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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/JLT.2019.2907786, Journal ofLightwave Technology

Abstract—This paper presents an original design for a volume

refractive index (RI) sensor for cell concentration detection based

on the unique resonant optical tunneling effect (ROTE). In this

design, the solution sample is introduced into the ROTE resonant

cavity, whose reflection spectrum presents a large shift of its

resonant dip in response to the tiny change of the solution RI.

Performance calibration using the polystyrene (PS) particle

solution indicates that the sensitivity is 19,000 nm/RIU and the

total Q factor is 620. Experiments with hepatoma cells have

obtained sensitivity values as high as 2.53 nm/(amol/ml) and a

detection limit of 1.2 × 105 cells/ml. Compared with previously

reported optical cell sensors, this original work implements the

ROTE mechanism for the first time and presents superior device

performance. Thus, the proposed design has a high potential for

use in biomedical applications, such as drug discovery, cell

research and medical diagnoses.

Index Terms—resonant optical tunneling effect, optical

biosensor, cell concentration, figure of merit.

I. INTRODUCTION

ELL concentration (number of cells/ml) is considered a

key indicator that reflects a series of cell processes, such as

viral infection [1-3], abnormal hematopoiesis [4], drug

reactions [5], and autoimmune disease [6]. Refractive index (RI)

measurements are widely used to quantitatively analyze

extremely small variations in the chemical components of a

solution. For example, 10-9 refractive index unit (RIU) is

equivalent to 1 femto-mol/L of salt in water. Recently, RI

measurements have been implemented and have real-time and

label-free methods of detecting cell concentrations at high

resolution [7].

Most of the current typical sensing mechanisms/structures of

RI sensors are based on near-field optics [8], such as optical

fiber Bragg grating (FBG) [9], long period fiber grating (LPG)

[10-11], photonic crystal/photonic crystal fiber (PCF) [12-13],

and whispering gallery mode (WGM) [14-18]. In addition, 2D

materials have been widely used in optical sensors because of

This study is financially supported by the National Natural Science

Foundation of China (No. 61501316, 61471255, 51622507, 51505324,

81602506 and 61377068), the Shanxi Provincial Foundation for Returned Scholars (2015-047), 863 project (2015AA042601), Excellent Talents

Technology Innovation Program of Shanxi Province (201605D211027),

Hundreds of Talents of Shanxi Province, and Research Grants Council of Hong Kong (N_PolyU505/13, 152184/15E and 152127/17E).

A. Q. Jian, L. Zou, G. Bai, Q. Q. Duan, Y. X. Zhang and S. B. Sang are with

Taiyuan University of Technology, MircoNano System Research Center,

College of Information and Computer Science, No. 79, Yingze Road (West),

their distinctive optical properties [19-21]. Y. J. Xiang et al.

designed a series of hybrid structure surface plasmon resonance

(SPR) sensors, in which 2D materials are employed for sensor

performance enhancement. For example, a graphene layer was

utilized to prevent the metal layer (Al) from oxidizing and to

increase both light and biomolecule adsorption to enhance the

sensitivity [22]. Moreover, the graphene layer acted as a

sensitive film to facilitate coupling between the two surface

plasmon polaritons (SPPs) modes, which are capable of high-

resolution RI sensing in the THz range [23]. Furthermore, MoS2

was found to be more absorptive of light energy and the

sensitivity can be further improved [24]. The heterostructures

of a limited number of black phosphorus (BP)-graphene/TMDC

(MoS2, WS2, MoSe2, WSe2) layers were also introduced to the

SPR sensors, and the performance of the various combinations

of 2D materials was compared [25].

Hyperbolic metamaterials, which are characterized by

hyperbolic dispersion, present a sensitive multilayer structure

and have drawn intensive research attention recently, and they

show considerable potential for RI sensing. Significant

sensitivity enhancement can be achieved for high-order modes

due to their spectral positions closer to the resonance of certain

permittivities [26] and stronger electromagnetic fields near the

interface [27]. Based on its unique characteristics, a compact

plasmonic biosensor platform has been developed with a

maximum of 30,000 nm/RIU and a record figure of merit (FOM,

which is defined as the ratio of the sensitivity to the full width

half maximum) of 590 [28].

