Patent Application: US-201313770157-A

Abstract:
an embodiment of the present invention relates to a photon - to - plasmon coupler for converting photons to plasmons or vice versa , said photon - to - plasmon coupler comprising a photonic waveguide for guiding photons , a plasmonic waveguide for guiding plasmons , and two plasmonic strip waveguides , each of said two plasmonic strip waveguides being connected to said plasmonic waveguide and embracing an end section of the photonic waveguide such that each of said plasmonic strip waveguides is optically coupled to the end section of the photonic waveguide .

Description:
the preferred embodiments of the present invention will be best understood by reference to the drawings , wherein identical or comparable parts are designated by the same reference signs throughout . it will be readily understood that the present invention , as generally described herein , could vary in a wide range . thus , the following more detailed description of the exemplary embodiments of the present invention , is not intended to limit the scope of the invention , as claimed , but is merely representative of presently preferred embodiments of the invention . fig1 shows a first exemplary embodiment of a photon - to - plasmon coupler 10 according to the present invention . the photon - to - plasmon coupler 10 comprises a photonic waveguide 20 for guiding photons . the photonic waveguide 20 is preferably a dielectric waveguide . the photon - to - plasmon coupler 10 further comprises a plasmonic waveguide 30 for guiding plasmons and two plasmonic strip waveguides 40 and 50 . the plasmonic waveguide 30 and the two plasmonic strip waveguides 40 and 50 are preferably made of metal . the two plasmonic strip waveguides 40 and 50 are connected to the plasmonic waveguide 30 and embrace an end section 21 of the photonic waveguide 20 such that each of the plasmonic strip waveguides 40 and 50 is optically coupled to the end section 21 of the photonic waveguide 20 . fig1 shows that the two plasmonic strip waveguides 40 and 50 form a y - shaped plasmonic strip waveguide structure 51 that converges towards the plasmonic waveguide 30 and embraces the end section 21 of the photonic waveguide 20 . the two plasmonic strip waveguides 40 and 50 are also referred to as v - shaped metal arms hereinafter . two stripe - like gaps 60 and 70 are formed between the y - shaped plasmonic strip waveguide structure 51 and the end section 21 of the photonic waveguide 20 . the width d of the gaps 60 and 70 strongly influences the coupling behaviour of the photon - to - plasmon coupler 10 . the ratio between the width d of the gaps 60 and 70 and the width wp of the plasmonic strip waveguides 40 and 50 is preferably between 0 . 01 and 2 . the width d of the gap 60 between the plasmonic strip waveguide 40 and the end section 21 of the photonic waveguide 20 preferably equals the width d of the gap 70 between the plasmonic strip waveguide 50 and the end section 21 of the photonic waveguide 20 . the plasmonic strip waveguides 40 and 50 preferably comprise a first section 42 and 52 that is coupled to the photonic waveguide 20 , and a second section 43 and 53 that is less coupled to the photonic waveguide 20 than the first section 42 and 52 or entirely decoupled from the photonic waveguide 20 . the width d of the gaps 60 and 70 between the first section 42 and 52 of both plasmonic strip waveguides 40 and 50 and the end section 21 of the photonic waveguide 20 is preferably at least partially constant along the propagation direction of the photons and plasmons . in addition , the waveguide width wp of the plasmonic strip waveguides 40 and 50 is at least partially or entirely constant along the propagation direction of the photons and plasmons . the ratio between the length l 2 of the second section 43 and 53 of the plasmonic strip waveguides 40 and 50 and the width wd of the photonic waveguide 20 in a middle section 22 is preferably between 1 and 4 . the end section 21 of the photonic waveguide 20 is preferably adiabatically tapered . in the embodiment shown in fig1 , the plasmonic waveguide 30 is a strip waveguide and forms a third plasmonic strip waveguide of the photon - to - plasmon coupler 10 . alternatively , the plasmonic waveguide 30 may be a slot waveguide that is connected to each of the plasmonic strip waveguides . such an embodiment is shown in fig1 . preferred materials for the plasmonic waveguide 30 and the two plasmonic strip waveguides 40 and 50 are silver , gold , copper , and aluminium . the photonic