1. Introduction

The interaction of light with periodic metallic nanostructures has become an area of intensive research. Negative refraction from meta-materials [1,2], extraordinary transmission through sub-wavelength holes [3], and giant optical activity in planar chiral nanostructures [4] represent artificially structured materials with unusual optical properties. Recently, polarized planewave transmission measurements through planar chiral structures [4] and elliptical nanohole arrays [5] have demonstrated large polarization rotations. These phenomena result from the interplay of the metal dispersive characteristics with the size and symmetries of the periodically repeated structures. For integrated optics applications, it is desirable to control and manipulate the mode polarization in a low loss, single mode dielectric waveguide [6]. This can be accomplished by placing metallic structures in close proximity to single mode dielectric waveguides resulting in optically anisotropic mode propagation characteristics. This hybrid approach, using low loss, high index contrast dielectric waveguides strongly interacting with metallic nanostructures, can be used to create new integrated on-chip optical devices [7].

Light confined in single mode dielectric waveguides can interact strongly with metals placed in close proximity to the waveguide core due to the mode tail in the dielectric cladding. This strong coupling between the mode and the metal surface can resonantly excite surface plasmons on the metal surface if the mode polarization has a component normal to the metal interface. Surface plasmon polaritons (SPP’s) are collective electromagnetic excitations of the metallic surface electron density that can confine light to distances small in comparison to the free space wavelength and provides a large electric field enhancement at the metal-dielectric interface[8]. The SPP’s on the metal surface act as a composite waveguide [9–12] and the guided light can directionally couple back and forth between the guided surface plasmon mode and mode in the dielectric waveguide [13, 14]. This asymmetric directional coupling is a resonant effect, but due to the optical loss of the guided surface plasmon mode can occur only over several coupling lengths before the mode is fully attenuated. However, if the metal length is kept below the characteristic plasmon coupling length, interesting and useful polarization effects are seen and can be exploited to make new photonic devices [14].

In this paper, we construct on-chip single mode waveguide optical rotators with integrated polarizers to examine the polarized transmission through the polarizer waveguide analyzer configuration. We find that when the polarizer and analyzer are crossed that the polarized transmission is not at a null but is shifted in angular displacement by up to 45 degrees and varies with the length of the device. Detailed simulations of the polarized transmission through the rotator device shows a clear non-linear resonance signal consistent with directional coupling into guided SPP’s. The proposed SPP directional coupling mechanism suggests that when the device structure is below the characteristic SPP coupling length we see giant polarization rotation and helical power flow in a single mode dielectric waveguide.

2. Experimental results

The polarization mode rotation devices studied in this work were fabricated using standard CMOS fabrication techniques. Figure 1 shows a schematic of the on-chip polarization rotation devices in the polarizer analyzer experimental setup. The integrated optical devices were fabricated by depositing a CVD oxide buffer layer, 2 microns thick, on top of a 300 mm silicon wafer. A silicon nitride layer, 0.3 microns thick, was deposited by PECVD on the oxide buffer layer, and waveguides were patterned by standard photolithography, and etched. A thick HDP oxide cladding was deposited on the nitride waveguide core and Cu metal electrodes for the rotation device and the integrated polarizer were formed using a standard Cu damascene process. The depth of the Cu rotation section is defined by timed etch of the oxide so that various Cu - nitride core separations could be studied. SEM cross-sections of the Cu electrode and Cu polarizer are shown in the lower panel of Fig. 1. A trapezoidal Cu etch profile in the rotator structure causes the lower width of the Cu near the nitride waveguide core to vary for various etch times. This variation will have an impact on the SPP guided modes allowed in the composite rotator structure shown in the $\overline{AB}$ cross-section of Figure 1. Another disadvantage of the damascene process for fabricating the Cu rotator is that a TaN/Ta buffer layer lies between the Cu and the oxide cladding. This buffer layer will alter the SPP dispersion relationship by modifying the effective permittivity of the Cu and the cladding in the region near the metal. Furthermore, the SEM profile reveals that the silicon nitride waveguide has a trapezoidal profile which moves the waveguide core upper edge away from the Cu rotator electrode and makes targeting the offset of the Cu rotator difficult to control. In the results presented in this paper, we will consider only under etched Cu rotator structures with an x offset of 40 nm and y offset of 60 nm from the upper waveguide core.

