1. Introduction

Single mode dielectric waveguides are essential elements in integrated optical components proposed for inter-chip and intra-chip signaling schemes [1]. High index contrast between waveguide core and cladding effectively confines light to transverse regions at or near the diffraction limit, and allows for low loss transmission of optical signals over large distances [2]. Surface plasmon polariton (SPP) waveguides consisting of metal thin films on dielectric substrates have been shown to confine light to regions smaller than the diffraction limit [3–6]. These SPP waveguide structures are intrinsically absorbing and dispersive at optical and infrared frequencies, and it is this attenuation and dispersion that limits the length scales over which SPP waveguides can be used to transmit optical signals [4,5]. Recent attempts to overcome this inherent limitation have utilized conventional dielectric waveguides to excite a guided surface plasmon mode [7].

A key requirement of these hybrid integration schemes is control over the mode polarization in the dielectric waveguide. Various mode polarization devices have been proposed in the past for metal clad waveguides [8] and fibers [9]. In these devices, thin metals are placed in contact with the slab waveguide or fiber core and SPP’s are launched in the thin metal films extinguishing the TM polarization. These methods are effective at producing very high extinction with acceptable insertion loss. In this paper, we examine the polarized transmission of a single mode dielectric waveguide in close proximity to large metallic electrode structures as a function of the offset distance between the waveguide core and the metallic electrodes, both experimentally and theoretically. Silicon nitride single mode waveguides with oxide cladding having high index contrast have been fabricated with copper metal electrodes placed on both sides of the waveguide utilizing standard CMOS processing. The mode structure in a single mode silicon nitride waveguide of square cross-section consists of two degenerate, propagating, predominantly linear polarization states as characterized by the effective index of refraction. The mode profile is Gaussian like in the waveguide core with evanescent mode tails extending into the oxide cladding dielectric. The introduction of a metal electrode in close proximity to the waveguide core has a dramatic effect on the mode profile by imposing boundary conditions at the metal-cladding interface. It is the discontinuity in the normal component of the electric field across the metal-cladding interface which allows for the excitation of a resonant surface plasmon and gives rise to the polarization of the mode in the waveguide.

2. Simulation of polarized transmission

Light propagation in single mode dielectric waveguide and metallic electrode structures has been simulated using 3D finite difference time domain (FDTD) solution to Maxwell’s equations [10]. In Fig. 1 is shown a schematic of the simulated structures. A silicon nitride waveguide core (red) with index of refraction 1.93 is surrounded by oxide cladding with index of 1.464. The nitride waveguides are square with dimensions of 0.3 μ, and have been chosen for single mode operation for λ=850 nm. Copper (Cu) metal electrodes (orange) are placed symmetrically about the waveguide core and the electrode waveguide core distance, d, is varied. The Cu metal electrode has index of refraction and extinction coefficient at 850 nm, n=0.084 and K=5.55, respectively, (real ε_m = -30.8 and imaginary ε_m = 0.9) and is modeled using Drude-Debeye dispersion in the FDTD simulations [10]. The mode profile and propagation constant for the single mode dielectric waveguides are determined from a frequency domain mode solver and the field profiles are used to source the FDTD simulation. The effective index for the single mode waveguide is degenerate for the two polarization states and is n_eff =1.590.

 

Fig. 1. Schematic of metallic electrode (orange)-single mode nitride (red) waveguide structure. Left (Right) schematic is top down (cross-sectional) view. In all simulations oxide cladding is assumed.

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The FDTD simulated polarized transmission through a 3 micron long Cu electrode structure is shown in Fig. 2a as a function of the metal-core separation. Two features are readily apparent: for metal–core separation of greater than 0.6 microns the transmission through the structure is unperturbed by the metal electrodes. This sets the minimum spacing requirements for electrode placement for various active devices fabricated using single mode waveguides. Secondly, a large transmission minimum at metal-core separation of 0.2 microns is observed for light polarized perpendicular to the metal-cladding interface. This selective polarization of the single mode waveguide can be attributed to resonant excitation of a surface plasmon mode on the Cu surface when the mode is polarized perpendicular to the metal. Furthermore the mode is preferentially transmitted with polarization parallel to the interface for metal – core separation in the range of 0.1 microns to 0.6 microns.

 

Fig. 2. (a) (Upper plot) Peak waveguide transmitted power through 3 micron long Cu metal electrode structure as a function of metal core separation, d. (b) (Lower plot) Eigenmode effective index computed for cross-section in fig. 1 as a function of metal core separation, d. E parallel and E perp. refers to largest E field amplitudes.