For these detection methods above, evanescent waves near

the two-media interface are exploited. The strong confinement

of the evanescent waves near the interface favors the strong

light-analyte interaction. However, the intensity of evanescent

waves decays exponentially with distance away from the

interface, which inevitably limits the spatial interaction depth

to the subwavelength range. These sensors cannot be used to

effectively measure the entire biological sample with a size

larger than the wavelength (e.g., eukaryotic cells at 10–100 µm)

or the samples/particles naturally suspended in the solution.

Taiyuan, 030024, Shanxi, China.(e-mail: [email protected];

[email protected]; [email protected]; [email protected];

[email protected]; [email protected]; Q. W. Zhang is with Key Laboratory of Specialty Fiber Optics and Optical

Access Networks, Shanghai University, Shanghai 200072, China

([email protected]). X. M. Zhang is with The Hong Kong Polytechnic University, Department of

Applied Physics, Hung Hom, Kowloon, Hong Kong SAR, China (e-mail:

[email protected]).

Highly sensitive cell concentration detection by

resonant optical tunneling effect

Aoqun Jian, Lu Zou, Gang Bai, Qianqian Duan, Yixia Zhang, Qianwu Zhang, Shengbo Sang, and

Xuming Zhang

C

mailto:[email protected]:[email protected]:[email protected]:[email protected]



However, in the case of volume RI sensing, light waves

completely propagate through the solution containing the

targeted analyte and interact with every particle in the shaft,

which is particularly useful for detecting samples with ultralow

concentrations. Volume RI sensing can be realized by some

classical methods/schemes, e.g., Fabry-Pérot (FP) etalon.

However, the complex fabrication process of a highly reflective

mirror with tiny absorption prevents its comprehensive

commercial application [29-30].

Since the first demonstration by Hayashi’s group [31], the

resonant optical tunneling effect (ROTE) has shown its unique

ability to bridge wave optics and quantum physics [32-37] and

has considerable potential for use in both theoretical studies

[38-39] and practical applications as photonic devices [40-43].

This study will present the first experimental demonstration of

a RI sensor based on the ROTE. This sensor overcomes the

spatial limitation of the evanescent field and can achieve high

sensitivity detection of whole cells. With simple fabrication, the

sensor successfully detects hepatoma cell concentrations with a

resolution of 1.2 × 105 cells/ml, and its FOM value is

comparable to that of other cutting-edge optical methods [7, 44].

II. MATERIAL AND METHODS

A. Concept and sensor design

The ROTE originates from a relatively simple phenomenon,

the optical tunneling effect (a.k.a., frustrated total internal

reflection, FTIR). When the incident angle θ is larger than the

critical angle of the interface between high and low RI media,

some of the evanescent light can pass through the total

reflection interface to form tunneled light if the low-RI layer is

thin enough [45]. Briefly, the ROTE refers to the resonance

effect of such tunneled light in a well-designed resonator, and

its structure consists of five layers with a high-low-high-low-

high distribution of RI, which are named in turn as follows:

input layer, first tunneling gap, central slab, second tunneling

gap, and output layer along the light propagating direction as

shown in Fig. 1a.

By using the finite difference time domain (FDTD) method,

the electric field distributions of the ROTE structure (one-

dimensional model) at the resonant wavelength are illustrated

in Fig. 1b (S-polarized light) and Fig. 1c (P-polarized light).

Fig. 1. (a) Schematic of the multilayer structure for the resonant optical

tunneling effect (ROTE). The electric field distributions of light propagation in the ROTE structure at the resonant wavelengths of reflection for (b) S-polarized

light and (c) P-polarized light. (d) Design of the ROTE sensor for the volume

RI detection.

