Enhanced light–matter interactions inplasmonic–molecular gas hybrid systemROY ZEKTZER, LIRON STERN, NOA MAZURSKI, AND URIEL LEVY*Department of Applied Physics, The Benin School of Engineering and Computer Science, The Center for Nanoscience and Nanotechnology,The Hebrew University of Jerusalem, Jerusalem 91904, Israel*Corresponding author: ulevy@mail.huji.ac.il

Received 7 December 2017; revised 13 March 2018; accepted 27 March 2018 (Doc. ID 315249); published 18 April 2018

Fascinating phenomena have been demonstrated in plasmonic materials due to their enhanced light–matter interac-tion and high sensitivity. Surface plasmon resonance (SPR), where resonance is obtained for a specific combination ofangle and wavelength of the incident light, is of particular interest for sensing applications, but is somewhat limiteddue to its relatively broad resonance line and the lack of referencing to a known source of absolute resonance. Wemitigate these deficiencies by exploiting the coupling between plasmonic and molecular resonance in a hybrid deviceconsisting of SPR and acetylene. The coupled system inherits the angular sensitivity, enhanced light–matter inter-actions, and miniaturization of the SPR, while the acetylene provides a narrow and accurate resonance in the telecomband. These qualities make our hybrid system very sensitive to minute variations in the incident angle. SPR is verysensitive to refractive index variations that originate from the highly dispersive nature of acetylene. Combined with thenarrow transition line of acetylene in the telecom band, this allows for the generation of a feedback signal for laserstabilization in a miniaturized volume. Taking advantage of these properties, we have stabilized a telecom laser toour hybrid system with a precision better than 300 kHz at 100 s. Furthermore, we have used the high sensitivity andaccuracy to demonstrate an angular sensor with angular resolution on the order of microradians. The ability to dem-onstrate a hybrid plasmonic–molecular coupled system in the telecom regime may enable a variety of other appli-cations, 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

OCIS codes: (020.0020) Atomic and molecular physics; (250.5403) Plasmonics; (240.6680) Surface plasmons; (020.3690) Line shapes

and shifts; (140.3425) Laser stabilization; (130.6010) Sensors.

https://doi.org/10.1364/OPTICA.5.000486

1. INTRODUCTION

In the last few years, there has been a growing interest in plas-monic devices due to their inherent advantages (e.g., the abilityto confine light at the nanometer scale) [1–13]. The enhancedelectromagnetic field in close proximity to metallic surfaces allowsthe observation of fascinating effects, such as strong nonlinearinteractions [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 attractivefor sensing applications [26–30], especially surface plasmon res-onance. Unfortunately, the performance of such devices may belimited by the high ohmic losses resulting in very broad resonan-ces. Furthermore, the plasmonic resonance is affected by environ-mental conditions that make such plasmonic devices less usefulfor applications where high accuracy is needed (e.g., in frequencyreferencing and atomic clocks). Clearly, there is great motivationto improve the performance of such devices [31,32].

In contrast, gas molecules such as acetylene (12C2H2) [33] andcarbon monoxide (12C16O), and alkali atomic vapors such as

rubidium [34] and cesium are characterized by their narrow tran-sition linewidths and high accuracy. While molecular transitioncan be affected by temperature and pressure variations, once theacetylene is sealed in a reference cell at room temperature, its pres-sure is quite stable and variations in the optical transition due tem-perature-driven pressure variations are small [35]. As such, they areoften used as frequency standards (e.g., for the stabilization oflasers). Laser stabilization is being used for applications such asatomic clocks [36–38], spectrum analyzers [39], and metrology[40,41]. In the past few years, we have observed a massive efforttoward the integration andminiaturization of atomic vapor cells inthe form of integrated nanophotonic–atomic devices, such as theatomic cladded wave guide (ACWG) [42,43], the atomic claddingmicroring resonator (ACMRR) [44–46], atomic cladded Mach–Zehnder interferometer [47], antiresonant reflecting optical wave-guides (ARROW) [48], and hollow core fibers [49]. A coupledplasmonic–atomic device has also been presented [17,50].While atomic vapors such as rubidium satisfy the need for stabi-lized sources in the near-infrared frequency regime (e.g., around

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780 nm wavelength for rubidium), there is a great need to stabilizethe light sources at the telecom regime and, for this purpose, theacetylene molecule is typically used as a reference source. Theacetylene ν1 � ν3 band offers a grid of absorption lines coveringmost of the telecommunications band. Indeed, hollow-core pho-tonic crystal fibers filled with acetylene have been used to demon-strate molecular spectroscopy in the telecom regime [51–53].

Here, we combine the advantages of the acetylene molecule toachieve an accurate and narrow linewidth in the telecom band andthe merits of plasmonics to achieve high sensitivity, strong fieldconfinement, and enhanced light–matter interactions at thenanoscale to demonstrate for what we believe is the first timean integrated coupled plasmonic–acetylene system. By doingso, we greatly enhance the performance of the SPR system, whilekeeping the interaction length of light with matter as short as pos-sible, supporting the miniaturization of our integrated device.The capability to control the narrow line shape of the coupledsystem combined with the ability to monitor minute changesusing the stabilization of lasers at the telecom regime makesour approach of plasmonic-enhanced light–molecular interactionin a gaseous phase a particular appealing one.

Following the experimental demonstration of the operationconcept, we demonstrate the two prominent applications: the sta-bilization of a laser source to the Fano signal, which provides laserstability better than 0.3 MHz; and an angular sensor, operating onthe basis of the linkage between the angle and wavelength of res-onance, combined with our new ability to stabilize the laser to theFano line shape that is detuned due to angular detuning in theSPR. Based on this approach, we have demonstrated angular res-olution better than 5 microradians.

