Fascinating phenomena have been demonstrated in plasmonic materials due to their enhanced light–matter interaction and high sensitivity. Surface plasmon resonance (SPR), where resonance is obtained for a specific combination of angle and wavelength of the incident light, is of particular interest for sensing applications, but is somewhat limited due to its relatively broad resonance line and the lack of referencing to a known source of absolute resonance. We mitigate these deficiencies by exploiting the coupling between plasmonic and molecular resonance in a hybrid device consisting of SPR and acetylene. The coupled system inherits the angular sensitivity, enhanced light–matter interactions, and miniaturization of the SPR, while the acetylene provides a narrow and accurate resonance in the telecom band. These qualities make our hybrid system very sensitive to minute variations in the incident angle. SPR is very sensitive to refractive index variations that originate from the highly dispersive nature of acetylene. Combined with the narrow transition line of acetylene in the telecom band, this allows for the generation of a feedback signal for laser stabilization in a miniaturized volume. Taking advantage of these properties, we have stabilized a telecom laser to our hybrid system with a precision better than 300 kHz at 100 s. Furthermore, we have used the high sensitivity and accuracy to demonstrate an angular sensor with angular resolution on the order of microradians. The ability to demonstrate a hybrid plasmonic–molecular coupled system in the telecom regime may enable a variety of other applications, such as chip-scale advanced spectroscopy, metrology, and chip-scale light sources.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
In the last few years, there has been a growing interest in plasmonic devices due to their inherent advantages (e.g., the ability to confine light at the nanometer scale) [1–13]. The enhanced electromagnetic field in close proximity to metallic surfaces allows the observation of fascinating effects, such as strong nonlinear interactions [14–19], an enhanced spontaneous emission rate [20–22], and local interactions with single quantum emitters [23–25], to name a few. Plasmonic effects are also very attractive for sensing applications [26–30], especially surface plasmon resonance. Unfortunately, the performance of such devices may be limited by the high ohmic losses resulting in very broad resonances. Furthermore, the plasmonic resonance is affected by environmental conditions that make such plasmonic devices less useful for applications where high accuracy is needed (e.g., in frequency referencing and atomic clocks). Clearly, there is great motivation to improve the performance of such devices [31,32].
In contrast, gas molecules such as acetylene ()  and carbon monoxide (), and alkali atomic vapors such as rubidium  and cesium are characterized by their narrow transition linewidths and high accuracy. While molecular transition can be affected by temperature and pressure variations, once the acetylene is sealed in a reference cell at room temperature, its pressure is quite stable and variations in the optical transition due temperature-driven pressure variations are small . As such, they are often used as frequency standards (e.g., for the stabilization of lasers). Laser stabilization is being used for applications such as atomic clocks [36–38], spectrum analyzers , and metrology [40,41]. In the past few years, we have observed a massive effort toward the integration and miniaturization of atomic vapor cells in the form of integrated nanophotonic–atomic devices, such as the atomic cladded wave guide (ACWG) [42,43], the atomic cladding microring resonator (ACMRR) [44–46], atomic cladded Mach–Zehnder interferometer , antiresonant reflecting optical waveguides (ARROW) , and hollow core fibers . A coupled plasmonic–atomic device has also been presented [17,50]. While atomic vapors such as rubidium satisfy the need for stabilized sources in the near-infrared frequency regime (e.g., around 780 nm wavelength for rubidium), there is a great need to stabilize the light sources at the telecom regime and, for this purpose, the acetylene molecule is typically used as a reference source. The acetylene band offers a grid of absorption lines covering most of the telecommunications band. Indeed, hollow-core photonic crystal fibers filled with acetylene have been used to demonstrate molecular spectroscopy in the telecom regime [51–53].
