1. Introduction

Surface plasmon polaritons (SPPs) are electromagnetic waves travelling along a metal-dielectric interface as a result of coupling of optical fields in dielectric to the oscillation of free electrons inside the metal [1]. The interest in SPPs has increased dramatically in recent past due to the possibility of their usage in guiding and routing in highly-integrated ultra-compact photonic circuits [2]. One of the limiting factors of SPP-based waveguide components in comparison to dielectric-based photonic counterparts is high propagation losses due to internal damping (ohmic loss) of radiation in metal, whose level increases with an increase in the mode confinement. But the fact that the same thin metal circuitry can be exploited to carry optical signals as well as electrical control gives SPP-based components an edge over photonic devices. As a result of this, signal modulation in SPP-based devices becomes preferable to realize than that in photonic devices due to reduction in the electrical power consumption and response time associated with electrical control signals. One of the very first demonstrations of this concept was realized with long-range SPP (LRSPP) thermo-optic modulator and switches where the same circuitry was used to guide the optical radiation and transmit the electrical signals that efficiently controlled the guidance [3,4]. It must be emphasized that in the above configurations, modulation was achieved using weakly guided SPP modes with a poor lateral confinement. In this context, dielectric-loaded SPP waveguides (DLSPPWs), where a dielectric ridge is placed on a metal surface and ensures a strong confinement for the SPP waves travelling along the metal-dielectric interface due to a high contrast in the effective index [5,6], represent a promising configuration. These plasmonic waveguides, by virtue of being naturally compatible with different dielectrics and industrial fabrication using large-scale UV lithography [7], are considered to be an attractive alternative to other plasmonic technologies. Recently, fiber in- and out-coupling of radiation guided by DLSPPWs using intermediate linearly tapered dielectric waveguide was realized at telecom wavelength [8]. Subsequently, development of fiber-coupled DLSPPW-based components, such as Mach-Zehnder interferometers, waveguide-ring resonators and directional couplers, whose operation at telecom wavelength is controlled via the thermo-optic effect by electrical signals transmitted through the same gold strips that support dielectric ridge of DLSPPWs was demonstrated [9]. In addition, partial propagation loss compensation using optical pumping was also achieved in DLSPPWs [10]. All these remarkable achievements make the DLSPPW configuration one of the most promising plasmonic technologies.

In this work, we extend further the DLSPPW-based portfolio of available functionalities by demonstrating the DLSPPW mode power monitoring realized via measuring variations in the resistance of metal stripes (supporting DLSPPW ridges) caused by heating due to the mode absorption, turning thereby inevitable propagation losses (damping) in plasmonic waveguides into a useful functionality. The DLSPPW power monitor is fabricated and characterized at telecom wavelengths exhibiting the µW-sensitivity, responsivities of up to ~1.8 µV/µW (for a bias voltage of 1 V) and a flat frequency response in the range of 50-550 Hz. Comparing to LRSPP-based power monitors [11], we obtain significant improvements in terms of the monitor length (being reduced from 1 mm to just 46 µm) and its responsivity, which is increased by ~20 times due to a reduction in the waveguide cross section. We also discuss possibilities for further improvement of the DLSPPW power monitor characteristics.

2. Operation principle

The operation principle of the investigated power monitor is similar to that explored before with long-range SPPs [11]. Let us consider the DLSPPW configuration with a polymer stripe of thickness d and width w on top of a metal layer of thickness t [Fig. 1(a) ], which transmits an SPP mode with power P(x), with x being the coordinate along the propagation direction.

 

Fig. 1 (a) Schematic representation of the end-fire in/out coupling arrangement [8] showing cleaved single-mode optical fibers and a fabricated sample with a polymer ridge and a gold stripe. (b) Schematic depth cross section of a DLSPPW interfaced via tapers with ridge optical waveguides. (c) Schematic layout of the investigated power monitor, with a microscope image of the actual structure (containing a 1-µm-wide PMMA ridge placed on a 4-µm-wide gold stripe) being incorporated, using a Wheatstone bridge configuration with the bias voltage being applied between internal (a) and external (c) contacts. The signal voltage is measured between internal (b) and external (d) contacts.