2. METHODS

Fabrication—Our integrated plasmonic–molecular device is illus-trated in Fig. 1(a). Light is coupled to a SPR mode, having its

evanescent tail expanding beyond the metal layer and inter-acting with the acetylene gas molecules. The device consistsof a 5 nm adhesion layer of Cr evaporated on a glass prism[15 × 15 × 15 mm3], followed by a 30 nm thick layer of evapo-rated gold. Given the fact that gold is a known catalyst [54], a5 nm thick protection layer of MgF2 is evaporated on top ofthe gold layer. Next, a glass chamber is epoxied [55] to the prism.Finally, the chamber is vacuum sealed, acetylene (50 Torr of(12C2H2)) is inserted, and the cell is pinched off. The end resultof this process in a standalone portable device can be seen inFig. 1(b).

Experimental setup—The measurement setup is depicted inFig. 1(c). The device is excited by a tunable laser in the telecomregime by using the Kretschmann configuration. We interrogatethe R9 line of acetylene [1520 nm, Fig. 1(d)]. The laser beam iscollimated, and its polarization is controlled via a half-wave plateto ensure transverse magnetic (TM) polarization excitation.

3. RESULTS

A. Simulations

The interaction of light with the acetylene molecules in our sys-tem is modeled by calculating the susceptibility of a quantumemitter that is reflected from a surface with a decaying field, fol-lowing [56,42]. This approach results in a Voight-like absorptionprofile. The linewidth is affected by three major broadeningmechanisms: 1—Doppler broadening, defined as Δω � kz · vAc,where vAc (430 m/s) is the most probable velocity of acetylene atroom temperature (295 K) and kz is the wave numbers of theplasmonic mode along the propagation direction; 2—Pressurebroadening, estimated as Δω � P�Torr� · 13�MHz∕Torr� [35],which can be approximated as 650 MHz; and 3—Transit timebroadening, which is the result of the finite interaction time be-tween the molecule and the plasmonic evanescent field giving riseto spectral broadening. The evanescent decay length is deducedfrom kT , which is the mode wavenumber in the transversedirection. Before calculating the susceptibility, we first need toextract the surface plasmon polariton (SPP) wave vector. In fact,k can be evaluated by attenuated total internal reflectionformalism [57,58], neglecting the presence of the acetylenemolecule. kz is given by 2π∕λn1n2 sin θ and kT is found asffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�n1 · 2π∕λ�2 − k2z

p, where θ is the incident angle, n1 is the re-

fractive index of acetylene, and n2 is the refractive index of theglass prism. This perturbative approach can be easily justifiedby the low molecular pressure. Using the above-mentioned pro-cedure, the effective refractive index of the SPR mode is found tobe 1.008 and the evanescent decay length is about 1 μm. Havingthe plasmonic mode wave vector in hand, we can now calculatethe Doppler and transit time broadened linewidths, which arefound to be ∼480 MHz and 30 MHz, respectively. The combi-nation of all, according to the Voight profile, can be calculatedaccording to f v � 0.5346 · f L �

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0.2166f 2

L � f 2G

p[59],

where f v is the Voigt linewidth, f L is the Lorentzian linewidthcorresponding to the homogeneous broadening, and f G is theGaussian linewidth corresponding to the Doppler broadening.This results in a total linewidth of about 950 MHz. Morein-depth discussion is provided in Supplement 1.

Having the refractive index of acetylene in hand, we can nowuse the attenuated total internal reflection formalism to deducethe transmission of our integrated plasmonic–molecular device

Fig. 1. (a) Illustration of the plasmonic–molecular device consisting ofa glass prism and a nanometric Au layer bonded to the gas cell. A laserbeam (thick red line) excites a plasmonic mode (red “wiggle”), whichinteracts with the molecules (blue dots) and is reflected off the structure.(b) Micrograph of the integrated plasmonic–molecular gas device.(c) Schematics of the experimental setup. (d) Absorption spectrum of12C2H2 taken from a reference cell with the R9 transition marked in red.

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by calculating the reflection coefficient from our four-layer struc-ture (acetylene, MgF2, Au, and Cr) and BK-7 prism. The refrac-tive index of gold was taken to be 1.1366� 10.236i [60].

In Figs. 2(a)–2(c), we present computer simulations of thepredicted light transmission obtained at three different incidentangles. The angle for which the transmission is at a minimum isdefined as 0 [Fig. 2(d)]. As can be observed, we can obtain a dis-persive-like line profile, with the specific shape strongly depend-ing on the incident angle with respect to the plasmonic resonance.Thus, by slightly tuning the incident angle, it is possible to sig-nificantly control the obtained spectral transmission. This is animportant degree of freedom that will be further discussed laterin this paper.

The interaction between the narrow resonance of acetyleneand the broad plasmonic resonance can also be explained in termsof the Fano line shape. While the original paper by Fano [61]describes the interaction between a narrow resonance and thecontinuum, it was shown that similar arguments can also be usedfor predicting the interaction between a discrete state and a broadresonance, as was discussed in [17,62,63]. The interaction be-tween molecular and plasmonic systems [64–66] has been usedto 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 Fanoresponse on demand, we provide a detailed discussion (seeSupplement 1), where we show that the three regimes predictedby Fano, namely anomalous dispersion, symmetric line shape,and normal dispersion can all be observed in our system simplyby tuning the angle of incidence.