Here, we combine the advantages of the acetylene molecule to achieve an accurate and narrow linewidth in the telecom band and the merits of plasmonics to achieve high sensitivity, strong field confinement, and enhanced light–matter interactions at the nanoscale to demonstrate for what we believe is the first time an integrated coupled plasmonic–acetylene system. By doing so, we greatly enhance the performance of the SPR system, while keeping the interaction length of light with matter as short as possible, supporting the miniaturization of our integrated device. The capability to control the narrow line shape of the coupled system combined with the ability to monitor minute changes using the stabilization of lasers at the telecom regime makes our approach of plasmonic-enhanced light–molecular interaction in a gaseous phase a particular appealing one.
Following the experimental demonstration of the operation concept, we demonstrate the two prominent applications: the stabilization of a laser source to the Fano signal, which provides laser stability better than 0.3 MHz; and an angular sensor, operating on the basis of the linkage between the angle and wavelength of resonance, combined with our new ability to stabilize the laser to the Fano line shape that is detuned due to angular detuning in the SPR. Based on this approach, we have demonstrated angular resolution better than 5 microradians.
Fabrication—Our integrated plasmonic–molecular device is illustrated in Fig. 1(a). Light is coupled to a SPR mode, having its evanescent tail expanding beyond the metal layer and interacting with the acetylene gas molecules. The device consists of a 5 nm adhesion layer of Cr evaporated on a glass prism , followed by a 30 nm thick layer of evaporated gold. Given the fact that gold is a known catalyst , a 5 nm thick protection layer of is evaporated on top of the gold layer. Next, a glass chamber is epoxied  to the prism. Finally, the chamber is vacuum sealed, acetylene (50 Torr of ()) is inserted, and the cell is pinched off. The end result of this process in a standalone portable device can be seen in Fig. 1(b).
Experimental setup—The measurement setup is depicted in Fig. 1(c). The device is excited by a tunable laser in the telecom regime by using the Kretschmann configuration. We interrogate the R9 line of acetylene [1520 nm, Fig. 1(d)]. The laser beam is collimated, and its polarization is controlled via a half-wave plate to ensure transverse magnetic (TM) polarization excitation.
The interaction of light with the acetylene molecules in our system is modeled by calculating the susceptibility of a quantum emitter that is reflected from a surface with a decaying field, following [56,42]. This approach results in a Voight-like absorption profile. The linewidth is affected by three major broadening mechanisms: 1—Doppler broadening, defined as , where (430 m/s) is the most probable velocity of acetylene at room temperature (295 K) and is the wave numbers of the plasmonic mode along the propagation direction; 2—Pressure broadening, estimated as , which can be approximated as 650 MHz; and 3—Transit time broadening, which is the result of the finite interaction time between the molecule and the plasmonic evanescent field giving rise to spectral broadening. The evanescent decay length is deduced from , which is the mode wavenumber in the transverse direction. Before calculating the susceptibility, we first need to extract the surface plasmon polariton (SPP) wave vector. In fact, can be evaluated by attenuated total internal reflection formalism [57,58], neglecting the presence of the acetylene molecule. is given by and is found as , where is the incident angle, is the refractive index of acetylene, and is the refractive index of the glass prism. This perturbative approach can be easily justified by the low molecular pressure. Using the above-mentioned procedure, the effective refractive index of the SPR mode is found to be 1.008 and the evanescent decay length is about 1 μm. Having the plasmonic mode wave vector in hand, we can now calculate the Doppler and transit time broadened linewidths, which are found to be and 30 MHz, respectively. The combination of all, according to the Voight profile, can be calculated according to , where is the Voigt linewidth, is the Lorentzian linewidth corresponding to the homogeneous broadening, and is the Gaussian linewidth corresponding to the Doppler broadening. This results in a total linewidth of about 950 MHz. More in-depth discussion is provided in Supplement 1.
Having the refractive index of acetylene in hand, we can now use the attenuated total internal reflection formalism to deduce the transmission of our integrated plasmonic–molecular device by calculating the reflection coefficient from our four-layer structure (acetylene, , Au, and Cr) and BK-7 prism. The refractive index of gold was taken to be .
