Phase-sensitivity-doubled surface plasmon resonance sensing via self-mixing interference

Pan Qi; Bowen Zhou; Zibang Zhang; Shiping Li; Ying Li; Jingang Zhong

doi:10.1364/OL.43.004001

The first surface plasmon resonance (SPR) biosensor was reported by Liedberg in 1983 [1]. Since then, the SPR has developed into a variety of types of biosensor structures [2–5]. SPR technology has advantages, including no need of purifying the analytical sample and no need of marking the biological samples. SPR technology is able to achieve real-time, in situ, and dynamic detection. Therefore, SPR technology has been widely used in biomedical research, clinical disease diagnosis, drug screening, environmental monitoring, and the research of biomolecular interaction in the field of food safety monitoring [6,7].

With the continuous development of life science and technology, SPR technology is expected to provide higher sensitivity in detection. It has been reported that the phase detection method can reach a resolution of $10^{- 8} RIU$ [8]. Although phase detection methods have the highest detection resolution, commercial SPR sensors using phase detection method are not common at present. It is because SPR phase detection is based on two-beam interference technology [9–12], requiring two optical channels. Thus, SPR phase detection requires complex equipment, strict requirements for its working environment, and harsh anti-vibration requirements. However, these requirements are difficult to satisfy simultaneously for common users, which makes the theoretical detection sensitivity hardly achieved in practice.

In this Letter, we report a simple, compact, and sensitivity-doubled SPR technology based on self-mixing interference (SMI). SMI refers to the phenomenon that the output light of the laser is reflected into the laser cavity by an object outside the cavity and interferes with the light in the cavity, resulting in the final output light of the laser being modulated by some property of the external object [13]. Thus, detecting the feedback light can demodulate the object information. Compared with the traditional interference system, the SMI system requires only one optical path and, therefore, is simple and compact. In addition, the SMI systems have the advantages of convenience for signal detection (can be detected by both the forward and backward leaking end of the laser, especially when detecting by the back of the leaking end, and it can be completely isolated from the light wave of the detector). Given these advantages, SMI systems have been widely used in the measurement of displacement, vibration, morphology, acceleration, and small angle [14–16]. Here we propose a SPR phase sensing technology based on SMI. Compared with two-beam interference and other single-beam SPR [17], more importantly, the light travels the SPR sensor twice, resulting in phase changes being doubled.

A Kretschmann-type SPR is shown in Fig. 1. The incident light is $p$ polarized. It enters the prism from the bottom surface at the angle of $θ$ . The light is then reflected by the gold film and reaches the photodetector (PD). For simplicity, we denote the prism, the gold film, and the sample as 1, 2, and 3, respectively. The reflection coefficient of light from prism to sample can be expressed as [18]

r_{1, 3} (θ) = \frac{r_{1, 2} (θ) + r_{2, 3} (θ) \exp [2 j d_{2} k_{z 2} (θ)]}{1 + r_{1, 2} (θ) r_{2, 3} (θ) \exp [2 j d_{2} k_{z 2} (θ)]}, (j = \sqrt{- 1}),

where

d_{2}

is the thickness of the gold film;

k_{z 2}

represents the wave number of the transmission light in the second optical medium along

Z

direction. It can be deduced that the reflectivity

R

and the phase

ϕ

of light from prism to sample are

R (θ) = | r_{1, 3} (θ) |,

ϕ = \arctan [\frac{Im (r_{1, 3})}{Re (r_{1, 3})}] .

Fig. 1. Schematic diagram of a Kretschmann-type SPR system.

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The equation of power for the laser SMI system under weak feedback condition is [19,20]

P = P_{0} [1 + K \cdot μ \cdot C \cos (ω τ)],

where

C

is the optical feedback intensity (when

C ≪ 1

, the system is in a state of weak feedback);

K

is a constant related to the laser itself only;

μ = N / τ c \sqrt{1 + α^{2}}

(

N

is the real part of the complex refractive index of the laser cavity;

c

is the speed of light;

τ

is the time of return for light in an external cavity;

α

is the line width broadening factor of the laser), and when the ratio of the external cavity length and the initial external cavity length is far less than 1,

μ

approximates a constant;

ω

is light frequency;

P

and

P_{0}

are output power with external cavity optical feedback and without external cavity optical feedback, respectively.

Figure 2 shows the diagram of the proposed SMI-based SPR system. The $p$ -polarized light emitted by the laser reaches the sample on the gold film surface through the excitation prism. The object beam carrying sample information is formed and exits from the coupling prism (the coupling prism and the excitation prism are made up of the rhombic prism, which ensures that the ejection light is in the same direction as the incident light). The light incidents on a mirror that is fixed on a piezoelectric ceramic transducer (PZT), and then is reflected back to the laser cavity by the mirror according to the original path. The SMI is formed with the laser inside the cavity. The phase shift of the SMI signal is realized by changing the optical path of the feedback light to the laser cavity through the PZT-driving mirror movement. The PD receives the interference signal at the backward leakage end of the laser. The prism is placed on the step rotating platform, and the $p$ -polarized light incident on the gold film is changed by rotating the platform. The attenuator is used to regulate the intensity of the feedback light.