Another way of looking at our hybrid system is from the pointof view of an SPR sensor. When the incident angle is detunedfrom 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 plas-monic resonance, the transmission line shape [Fig. 2(b)] resem-bles the imaginary part of the refractive index [Fig. 2(f )]. In fact,when the incident angle is tuned to resonance, a minute change of10−6 in the imaginary or the real part of the refractive index willmodify the normalized transmission by 1.34 · 10−4 or 2.18 · 10−6,respectively. On the other hand, when the angle is detuned to−0.116° from resonance, the same change will modify the trans-mission by 0.9 · 10−4 or 2.64 · 10−4, respectively. Thus, at zeroangle detuning from resonance, the SPR sensor is more sensitiveto changes in the imaginary part of the refractive index. However,when the angle is detuned from resonance, higher sensitivity tovariations in the real part of the refractive index is observed.

Interestingly, for zero detuning we observe the symmetric lineshape presented as a peak instead of an absorption dip as would beexpected in a stand-alone acetylene cell. While this might seem abit surprising, one should always remember that the Fano lineshape is a result of the interplay between two resonances andthe line shape strongly depends on the coupling and dampingin the system. Here, due to the high losses of the plasmonic op-tical mode, it is reasonable to assume that in most cases the SPRwill be undercoupled (i.e., the loss of the plasmonic mode is largerthan the coupling loss). By reducing the gold layer thickness, onecan increase the coupling loss up to the point that overcoupling isachieved. To further study this latter issue, we have calculated thetransmission of light through the hybrid system as a function ofangle, assuming at zero detuning for the case of 30 nm gold layerthickness (undercoupling, red curve), and for the case where thegold thickness is reduced to 9 nm (overcoupled regime, bluecurve), as can be seen in Fig. 3(a). We have also calculatedthe transmission for the two cases as a function of laser detuningat resonance angles [Fig. 3(b)], which are 42.2° for the under-coupled case and 43.65° for the overcoupled case.

In the case of undercoupling, the increase in the mode lossesdue to the acetylene absorption takes the system further awayfrom critical coupling and the transmission becomes larger, inthe form of an acetylene resonance peak. However, for the caseof an overcoupled SPR, the increase in loss due to the acetyleneabsorption pushes the system toward critical coupling, and theoverall transmission is reduced, as manifested by the dip in

Fig. 2. (a)–(c) Simulated transmission of the coupled system at differ-ent incident angles normalized via dividing the raw data by a fit to thebare SPP resonance (excluding the acetylene contribution). (d) Simulatedsurface plasmon resonance at zero detuning. The three circles denotethe angles for which the results of Figs. 2(a)–2(c) were calculated.(e)–(f ) Simulated imaginary and real part of the refractive index ofthe R9 line of 12C2H2.

Fig. 3. (a) Calculated surface plasmon resonance for 30 nm gold layerthickness (under coupled regime, red) and for 9 nm thickness (overcoupled regime, purple). (b) Calculated transmission of the coupled sys-tem at a SPR resonance incident angle for 30 nm gold layer thickness(under coupled regime, red), and for 9 nm thickness (overcoupledregime, purple). Both transmissions are normalized by dividing theraw data by a fit to the bare SPP resonance (excluding the acetylenecontribution).

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transmission. It is interesting to see the strong effect acetylene hason the coupling condition of the SPR [Fig. 3(b)]. Such effectcould be very stimulating for slow and fast light research. In par-ticular, having dispersive media integrated with SPR results in adispersive-like coupling nature and slow/fast light effects. Thisalso has been reported in other systems [67–69].

B. Measurement

In Fig. 4, we present the measured transmission spectra of ourhybrid plasmonic–molecular device, first as a function of theincident angle (panel a) and then as a function of the frequencydetuning for three different incident angles (panels b–d, the anglesare denoted as circles in panel a). As a reference, we have recordedsimultaneously the acetylene absorption line using a referenceacetylene cell (blue lines, not in scale in the y axis). The threepresented spectra correspond to the three different Fano conditionsof anomalous dispersion symmetrical line shape and normaldispersion. 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 theirshape to the calculations. To further compare the two sets, wepresent in Fig. 5(a) more detailed set of measurements and com-puter simulations that clearly show the trend of gradually movingfrom a normal dispersion at negative angles to an anomalousdispersion in positive angles, through observing a symmetric lineshape at a zero detuning angle. We can also observe that the shiftin the transmission peak and the contrast is stronger at negativeangles, which relates to the asymmetrical line shape of the SPR.While the measured and the simulated curves resemble each otherin their shape, some discrepancy is observed, most probably dueto the fact that the fabricated gold layer is of lower quality com-pared to the value we have used for the simulations. Furthermore,surface roughness was not taken into account. This is also in linewith the extracted propagation length, which was found to be

slightly lower than the simulated value (see discussion later inthe paper).

After examining the light–molecule interactions and the lineshape properties, we address potential applications for such a de-vice. The first, and perhaps the most obvious choice, is to takeadvantage of the accuracy and the stability of acetylene absorptionlines to demonstrate an integrated and miniaturized reference cell.

To address the above-mentioned application, we have mea-sured the stability of our device by recording the beat notebetween two lasers, one stabilized to a reference acetylene cell(13C2H2, R29) and the other to our plasmonic cell (12C2H2, R9).Furthermore, we have compared the stability of our system tothe stability of a free-running laser by beating it against the samereference acetylene cell (13C2H2, R29). Finally, to estimate ouroptimum locking accuracy, we have recorded the beat note be-tween the reference acetylene cell and another reference acetylenecell (12C2H2, R9). We have set the incident angle to 0 (definedas the plasmonic resonance angle) to achieve the highest contrast.The experimental setup used to lock the lasers is presentedin Fig. 6(a).

