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Nonlinear interferometric surface-plasmon-resonance sensor

Hailong Wang, Zhongxing Fu, Zhihao Ni, Xiong Zhang, Chunliu Zhao, Shangzhong Jin, Jietai Jing

Published Mar 13, 2021• 8 citations

Abstract

A nonlinear interferometer can be constructed by replacing the beam splitter in the Mach-Zehnder interferometer with four-wave mixing (FWM) process. Meanwhile, the conventional surface plasmon resonance (SPR) sensors can be extensively used to infer the information of refractive index of the sample to be measured via either angle demodulation technique or intensity demodulation technique. Combined with a single FWM process, a quantum SPR sensor has been realized, whose noise floor is reduced below standard quantum limit with sensitivity unobtainable with classical SPR sensor. Therefore, in this work we have theoretically proposed a nonlinear interferometric SPR sensor, in which a conventional SPR sensor is placed inside nonlinear interferometer, which is called as I-type nonlinear interferometric SPR sensor. We demonstrate that near resonance angle I-type nonlinear interferometric SPR sensor has the following advantages: its degree of intensity-difference squeezing, estimation precision ratio, and signal-noise-ratio are improved by the factors of 4.6 dB, 2.3 dB, and 4.6 dB respectively than that obtained with a quantum SPR sensor based on a single FWM process. In addition, the theoretical principle of this work can also be expanded to other types of sensing, such as bending, pressure, and temperature sensors based on a nonlinear interferometer.

DOI: 10.1364/oe.421217

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A nonlinear interferometer can be constructed by replacing the beam splitter in the Mach-Zehnder interferometer with four-wave mixing (FWM) process. Meanwhile, the conventional surface plasmon resonance (SPR) sensors can be extensively used to infer the information of refractive index of the sample to be measured via either angle demodulation technique or intensity demodulation technique. Combined with a single FWM process, a quantum SPR sensor has been realized, whose noise floor is reduced below standard quantum limit with sensitivity unobtainable with classical SPR sensor. Therefore, in this work we have theoretically proposed a nonlinear interferometric SPR sensor, in which a conventional SPR sensor is placed inside nonlinear interferometer, which is called as I-type nonlinear interferometric SPR sensor. We demonstrate that near resonance angle I-type nonlinear interferometric SPR sensor has the following advantages: its degree of intensity-difference squeezing, estimation precision ratio, and signal-noise-ratio are improved by the factors of 4.6 dB, 2.3 dB, and 4.6 dB respectively than that obtained with a quantum SPR sensor based on a single FWM process. In addition, the theoretical principle of this work can also be expanded to other types of sensing, such as bending, pressure, and temperature sensors based on a nonlinear interferometer.

Surface plasmon resonance (SPR) sensors can reach the quantum noise limit of the optical readout field in various configurations. We demonstrate that two-mode intensity squeezed states produce a further enhancement in sensitivity compared with a classical optical readout when the quantum noise is used to transduce an SPR sensor signal in the Kretschmann configuration. The quantum noise reduction between the twin beams when incident at an angle away from the plasmonic resonance, combined with quantum noise resulting from quantum anticorrelations when on resonance, results in an effective SPR-mediated modulation that yields a measured sensitivity 5 dB better than that with a classical optical readout in this configuration. The theoretical potential of this technique points to resolving particle concentrations with more accuracy than is possible via classical approaches to optical transduction.

We investigate the use of twin-mode quantum states of light with symmetric statistical features in their photon number for improving intensity-sensitive surface plasmon resonance (SPR) sensors. For this purpose, one of the modes is sent into a prism setup where the Kretschmann configuration is employed as a sensing platform and the analyte to be measured influences the SPR excitation conditions. This influence modifies the output state of light that is subsequently analyzed by an intensity-difference measurement scheme. We show that quantum noise reduction is achieved not only as a result of the sub-Poissonian statistical nature of a single mode, but also as a result of the nonclassical correlation of the photon number between the two modes. When combined with the high sensitivity of the SPR sensor, we show that the use of twin-mode quantum states of light notably enhances the estimation precision of the refractive index of an analyte. With this we are able to identify a clear strategy to further boost the performance of SPR sensors, which are already a mature technology in biochemical and medical sensing applications.

Conventional interferometers make precision measurements by analyzing the position of interference fringes while nonlinear interferometers rely upon a sensitive measurement of phase difference. We detect this phase sensitivity using a correlated probe and conjugate beam that have undergone four-wave mixing inside a hot Rubidium-85 vapor cell. By placing a piece of glass into the path of the probe we observe a phase shift that indicates a successful nonlinear interferometer. We now plan to place into the probe path oils with known indices of refraction on plasmonic media and measure the resulting phase shifts. These results will then allow us to back-calculate an unknown material’s index of refraction simply by observing the phase shift with a level of sensitivity greater than conventional interferometers. Continued research in the field of interferometry utilizing nonlinear processes should provide even greater sensitivity in precision measurements and applications across a range of scientific disciplines.

A surface plasmon resonance (SPR) refractive index sensing technique based on the optimal pre-and post-selection (PPS) is put forward. The intensity contrast ratio (ICR) is introduced to estimate the precision of this sensing technique. Compared with the traditional sensing techniques, our method shows that the ICR can be improved by about two orders of magnitude with optimal pre-and post-selected states. It is also proved that our sensing technique has a large tolerance for the metal film thickness and the incident angle. Remarkably, the method greatly reduces the cost of experiments, which is significant for promoting the widespread applications of SPR sensors.

A nonlinear interferometer uses nonlinear elements as beam splitters to split and to recombine optical waves for interference. As a result, the interference fringe size has a nonlinear dependence on the intensity of the field for phase sensing and leads to an enhanced phase signal. In this paper, a practical scheme of nonlinear interferometry for precision phase measurement is analyzed with parametric amplifiers as the nonlinear beam splitters. It is found that the signal due to phase shift is enhanced by a factor of the amplification gain as compared to a linear interferometer with the same phase-sensing light intensity while the quantum noise is kept at the vacuum level, thus, effectively increasing the signal-to-noise ratio (SNR) beyond the standard quantum limit. Furthermore, the scheme is not as sensitive to the detection loss as the linear scheme with a squeezed state for noise reduction. However, losses inside the interferometer limit the enhancement factor in SNR. We apply the concept to a Michelson interferometer but with parametric amplifiers involved for gravitational-wave detection. We find that effective power is increased by the gain of the amplifiers without actually increasing the cycling power inside the interferometer. Furthermore, the full benefits with squeezed input and variational output or the combination of a quantum nondemolition interferometer for sensitivity beyond the standard quantum limit apply here with even better results. Such a nonlinear interferometer will find wide applications in precision measurements.