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:
[0001]    The present invention relates to photon-to-plasmon couplers for converting photons to plasmons or vice versa. 
       BACKGROUND OF THE INVENTION 
       [0002]    During the last decade the field of quantum plasmonics has developed into a fast growing research area [1]. For quantum optics experiments on a chip and for the miniaturization of optical applications, plasmons promise unique opportunities since they can beat the diffraction limit of light, reaching extremely high electromagnetic energy densities and low mode volumes [2]. Thus, plasmonic structures offer the tools necessary to achieve a higher level of control to light-matter interactions on a nanometer scale. 
         [0003]    A key step in order to make use of these features is an efficient and controlled in- and out-coupling of plasmons to and from plasmonic structures [3]. For example, in proposed single-photon transistors [4] efficient photon-to-plasmon waveguide coupling is crucial. Furthermore, on-chip detection of plasmons is challenging [5] so that scattering of plasmons into photons and their subsequent detection with standard optical technology seems more feasible at present. Therefore, a number of photon-to-plasmon coupler schemes have been numerically investigated in two dimensions (2D) [6-8] and three dimensions (3D) [9-16] some of which have been fabricated in recent years [9-11]. 
         [0004]    Nevertheless, the above coupler schemes exhibit certain shortcomings in particular with respect to quantum plasmonics, so that novel designs are required. Specifically, these designs should allow for easy and reliable fabrication, e.g. via standard electron beam techniques. 
       OBJECTIVE OF THE PRESENT INVENTION 
       [0005]    An objective of the present invention is to present a photon-to-plasmon coupler that is easy to fabricate and provides a good coupling efficiency between photonic and plasmonic waveguides. 
       BRIEF SUMMARY OF THE INVENTION 
       [0006]    An embodiment of the invention is directed 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.       
 
         [0011]    This embodiment of the present invention exhibits a very high coupling efficiency. The coupling results from an evanescent field between the plasmonic strip waveguides and the photonic waveguide. The coupling efficiency has been confirmed by 3D-simulation of the results which are described further below with reference to the figures. 
         [0012]    Preferably, the two plasmonic strip waveguides form a Y-shaped plasmonic strip waveguide structure that converges towards the plasmonic waveguide and embraces the end section of the photonic waveguide. 
         [0013]    Two stripe-like gaps may be formed between the Y-shaped plasmonic strip waveguide structure and the end section of the photonic waveguide. Via the width of the gap, the coupling behaviour may be optimized. The ratio between the width of the gap and the width of the plasmonic strip waveguides is preferably between 0.01 and 2. 
         [0014]    The width of the gap between one of the plasmonic strip waveguides and the end section of the photonic waveguide preferably equals the width of the gap between the other one of the plasmonic strip waveguides and the end section of the photonic waveguide. 
         [0015]    The width of the gap between the first section of each of the plasmonic strip waveguides and the end section of the photonic waveguide may be at least partially constant along the propagation direction of the photons and plasmons. 
         [0016]    Preferably, the waveguide width of the plasmonic strip waveguides is at least partially or entirely constant along the propagation direction of the photons and plasmons. The plasmonic strip waveguides are preferably plasmonically decoupled from one another by the end section of the photonic waveguide. 
         [0017]    Each of the plasmonic strip waveguides preferably comprises a first section being coupled to the photonic waveguide, and a second section that is less coupled to the photonic waveguide than the first section or entirely decoupled from the photonic waveguide. 
         [0018]    The ratio between the length of the second section of each of the plasmonic strip waveguides and the width of the photonic waveguide is preferably between 1 and 4. 
         [0019]    The photonic waveguide may comprise a middle section adjacent to the end section. The waveguide width of the middle section of the photonic waveguide may be larger than the width of each of the plasmonic strip waveguides. Alternatively, the waveguide width of the middle section of the photonic waveguide and the width of each plasmonic strip waveguide may be equal. 
         [0020]    The end section of the photonic waveguide is preferably tapered, e.g. adiabatically tapered. The term “adiabatically tapered” refers to a taper that changes its waveguide width so smoothly that the additional losses caused by the taper are negligible. 
         [0021]    The plasmonic waveguide may be a strip waveguide and may form a third plasmonic strip waveguide of the photon-to-plasmon coupler. Alternatively, the plasmonic waveguide may be a slot waveguide that is connected to each of the plasmonic strip waveguides. 
         [0022]    The width of each of the plasmonic strip waveguides is preferably either smaller than the width of the plasmonic waveguide or as large as the width of the plasmonic waveguide. 
         [0023]    A further 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, that converge towards the plasmonic waveguide and form a Y-shaped plasmonic strip waveguide structure,   said Y-shaped plasmonic strip waveguide structure being optically coupled to an end section of the photonic waveguide.       
 
         [0028]    As discussed above, a Y-shaped plasmonic strip waveguide structure supports an evanescent coupling between the two plasmonic strip waveguides and the photonic waveguide. 
         [0029]    A further 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 coupled to an end section of the photonic waveguide but separated from the end section of the photonic waveguide by a gap.       
 