The measured stability over time is presented in Fig. 6(b) as anAllan variance scheme. As can be seen, the laser that is locked toour cell shows an order of magnitude improvement in stability ascompared to the free laser, and the obtained instability goesdown below 0.3 MHz (δf ∕f � 1.3 · 10−9) (see the pink curveas opposed to black curve). Such a stability level is already suffi-cient for a large variety of applications, such as wavelength divi-sion multiplexing (WDM) [70–72]. Considering the significant

Fig. 4. (a) Measured transmission of the coupled system as a functionof incident angle, maximum measured transmission was normalized to 1.(b)–(d) Measured transmission of the coupled system as a function offrequency detuning at three different incident angles, denoted as circlesin panel a. The transmission spectra are normalized by dividing the rawdata by a fit to the SPP resonance excluding the acetylene contribution.

Fig. 5. Measured (red) and simulated (blue) transmission of thecoupled system at different incident angles.

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miniaturization, such an achievement should not be underesti-mated. While this result is a significant step forward, however,there is still room for further improvement. As a reference, thesame locking approach was used to achieve instability lower than40 kHz, using a large cell as a reference. One of the major param-eter that can be further improved is the temperature stability. Infact, in SPR-based systems, temperature fluctuations are trans-lated to fluctuations in the SPR angular or wavelength spectrumand, as a result, affect the obtained response. We have simulatedthe effect of temperature fluctuations, taking into account thethermo-optic coefficient of glass to be 0.3 · 10−5 �K�−1, and alsoconsidering the temperature-dependent plasma frequency of gold[73]. The simulation results are depicted in Fig. 7. In Fig. 7(a), weshow the effect of temperature deviation on the Fano line shape,whereas in Fig. 7(b) we plot the spectral shift of the peak as afunction of temperature variation. As can be seen, a frequencydrift of 1.4 MHz∕K is expected. Thus, our measured instabilityimplies temperature fluctuations of the order of 0.2 deg in 100 s.

Clearly, the stability of our system can be further improved bythermal stabilization. Temperature stabilization down to 3 [mK]is feasible [74] and, based on the above discussion, will result infrequency fluctuations of less than 5 kHz. In such a case, thermalstability will no longer be a limiting factor. Another relevantparameter is the resonance linewidth. Frequency stabilization is

directly related to the resonator’s Q factor, according to theAllan deviation equation in a shot-noise-limited region, Δf ∝N∕�S · Q� · τ−0.5 [75], where Q is the Q factor, S is the signal,N is the noise, and τ is the averaging time. Pressure broadeningaffects the linewidth of our device. Reducing the pressure will re-duce the gas density and result in a narrower line. On the otherhand, lower pressure will unfortunately lead to a lower signal con-trast. The two effects will counteract each other and would notresult in a significant improvement, if any. The signal can beincreased by increasing the propagation length of the plasmon.Our signal contrast corresponds to a propagation length of75 μm, while the theoretical propagation length of such a modeis 114 μm, considering the effective index of gold we took in oursimulation (1.1366� 10.236i) that has shown better contrastthan our measurement. The resonance effects allow us to get along propagation length in a small volume and can be improvedby depositing high-quality Au layers, which will result in lessOhmic losses and higher Q factors.

Another source of instability is related to mechanical fluctua-tions, which may affect the incident angle and thus will modifythe system’s response. While these instabilities are undesirable forapplications such as frequency stabilization, the sensitivity to aslight change in the incident angle and the temperature can beused for an angular sensor or a temperature sensor. Such sensorscould offer superior performance compared to bare plasmonic sys-tems. To demonstrate this feature, we have measured the beatsignal between a laser locked to our hybrid plasmonic–molecularsystem and a laser locked to a reference cell as a function ofincident angle. The obtained results are shown in Fig. 8.

While the shift in frequency is not linear with the angle, forsmall deviations from the angle of plasmonic resonance, the sen-sitivity can be estimated as ∼1.2 GHz∕deg . This factor, com-bined with the high-frequency stability of more than 300 kHzat 100 s, translates to an angular resolution better than 0.25 millidegree (4.4 μRad).

Fig. 6. (a) Frequency stabilization scheme. Two loops are presented.The right loop (purple) represents a telecom laser locked to our hybriddevice. The left loop (orange) represents a telecom laser locked to anacetylene reference cell. (b) Allan deviations of the beating signal betweena laser locked to an acetylene reference cell (13C2H2, R29) to a free run-ning laser (black), laser locked to our hybrid device (pink), and a laserlocked to an acetylene (13C2H2, R9) reference cell (green).

Fig. 7. (a) Simulated transmissions of our coupled system as functionof temperature at a resonance angle of the SPR. (b) Simulated driftof the maximum transmission of our coupled system as a function oftemperature.

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As seen in Fig. 5, the signal contrast decreases as we detune thesystem further away from the SPR resonance. This result is ex-pected to affect our ability to lock the system. Another importantparameter is the angular window of operation (i.e., the range ofdetuning angles for which the change in peak frequency is stilllinear with angle detuning). Next we discuss these issues in detail.