Fig. 2. SMI-based SPR system.

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As shown in Fig. 2, $p$ -polarized light interacts with the sample twice, back and forth. Consequently, the intensity and the phase of the light change twice. According to Eqs. (2) and (3), the relation among intensity, phase, and incidence angle can be expressed as

R^{'} (θ) = | r_{1, 3} (θ) | \times | r_{1, 3} (θ) |,

ϕ^{'} = 2 \arctan [\frac{Im (r_{1, 3})}{Re (r_{1, 3})}] .

$P$ -polarized light takes two SPR effects and then returns to the laser cavity. It interferes with the light in the laser cavity. The feedback intensity of $P$ is related to $R^{'} (θ)$ . Using $ϵ \cdot R^{'} (θ)$ to replace the light feedback intensity coefficient $C$ , the intensity and phase equation of the SMI-based SPR model can be expressed as

P = P_{0} [1 + K \cdot μ \cdot ϵ \cdot R^{'} (θ) \cos (4 π \frac{L_{0} + Δ L}{λ} + ϕ^{'})],

ϕ_{SMI} = 4 π \frac{L_{0} + Δ L}{λ} + ϕ^{'},

where

ϵ

is one of the parameters of the optical feedback intensity that can be set manually. By tuning this parameter, the SMI is set under weak feedback state to ensure that the SMI signal obtained by the system is approximately sinusoidal;

L_{0}

is the initial distance from the mirror to the laser cavity;

Δ L

is the moving distance of PZT, which is carrying the mirror;

λ

is the wavelength of the laser.

The intensity and phase of the sample are both related to the angle of incidence and the refractive index of the sample. If the incident angle of the light is known, the relationship among the intensity, phase, and change of the refractive index of the sample can be calculated. In our experiment, the refractive index of the prism is 1.516 (K9 glass). The thickness of the gold film is 50 nm. The dielectric constant of the gold film is $- 13.4 + 1.4 j$ . $λ = 632.8 nm$ . The incidence angle is the SPR resonance angle of distilled water (70.5°). $L_{0} = 400 mm$ . The range of change in the refractive index of the sample is from 1.30 to 1.37. Let $P_{0} = 1$ , $K \cdot μ \cdot ϵ = 0.1$ (when the system is in a weak feedback condition); the refractive index of the sample $n$ and $Δ L$ are both related to time $t$ . Suppose $n = 1.30 + v t$ , where $v$ is the speed of change in the refractive index of the sample; suppose $Δ L = v^{'} t$ , where $v^{'}$ is the moving speed of PZT. Then Eq. (7) can be written with $n$ as variable. Assuming $v = 10^{- 3} RIU / s$ , $v^{'} = 200 nm / s$ , the obtained simulation interference signals are as shown in Fig. 3. According to Eqs. (2), (3), (7), and (8), the simulated relationship between the reflectivity and the refractive index of the sample, and the relationship between the phase and the refractive index of the sample are shown in Fig. 4.

Fig. 3. Interference signal in the SMI-based SPR model.

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Fig. 4. Relation curve among intensity, phase, sensitivity, and refractive index. (a) Relationship among the intensity, phase, and refractive index with traditional two-beam interferometer, (b) relationship among the intensity, phase, and refractive index with the SMI, (c) relationship between the sensitivity and the refractive index with traditional two-beam interferometer, and (d) relationship between the sensitivity and the refractive index with the SMI.

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As Fig. 4 shows, the refractive index corresponding to the minimum intensity of the light wave is the resonance refractive index. The intensity changes slowly, and the phase changes rapidly near the resonance refractive index, indicating that the phase has a high sensitivity in this position. Within the same change range of the refractive index near this position (shown in the A-B section in Fig. 4), the phase change of SPR based on the SMI is twice that of the SPR phase change of a traditional two-beam interferometer (shown in the C-D section in Fig. 4).

Sensitivity is generally used to measure the measured value of SPR, quantitatively evaluated by the intensity or the slope of the phase curve. The relationship between the sensitivity of intensity and the refractive index of the sample, and the sensitivity of the phase and the refractive index of the sample are separately defined as

S_{r} = | \frac{d R}{d n} |,

S_{ϕ} = | \frac{d ϕ}{d n} |,

where

S_{r}

is the sensitivity of reflectivity, and

S_{ϕ}

is the sensitivity of the phase. The sensitivity in Figs. 4(a) and 4(b) can be calculated according to Eqs. (9) and (10). In Figs. 4(c) and 4(d), the blue curve represents the first derivative of the intensity of SPR signal with respect to the refractive index of the sample. The red curve represents the first derivative of the phase of SPR signal with respect to the refractive index of the sample. It can be seen that around the resonance angle, the SPR phase detection sensitivity of the SMI is twice as much as that of the two-beam interference SPR.

