Quantum spectroscopy of plasmonic nanostructures

We use frequency entangled photons, generated via spontaneous parametric down conversion, to measure the broadband spectral response of an array of gold nanoparticles exhibiting Fano-type plasmon resonance. Refractive index sensing of a liquid is performed by measuring the shift of the array resonance. This method is robust in excessively noisy conditions compared with conventional broadband transmission spectroscopy. Detection of a refractive index change is demonstrated with a noise level 70 times higher than the signal, which is shown to be inaccessible with the conventional transmission spectroscopy. Use of low photon fluxes makes this method suitable for measurements of photosensitive bio-samples and chemical substances.


Introduction
New insights in understanding the behavior of materials at the nano-scale and progress in nanofabrication capabilities have triggered great interest in the study of plasmonic nanostructures. One practical application of these structures is the development of sensing technology. Plasmonic sensors benefit from their bio-compatibility and high sensitivity [1][2][3][4].
With the sensitivity of the sensors approaching the atto-Molar scale, as well as for sensing of photosensitive substances, it is important that the analyte is not damaged or modified by the probing light. This brings the requirement of using extremely small doses of light, possibly down to the level of single photons, and highly sensitive equipment for the readout of the sensor response. For sensing with low photon counts, the main practical issue is careful suppression of the influence of the background noise. This is challenging with conventional spectroscopy but quantum optics can be exploited to effectively address this issue [5][6][7].
In this work, we demonstrate advantages of using frequency entangled photons, generated via spontaneous parametric down conversion (SPDC), in revealing the spectroscopic response of a plasmonic refractive index sensor under noisy conditions. The technique operates at a single photon level and is more robust to environmental noise, compared to conventional transmission spectroscopy.

Quantum spectroscopy
In the SPDC a pump photon travelling in a medium with quadratic susceptibility occasionally splits into a pair of photons, referred to as signal and idler [23,24]. Signal and idler photons are created almost simultaneously (within tens of fs) with their energies and momenta obeying the conservation laws: where , and ⃗ are the energies and the wave vectors of the pump, signal and idler photons respectively. Signal and idler photons are detected with two single photon avalanche photodiodes (APD). Their pairwise correlation is measured by an electronic coincidence circuit, which produces a signal (coincidence) if APD counts arrive within the fixed time window typically of about several ns. Dedicated techniques, allow obtaining the widths of the SPDC spectra in a given spatial mode in the range of several hundreds of nanometers [25][26][27][28].
The sample under investigation is placed in the path of one of the photons (idler) and the frequency selection is performed over another photon (signal) by a monochromator [29][30][31][32][33], see Fig. 1(a). Since the sum of energies of the down-converted photons is equal to the energy of the pump, spectral selection over the signal photon defines the frequency of the correlated idler photon. Following [29], the number of coincidences between two APDs is proportional to the spectral function of the sample ( ) at the frequency of the idler photon In contrast to the conventional transmission spectroscopy, the spectral selection is performed in the channel without the structure under test. Following the analogy with imaging experiments, we refer to the method as quantum (ghost) spectroscopy.
The remarkable feature of the quantum spectroscopy is its robustness against the environmental noise, which allows conducting measurements at extremely low photon fluxes.
The noise typically includes background optical noise and electronic noise of the APDs. Let us denote the number of SPDC photocounts as where is the number of photon pairs, produced by the SPDC source, and is the quantum efficiency of signal and idler channel, respectively. The number of coincidences is proportional to the probability of joint detection by the APDs in two channels: Assuming that noise photocounts of the two APDs are uncorrelated, the number of noise coincidences is given by accidental overlap of photocounts within the time window of the coincidence circuit . It also includes components due to accidental overlap of SPDC and noise photocounts: where N s and N i are the number of noise photocounts of APDs in signal and idler channels, respectively. The total number of coincidences is given by: Even though , the number of noise coincidences R N is strongly suppressed compared to ( ), because of a narrow coincidence time window . Thus the spectral response of the structure can be revealed from even under excessive noise situations.

Comparison to the conventional transmission spectroscopy
In conventional transmission spectroscopy, the sample is placed between the light source and the monochromator; the transmission spectrum is obtained directly from APD photocounts, see Fig. 1(b). The signal-to-noise ratio (SNR) for the transmission spectroscopy is given by . For the quantum spectroscopy SNR is given by (3,4), where it is assumed that . The ratio of the two SNRs is given by: .
The advantage in the SNR for the quantum spectroscopy is provided by the use of high quantum efficiency, low noise APD in the idler channel, and the narrow coincidence time window .