Our Fano-like signal can be simply considered as a derivativeof the narrow resonance (acetylene) by the broad resonance(SPR). As such, to obtain the largest detuning range for whichthe shift is still linear with detuning, one should seek a signal witha parabolic-shaped resonance. Unfortunately, SPR does not have aparabolic line shape and thus the change in the peak frequency ofthe signal is not linearly varying with the angle. Furthermore, thecontrast of the signal is not constant. Instead, the contrast is de-creasing as the angle is detuned from resonance due to a simplereason: One must couple light into the acetylene to probe its re-sponse. Clearly, as we detune away from the plasmonic resonance,no light is coupled into the surface waves and the acetylene cannotbe probed. Obviously, the Q factor of the signal will also beaffected 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 arefractive index of n � 1.1366� 10.236i. This previously pub-lished value was found to provide an SPR line shape that closelyresembles our measurements. The simulation results are displayedin Fig. 9. Three values of gold layer thicknesses have been con-sidered, 25 nm (solid blue), 30 nm (solid, red representing thegold thickness found in our device), and 35 nm (solid green).Furthermore, to estimate what could be the results assuming agold layer with optimal quality would have been used, we haverepeated these simulations assuming a better (yet realistic) layer ofgold (n � 0.56233� 9.4769i) [76]. For the latter, we haveassumed 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 beseen, the Q factor can be improved by a factor of about 2 byevaporating 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 anoptimal gold layer is shown to be helpful, increasing the contrastby nearly threefold. We can also observe that by decreasing thegold width we increase the coupling losses and, as explained

earlier, gets closer to critical coupling. In such a case, more lightis coupled to the mode and a higher contrast is obtained. Theseresults point toward a clear path to improve our device, simply byoptimization of the gold layer’s quality and thickness. In Fig. 9(c)we present the peak position as a function of the detuningangle alongside a linear fit to the curve (black dots). One canclearly observe that, for small angle variations in the range−0.1 < θ < 0.01, the change in the peak position as a functionof the angle is linear for our device. For the set of devices with anoptimal layer of gold (dashed lines), a high sensitivity is obtained,up to 11 GHz/degree, at the expense of a reduced range oflinearity now estimated to be within the angle detuning of∼−0.05 < θ < 0.01 from resonance. To better estimate the im-plications on our capability to lock the system at these variousdetuning 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 param-eter is proportional to the multiplication S · Q , which is inverselyproportional to our frequency instability. The results are pre-sented in Fig. 9(d). As can be seen, the locking factor of oursimulated device shows a FWHM of about 0.1 deg while the de-vices with higher Q factor will mostly show a FWHM of about0.035 deg. These values define the range of angles that can bemeasured 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 Q factorwill show higher sensitivity at the expense of a narrower angularbandwidth. We thus conclude that if one is seeking a large angularbandwidth, the Q factor should be moderate, and the limitedsensitivity should be compensated for using high-quality lockingsetups and a high signal-to-noise ratio. On the other hand, if thesignal-to-noise ratio is limited, it is still possible to track the

Fig. 8. Measured beating signal between a laser locked to our hybriddevice and a laser locked to a reference cell as a function of the incidentangle.

Fig. 9. Simulations of devices based on our deposited gold layer quality(n � 1.1366� 10.236i), having thickness of 25 nm (solid blue), 30 nm(solid red), and 35 nm (solid green). For comparison, we alsoprovide simulations for devices with an optimal quality of gold layer(n � 0.56233� 9.4769i) with a thickness of 35 nm (dashed blue),40 nm (dashed red), and 45 nm (dashed green). (a) Light transmissionaround the surface plasmon resonance at zero wavelength detuning.(b) Contrast of the Fano signal. (c) Peak position as a function of angledetuning. (d) Locking factor, defined as the contrast divided by theFWHM, as a function of angle detuning. For panels b, c, and d, zeroangle was defined as the resonance angle.

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angle with high precision, at the expense of limited angularbandwidth.

Following the obtained results and the discussion above, thepractical angular bandwidth of our device is about 0.1°, and theangular resolution is about 0.25 milli degree. Further improve-ment in locking quality and further noise reduction is expectedto provide even better angular resolution. These improvements,together with improving the Q factor of the SPR, will make ourdevice even better in its performance compared to other SPR- andprism-based angular sensors [28,77]. Similar to our approach,these techniques are also limited by nonlinearity and contrastreduction as the angle is detuned from resonance. Even moreso, these techniques are based on two prisms rather than one,which makes their implementation more cumbersome and lessstable.

4. CONCLUSIONS

We have demonstrated a hybrid plasmonic–molecular devicebased on an SPR configuration integrated with an acetylene cell.The approach allows degrees of freedom in controlling the ob-tained line shape in the form of a Fano response. In fact, the lineshape can be easily switched from normal dispersion to an anoma-lous dispersion of transmission simply by tuning the angle of in-cidence. Unlike a conventional SPR, where a dip in transmissionis observed at the critical angle, here we can demonstrate a peak intransmission due to the interplay between coupling and loss.Essentially, the additional absorption of the acetylene shifts thesystem to be under-coupled, and thus higher transmission isobtained.

Following the fundamental demonstration of line shape con-trol, we have also demonstrated two potential applications. First,taking advantage of the narrow resonance line of acetylene and itsabsolute accuracy, and combined with the flexibility and field en-hancement of plasmonics, we have used our hybrid approach tostabilize telecom band lasers to a level better than 300 kHz at100 s. This paves the way toward using our device in applicationssuch as wavelength division multiplexing (WDM). We have alsodemonstrated the usefulness of our device as an angular sensor,having resolution in the microradians regime. Such merits couldnot be achieved by a stand-alone plasmonic device due to its rel-atively broad linewidth. On the other hand, the use of acetyleneby itself, without being combined with a plasmonic device, lacksthe properties of angular sensitivity, field enhancement, a highdegree of control over the line shape, and enhanced light–matterinteractions. It is therefore the hybridization of the two disciplinesthat we believe makes our device unique from the fundamentalpoint of view and attractive from the application standpoint. Onepossible application that can benefit from the angular sensitivityand the accuracy of acetylene is the angular stabilization ofmechanical systems. It should also be mentioned that the degreeof control over the narrow line shape may become helpful instudying other fundamental phenomena and addressing addi-tional applications (e.g., slow light and electromagnetically in-duced transparency).

Funding. H2020 European Research Council (ERC) (ERC-LIVIN 648575); Israeli Ministry of Science and Technology.