In order to verify the feasibility of the proposed technique, the process of the change in the refractive index caused by the dissolution of NaCl particles is monitored by the experimental device shown in Fig. 2. The light source is a linearly polarized He–Ne laser (power 0.5 MW, working wavelength 632.8 nm), and its polarization direction is adjusted to the relative P direction of the mirror surface coated with the thickness of 50 nm gold film, which is on the excitation prism. The attenuator is used to regulate the intensity of the feedback light, so as to make the SMI in the weak feedback state. To ensure that the light beam transmitted by the prism is consistent with the laser beam direction, the two same isosceles right-angled prisms are applied to the synthesis of a trapezoid prism. The parameters of each single prism are: $n = 1.5163$ , and waist length and thickness are both 32.5 mm. The reflection coefficient of the reflector is greater than 92%; PZT is the P-625.1CD type piezoelectric ceramic platform of the PI company (the stroke is 500 μm, and the resolution is 1.4 nm); the PZT controller is the E-625 type piezoelectric controller of the PI company; the stepping stage is driven by the stepping motor, and the rotation step is set to 0.1°; the PD is a Hamamatsu S7686 type PD; the signal processing circuit converts the photocurrent to the voltage signal, amplifiers, and filters; the PCI6220 data acquisition card of the National Instruments Company is used to collect the photoelectric signal and control the stepping stage, and the sampling rate of PCI6220 is 250 k samples/s. We use signal averaging (single-point acquisition 2000 times and then averaged) and a hardware low-pass filter to improve the signal-to-noise ratio.

The 30 μl distilled water is dripped into the sample pool with a pipette. The rotation of the stepping stage with a trapezoid prism is controlled by a stepping stage controller. The angle of the $p$ -polarized light incident to the gold film is slightly greater than the resonance angle of the distilled water (the resonance angle of the distilled water is about 70.5°, and the incident angle is adjusted to 72° in the experiment). The light beam after the coupling prism is kept parallel to the incident direction and is vertically incident to the mirror. The reflector is driven by the PZT controller in a translation motion (the moving step is 20 nm, and the moving range is 60 μm), and the SMI signal is detected. Then 7.5 mg NaCl particles are added to the sample pool to dissolve into the distilled water in the sample pool. The recording curve of the change of the refractive index caused by the solution of NaCl particles is obtained as shown in Fig. 5.

Fig. 5. SPR recording curve of refractive index change caused by dissolution of NaCl particles.

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The interference signal of distilled water is measured before the addition of NaCl particles, as shown in the A-B section in Fig. 5. When the NaCl particles are added to the distilled water (in order to make the refractive index of the sample near the incident light spot continue to change slowly, the position of the addition deviates from the spot), the refractive index of samples near the incident light spot gradually becomes larger as the particles dissolve in distilled water. The SPR resonance angle of the sample increases gradually, and the resonance peak shifts to the direction of angle that is larger than the resonance angle of the distilled water, as shown in the B-C section in Fig. 5. The C position indicates that the incident angle of polarized light on the gold film changes to the SPR resonance angle of the sample. The C-D section in Fig. 5 indicates that the resonance peak is shifting continually. During the monitoring time (the displacement modulation is 60 μm, and it takes $\sim 72 s$ ), the sample solution is not saturated (the refractive index of the sample is not stable). If the monitoring time is prolonged, the vibration amplitude of the interference signal will tend to be stable.

In order to observe the relationship between the intensity and phase in the dissolution process of the NaCl particles, the intensity of the vibration amplitude of the SMI signal is expressed by valley–peak subtraction, and the phase of the SMI signal is obtained by the Fourier transformation fringe phase analysis method. The relationship between the intensity/phase curve of the signal and time in the whole measurement process is shown in Fig. 6.

Fig. 6. Relationship curve between the intensity and the phase change of NaCl particles during the dissolution process with time.

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Figure 7 shows the sensitivity curves of amplitude and phase versus time. As shown in Figs. 6 and 7, the intensity of reflection is the weakest at about 22 s, indicating that at a fixed angle of incidence (72°), the refractive index of the NaCl solution is the SPR resonance refractive index at this time, and the sensitivity of the intensity is low at this point, but the phase changes obviously. The maximum value of phase change is about 3 rad, which is consistent with the simulation results in Fig. 4(b), and that is double of the phase change for two-beam SPR. The phase sensitivity is twice as much as that of the conventional interferometric SPR. Therefore, the detection limit of our proposed method can theoretically be half that of the traditional method.

Fig. 7. Intensity and phase sensitivity of NaCl particles in the dissolution process.

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In summary, we propose an SMI-based SPR phase sensing technique that allows for a simple and compact configuration. The technique can also achieve double phase sensitivity in comparison with existing phase detection SPR techniques. The proposed technique is experimentally demonstrated by monitoring the change process of NaCl solution refractive index. The results demonstrate the phase sensitivity doubling capability of the proposed technique. The proposed technique adds much practicability to SPR sensing technology.

Funding

National Natural Science Foundation of China (NSFC) (61605063); Natural Science Foundation of Guangdong Province (2014A030310483, 2015A030310458); Guangdong Province Higher Vocational Colleges & Schools Pearl River Scholar Funded Scheme (GDHVPS) (2016).

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Phase-sensitivity-doubled surface plasmon resonance sensing via self-mixing interference

Abstract

Funding

REFERENCES

Cited By

Figures (7)

Equations (10)

Optics Letters