 

Fig. 1. Schematic of the test chip in the polarizer analyzer experimental setup. The test chip consists of dielectric single mode Si₃ N₄ waveguides with Cu rotator section and integrated Cu polarizer. $\overline{AB}$ cross-section shows the polarization rotator structure consisting of a Cu electrode located near the waveguide core. $\overline{CD}$shows the cross-section for the integratedpolarizer.

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The polarized transmission experimental setup is shown in Fig 1. A fiber coupled diode laser at 850 nm is used as a point source which is collimated and passed through the input control polarizer. The polarized light is then focused and end-fired into the single mode silicon nitride waveguide. The silicon nitride waveguide thickness is 0.3 um and the design width is drawn at 0.35 um at the base of the trapezoidal etch profile of the waveguide. The dimensions were chosen such that the mode effective index in the nitride waveguide is degenerate for the two polarization states of the eigenmode. This eliminates any mode birefringence which could potentially influence the initial polarization state of the mode incident on the polarization rotation structure. Residual birefringence in the mode will result in a slight elliptically polarized mode incident on the polarization rotation structure as the input polarization angle is varied. Various Cu rotator lengths and design offset distances have been studied with various etch times to manipulate the incident mode. An integrated polarizer is used as the analyzer and is made using a 250 micron long thin Cu metal 500 nm over the nitride core. The integrated polarizer (Fig. 1 $\overline{CD}$ cross-section) is designed to pass only the E_x mode and extinguish the E_y mode. The output transmission is collected by a multimode fiber butted to the waveguide cleave and measured in a fiber coupled power meter. The polarized transmission through the rotator structure and the integrated polarizer is obtained by aligning the single mode guide and the collection fiber and optimizing the collected power. Each angular measurement is re-optimized. The polarized transmission data is obtained by normalizing the transmitted power through the rotator analyzer structure by the transmitted power through the waveguide with no polarizer or rotator structure. This normalization removes any residual input polarization from the laser and fiber source. The absolute power of the measured data will vary depending on cleave, laser parameters, and alignment, but the polarized transmission spectrum is very repeatable.

 

Fig. 2. Polarized Transmission through an on-chip polarizer analyzer. The polarization rotation Cu electrode is defined by timed etch (80 second etched sample) and is approximately 60 nm above the nitride dielectric waveguide core (SEM image). The inset shows the polarized transmission on a linear scale.

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In Fig. 2, the measured polarized transmission through the on-chip polarizer analyzer sample is shown as function of the input polarization angle and Cu metal length. The input polarization angles of 0 Degrees correspond to an E_y polarized mode in the nitride waveguide, and ±90 Degrees corresponding to the E_x mode polarization. The polarized transmission for the polarizer only is shown in Fig. 2. The polarizer has a minimum transmitted intensity for the E_y polarized mode (0 degrees) with an extinction depth of 20 dB for the E_y polarized mode. If the Cu rotator did not affect the mode polarization, we would expect the minimum in the polarized transmittance to occur with the E_y polarized mode at 0 degrees. The polarized transmission spectrum shows a resonant angular displacement as a function of Cu length. The polarized transmission null shifts from about -20 degrees for 3 micron long Cu to about -40 to -45 degrees for 5 micron long Cu as the input mode polarization is rotated into the Cu rotator cusp (See inset). This corresponds to a specific rotation of the mode polarization of ~10⁴ Degrees/mm for the 5 micron length. The 4 micron and 6 micron length sample show a significantly weaker resonance and the mode extinction seems to saturate at a rotation of -40 Degrees for Cu rotator lengths greater than 5 microns. The inset of Fig. 2 displays the polarized transmission on a linear scale which shows the expected periodic behavior of the rotator angular spectrum. The optical loss of the Cu rotator can be quite high, up to 60%. This loss can be reduced by further coating of the sample with oxide, thereby eliminating the Cu-air interface which is responsible for some of the optical loss.