         [0034]    As discussed above, the width of the gap provides a further parameter for optimizing the evanescent coupling between the two plasmonic strip waveguides and the photonic waveguide. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0035]    In order that the manner in which the above-recited and other advantages of the invention are obtained will be readily understood, a more particular description of the invention briefly described above will be rendered by reference to specific embodiments thereof which are illustrated in the appended figures. Understanding that these figures depict only typical embodiments of the invention and are therefore not to be considered to be limiting of its scope, the invention will be described and explained with additional specificity and detail by the use of the accompanying drawings: 
           [0036]      FIG. 1  shows a first exemplary embodiment of a photon-to-plasmon coupler according to the present invention. 
           [0037]      FIG. 2  shows the energy flux Φ along the surface plasmon waveguide after the coupling process of the coupler shown in  FIG. 1 . The flux is normalized to the incoming energy flux Φ0. The fast decay at the beginning corresponds to scattered light whereas the slow decay fits to the predicted waveguide damping and thus corresponds to the guided plasmon mode. The intensity value at a propagation length of zero gives the coupling efficiency η. 
           [0038]      FIG. 3  shows—with respect to the coupler shown in FIG.  1 —the field distribution (intensity) of the momentum-matched guided (a) dielectric and (b) plasmonic mode. 
           [0039]      FIG. 4  shows—with respect to the coupler shown in FIG.  1 —a top view on electrical field distribution (component parallel to SiO2 surface) at the interface between air and the SiO2-substrate with the mesh of the coupler geometry (only upper half). 
           [0040]      FIG. 5  shows—with respect to the coupler shown in FIG.  1 —the dependence of the coupling efficiency on the taper-length L 1  starting from the optimized structure revealing an oscillatory behavior. The solid line is fit of the data with the analytic model A*exp(−Bx)*cos(Cx)+D. 
           [0041]      FIG. 6  shows—with respect to the coupler shown in FIG.  1 —the wavelength dependence of the coupling efficiency η of the optimized structure. The solid line is a guide for the eye. 
           [0042]      FIGS. 7-15  show an exemplary embodiment of process steps for fabricating the photon-to-plasmon couplers of  FIGS. 1 and 16 . 
           [0043]      FIG. 16  shows a second exemplary embodiment of a photon-to-plasmon coupler according to the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0044]    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. 
         [0045]    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. 
         [0046]      FIG. 1  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. 
         [0047]    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. 
         [0048]    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 . 
         [0049]      FIG. 1  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. 
         [0050]    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 . 
         [0051]    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 . 
         [0052]    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 . 
         [0053]    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. 
         [0054]    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. 
         [0055]    The end section  21  of the photonic waveguide  20  is preferably adiabatically tapered. 
         [0056]    In the embodiment shown in  FIG. 1 , the plasmonic waveguide  30  is a strip waveguide and forms a third plasmonic strip waveguide of the photon-to-plasmon coupler  10 . 
         [0057]    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  FIG. 16 . 
         [0058]    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. 
         [0059]    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. 
         [0060]    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. 
         [0061]    The photon-to-plasmon coupler  10  shown in an exemplary fashion in  FIG. 1  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. 
         [0062]    The rectangular dielectric waveguide  20  of the photon-to-plasmon coupler  10  shown in  FIG. 1  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. 
         [0063]    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  FIG. 1 ). 
         [0064]    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. 
         [0065]    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. 
         [0066]    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. 
         [0067]    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. 
         [0068]    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. 
         [0069]    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. 
         [0070]      FIG. 2  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. 
         [0071]    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  FIG. 3 . 
         [0072]    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. 
         [0073]    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  FIG. 4 . 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. 
         [0074]    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 ( FIG. 5 ). 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 . 
         [0075]      FIG. 6  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. 
         [0076]    In conclusion, an easy-to-fabricate, versatile photon-to-plasmon coupler for on-chip quantum plasmonics has been presented. In contrast to prior art, the focus is on shorter wavelength in the visible spectral range. By using FEM combined with the Taguchi-method a very time-efficient optimization and computation approach executable on conventional PCs has been presented. To avoid overestimated coupling efficiency a simple but reliable method based on the decay of coupled plasmons has been introduced. 
         [0077]      FIGS. 7-15  show exemplary method steps for fabricating the couplers  10  that are shown in  FIGS. 1 and 16 . The method steps start from a layer structure comprising a silicon wafer  100 , a SiO2-layer  110 , and a SiN-layer  120  as shown in  FIG. 7 . 
         [0078]      FIGS. 8 ,  9  and  10  show the fabrication of the photonic strip waveguide  20 . The SiN-layer  120  is structured by a lithography step that includes a photo resist layer  130  and an etch step. The photonic strip waveguide  20  is formed by a remaining strip in the SiN-layer  120 . 
         [0079]    Thereafter, the two plasmonic strip waveguides  40  and  50  are fabricated. This is shown in  FIGS. 12-15 . The photonic strip waveguide  20  is covered by a second photoresist layer  140 . Then, a metal layer  150  is deposited thereon. By removing the buried photoresist layer  140  the photonic strip waveguides  40  and  50  are completed. 
       REFERENCE NUMERALS 
       [0000]    
       
           10  photon-to-plasmon coupler 
           20  photonic waveguide 
           21  end section 
           22  middle section 
           30  plasmonic waveguide 
           40  plasmonic strip waveguide 
           42  first section 
           43  second section 
           50  plasmonic strip waveguide 
           51  Y-shaped plasmonic strip waveguide structure 
           52  first section 
           53  second section 
           60  stripe-like gap 
           70  stripe-like gap 
           100  silicon wafer 
           110  Si02-layer 
           120  SiN-layer 
           130  photo resist layer 
           140  photo resist layer 
           150  metal layer 
         D width of the gaps 
         De distance 
         L 1  length 
         L 2  length 
         Wd width of the photonic waveguide 
         Wp width of plasmonic strip waveguide 
       
     
       LITERATURE 
       [0000]    
       
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