waveguide 20 is preferably a dielectric waveguide which may consist of or comprise silicon , silicon dioxide , silicon nitride , gallium phosphide , and / or acrylic glass . typical sizes of the photonic waveguide 20 are heights from 50 nm to 5 μm and widths of 100 nm to 10 μm . the typical sizes of the plasmonic waveguides 30 , 40 and 50 are widths of 50 nm to 10 μm and heights of 10 nm to 300 nm . the photon - to - plasmon coupler 10 may be optimized with simulation tools . the explanations hereinafter and the results discussed with regard to specific dimensions of photon - to - plasmon couplers are to be understood as exemplary , only . the photon - to - plasmon coupler 10 shown in an exemplary fashion in fig1 may exhibit a strong evanescent field at frequencies corresponding to 780 nm vacuum wavelength which is accessible with single emitters . for characterization and optimization a full 3d simulation of the structure has been performed and the coupling efficiency η has been calculated . the rectangular dielectric waveguide 20 of the photon - to - plasmon coupler 10 shown in fig1 is tapered at one end . the increasing evanescent part of the waveguide &# 39 ; s electromagnetic field couples over gaps 60 and 70 to the v - shaped metal arms 40 , 50 which merge with the plasmonic waveguide near the taper tip into a straight rectangular metal waveguide 30 for surface plasmons . the coupler - structure is completely defined by both waveguide &# 39 ; s cross sections ( which are fixed after matching their effective refractive indices ) and four free parameters : i ) the distance de of the metal arms from the dielectric waveguide at their ends , i ) the width d of the gaps 60 and 70 between dielectric and metal in the taper region , iii ) the width wp of the metal arms , and iv ) the length l 1 of the tapered region ( see fig1 ). the materials considered here are silicon - nitride ( si3n4 ) for the dielectric and gold ( au ) for the plasmonic waveguides on a silica - substrate ( sio2 ). the structure has been optimized for a wavelength of 780 nm with the relative permeabilities ∈′+ i ∈″ of 3 . 99 ( si3n4 ), 2 . 37 ( sio2 ) and − 22 . 46 + i1 . 39 ( au ). these values respectively correspond to refractive indices n ′+ in ″ of 1 . 9974 , 1 . 5388 and 0 . 1754 + i4 . 9123 . since coupling of single emitters to the structures on the chip for example by nano - manipulation techniques is desired , gold has been chosen over silver because it does not oxidize and thus can be used without protective capping layers . silicon nitride on sio2 is chosen for convenience , as it is commercially available grown on silicon wavers , nicely processable by lithography and widely used in waveguiding . compared to silicon , si3n4 has a wide bandgap and is used for integrated optical structures in the visible spectral range . this general coupler - scheme fulfils heavy demands for easy fabrication since it only requires standard e - beam lithography methods . for the simulations a commercial fem maxwell &# 39 ; s equations - solver ( jcmwave ) has been used which allows for full 3d computations and supports non - uniform and adaptive meshing . fem generates relatively fast and accurate simulation results for setups involving metals and complex 3d geometries , also convergence checks are straight - forward . in order to optimize the structure towards a high coupling efficiency the taguchi - method has been used which is well known in the field of design of experiments ( doe ). taguchi &# 39 ; s statistical method strongly reduces the number of computational runs . in this case with 4 parameters ( de , d , wp , l 1 ) where each is varied over a reasonable range in 3 steps ( levels ), the number of required runs can be reduced to 9 ( instead of 3 4 = 81 generally needed to check all possible combinations of 4 parameters and 3 levels ). the combination of fem with the taguchi - method makes the approach very time - efficient . first , the performance of the uncoupled photonic and plasmonic waveguides is investigated . with a propagating mode solver it is searched for thickness and height of the rectangular waveguides where single mode operation is ensured . the importance of these first calculations is threefold : i ) a field distribution for the dielectric waveguide is computed which can be used as a source for the full coupler computations , ii ) the effective refractive indices n eff ( and thus their propagation constants β = 2π * re ( n eff )/ λ ) of the dielectric and those of the plasmonic modes can be matched , and