In Figs. 2(a)–2(c), we present computer simulations of the predicted light transmission obtained at three different incident angles. The angle for which the transmission is at a minimum is defined as 0 [Fig. 2(d)]. As can be observed, we can obtain a dispersive-like line profile, with the specific shape strongly depending on the incident angle with respect to the plasmonic resonance. Thus, by slightly tuning the incident angle, it is possible to significantly control the obtained spectral transmission. This is an important degree of freedom that will be further discussed later in this paper.
The interaction between the narrow resonance of acetylene and the broad plasmonic resonance can also be explained in terms of the Fano line shape. While the original paper by Fano  describes the interaction between a narrow resonance and the continuum, it was shown that similar arguments can also be used for predicting the interaction between a discrete state and a broad resonance, as was discussed in [17,62,63]. The interaction between molecular and plasmonic systems [64–66] has been used to evaluate molecular properties and plasmonic device properties, taking advantage of the coupling between the two systems. To clarify the flexibility of our platform in controlling the Fano response on demand, we provide a detailed discussion (see Supplement 1), where we show that the three regimes predicted by Fano, namely anomalous dispersion, symmetric line shape, and normal dispersion can all be observed in our system simply by tuning the angle of incidence.
Another way of looking at our hybrid system is from the point of view of an SPR sensor. When the incident angle is detuned from resonance, the transmission line shape [Figs. 2(a) and 2(c)] resembles the real part of the acetylene refractive index [Fig. 2(e)]. On the other hand, when the incident angle is tuned to the plasmonic resonance, the transmission line shape [Fig. 2(b)] resembles the imaginary part of the refractive index [Fig. 2(f)]. In fact, when the incident angle is tuned to resonance, a minute change of in the imaginary or the real part of the refractive index will modify the normalized transmission by or , respectively. On the other hand, when the angle is detuned to from resonance, the same change will modify the transmission by or , respectively. Thus, at zero angle detuning from resonance, the SPR sensor is more sensitive to changes in the imaginary part of the refractive index. However, when the angle is detuned from resonance, higher sensitivity to variations in the real part of the refractive index is observed.
Interestingly, for zero detuning we observe the symmetric line shape presented as a peak instead of an absorption dip as would be expected in a stand-alone acetylene cell. While this might seem a bit surprising, one should always remember that the Fano line shape is a result of the interplay between two resonances and the line shape strongly depends on the coupling and damping in the system. Here, due to the high losses of the plasmonic optical mode, it is reasonable to assume that in most cases the SPR will be undercoupled (i.e., the loss of the plasmonic mode is larger than the coupling loss). By reducing the gold layer thickness, one can increase the coupling loss up to the point that overcoupling is achieved. To further study this latter issue, we have calculated the transmission of light through the hybrid system as a function of angle, assuming at zero detuning for the case of 30 nm gold layer thickness (undercoupling, red curve), and for the case where the gold thickness is reduced to 9 nm (overcoupled regime, blue curve), as can be seen in Fig. 3(a). We have also calculated the transmission for the two cases as a function of laser detuning at resonance angles [Fig. 3(b)], which are 42.2° for the undercoupled case and 43.65° for the overcoupled case.
In the case of undercoupling, the increase in the mode losses due to the acetylene absorption takes the system further away from critical coupling and the transmission becomes larger, in the form of an acetylene resonance peak. However, for the case of an overcoupled SPR, the increase in loss due to the acetylene absorption pushes the system toward critical coupling, and the overall transmission is reduced, as manifested by the dip in transmission. It is interesting to see the strong effect acetylene has on the coupling condition of the SPR [Fig. 3(b)]. Such effect could be very stimulating for slow and fast light research. In particular, having dispersive media integrated with SPR results in a dispersive-like coupling nature and slow/fast light effects. This also has been reported in other systems [67–69].