Except for the length of the central slab (15 μm), which is

shortened to save the simulation resource and time, the

parameters involved in the simulation are equivalent to the

values shown in TABLE I. For both polarization states, the

electric field tends to decrease in the first tunneling gap and then

form a locally enhanced mode in the central slab, similar to a

TABLE I

PARAMETERS OF THE RESONANT OPTICAL TUNNELING EFFECT (ROTE)

MULTILAYERED STRUCTURE

Parameter Symbol Value

Incidence angle α 61°

Width of tunneling gap d 3 μm

Width of central slab g 300 μm

Refractive index of input and

output layers nin, nout 1.59+9.84 × 10

-9 i

Refractive index of the

tunneling gaps n1 1.308+5 × 10

-6 i

Refractive index of central slab n2 To be determined



standing wave, before it finally decays in the second tunneling

gap. These two graphs show that the incident wave propagates

across the whole ROTE structure, thereby enabling volume RI

sensing.

According to our previous study [40], the ROTE

transmission is more sensitive to RI changes in the central slab

than to that of the tunneling gaps. Therefore, the central slab is

chosen as the sensing element rather than the tunneling gaps. A

schematic diagram of the sensor based on ROTE is shown in

Fig. 1d. In this study, K9 prisms coated with low-RI polymer

layers are used to form the photonic barriers and the cell

solution injected between the two photonic barriers acts as the

central slab. The polymer layer (MY-131 series, RI = 1.308 RIU)

forms a low-RI dielectric layer between the prism (RI = 1.59

RIU) and the liquid sample to be tested (RI = 1.35–1.37 RIU).

In this way, the RI distribution has the order of high-low-high-

low-high, which meets the requirement of the ROTE. The

detailed parameters of the sensor device are listed in TABLE I.

Because the ROTE peak/dip of the S-polarized light is much

sharper than that of P-polarized light (by a factor of 1000 [40]),

the sensor is chosen to work in the S-polarized state in the

following experiments to achieve a better performance.

B. Preparation of the ROTE multilayered structure

Because the triangular prism is too heavy to be safely fixed

on the spin coating machine, the low-RI polymer film cannot

be directly coated on the triangular prism surface. Thus, it is

coated on a glass slide with the same material (K9) as the

triangular prism. Then, the glass slide is seamlessly adhered to

the triangular prism reflector by a UV curing adhesive. Because

the thickness of the low-RI medium strongly influences the

experimental results, it is carefully checked by ellipsometry

before the experiment.

C. Experimental setup

The schematic diagram of the experimental setup is shown in

Fig. 2a. Because of the low absorption of the cell in the near

infrared and infrared wavelengths, a tunable infrared fiber laser

(TIFL, New Focus TLB-6700) is employed as the light source

to reduce the influence of the laser thermal effect on cell

physiology. The polarization state of the emitted laser is tuned

to be S-polarized by a fiber polarization controller (FPC) and

verified by a polarization splitting prism (not shown in Fig. 2a).

Before the incident laser is collimated by the single mode fiber

(SMF) collimator, an optical fiber attenuator is utilized to adjust

the laser intensity. In the experiment, the incident angle (61°) is

greater than the total internal reflection angle by 1°. Finally, the

reflected laser is collected by a photodetector (New Focus

1811-FC-AC), recorded together with the synchronous signal

from the laser by a digital storage oscilloscope (DSO, GDS-

2302A), and further transferred as the reflection spectrum of the

ROTE structure.

In the experiments, the position of the reflected spot is

recorded and the incident angle can be calculated based on

geometric relationships. The thickness of the low RI film is

measured by an ellipsometer (AST SE200BA) in advance.

According to the theoretical study, the free spectral range (FSR)

of the ROTE reflection spectrum is mainly determined by the

incident angle, the width of the gap and the RI of the medium

in the gap. When the incident angle and RI are input as

constants, the FSR is only dependent on the separation of the

prisms. Therefore, the width of the analyte region can be

derived by fitting the experimental curve in the case of the gap

filled with the liquid using a definite RI. Before every series of

cell density measurements, the gaps are filled with the RI

matching fluid and the FSR is utilized as a reference for the

separation adjustment. Thus, the sensor is calibrated and the

uniformity of the analyte’s thickness is ensured in the

experiment. Different analyte solutions are prepared with

different concentrations, and the RIs of these solutions are

measured by a commercial digital RI detector (AR200 digital

hand-held refractometer). Then, one of the solutions is injected

into the gap (i.e., the central slab of the ROTE) between the two

triangular prisms with proper pressure to overcome the surface

tension. The thickness of the liquid analyte layer is equal to the

width of the gap. Because the irradiations out of resonance are

totally reflected at the high-low RI interface, their intensities are

considered to be the reference for output normalization. After

each measurement, the gap is washed with alcohol and fully

dried to restore the initial operation conditions. Finally, the

wavelength shift of the ROTE characteristic dip in the reflected

spectrum is recorded for further analysis.