See Supplement 1 for supporting content.

REFERENCES

1. E. A. Ash and G. Nicholls, “Super-resolution aperture scanning micro-scope,” Nature 237, 510–512 (1972).

2. M. Stockman, “Nanofocusing of optical energy in tapered plasmonicwaveguides,” Phys. Rev. Lett. 93, 137404 (2004).

3. B. Desiatov, I. Goykhman, and U. Levy, “Plasmonic nanofocusing oflight in an integrated silicon photonics platform,” Opt. Express 19,13150–13157 (2011).

4. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, and T. W. Ebbesen, “Channelplasmon-polariton guiding by subwavelength metal grooves,” Phys. Rev.Lett. 95, 046802 (2005).

5. S. Raza, N. Stenger, A. Pors, T. Holmgaard, S. Kadkhodazadeh, J. B.Wagner, K. Pedersen, M. Wubs, S. I. Bozhevolnyi, and N. A. Mortensen,“Extremely confined gap surface-plasmon modes excited by electrons,”Nat. Commun. 5, 4125 (2014).

6. D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffrac-tion limit,” Nat. Photonics 4, 83–91 (2010).

7. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W.Ebbesen, “Channel plasmon subwavelength waveguide componentsincluding interferometers and ring resonators,” Nature 440, 508–511(2006).

8. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon sub-wavelength optics,” Nature 424, 824–830 (2003).

9. A. Melikyan, L. Alloatti, A. Muslija, D. Hillerkuss, P. C. Schindler, J. Li, R.Palmer, D. Korn, S. Muehlbrandt, D. Van Thourhout, B. Chen, R. Dinu,M. Sommer, C. Koos, M. Kohl, W. Freude, and J. Leuthold, “High-speedplasmonic phase modulators,” Nat. Photonics 8, 229–233 (2014).

10. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L.Brongersma, “Plasmonics for extreme light concentration and manipula-tion,” Nat. Mater. 9, 193–204 (2010).

11. E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photonsorters for spectral and polarimetric imaging,” Nat. Photonics 2, 161–164 (2008).

12. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang,“A hybrid plasmonic waveguide for subwavelength confinement andlong-range propagation,” Nat. Photonics 2, 496–500 (2008).

13. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscaledimensions,” Science 311, 189–193 (2006).

14. D. C. Marinica, A. K. Kazansky, P. Nordlander, J. Aizpurua, and A. G.Borisov, “Quantum plasmonics: nonlinear effects in the field enhance-ment of a plasmonic nanoparticle dimer,” Nano Lett. 12, 1333–1339(2012).

15. B. Sharma, R. R. Frontiera, A.-I. Henry, E. Ringe, and R. P. Van Duyne,“SERS: materials, applications, and the future,” Mater. Today 15(1-2),16–25 (2012).

16. M. Danckwerts and L. Novotny, “Optical frequency mixing at coupledgold nanoparticles,” Phys. Rev. Lett. 98, 026104 (2007).

17. L. Stern, M. Grajower, and U. Levy, “Fano resonances and all-opticalswitching in a resonantly coupled plasmonic-atomic system,” Nat.Commun. 5, 4865 (2014).

18. I.-Y. Park, S. Kim, J. Choi, D.-H. Lee, Y.-J. Kim, M. F. Kling, M. I.Stockman, and S.-W. Kim, “Plasmonic generation of ultrashort ex-treme-ultraviolet light pulses,” Nat. Photonics 5, 677–681 (2011).

19. D. E. Chang, A. S. Sorensen, E. A. Demler, and M. D. Lukin, “A single-photon transistor using nanoscale surface plasmons,” Nat. Phys. 3, 807–812 (2007).

20. L. Rogobete, F. Kaminski, M. Agio, and V. Sandoghdar, “Design of plas-monic nanoantennae for enhancing spontaneous emission,” Opt. Lett.32, 1623–1625 (2007).

21. V. K. Komarala, Y. P. Rakovich, A. L. Bradley, S. J. Byrne, Y. K. Gun’ko,N. Gaponik, and A. Eychmüller, “Off-resonance surface plasmon en-hanced spontaneous emission from CdTe quantum dots,” Appl. Phys.Lett. 89, 253118 (2006).

22. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A.Scherer, “Surface-plasmon-enhanced light emitters based on InGaNquantum wells,” Nat. Mater. 3, 601–605 (2004).

23. D. E. Chang, A. Sørensen, P. Hemmer, and M. Lukin, “Strong couplingof single emitters to surface plasmons,” Phys. Rev. B 76, 35420(2007).

24. T. H. Taminiau, F. D. Stefani, F. B. Segerink, and N. F. van Hulst, “Opticalantennas direct single-molecule emission,” Nat. Photonics 2, 234–237(2008).

Research Article Vol. 5, No. 4 / April 2018 / Optica 492

25. D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Quantumoptics with surface plasmons,” Phys. Rev. Lett. 97, 53002 (2006).

26. J. Homola, “Surface plasmon resonance sensors for detection of chemi-cal and biological species,” Chem. Rev. 108, 462–493 (2008).

27. J. R. L. Guerreiro, M. Frederiksen, V. E. Bochenkov, V. De Freitas,M. G. F. Sales, and D. S. Sutherland, “Multifunctional biosensor basedon localized surface plasmon resonance for monitoring small molecule-protein interaction,” ACS Nano 8, 7958–7967 (2014).

28. S.-F. Wang, M.-H. Chiu, C.-W. Lai, and R.-S. Chang, “High-sensitivitysmall-angle sensor based on surface plasmon resonance technologyand heterodyne interferometry,” Appl. Opt. 45, 6702–6707 (2006).

29. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. VanDuyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7,442–453 (2008).

30. N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos,“Nanoantenna-enhanced gas sensing in a single tailored nanofocus,”Nat. Mater. 10, 631–636 (2011).

31. A. Shalabney and I. Abdulhalim, “Sensitivity-enhancement methods forsurface plasmon sensors,” Laser Photon. Rev. 5, 571–606 (2011).

32. M. A. Schmidt, D. Y. Lei, L. Wondraczek, V. Nazabal, and S. A. Maier,“Hybrid nanoparticle-microcavity-based plasmonic nanosensors withimproved detection resolution and extended remote-sensing ability,”Nat. Commun. 3, 1108 (2012).

33. P. Balling, M. Fischer, P. Kubina, and R. Holzwarth, “Absolute frequencymeasurement of wavelength standard at 1542 nm: acetylene stabilizedDFB laser,” Opt. Express 13, 9196–9201 (2005).

34. H. S. Moon, W. K. Lee, L. Lee, and J. B. Kim, “Double resonance opticalpumping spectrum and its application for frequency stabilization of alaser diode,” Appl. Phys. Lett. 85, 3965–3967 (2004).

35. S. L. Gilbert and W. C. Swann, “Acetylene 12C2H2 absorption referencefor 1510 nm to 1540 nm wavelength calibration—SRM 2517a,” NISTSpecial Publication 260-133 (2001).

36. S. B. Papp, K. Beha, P. Del’Haye, F. Quinlan, H. Lee, K. J. Vahala, andS. A. Diddams, “Microresonator frequency comb optical clock,” Optica 1,10–14 (2014).

37. P. Wolf and G. Petit, “Satellite test of special relativity using the globalpositioning system,” Phys. Rev. A 56, 4405–4409 (1997).

38. S. Knappe, V. Shah, P. D. D. Schwindt, L. Hollberg, J. Kitching, L. A.Liew, and J. Moreland, “A microfabricated atomic clock,” Appl. Phys.Lett. 85, 1460–1462 (2004).

39. ADVANTEST, “Q8384 optical spectrum analyzer,” (2001).40. J. L. Hall, “Stabilized lasers and precision measurements,” Science 202,

147–156 (1978).41. K. M. Evenson, J. S. Wells, F. R. Petersen, B. L. Danielson, G. W. Day,

R. L. Barger, and J. L. Hall, “Speed of light from direct frequency andwavelength measurements of the methane-stabilized laser,” Phys.Rev. Lett. 29, 1346–1349 (1972).

42. L. Stern, B. Desiatov, I. Goykhman, and U. Levy, “Nanoscale light-matterinteractions in atomic cladding waveguides,” Nat. Commun. 4, 1548(2013).

43. L. Stern, B. Desiatov, N. Mazurski, and U. Levy, “Strong coupling andhigh-contrast all-optical modulation in atomic cladding waveguides,”Nat. Commun. 8, 14461 (2017).

44. L. Stern, R. Zektzer, N. Mazurski, and U. Levy, “Enhanced light-vaporinteractions and all optical switching in a chip scale micro-ring resonatorcoupled with atomic vapor,” Laser Photon. Rev. 10, 1016–1022 (2016).

45. R. Ritter, N. Gruhler, W. H. P. Pernice, H. Kübler, T. Pfau, and R. Löw,“Coupling thermal atomic vapor to an integrated ring resonator,” New J.Phys. 18, 103031 (2016).

46. L. Stern and U. Levy, “Transmission and time delay properties of anintegrated system consisting of atomic vapor cladding on top of a microring resonator,” Opt. Express 20, 28082–28093 (2012).

47. R. Ritter, N. Gruhler, W. Pernice, H. Kübler, T. Pfau, and R. Löw, “Atomicvapor spectroscopy in integrated photonic structures,” Appl. Phys. Lett.107, 041101 (2015).

48. W. Yang, D. B. Conkey, B. Wu, D. Yin, A. R. Hawkins, and H. Schmidt,“Atomic spectroscopy on a chip,” Nat. Photonics 1, 331–335 (2007).

49. S. Ghosh, A. R. Bhagwat, C. K. Renshaw, S. Goh, A. L. Gaeta, and B. J.Kirby, “Low-light-level optical interactions with rubidium vapor in a pho-tonic band-gap fiber,” Phys. Rev. Lett. 97, 023603 (2006).

50. S. A. Aljunid, E. A. Chan, G. Adamo, M. Ducloy, D. Wilkowski, and N. I.Zheludev, “Atomic response in the near-field of nanostructured plas-monic metamaterial,” Nano Lett. 16, 3137–3141 (2016).

51. F. Benabid, F. Couny, J. C. Knight, T. A. Birks, and P. St. J. Russell,“Compact, stable and efficient all-fibre gas cells using hollow-core pho-tonic crystal fibres,” Nature 434, 488–491 (2005).

52. S. Ghosh, J. E. Sharping, D. G. Ouzounov, and A. L. Gaeta, “Resonantoptical interactions with molecules confined in photonic band-gap fibers,”Phys. Rev. Lett. 94, 093902 (2005).

53. F. Benabid, P. Light, F. Couny, and P. St. J. Russell, “Electromagnetically-induced transparency grid in acetylene-filled hollow-core PCF,” Opt.Express 13, 5694–5703 (2005).

54. M. Conte, A. F. Carley, C. Heirene, D. J. Willock, P. Johnston, A. A.Herzing, C. J. Kiely, and G. J. Hutchings, “Hydrochlorination of acetyleneusing a supported gold catalyst: a study of the reaction mechanism,”J. Catal. 250, 231–239 (2007).