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In the steady-state regime the SPP power absorbed by the metal stripe is dissipated into the top polymer ridge provided that the substrate thermal conductivity is significantly smaller than that of the polymer (the most favorable case for the considered power monitoring). The power dissipated per unit length can then be evaluated as $Q~\kappa \Delta Tw/d$, where κ is the polymer thermal conductivity and $\Delta T$ is the increase of the metal stripe temperature due to the absorption of the SPP mode power, resulting in the following estimate [11]:

Here, ${\alpha }_{abs}$ is the coefficient of SPP absorption by the metal stripe, $P_{in}$ is the power coupled in the SPP mode and ${\alpha }_{pr}$ is the SPP attenuation coefficient that can, in principle, have also other contributions, e.g. from the SPP mode scattering by waveguide imperfections. Note that, in this case, the heat dissipation is considered to be one-sided (instead of the symmetrical two-sided dissipation considered previously for long-range SPPs [11]), because of the potential possibility of choosing different materials for a substrate and a ridge. The temperature rise causes an increase in the metal resistivity and, consequently, in the stripe resistance that can be evaluated using Eq. (1) as follows

Here, L is the length of the considered metal stripe and ${\alpha }_{th}$ is the thermal resistance coefficient of metal. It is clearly seen [Eq. (2)] that the resistance increases linearly with the in-coupled power and, thereby, with the transmitted SPP power. This allows measurements of the metal stripe resistance (or its variations) for the purpose of monitoring of the transmitted SPP power.

In our experiments [Fig. 1(c)], an external Wheatstone bridge configuration was used to monitor changes in the DLSPPW gold stripe resistance. For the balanced bridge being constructed to ensure the maximum response of the Wheatstone bridge, i.e., when $R_1=R_2=R_3=R_4^0$ with the latter resistance being that of the DLSPPW metal stripe in the absence of the SPP radiation [11], the signal voltage can be expressed using Eq. (2) as follows

3. Experimental arrangement

The waveguide structures were fabricated by deep UV lithography (wavelength of ~250 nm) with Süss Microtech MJB4 mask aligner in the vacuum contact mode. Poly-methyl-methacrylate (PMMA) resist of thickness ~1 µm was spin-coated on a (~750-µm-thick) magnesium fluoride (MgF₂) substrate containing a patterned 50-nm-thick gold film. The fabricated sample contained a 1-µm-wide PMMA ridge forming a straight DLSPPW connected (via funnel structures of ~25 µm in length) on both sides to 10-µm-wide (purely dielectric) ridge polymer waveguides (RPWs) outside the gold region [Fig. 1(a)]. Funnel structures were used to efficiently interface the DLSPPW mode and the RPW (fundamental) modes that were interfaced in turn at the sample facets with the fundamental modes of single-mode polarization-maintaining (PM) fibers employed for in- and out-coupling of laser radiation. The width of access RPWs was chosen to be 10 µm in order to match with the dimension of a single-mode fiber of core diameter of ~10 µm [8]. The final step of the fabrication process was a cleavage of the sample perpendicular to the RPWs resulting in ~2-mm-long access RPWs leading towards each side of the DLSPPW area. It should be mentioned that the edge quality of the cleavage affects the level of coupling loss for end-fire coupling. For the Wheatstone bridge arrangement, ultrasonic wire bonding was used to connect aluminum wires to ~200 × 500 µm² bonding pads on the sample. These wires were then connected to the (external) Wheatstone bridge resistors having the resistance close to the estimated resistance (~49 Ω) of a 4-µm-wide and 46-µm-long DLSPPW gold stripe (whose resistance was to be monitored [Fig. 1(c)]. It should be noted that the straight DLSPPW section was electrically isolated from the funnel structures with 1.5-µm-wide gaps. These gaps introduce additional scattering loss which is yet to be quantified.