Fig. 2. Experimental setup of the ROTE sensor. (a) Entire measurement system

that utilizes a tunable infrared laser (TIFL) to sweep the wavelength range to detect the reflection spectrum; and (b) close-up and (c) photograph of the ROTE

structure.

III. RESULTS AND DISCUSSION

A. Performance calibration using polystyrene particles

The sensor performance is first calibrated using polystyrene

(PS) particles, which have equivalent properties as the material

of interest, before the sensor is used to measure real cells. The

PS is an optically transparent material, and the dispersed PS

particles in aqueous solution are similar to the cells in culture

fluid. Therefore, PS particles are often used as a substitute for

cell experiment. The concentration of the PS particle solution



can be evaluated with ultrahigh accuracy by weighing the dry

Fig. 3. (a) Shift of the resonant dip with the change of the RI of the analyte. (b)

Measured thermal drift as a function of the test time. (c) Enlarged view of the

resonant wavelength shift. The experimental reflection spectra are compared with the simulation results.

PS particles to be dissolved. These particles are utilized to

mimic the cell solution and to preliminarily characterize the

performance of the ROTE sensor. In the experiment, different

amounts of PS particles (5 µm diameter, standard deviation ≤

0.027 µm, Duke Scientific Corp.) are dissolved in anhydrous

ethanol as the target analyte. Because the RI of the PS particles

(1.590 RIU) is larger than that of anhydrous ethanol (1.361

RIU), a higher concentration of PS particles in the mixed

solution would result in a greater RI. The experimental results

indicate that the ROTE absorption dip in the reflection spectrum

experiences a redshift as the RI of the intermediate analyte layer

increases (Fig. 3a). The sensitivity obtained is 19,000 nm/RIU,

and the Q value of the ROTE absorption dip is 620.

Because long-term laser transmission will directly heat the

analyte in the central slab and change its RI during the

measurement, the variations in the ROTE resonant wavelength

over the test time under a particular laser power are recorded

(Fig. 3b). The resonant wavelength has a linear relationship

with the measured time, and the slope is ‒5 pm/min. To avoid

this problem, the thermal drift is removed in all measurements

in this study. A close-up of the ROTE reflection spectrum is

presented in Fig. 3c to clearly show the details of the

wavelength shift due to the RI variation. The experimental

results are consistent with the theoretical analysis obtained by

the transfer matrix method (TMM), and additional details on

this method can be found in the authors’ previous work [40].

The slight difference between the theoretical and experimental

results may be related to certain negligible factors, such as the

optical dispersion of the materials involved in the system (low

RI polymer and liquid analyte) and the parallelization of the

prisms.

B. Q factor analysis of the ROTE dip

The experimental ROTE reflection spectrum and the

simulation results are shown in Fig. 4. According to Gansch et

al. [46], the total Q factor of the resonator can be written as

follows:

radabsstrtotal QQQQ

1111 (1)

where Qrad is the Q factor due to the coupling loss of the

incident light, Qstr accounts for the loss of reflection and

refraction in the model structure, and Qabs originates from the

loss of material absorption.

The values of these Q factors can be obtained from the

simulation and the experiment. For instance, Qstr can be

determined from the simulation without considering the

material absorption (the red curve in Fig. 4). However, if the

complex value of RI is used when determining the material

absorption (the orange curve in Fig. 4), the ROTE characteristic

dip becomes significantly broader, and a value of Qabs = 650 is

obtained by comparing these two simulation curves. Based on

the experimentally measured spectrum (the green curve in Fig.

4), a value of Qtotal = 620 is directly obtained. Then, a

comparison of the differences between the simulated and the

experimental spectra generates a Qrad value of 1.3 × 104. To

achieve a high quality factor, we improve our device based on

multiple aspects, such as selecting low absorption materials and

optimizing the structural dimensions. Compared with the

simulations performed by our group, negative factors remain in

the experiment, such as the parallelization of the prisms, which

leads to a decline in the Q factor.