The plasmonic array sensor
We use an array of metal nanoparticles which has a narrow Fano-type plasmon resonance, due to diffractive coupling of localized surface plasmons [34][35][36][37][38][39]. The array acts as a metallic grating, and when the wavelength of incident light gets close to the Rayleigh cut-off wavelength, the diffracted wave propagates along the surface [40]. This effect is referred to as Wood-Rayleigh's anomaly. If the anomaly wavelength is close to the plasmon resonance of individual nanoparticles, then the collective plasmonic mode is excited.
Excitation of the mode results in a narrow Fano-type resonance in the transmission spectrum of the array. Position and shape of the Fano resonance depend on the shape of the nanoparticles, distance between them, and refractive index of the surrounding medium. High sensitivity to the local change of the refractive index as well as high quality (Q) factor of the nanoparticle array resonance constitute the basis for its sensing applications [37,41].
The nanoparticle array is fabricated using a combined method of nanosphere lithography with femtosecond laser-induced transfer which allows production of large-scale periodic arrays of spherical nanoparticles [37]. where Q is defined as the ratio of the resonance wavelength to the resonance width, defined from the fit using the Fano formula (see details below).
The refractive index sensitivity is measured by removing the cover PDMS layer and adding testing glycerin-water solutions with different concentration on top of the array. The sensitivity is calculated as a ratio of the resonance shift in nm to the change of the refractive index of the testing solution.

Experimental setup
The quantum spectroscopy setup is shown in Fig. 1(a). Three bulk BBO crystals (Dayoptics) with the thickness of 0.3 mm, 0.5 mm and 0.5 mm are pumped by a continuous wave vertically polarized diode laser at 407 nm (Omicron PhoxX-405-60). The BBOs are cut for type-I collinear SPDC. One of the BBOs is set for the frequency degenerate regime while another two are detuned from the degenerate regime by tilting their optical axis [26]. The resulting SPDC light source has a spectral width of ~250 nm, and is shown in Fig. 3. The pump is eliminated by a UV-mirror, and the SPDC is split by a non-polarizing beamsplitter Results of the quantum spectroscopy are compared with those obtained by the transmission spectroscopy, see Fig. 1(b) for the experimental set-up. The light from the lamp after the single mode fiber (SMF) is sent through the sample under investigation, using the same optical system as described above, and then coupled into the monochromator. APD photocounts are recorded versus the wavelength, selected by the monochromator.
The experimental procedure in both cases includes transmission measurements of the samples substrate and the array. The resulting transmission spectrum is calculated as the ratio of the array and the substrate spectra.

Results and discussion
To ensure that the SPDC bandwidth fully covers the range of the structure's Fano resonance, we measure the sample transmission with the quantum spectroscopy set-up. The nanoparticle array is covered by a layer of PDMS to create homogeneous surroundings. The refractive index of the PDMS is about 1.4 [42]. The obtained spectrum is shown in Fig. 4. It reveals the Fano-type resonance with the distinctive asymmetrical shape. The gray solid curve in Fig.4 shows the fitting of the experimental results with the Fano formula [38,39] with the following parameters: resonance wavelength λ R = 806 nm, resonance width Δλ = 30 For experiments with actual light sensitive structures it would be advantageous to place the sample just after the monochromator in the signal beam. In this case the sample will be illuminated by a spectrally filtered light with fewer photons, compared to the present configuration. However, since the total number of detected photon pairs will remain the same there will be no improvement in the resulting SNR.
The ratio can be significantly increased by using an additional monochromator in the idler arm. The two monochromators should select exactly conjugated frequencies of signal and idler photons, given by Eq. (1). It would be feasible to decrease by at least 2 orders of magnitude. Furthermore by using commercially available low-jitter APDs (~50 ps), and time-to-digital converters with timing resolution on the order of ~10 ps [44] it would be possible to set the coincidence time window to about ~100 ps. Given this, it is feasible to reach the ratio as high as .

Conclusion
In The developed approach will contribute to further progress in application of plasmonic sensors. In particular, it would allow non-disturbing measurements of ultra-small concentrations of chemicals (at atto-molar scale), and sensing of photo-sensitive substances, which can be affected by the probing light.