4. Optical characterization

The adjustment of the in-coupling PM fiber with respect to the input RPW was accomplished by monitoring the output facet of the sample with the help of far-field microscopic arrangement. The mode field diameter of 1-µm-thick and 10-µm-wide RPWs is well matched with that of a standard PM single-mode fiber used in this experiment [8]. The overall, i.e. fiber-to-fiber, power loss was found to be at the level of ~55 dB for the wavelength range of 1450-1525 nm, which was significantly larger than the loss measured previously with the DLSPPWs placed on an unstructured 100-µm-wide gold stripe [8] but of the same order of magnitude as the loss obtained with the thermo-optic DLSPPW-based components [9]. Considering the propagation loss (~12 dB at λ ≈1550 nm) calculated for 100-µm-long DLSPPWs [13] and corroborated in our experiments [8], the propagation loss in the straight DLSPPW section used for power monitoring can be estimated to be ~5 dB. Other factors contributing to the insertion loss are the fiber-RPW and RPW-DLSPPW coupling losses as well as the gap between DLSPPWs and funnel structure. The amount of the fiber-RPW coupling loss can be significantly reduced by improving the quality of RPW cleaved edges and also by using an in-coupling fiber with smaller diameter. Some improvements are also expected for the RPW-DLSPPW coupling when properly adjusting the PMMA thickness [8].

The responsivity of the investigated power monitor was evaluated by first balancing the Wheatstone bridge in the absence of the DLPPW excitation and then measuring the signal voltage for different laser powers and at different wavelengths (Fig. 2 ). The input power to the DLSPPW was evaluated, using the measured fiber-to-fiber loss and arriving at the conversion factor of 22 dB, to be in the range of µW, showing a high sensitivity of the power monitor. It should be mentioned that the Wheatstone bridge was practically impossible to perfectly balance mainly because of small variations in the resistance of different arms, most probably due to temperature fluctuations. Nevertheless, changes in the signal voltage were found linear with respect to the input laser power, showing the possibility of monitoring the (DLSPPW mode) power-induced changes in the stripe resistance (Fig. 2). The slope of the response, which defines the responsivity of the power monitor, was observed to increase with the wavelength. The possible reason for this behavior is that the actual power delivered to the DLSPPW was different at different wavelengths mainly because of variations in the fiber-RPW and RPW-DLSPPW coupling efficiencies. It should be mentioned that the units to represent the responsivity, e.g., 1.8 µV/µW at 1525 nm, were chosen to emphasize the range of measurements performed.

 

Fig. 2 Signal voltage measured as a function of the input (with respect to the DLSPPW) optical power (P_in), whose level was estimated from the insertion fiber-to-fiber loss, for the bias voltage of 1 V at three different wavelengths. Slopes of linear fits to the experimental data provide the responsivity for each wavelength.

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The responsivity of the considered DLSPPW-based power monitor can be estimated with the help of Eq. (3). Using the typical DLSPPW propagation loss${\alpha }_{pr}~2\cdot {10}^{-2}$µm⁻¹ [8], thermal resistance coefficient ${\alpha }_{th}~3\cdot {10}^{-3}$K⁻¹ for gold [14], polymer thermal conductivity $\kappa ~0.2$ W/mK [15], d = w = 1 µm and L = 46 µm, we evaluate the power monitor responsivity to be ~49 µV/µW for the bias voltage of 1 V. The difference between this value and one that obtained from the experiment is primarily due to the approximation of one-sided heat dissipation used when obtaining Eq. (1), whereas in the current realization the heat generated in the gold stripe dissipates also in air and, most importantly, into the MgF₂ substrate, whose thermal conductivity is 130 times larger than that of PMMA [15]. This circumstance entails that the main amount of heat is dissipated into the substrate with a huge thermal capacity as compared to the PMMA ridge, decreasing drastically the steady-state temperature of the DLSPPW and its gold stripe. This situation represents thereby the worst case scenario instead of the most favorable case considered when deriving the above relations [Eqs. (1-3)]. It should be emphasized here that the choice of MgF₂ was dictated by the availability of a low refractive index (~1.37) substrate in order to ensure efficient guiding by RPWs [8], an important requirement for the realization of fiber-to-fiber transmission characterization. Note that, even in this case, the measured responsivity was significantly larger (by ~20 times) than that obtained previously with long-range SPP waveguides [11].