In Fig. 4, we present the measured transmission spectra of our hybrid plasmonic–molecular device, first as a function of the incident angle (panel a) and then as a function of the frequency detuning for three different incident angles (panels b–d, the angles are denoted as circles in panel a). As a reference, we have recorded simultaneously the acetylene absorption line using a reference acetylene cell (blue lines, not in scale in the axis). The three presented spectra correspond to the three different Fano conditions of anomalous dispersion symmetrical line shape and normal dispersion. The plasmonic resonance angle is defined as 0.
By comparing the measured results to the calculations (Fig. 2), one may observe that the measurements are very similar in their shape to the calculations. To further compare the two sets, we present in Fig. 5(a) more detailed set of measurements and computer simulations that clearly show the trend of gradually moving from a normal dispersion at negative angles to an anomalous dispersion in positive angles, through observing a symmetric line shape at a zero detuning angle. We can also observe that the shift in the transmission peak and the contrast is stronger at negative angles, which relates to the asymmetrical line shape of the SPR. While the measured and the simulated curves resemble each other in their shape, some discrepancy is observed, most probably due to the fact that the fabricated gold layer is of lower quality compared to the value we have used for the simulations. Furthermore, surface roughness was not taken into account. This is also in line with the extracted propagation length, which was found to be slightly lower than the simulated value (see discussion later in the paper).
After examining the light–molecule interactions and the line shape properties, we address potential applications for such a device. The first, and perhaps the most obvious choice, is to take advantage of the accuracy and the stability of acetylene absorption lines to demonstrate an integrated and miniaturized reference cell.
To address the above-mentioned application, we have measured the stability of our device by recording the beat note between two lasers, one stabilized to a reference acetylene cell (, R29) and the other to our plasmonic cell (, R9). Furthermore, we have compared the stability of our system to the stability of a free-running laser by beating it against the same reference acetylene cell (, R29). Finally, to estimate our optimum locking accuracy, we have recorded the beat note between the reference acetylene cell and another reference acetylene cell (, R9). We have set the incident angle to 0 (defined as the plasmonic resonance angle) to achieve the highest contrast. The experimental setup used to lock the lasers is presented in Fig. 6(a).
The measured stability over time is presented in Fig. 6(b) as an Allan variance scheme. As can be seen, the laser that is locked to our cell shows an order of magnitude improvement in stability as compared to the free laser, and the obtained instability goes down below 0.3 MHz () (see the pink curve as opposed to black curve). Such a stability level is already sufficient for a large variety of applications, such as wavelength division multiplexing (WDM) [70–72]. Considering the significant miniaturization, such an achievement should not be underestimated. While this result is a significant step forward, however, there is still room for further improvement. As a reference, the same locking approach was used to achieve instability lower than 40 kHz, using a large cell as a reference. One of the major parameter that can be further improved is the temperature stability. In fact, in SPR-based systems, temperature fluctuations are translated to fluctuations in the SPR angular or wavelength spectrum and, as a result, affect the obtained response. We have simulated the effect of temperature fluctuations, taking into account the thermo-optic coefficient of glass to be , and also considering the temperature-dependent plasma frequency of gold . The simulation results are depicted in Fig. 7. In Fig. 7(a), we show the effect of temperature deviation on the Fano line shape, whereas in Fig. 7(b) we plot the spectral shift of the peak as a function of temperature variation. As can be seen, a frequency drift of is expected. Thus, our measured instability implies temperature fluctuations of the order of 0.2 deg in 100 s.