2. Simulation results

The simulated polarized transmission through the polarization rotator is performed utilizing a 3D finite difference time domain (FDTD) solution to Maxwell’s equations [16]. FDTD allows for the simulation of dispersive metals and since it is a time domain method, we can examine the coupling of modes in time in the composite metal/dielectric waveguide structure. At optical and infrared wavelengths, metals can be modeled in FDTD using a free-electron Drude model,

where ω_pl is the plasma frequency of the metal, and γ is the damping rate. The dispersion relation for the Cu permittivity gives Re(ε_m (ω ₀))=-30.8 and Im(ε_m (ω ₀))=0.94 at the central excitation frequency, ω ₀, corresponding to a wavelength of 850 nm.. The last term in Eq. (1) represents the frequency dependent contribution from the finite conductivity of the Cu [6]. Surface plasmon polaritons are surface bound states of an optical field at a metal dielectric interface. SPP’s can propagate over large distances as guided modes and confine light to regions small compared to the wavelength of light. SPP’s are intrinsically lossy and can be excited by the evanescent mode tail in a single mode waveguide. The surface plasmon dispersion relationship for the infinite metal surface [8] is

and the condition for SPP excitation is Re(ε_m (ω ₀))+ε_c<0, where ε_c is the dielectric permittivity of the cladding, and the polarization of the incident light must have a component perpendicular to the metal-dielectric interface. For Cu metal electrodes, the surface plasmon effective index (effective extinction) is n_spp=1.517 (K_spp=1.78×10^-3) and is bound between the core index and the cladding index, thus allowing phase matching by the single mode dielectric waveguide. A mode polarized perpendicular to the metal interface can directionally couple light into a guided SPP mode [14] with the characteristic coupling length

dictated by the surface plasmon effective index and the mode effective index for that particular polarization. For Cu metal electrodes and the single mode waveguide geometry parameters discussed above, the SPP coupling length is L ~4 to 5 microns. The coupling distance sets the length scale over which the incident optical field is completely transferred into a guided surface plasmon. Previously, we have demonstrated that in the strong coupling regime, novel polarization phenomena can be observed on short length scales due to directional coupling into guided surface plasmon modes. This directional coupling occurs between the mode in the dielectric waveguide and the guided surface plasmon mode on the metal surface and can result in complete mode polarization in as little as 4 microns of length. In the polarization rotation structure, the metal is located at the corner of the waveguide and there are two independent surfaces which can support SPP’s polarized normal to the surfaces. This additional mode creates the polarization rotation and leads to very large field enhancements at corners. Similar corner resonances have been predicted and observed for SPP channel waveguides. [17, 18]

 

Fig. 3. Simulated Polarized transmission using Finite Difference Time Domain solution to Maxwell’s equations. The cross-section of the polarization device is shown, the nitride waveguide core is show in blue and the Cu electrode 60 nm from edge is red. The inset is the polarized transmission on a linear scale.

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In Fig. 3, we show the FDTD computed polarized transmission through the polarization rotation structures shown in cross-section in the inset of Fig. 3 for various lengths of Cu metal electrodes. The Cu polarization rotator is modeled using the standard Drude dispersion relationship in Eq. (1). The silicon nitride waveguide and the Cu metal rotator is modeled with a rectangular rather than trapezoidal cross-section, and the thin TaN/Ta barrier layer is neglected in the simulations. The rectangular profiles shown in the inset of Fig. 3 reduce the spurious loss introduced by the stair-cased FDTD grid. The Cu electrode is placed 60 nm from the nitride waveguide core. The mode is sourced in the plane of the waveguide and the input polarization is rotated to simulate the control polarizer. The polarized transmission is computed on an output plane after the Cu rotator structure by computing the complex |E_x| amplitude to model the analyzer. The maximum transmitted intensity |E_x|² is plotted in Fig. 3 as a function of the input polarization angle. The simulated polarized transmission as a function of the length has the same resonant structure seen in the experiment and is in qualitative agreement with the experimental data of Fig. 2. The polarized transmission null rotates from 0 degrees to -50 degrees as the length is varied, and saturates at -50 degrees. The saturation in the rotation at -50 degrees occurs when the input mode polarization points toward the Cu metal corner. The overall loss in the simulation is approximately 30% compared to 60% loss measured experimentally.

 

Fig. 4. Upper panels show the computed electric fields in the center of the polarization rotation device of various lengths. Strong field enhancements are seen at the corners of the Cu electrodes indicating excitation of surface plasmon polaritons. Lower panel illustrates the directional coupling mechanism for the rotation of the input mode (E_y ¹¹). (a) Input mode directional coupling into y-SPP. (b) Inter-plasmon coupling into x-SPP and back coupling into dielectric waveguide. The green arrow indicates the mode polarization and the red arrows indicates the directional coupling.