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2.1 Guided surface plasmon excitation

Surface plasmons are collective bound states of the electromagnetic field and the nearly free electrons in the metal localized at the metal-dielectric interface [11]. The surface plasmon dispersion relationship is

where ε_m (ω) is the frequency dependent dielectric function for the Cu, and ε_c is the cladding dielectric constant. A surface plasmon excitation can exist if Re(ε_m(ω)) < -ε_c.

The surface plasmon wavevector, k_sp, can be expressed in terms of an effective index (N_sp) and extinction coefficient (K_sp), which for Cu and oxide at 850 nm gives, 1.51 and 0.0017, respectively. It is well established that plasmons can be excited by various evanescent coupling schemes [3,12]. The coupling of incident photons to surface plasmon modes requires energy and momentum conservation and depends on the incident polarization having a component normal to the surface. The evanescent tail of the mode in the dielectric waveguide can readily excite a surface plasmon resonance [7]. Alternatively, one can think of a mode localized in the single mode waveguide core as phase matched to the surface plasmon. This occurs if the effective index of the composite mode is equal to the plasmon effective index, N_sp. Thus the asymmetric transfer of power from the dielectric waveguide into a guided surface plasmon mode occurs as in the standard coupled mode theory. The mode effectively tunnels from the single mode dielectric waveguide core to the guided surface plasmon mode which depends on the metal electrode/waveguide core separation. Figure 2b shows the eigenmode effective index for the metal/ dielectric waveguide structure cross-section (see Fig. 1) as a function of the metal/waveguide core separation. The two polarization states are degenerate above a metal core separation of 0.65 microns consistent with FDTD results approaching the single mode waveguide effective index of 1.59. At a metal core separation of 0.2 microns, the perpendicular polarized mode effective index is matched to the surface plasmon index, while the parallel polarized mode index is matched approximately to the single mode dielectric waveguide effective index. This matching for the perpendicular polarization represents the onset of the resonant excitation of guided surface plasmons for separations in the range of 0.2 to 0.65 microns. These guided surface plasmons are intrinsically lossy, with the loss governed by the effective extinction coefficient, K_sp. In general, the propagation eigenvalues for the metal/waveguide cross-section obtained by the eigenmode solver are complex and have been selected based on having extinction coefficients less than K_max=0.01, where K_max > K_sp. Other higher order modes could be obtained by increasing the maximum extinction coefficient, however these modes are more highly attenuated.

2.2 Asymmetric directional coupling

In the proceeding section, the resonant excitation of the guided surface plasmon mode from the input single mode dielectric waveguide has been attributed to asymmetric coupling between the lossless input mode and the lossy guided surface plasmon mode. Coupled mode theory predicts a weak reverse coupling from the guided surface plasmon mode into the dielectric waveguide which is a strong function of the metal electrode length. Figure 3 shows electric field profiles for input mode polarized perpendicular to the metal surface for a long electrode structure of 8 microns. For a metal core separation of 0.2 microns (upper plot of Fig. 3), the electric field shows a pronounced amplitude minimum after approximately 3.5 microns into the metal electrode structure. The electric field amplitude sliced along the dielectric waveguide core is shown in the inset of Fig. 3. It clearly shows the amplitude minimum at 3.5 micron, and regeneration of an attenuated guided mode in the dielectric core beyond the 3.5 micron length. The lower panel of Fig. 3 shows the electric field profile for a metal core separation of 0.6 microns. At 0.6 microns separation the mode propagates essentially undisturbed through the metal electrode structure. This corresponds to the point where the two modes in the composite metal structure are degenerate and equal to the mode effective index of the dielectric waveguide with no metal electrode structure.

Figure 4 shows the electric field profiles for input mode polarization parallel to the metallic electrode surface for the two electrode separations of 0.2 (upper) and 0.6 microns (lower), respectively. It is clear that this polarization only undergoes attenuation and does not resonantly couple to surface plasmons. Furthermore, by choosing a metallic electrode length as short as 3–4 microns for the 0.2 micron metal core separation will result in nearly 100% transmission of waveguide mode polarized parallel to metal electrode surface.

 

Fig. 3. Electric field profiles for 8 micron long metallic electrode with polarization perpendicular to metal surface. Upper (Lower) plot is for electrode core separation 0.2 (0.6) microns. Inset shows slice along waveguide core (black line).

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Fig. 4. Electric field profiles for 8 micron long metallic electrode with polarization parallel to metal surface. Upper (Lower) plot is for electrode core separation 0.2 (0.6) microns.

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3. Experimental results

Preliminary measurements of the polarized transmission through several structures shown in Fig. 5 have been performed. The experimental setup for the measurement of the polarized transmission is shown schematically in Fig. 5. A CW laser diode operating at 850 nm is coupled to a single mode fiber (SMF) and used as a point source for collimating an input beam. The collimated beam is passed through a Glan Thompson polarizer, which is varied to control the input polarization state in the single mode waveguide, and focused onto the coupling region of the single mode waveguide. The output of the single mode waveguide is collected with a multi-mode fiber (MMF) and the transmitted power is measured for the two orthogonal polarization states.