The power monitor responsivity of 1.8 µV/µW measured at λ = 1525 nm for the bias voltage of 1 V implies that a signal voltage of ~0.2 mV will be obtained by using a moderate optical power of 1 mW and bias voltage of 0.1 V. Such a voltage should be possible to measure reliably, because the thermal noise limit is much smaller: $\delta V~4{\left(kTR\Delta f\right)}^{0.5}$~0.6 µV, where k is the Boltzman’s constant, R is estimated to be ~49 Ω, T ~300 K is the resistor temperature and $\Delta f$ = 1 kHz, which is a typical measurement bandwidth used with thermo-optical components [3]. Modulation response of the power monitor was studied by chopping the input laser light at various frequencies with the signal voltage being measured by a lock-in amplifier (Fig. 3 ).

 

Fig. 3 Signal voltage as a function of the frequency of modulation of the input laser radiation. Duty ratio of 50% was kept constant through the conducted measurements.

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It was observed that the signal voltage level for low (< 50 Hz) and high (> 550 Hz) frequencies is strongly frequency dependent, indicating the occurrence of two rather different in speed processes: very slow heating of the substrate (time constant of a few seconds [9]) and (relatively) fast heating of the polymer ridge (and environmental air as the gold stripe width is larger than that of polymer ridge). This non-monotonous behavior might represent problems for power monitoring of varying in time radiation. However, we should emphasize that the situation can be radically changed by using another low-index substrate material instead of MgF₂, for example a low-index polymer. Yet another possible strategy might be to make use of a recently reported silicon-on-insulator (SOI) configuration for DLSPPWs, in which efficient in- and out-coupling between SOI photonic waveguides and DLSPPWs was successfully realized [16]. In this configuration, a gold film is placed directly on a silica layer, whose thermal conductivity is significantly smaller than that of MgF₂ [15].

5. Conclusions

We have demonstrated a method to monitor the transmitted SPP mode power in DLSPPW-based components. Our approach takes advantage of the inevitable DLSPPW mode absorption by an underlying metal stripe that results in the stripe heating and, consequently, its resistance change. The method being similar to that reported previously for long-range SPP waveguides [11] is based on stripe resistance measurements using a Wheatstone bridge configuration. The investigated waveguide configuration consisted of a 1-µm-thick and 10-µm-wide polymer ridges tapered laterally to a 1-µm-wide ridge placed on a 50-nm-thin and 4-µm-wide gold stripe supported by MgF₂ substrate. Using single-mode polarization-maintaining fiber for in- and out-coupling of radiation, the DLSPPW mode power monitoring at telecom wavelengths has been realized with the responsivities of up to ~1.8 µV/µW (for a bias voltage of 1 V) showing weak wavelength dependence. The investigated power monitor has exhibited a flat frequency response in the range of 50-550 Hz. It should be noted that the above characteristics can be significantly improved by using another (than MgF₂) substrate material with a lower thermal conductivity.

The demonstrated power monitoring extends further the existing and already impressive portfolio of DLSPPW-based photonic functionalities, which includes passive [12], active [10] and wavelength-selective components [17], fiber-coupled thermo-optically controlled devices [9] and SOI-based waveguide-ring resonators interfaced with photonic waveguides [16]. We would like to emphasize that the demonstrated power is fundamentally noninvasive, and can be conducted in any place of a plasmonic circuit and operated even in parallel with other means of radiation control [9]. In the context of DLSPPW-based photonic circuits, optical power monitors combined with wavelength-sensitive thermo-optic components can make it possible to selectively block or equalize one or more of the signal channels dynamically, performing thereby internally control of the transmitted optical power, e.g. variable optical attenuation. Recent development of SOI-based DLSPPW components [16] might provide a way of introducing DLSPPW-based plasmonics into the SOI photonics platform, making the realization of on-chip plasmonic devices feasible.