iii ) the damping of the surface plasmons in the metal waveguide can be derived . with the source thus generated , the simulations of the coupler can be performed . a very important step in coupler design is a precise and reliable evaluation of the coupling efficiency η . the evaluation method uses the fact that only the guided field , i . e . the plasmon will be confined to the metallic waveguide over longer distances in contrast to scattered fields . therefore , a total of 5 μm of plasmon waveguide is retained in the computational domain and the poynting vector fields in planes perpendicular to the propagation direction in equal steps along the waveguide are exported . by summing up over all points of the exported fields the flux φ can be obtained through these surfaces . fig2 shows the results for the optimized structure where a fast decay followed by a slower exponential decay can be clearly observed . the latter is fit with a mono - exponential model f ( z )= a0 exp (− αz ) where α is the attenuation constant of the plasmon mode derived from the propagating mode solver ( α = 4π im ( n eff )/ λ ). the amplitude a0 which is the only open parameter of the fit gives us the coupling efficiency η directly after the coupler , i . e . where the metal stripe waveguide begins ( after normalization to the source field &# 39 ; s energy - flux φ0 ). it is noted that the method is independent of assumptions regarding power - orthogonality . this is in contrast to several other methods that have been utilized in prior art . it is also emphasized that the method used here does not simply place a “ monitor ” at the end of the coupler which would easily lead to an overestimated coupling efficiency η . for both waveguides two guided modes are found , a purely te and tm mode for the dielectric waveguide , whereas there are two tem modes for the metal waveguide . the field distributions of the momentum - matched modes for both waveguides are depicted in fig3 . an n eff - diel of 1 . 6886 for the te mode of the dielectric waveguide with a height of 300 nm and a width of 510 nm and an n eff - metal of 1 . 6871 + i0 . 0166 for the metallic waveguide with a height of 50 nm and a width of 400 nm is found , respectively . the imaginary part of n eff - metal corresponds to a decay constant of α = 3 . 74 μm . the te mode has been chosen due to geometric reasons : since its evanescent field is pronounced at the sides of the waveguide it will couple over the gap in the tapered region and its polarization parallel to the silica - substrate sio2 surface is well suited to polarize the metal arms and thus excite plasmons . now the coupler problem is computed . after the taguchi - optimization the best coupling efficiency of η = 47 % is found for the parameters de = 100 nm , d = 24 nm , wp = 120 nm and l 1 = 1030 nm . the mesh of the coupler problem and the field distribution are shown in fig4 . it is pointed out that by capping the structure with a higher index dielectric than air and using silver instead of gold , higher coupling efficiencies η &# 39 ; s above 60 % can easily be reached . a drawback of the taguchi - method is the missing insight into the importance of the individual parameters on the result . in order to analyze effects caused by imperfections in fabrication four parameter scans have been performed . starting from the optimized structure the parameter may be varied while keeping the others fixed . whereas the three parameters de , d and wp show only moderate influence on the coupling efficiency η the scan of the taper length l 1 reveals a clear oscillatory behavior ( fig5 ). this reflects the working principle of the coupler design : the evanescent part of the dielectric mode excites surface plasmons in the v - shaped metal arms , the electromagnetic energy is then coupled back and forth between the inner and outer edge of the arms while propagating towards the taper - tip . the coupling efficiency η is at its maximum when the taper length l 1 is such that most of the electromagnetic energy has coupled to the outer side and fits to the field distribution of the guided plasmon mode . at the same time the taper length l 1 has to be kept as short as possible because of dissipative attenuation in the metal arms 40 and 50 . fig6 shows the spectral bandwidth of the coupler by scanning over a variety of input frequencies ( dielectric constants taken from ref . 25 ). from this a broad bandwidth of approximately 220 nm can be extracted . in conclusion , an easy - 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