 

Fig. 5. Schematic of experimental set up (upper figure). Lower image shows two Cu electrodes (L=~70 microns) with single mode waveguide in center of electrode structure. Waveguide core is 0.35 microns wide and metal waveguide separation ~1.4 microns.

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The polarized transmittance for three different Cu-waveguide structures was measured with Cu-core separation of 1.4, 0.3, and 0.2 microns with a fixed length of 70 microns. It is important to note that the metal electrode length is much longer than the simulated electrode length of the previous section. These structures have not been optimized for polarizing the single mode waveguide and are meant only to qualitatively validate the simulated predictions. The polarized transmittance for a straight guide with no Cu electrodes is measured as a reference. The normalized transmittance for the transmitted mode provides a convenient measure of the mode polarization and is defined as

where T _⊥ and T _∥ are the transmitted power for the perpendicular and parallel mode polarization, respectively. The transmitted power utilized in Eq. 2 is referenced to the straight waveguide polarized transmittance with no Cu metal to account for any residual polarization difference that may arise due to waveguide asymmetry or polarization at the input fiber.

Table 1. Normalized transmittance and extinction ratio for various waveguide core/ metal electrode separations (L=70 micron long metal electrode structures).

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Table 1 shows the normalized transmittance for the 3 Cu-waveguide core spacing. The normalized transmittance for the narrow spacing cases of 0.2 and 0.3 show that the output mode is completely (~98%) polarized parallel to the metal electrode on exit. The larger separation case (1.4 microns) results in normalized transmittance for the parallel polarization is 70% and 30% for the perpendicular polarization relative to the straight guide with no metal at 52% and 48% respectively. This means that the output has a residual polarization of 18% relative to the straight waveguide with no metal and differs from the theoretical 50%–50% predicted by simulation.

Table 2. Insertion loss for each polarization vs. metal electrode separation (70 micron length)

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Table 2 shows the computed insertion loss for the three 70 micron long waveguide metal electrode structures. The smaller metal core separation (0.2–0.3 microns) has nearly 6.0 dB insertion loss for polarization parallel to the metal interface with 0.6 dB loss for the larger spacing (1.4 microns). For the polarization perpendicular to the metal interface, the insertion loss increases to approximately 23 dB for the smaller separation as expected. The insertion loss for the large spacing increases to 4 dB.

The large insertion loss of 4 dB for perpendicular polarization, and the residual polarization for the largest spacing indicates that the coupling to surface plasmons occurs at larger spacing than predicted by simulation. Several factors influence the mode extent and hence the coupling to surface plasmons. The largest contribution comes from the fact that the single mode waveguide is asymmetrically placed between the metal electrodes for the 1.4 micron separation. The separation on the upper electrode shown in Fig. 5 is approximately 1.2 microns, while the lower electrode is 1.4 microns from the core. This asymmetry will impact the coupling distance and the polarized transmission. Another factor present in the experimental data and absent in simulation is waveguide loss from nitride line edge roughness in the metal electrode region. The simulations are for perfectly smooth waveguide sidewalls and do not include any sidewall roughness. Finally, the copper metal electrodes have been made in a standard CMOS process and are encapsulated in a thin barrier metal layer. This barrier layer will impact the surface plasmon dispersion and the coupling to surface plasmons.

These preliminary results indicate that mode polarization does occur when the light is polarized perpendicular to the metal surface, but requires further investigation on more structures to further map out the coupling to surface plasmons at the metal electrode cladding interface.

4. Conclusions

We have demonstrated that near complete polarization of a mode in a dielectric waveguide can be achieved by placing metal electrode structures in close proximity to the waveguide core. The polarization occurs due to resonant excitation of a guided surface plasmon mode when the input polaration is perpendicular to the metal interface. Asymmetric directional coupling between the surface plasmon guided mode and the single mode dielectric waveguide has been observed. For Cu metallic electrodes, FDTD simulations indicate an optimal offset distance of 0.2 microns and an electrode length of 3 to 4 microns will result in near total mode polarization parallel to the metal surface. Preliminary experiments on longer structures validate the prediction of total polarization of the transmitted mode for electrode separations of 0.2 and 0.3 microns, respectively. However, the fabricated Cu electrode structures are made using a dual Damascene process and have a thin barrier layer between the Cu and the cladding oxide. The influence of the barrier layer on the plasmon dispersion and a more complete set of electrode separations will be presented in future work.