imposes the development of a polarization diversity scheme [7]. Polarization diversity schemes have already been demonstrated with silicon photonics and rely on polarization separators and polarization converters. A polarization separator can be as simple as a directional coupler [8,9], whereas the polarization converter is usually more difficult to implement. Many different types of polarization converters have been reported in the literature [10–13], including highly compact hybrid silicon plasmonic converters [14–16]. In this work, we investigate numerically an original design of a compact, low-loss DLSPPW-based polarization converter. More importantly, and beyond the intrinsic performance of the converter, we investigate the thermooptical properties of our configuration. We show that the performance of our converter is only marginally impacted by a temperature change of several tenths of degrees, making our design appealing for integration into a fluctuating temperature environment, such as a thermooptical reconfiguration plateform. A schematic view of the plasmonic polarization converter we consider is shown in Fig. 1. A metallic dihedron is created by coating with gold the vertical and horizontal sides of a dielectric step. A dielectric ridge is then formed at the inner corner of the dihedron. This 0146-9592/14/030697-04$15.00/0
ridge has two adjacent sides in contact with the metal. In this Letter, this configuration will be denoted as a dihedron DLSPPW. From a practical point of view, such a structure could be obtained by a deep etching process followed by a metal evaporation under a tilted angle and a subsequent dielectric ridge fabrication using lithography and dry etching. We investigate the optical and thermo-optical properties of the dihedron DLSPPW by means of 2D and 3D finite element method (FEM) software [17]. Knowing the basic properties of standard DLSPPWs [2], one can anticipate that in the presence of a vertical wall of sufficient height (in the range of 2 μm at telecom wavelengths [18]), a plasmonic mode will be supported by the vertical metal–polymer interface. We investigate the interplay of this vertical plasmonic mode with the horizontal one by performing a 2D FEM analysis of the computational situation depicted in Fig. 2(a). The dihedron DLSPPW is composed of a polymer ridge (n 1.535) with a cross section wg × hg . In this Letter, we consider polymer ridges with a fixed width wg 800 nm supporting a single plasmon mode along the horizontal direction for heights hg around wg . In addition, we use optically thick metal films with a thickness of t 100 nm, roughly 10 times the skin depth of gold (nAu 0.55 i11.5 [19]) at λ0 1.55 μm in such a way that the dielectric step supporting the vertical film can be safely disregarded as long as plasmon modes confined at the inner metal interfaces are of interest. Figure 2(b) shows the dispersion of the real effective index of the two
Fig. 1. Schematic view of the dihedron DLSPPW. © 2014 Optical Society of America
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OPTICS LETTERS / Vol. 39, No. 3 / February 1, 2014
Fig. 2. (a) Schematic view of the 2D dihedron DLSPPW investigated numerically. (b) For wg 800 nm, real effective index of the vertical and horizontal DLSPPW mode as a function of hg . (c) Electric field modulus distribution for the horizontal mode when hg 900 nm. (d) Electric field modulus distribution for the vertical mode when hg 900 nm. (e) and (f) For hg wg 800 nm, electric field modulus distribution for the two supermodes. Solid arrows, supermode transverse polarization.
modes supported by the dihedron DLSPPW (wg 800 nm) when the waveguide height hg is varied. For hg < wg (or hg > wg ) the larger effective index mode is confined along the horizontal (or vertical) metal–polymer interface. The dominant electric field component of these modes is perpendicular to the metal–polymer interface on which the mode is peaked. As shown by the field intensity distributions displayed in Figs. 2(c) and 2(d), the two modes are repelled away from the inner corner of the dihedron owing to the boundary condition for their dominant electric field component at the tangential metal wall. Thus the effective index of each dihedron mode is lower as compared to the modes of a standard (single metal interface) DLSPPW of the same cross section. In this way, a dihedron waveguide with a given cross section can be single mode along one given metal interface, whereas the corresponding single interface DLSPPW would be multimode for the same polymer ridge cross
section. For the dielectric ridge nearly symmetric (hg ≃ wg ), the polarization of the eigenmodes departs from the quasi-TE or quasi-TM and becomes more hybrid with significant components of the electric field perpendicular to both metallic walls. When the dielectric ridge is made symmetric (hg wg ), the dispersion curves feature an anticrossing due to the hybridization of the DLSPPW modes supported by the horizontal and vertical interfaces. The resulting supermodes feature either in-phase or out-of-phase transverse electric field E x and E z components leading to a polarization respectively aligned with the symmetry axis of the dihedron [noted 45° in Fig. 2(e)] or perpendicular to that axis [noted 135° in Fig. 2(f)]. These two supermodes are the basic ingredients of the dual-mode interferometer plasmonic polarization converter we investigate in this work. For the symmetric dihedron DLSPPW, the two supermodes feature a very similar field intensity distribution with slightly different field confinement within the polymer and accordingly different real effective indices 45 such that Δneff n135 eff − neff 1.332 − 1.304 0.028. The damping distance given by LSPP λo ∕4πn0eff where n0eff is the effective index imaginary part is found to be around 41 μm (or 36 μm) for the 135° (or 45°) polarization. From this modal analysis, we conclude that if excited simultaneously, the interference of the two supermodes should create a beating pattern along the symmetric dihedron DLSPPW with a half-beating length of LHB λ0 ∕2Δneff 27.7 μm. Figure 3(a) shows the full 3D FEM modeling of the propagation along a 30 μm long symmetric dihedron DLSPPW when a quasi-TM polarized mode of a standard DLSPPW is used as an input field. As expected from the 2D eigenmode analysis, we observe a beating with a length of 29.8 μm leading to an efficient polarization conversion at the output of the 30 μm long dihedron DLSPPW. The polarization conversion efficiency is quantitatively evaluated by computing the extinction ratio (ER) defined by [10] ERTM→TE 10 log10
out P TM ; P out TE
(1)
out where P out TE and P TM are the flux through the output cross section of the finite-length device of the time average Poynting vector associated with the dominant electric field component E x (or E z ) for TE (or TM) polarization.
Fig. 3. Dihedron DLSPPW quasi-TM to quasi-TE polarization conversion obtained by 3D FEM calculation. (a) Input and electric field map distribution. (b) Electric field distribution along the device. (c) Output electric field map distribution.
February 1, 2014 / Vol. 39, No. 3 / OPTICS LETTERS Table 1. Polarization Converter Performance and Comparison to Previous Numerical (n.) and/or Experimental (e.) Worksa Dihedron Ref. [11] Ref. [12] Ref. [13] Ref. [15,16] n./e. n. e. e. n./e. Material Au/Poly. L (μm)