Clearly, the stability of our system can be further improved by thermal stabilization. Temperature stabilization down to 3 [mK] is feasible  and, based on the above discussion, will result in frequency fluctuations of less than 5 kHz. In such a case, thermal stability will no longer be a limiting factor. Another relevant parameter is the resonance linewidth. Frequency stabilization is directly related to the resonator’s factor, according to the Allan deviation equation in a shot-noise-limited region, , where is the factor, is the signal, is the noise, and is the averaging time. Pressure broadening affects the linewidth of our device. Reducing the pressure will reduce the gas density and result in a narrower line. On the other hand, lower pressure will unfortunately lead to a lower signal contrast. The two effects will counteract each other and would not result in a significant improvement, if any. The signal can be increased by increasing the propagation length of the plasmon. Our signal contrast corresponds to a propagation length of 75 μm, while the theoretical propagation length of such a mode is 114 μm, considering the effective index of gold we took in our simulation () that has shown better contrast than our measurement. The resonance effects allow us to get a long propagation length in a small volume and can be improved by depositing high-quality Au layers, which will result in less Ohmic losses and higher factors.
Another source of instability is related to mechanical fluctuations, which may affect the incident angle and thus will modify the system’s response. While these instabilities are undesirable for applications such as frequency stabilization, the sensitivity to a slight change in the incident angle and the temperature can be used for an angular sensor or a temperature sensor. Such sensors could offer superior performance compared to bare plasmonic systems. To demonstrate this feature, we have measured the beat signal between a laser locked to our hybrid plasmonic–molecular system and a laser locked to a reference cell as a function of incident angle. The obtained results are shown in Fig. 8.
While the shift in frequency is not linear with the angle, for small deviations from the angle of plasmonic resonance, the sensitivity can be estimated as . This factor, combined with the high-frequency stability of more than 300 kHz at 100 s, translates to an angular resolution better than 0.25 milli degree (4.4 μRad).
As seen in Fig. 5, the signal contrast decreases as we detune the system further away from the SPR resonance. This result is expected to affect our ability to lock the system. Another important parameter is the angular window of operation (i.e., the range of detuning angles for which the change in peak frequency is still linear with angle detuning). Next we discuss these issues in detail.
Our Fano-like signal can be simply considered as a derivative of the narrow resonance (acetylene) by the broad resonance (SPR). As such, to obtain the largest detuning range for which the shift is still linear with detuning, one should seek a signal with a parabolic-shaped resonance. Unfortunately, SPR does not have a parabolic line shape and thus the change in the peak frequency of the signal is not linearly varying with the angle. Furthermore, the contrast of the signal is not constant. Instead, the contrast is decreasing as the angle is detuned from resonance due to a simple reason: One must couple light into the acetylene to probe its response. Clearly, as we detune away from the plasmonic resonance, no light is coupled into the surface waves and the acetylene cannot be probed. Obviously, the factor of the signal will also be affected by the line shape.
To explore the operation range and the linearity of our device, we have simulated its performance, assuming a gold layer with a refractive index of . This previously published value was found to provide an SPR line shape that closely resembles our measurements. The simulation results are displayed in Fig. 9. Three values of gold layer thicknesses have been considered, 25 nm (solid blue), 30 nm (solid, red representing the gold thickness found in our device), and 35 nm (solid green). Furthermore, to estimate what could be the results assuming a gold layer with optimal quality would have been used, we have repeated these simulations assuming a better (yet realistic) layer of gold () . For the latter, we have assumed gold layer thicknesses of 35 nm (dashed blue), 40 nm (dashed red), and 45 nm (dashed green).