55. Thorlabs, “Thorlabs—TS10 vacuum epoxy, low vapor pressure—Twopart,” https://www.thorlabs.com/thorproduct.cfm?partnumber=TS10.

56. M. Ducloy, “Nonlinear selective reflection from an atomic vapor at arbi-trary incidence angle,” Phys. Rev. A 38, 5197–5205 (1988).

57. C. C. Katsidis and D. I. Siapkas, “General transfer-matrix method for op-tical multilayer systems with coherent, partially coherent, and incoherentinterference,” Appl. Opt. 41, 3978–3987 (2002).

58. R. Kondo, S. Tojo, T. Fujimoto, and M. Hasuo, “Shift and broadening inattenuated total reflection spectra of the hyperfine-structure-resolved D2line of dense rubidium vapor,” Phys. Rev. A 73, 062504 (2006).

59. J. J. Olivero and R. L. Longbothum, “Empirical fits to the Voigt line width:a brief review,” J. Quant. Spectrosc. Radiat. Transf. 17, 233–236 (1977).

60. L. Gao, F. Lemarchand, and M. Lequime, “Comparison of differentdispersion models for single layer optical thin film index determination,”Thin Solid Films 520, 501–509 (2011).

61. U. Fano, “Effects of configuration interaction on intensities and phaseshifts,” Phys. Rev. 124, 1866–1878 (1961).

62. V. Giannini, Y. Francescato, H. Amrania, C. C. Phillips, and S. A. Maier,“Fano resonances in nanoscale plasmonic systems: a parameter-freemodeling approach,” Nano Lett. 11, 2835–2840 (2011).

63. P. Alonso-Gonzalez, M. Schnell, P. Sarriugarte, H. Sobhani, C. Wu, N.Arju, A. Khanikaev, F. Golmar, P. Albella, L. Arzubiaga, F. Casanova,L. E. Hueso, P. Nordlander, G. Shvets, and R. Hillenbrand, “Real-spacemapping of Fano interference in plasmonic metamolecules,” Nano Lett.11, 3922–3926 (2011).

64. D. Dregely, F. Neubrech, H. Duan, R. Vogelgesang, and H. Giessen,“Vibrational near-field mapping of planar and buried three-dimensionalplasmonic nanostructures,” Nat. Commun. 4, 2237 (2013).

65. E. J. Osley, C. G. Biris, P. G. Thompson, R. R. F. Jahromi, P. A.Warburton, and N. C. Panoiu, “Fano resonance resulting from a tunableinteraction between molecular vibrational modes and a double con-tinuum of a plasmonic metamolecule,” Phys. Rev. Lett. 110, 087402(2013).

66. F. Neubrech, A. Pucci, T. W. Cornelius, S. Karim, A. García-Etxarri, andJ. Aizpurua, “Resonant plasmonic and vibrational coupling in a tailorednanoantenna for infrared detection,” Phys. Rev. Lett. 101, 157403(2008).

67. M. Sandtke and L. Kuipers, “Slow guided surface plasmons at telecomfrequencies,” Nat. Photonics 1, 573–576 (2007).

68. Y. Xu, J. Zhang, and G. Song, “Slow surface plasmons in plasmonic gra-ting waveguide,” IEEE Photon. Technol. Lett. 25, 410–413 (2013).

69. G. Wang, H. Lu, and X. Liu, “Trapping of surface plasmon waves ingraded grating waveguide system,” Appl. Phys. Lett. 101, 013111(2012).

70. K. Igarashi, T. Tsuritani, I. Morita, K. Katoh, and K. Kikuchi, “Frequencystabilization of multiple semiconductor lasers for Nyquist-WDM transmis-sion systems,” in Optical Fiber Communication Conference andExposition and the National Fiber Optic Engineers Conference (OFC/NFOEC) (2013), Vol. 2, paper OTu2I.6.

71. M. Koga and M. Teshima, “Wavelength standards and stabilization forWDM networks,” in Optical Fiber Communication Conference and theInternational Conference on Integrated Optics and Optical FiberCommunication (OFC/IOOC) (IEEE, 1999), pp. 151–151b.

72. M. Happach, D. De Felipe, V. Friedhoff, M. Kleinert, C. Zawadzki, M.Moehrle, N. Keil, W. Hofmann, and M. Schell, “Temperature-tolerantwavelength-setting and -stabilization in a polymer-based tunable DBRlaser,” J. Light. Technol. 35, 1797–1802 (2017).

73. A. K. Sharma and B. D. Gupta, “Influence of temperature on the sensi-tivity and signal-to-noise ratio of a fiber-optic surface-plasmon resonancesensor,” Appl. Opt. 45, 151–161 (2006).

Research Article Vol. 5, No. 4 / April 2018 / Optica 493

74. A. N. Naimushin, S. D. Soelberg, D. U. Bartholomew, J. L. Elkind, andC. E. Furlong, “A portable surface plasmon resonance (SPR) sensor sys-tem with temperature regulation,” Sens. Actuators B 96, 253–260 (2003).

75. R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J.Munley, and H. Ward, “Laser phase and frequency stabilization using anoptical resonator,” Appl. Phys. B 31, 97–105 (1983).

76. A. D. Rakić, A. B. Djurišić, J. M. Elazar, and M. L. Majewski, “Opticalproperties of metallic films for vertical-cavity optoelectronic devices,”Appl. Opt. 37, 5271–5283 (1998).

77. H.-L. Hsieh, J.-Y. Lee, L.-Y. Chen, and Y. Yang, “Development ofan angular displacement measurement technique through birefringenceheterodyne interferometry,” Opt. Express 24, 6802–6813 (2016).

Research Article Vol. 5, No. 4 / April 2018 / Optica 494