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The resonant behavior seen in the polarized angular transmission spectra can be examined by evaluating the mode profiles in the metal electrode waveguide rotator structure. In Fig. 4 (upper panel) is shown the sequence of the complex E_x and E_y field amplitudes in the center of the polarization rotation structures for various electrode lengths. All the results are for input E_y mode polarization (0 degrees). The sequence shows a clear indication that SPP’s are excited at the Cu metal surfaces for both polarization components, with strong field enhancement at the Cu metal corners. The effect of the directional coupling from the waveguide into the guided SPP modes and their inter-coupling can be seen by monitoring the peak E_y and E_x amplitudes as the length of the Cu rotator is increased. The peak E_x amplitude occurs for the 3 micron long rotator at the Cu metal corner, but the peak E_y amplitude in the center of the guide decreases monotonically with increasing length. The lower panel of Fig. 4 illustrates the SPP directional coupling mechanism responsible for the rotation of the mode. Figure 4(a) represents the incident mode field corresponding to the no metal case superimposed on the metal electrode structure. The SPP modes are represented schematically on the Cu electrode surface. The incident mode is not an eigenmode of the composite structure, and has considerable overlap with the SPP eigenmodes in the composite structure. The dominant polarization E_y excites an SPP eigenmode on the y normal surface shown schematically in Fig. 4(a). This SPP can directionally couple into an SPP eigenmode on the x normal surface by simply turning the corner as indicated by the diagonal red arrow in Fig. 4(b). This inter-plasmon directional coupling, followed by back-coupling into the dielectric waveguide, rotates the polarization with a specific handedness. The back-coupling step is typically not total and results in scattering loss for the single metal rotator structure. This is completely analogous to the directional coupling between two parallel dielectric waveguides in close proximity to one another. In the two waveguide case, a mode launched in the right waveguide will couple to the left guide completely transferring from the right to the left guide in the characteristic coupling length [6]. This is due to the fact that the input mode localized in the right waveguide is not an eigenmode of the two waveguide system, but is a superposition of symmetric and anti-symmetric eigenmodes, and hence coupled. This allows for the left and right waveguides to exchange energy in time, as in coupled harmonic oscillators, resulting in the characteristic beating phenomena. In the polarization rotation structure, the eigenmodes are more complex than the two dielectric waveguide case and leads to more complex intermodal directional coupling behavior. The eigenmodes consist of SPP like modes localized at the metal surfaces and dielectric waveguide modes localized in the dielectric media. The SPP like eigenmodes in the metal electrode waveguide surface depend on the electrode offset distance as well as the dimensions of the Cu electrode. Furthermore, the eigenmodes are intrinsically lossy, and therefore the directional coupling is only efficient in lengths less than the directional coupling length.

 

Fig. 5. Time averaged Poynting vector streamlines. (a) A 3 micron rotator metal electrode on left side of waveguide. (b) identical structure with metal on right side of waveguide. (c) no metal case. The incident mode is E_y polarized in all cases indicated by green arrow.

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The inter-plasmon directional coupling mechanism gives a sense or handedness to the polarization rotation as indicated in the bottom panel of Fig. 4(b). The induced optical vorticity arises due to the symmetry of the input mode and the close proximity of two planar surfaces which can support surface plasmons. Figure 5 shows the time averaged Poynting vector streamlines for the 3 micron long rotator case (upper panels) and the waveguide only (lower panel). The rotational sense dictated by the SPP coupling mechanism is clearly evident in the Poynting vector flows. This indicates a helical power flow [19] as the mode propagates along the waveguide axis, while in the waveguide without the Cu metal rotator, the power flow remains irrotational. Figures 5(a) and 5(b) show the Poynting vector streamlines for mirror symmetric Cu rotator electrode structures. The rotational sense is reversed for the mirror symmetric rotator [clockwise in Fig. 5(a), and counter-clockwise in Fig. 5(b)], and is predicted by the directional coupling mechanism. Furthermore, if the input mode polarization is changed from E_y to E_x the rotational sense is reversed. The induced optical vorticity is generated by the directional coupling into the guided SPP modes in the composite rotator structure, and the scattering loss from the SPP modes is apparent by the streamlines emerging from the back side of the metal electrode.