In Fig. 9(a) we plot the calculated SPR resonances. As can be seen, the factor can be improved by a factor of about 2 by evaporating a layer of gold with optimal quality. In Fig. 9(b), we plot the calculated contrast of our Fano signal for the devices. Our current device achieves a contrast of about 6, whereas an optimal gold layer is shown to be helpful, increasing the contrast by nearly threefold. We can also observe that by decreasing the gold width we increase the coupling losses and, as explained earlier, gets closer to critical coupling. In such a case, more light is coupled to the mode and a higher contrast is obtained. These results point toward a clear path to improve our device, simply by optimization of the gold layer’s quality and thickness. In Fig. 9(c) we present the peak position as a function of the detuning angle alongside a linear fit to the curve (black dots). One can clearly observe that, for small angle variations in the range , the change in the peak position as a function of the angle is linear for our device. For the set of devices with an optimal layer of gold (dashed lines), a high sensitivity is obtained, up to 11 GHz/degree, at the expense of a reduced range of linearity now estimated to be within the angle detuning of from resonance. To better estimate the implications on our capability to lock the system at these various detuning angles, we define a merit function of “locking factor” given by the contrast divided by the full width at half maximum (FWHM) of the signal. In fact, it can be shown that this parameter is proportional to the multiplication , which is inversely proportional to our frequency instability. The results are presented in Fig. 9(d). As can be seen, the locking factor of our simulated device shows a FWHM of about 0.1 deg while the devices with higher factor will mostly show a FWHM of about 0.035 deg. These values define the range of angles that can be measured without a significant decrease in the locking stability. Not surprisingly, we observe the conservation of the sensitivity-angular bandwidth product. A device with a better factor will show higher sensitivity at the expense of a narrower angular bandwidth. We thus conclude that if one is seeking a large angular bandwidth, the factor should be moderate, and the limited sensitivity should be compensated for using high-quality locking setups and a high signal-to-noise ratio. On the other hand, if the signal-to-noise ratio is limited, it is still possible to track the angle with high precision, at the expense of limited angular bandwidth.
Following the obtained results and the discussion above, the practical angular bandwidth of our device is about 0.1°, and the angular resolution is about 0.25 milli degree. Further improvement in locking quality and further noise reduction is expected to provide even better angular resolution. These improvements, together with improving the factor of the SPR, will make our device even better in its performance compared to other SPR- and prism-based angular sensors [28,77]. Similar to our approach, these techniques are also limited by nonlinearity and contrast reduction as the angle is detuned from resonance. Even more so, these techniques are based on two prisms rather than one, which makes their implementation more cumbersome and less stable.
We have demonstrated a hybrid plasmonic–molecular device based on an SPR configuration integrated with an acetylene cell. The approach allows degrees of freedom in controlling the obtained line shape in the form of a Fano response. In fact, the line shape can be easily switched from normal dispersion to an anomalous dispersion of transmission simply by tuning the angle of incidence. Unlike a conventional SPR, where a dip in transmission is observed at the critical angle, here we can demonstrate a peak in transmission due to the interplay between coupling and loss. Essentially, the additional absorption of the acetylene shifts the system to be under-coupled, and thus higher transmission is obtained.
Following the fundamental demonstration of line shape control, we have also demonstrated two potential applications. First, taking advantage of the narrow resonance line of acetylene and its absolute accuracy, and combined with the flexibility and field enhancement of plasmonics, we have used our hybrid approach to stabilize telecom band lasers to a level better than 300 kHz at 100 s. This paves the way toward using our device in applications such as wavelength division multiplexing (WDM). We have also demonstrated the usefulness of our device as an angular sensor, having resolution in the microradians regime. Such merits could not be achieved by a stand-alone plasmonic device due to its relatively broad linewidth. On the other hand, the use of acetylene by itself, without being combined with a plasmonic device, lacks the properties of angular sensitivity, field enhancement, a high degree of control over the line shape, and enhanced light–matter interactions. It is therefore the hybridization of the two disciplines that we believe makes our device unique from the fundamental point of view and attractive from the application standpoint. One possible application that can benefit from the angular sensitivity and the accuracy of acetylene is the angular stabilization of mechanical systems. It should also be mentioned that the degree of control over the narrow line shape may become helpful in studying other fundamental phenomena and addressing additional applications (e.g., slow light and electromagnetically induced transparency).
H2020 European Research Council (ERC) (ERC-LIVIN 648575); Israeli Ministry of Science and Technology.
See Supplement 1 for supporting content.
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