The polarization rotation for the single Cu electrode structure is seen to saturate at 45 degree rotation, and is limited by the symmetry of the structure. In Fig. 6, we consider the polarization rotation in a symmetric Cu electrode structure [see inset of Fig. 6(a)] where the electrodes are placed along the diagonal of the waveguide core and the x offset is varied for both electrodes. Figure 6(a) shows the calculated polarization rotation angle parametrized by the electrode offset for 5 micron long Cu metal electrodes. The polarization rotation angle increases continuously below 400 nm offsets, and approaches 90 degree rotation for offsets below 100 nm. The polarized transmission through the 5 micron long rotator structure is shown in Fig. 6(b), and is approximately independent of the input mode polarization. The dual Cu electrode rotator has low transmission loss (15–20%) for mode rotations of ~90 degrees. For electrode offsets greater than 400 nm, the input mode does not interact strongly with the Cu electrodes and no polarization effects are observed. In Fig. 6(c), the transverse field amplitudes are shown for the symmetric rotator structure indicating that the input E_x ¹¹ mode is converted into the E_y ¹¹ mode. This demonstrates that at least in principle, 90 degree mode rotation is possible with improved transmission throughput.

 

Fig. 6. Simulated polarization rotation and transmission through symmetric Cu electrode structure versus electrode offset distance for 5 micron long rotator structure. (a) Rotation angle and Ex Degree of polarization for Ex input polarization. (b) Polarized transmission for Ex and Ey input polarized mode. (c) Complex transverse field amplitudes for 100 nm Cu electrode offset sliced through center of dielectric waveguide core.

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3. Conclusions

We have fabricated on-chip single mode dielectric waveguides with an integrated polarization rotator and an analyzing polarizer. We have presented the measured polarized transmission spectrum through the polarizer-rotator-analyzer configuration as a function of the input mode polarization angle. The measured polarization spectrum shows a non-linear resonant rotation as a function of the Cu rotator length. The polarization rotation is evident by the angular shift in the transmission null as the input mode polarization is rotated toward the Cu metallic corners of the rotator structure. We find that short Cu rotator electrodes, placed diagonally to the waveguide core symmetry axis and in close proximity to the waveguide core, can effectively rotate the polarization by 45 degrees in 5 microns length. The polarization rotation is a function of the Cu rotator length and is seen to saturate when the input mode polarization is directed at the Cu rotator corners and the Cu rotator length exceeds the SPP characteristic coupling length. The mode polarization rotation depends on the details of the Cu rotator cross-section and the relative position of the Cu metal surfaces to the waveguide core, and directly impacts the propagation and eigenmode profile in the rotator waveguide composite structure. The damascene process for the Cu rotator fabrication is not ideal due to the etch definition of the position and the inherent barrier layer which modifies the SPP dispersion relationship. Both of these factors contribute to the rotational loss. While the measured loss is quite high, 50–60%, the loss can be mitigated by improved waveguide and rotator design and by overcoating the sample to remove Cu-air interface.

FDTD simulations of the polarized transmission through the 3D polarization rotation structure and analyzer show a similar non-resonant rotation of the input mode polarization. The simulations indicate the mode in the dielectric waveguide resonantly excites SPP modes on the Cu electrode metal surfaces. The observed polarization rotation mechanism is seen to be directional coupling into guided SPP modes in the rotator waveguide structure. The inter-plasmon coupling at the metallic corners gives the rotation its handedness and is seen to lead to helical power flow in the dielectric waveguide. The metal electrodes place offset from the waveguide symmetry axes seems to induce circular birefringence in the waveguide, as seen by the helical Poynting vector and the transformation of the linearly polarized input mode into a linearly polarized output mode. Further study of the complex eigenmodes in the metal electrode waveguide cross-section is necessary to determine the polarization state of the output mode and its dependence on the chiral symmetry of the structure. Recent work suggests that the optical inhomogeneity and anisotropy of the media can impart angular momentum to the mode [19], and results in optical vortices [19,20]. The off-axis Cu rotator structure creates an effective optically anisotropic waveguide media and results from the two perpendicular metal surfaces supporting SPP like eigenmodes. Simulations of symmetric electrode configurations along the diagonal of the waveguide suggest that 90 degree rotations are possible on the same length scale. This represents an efficient means of controlling and manipulating the mode polarization in compact integrated optical devices used for optical information processing and signaling.