Fig. 4. Comparison of the reflection spectra of the ROTE sensor with the FP

etalon. The ROTE spectra are obtained from the experiment and the simulations

under different conditions (with/without absorption).

Based on Eq. (1), the calculated value of Qstr is 1.28 × 106,

which is very high and demonstrates that the ROTE structure is

an excellent resonator. For further comparison, the reflection

spectrum of an ideal FP etalon with 99.6% reflectivity mirrors

is also plotted in Fig. 4. The cavity length of the FP etalon is

equivalent to the effective length of the ROTE structure. The

FP cavity has a Qstr value of 3 × 105, which is lower than that of

the ROTE structure by one order of magnitude. Since a higher

Q factor is more favorable for a higher resolution of volume

sensing, the ROTE structure is used in this work to detect the

cell concentration instead of the classical FP cavity.

The loss of energy is mainly caused by absorption by the

material in the system, which includes three parts (materials),

such as the prism (glass), the low-RI layer (polymer), and the

analyte solution (alcohol solution with PS particles). The main

source of absorption is from the liquid analyte due to its high

RI imaginary part and its large thickness (~300 μm). A dilemma

arises when we try to detect a low concentration solution based

on RI because higher sensitivity indicates a stronger light-

analyte interaction, which also induces stronger absorption of

the solvent (typically water or phosphate buffered solution, PBS)

and thus a lower Q factor and reduced sensor resolution.

Therefore, prerequisites for excellent sensor performance

include the reasonable optimization of parameters and a

consideration of the balance between sensitivity and the Q

factor.

C. Cell detection experiments

Hepatoma cells of different concentrations are used as the

analyte to be measured in this experiment. The initial cell

amount is counted on a hemocytometer. Pure cells are separated

from the cell culture fluid by centrifugation. Then, different

amounts of cell-containing solutions (2, 2.2, 2.4, 2.6, and 2.8 µl)

are extracted using a pipette before they are mixed with 500-µl

RI matching solution (Cargille AA, 1.4580 RIU), which can

maintain the cell morphology during the measurement process.

Five different concentrations of cells are prepared (1.19 × 105,

2.39 × 105, 3.59 × 105, 4.79 × 105, and 5.99 × 105 cells/ml). Fig.

5a shows the ROTE reflection spectra of the five sample

solutions. The RI variations can be retrieved by the shift of the

ROTE dip. Fig. 5b plots the dip wavelength as a function of the

cell concentration (the Q factor is approximately equal to 950).

The sensitivity reaches as high as 2.53 nm/(amol/ml), and the

cell concentration of 1.2 × 105 cells/ml can be easily

discriminated.

Fig. 5. (a) ROTE dip presents a redshift as the cell concentration of the analyte

increases. (b) Dependence of the ROTE resonant wavelength on the cell concentration.

TABLE II compares our ROTE sensors with some other

classical cell sensors in the literature, such as localized surface

plasmon resonance (LSPR) sensors [44], FP etalons [47], titled

TABLE II

COMPARISON OF OUR ROTE SENSOR WITH OTHER CLASSICAL SENSORS IN

THE LITERATURE

Working

principle

Sensitivity

(nm/RIU) FOM

Detection Limit

(cells/ml)

LSPR [44] 535 104~106

FP etalon [47] 1013

LSPR + FP etalon [49] 496 ~104

TFBG [7] 180 2500 ~105

PCF [48] 38000 4.6×10-7 RIU

ROTE 19000 7600 1.2 × 105

LSPR, localized surface plasmon resonance FP, Fabry–Pérot

TFBG, tilted fiber Bragg grating PCF, photonic crystal fiber



fiber grating (TFBG) sensors [7] and PCF sensors [48]. From

TABLE II, the ROTE sensor is superior in sensitivity and

comparable in FOM. In addition, the detection limit of the

ROTE sensor is among the best. These findings demonstrate the

excellent performance of our ROTE cell concentration sensor.

IV. CONCLUSIONS

In this study, ultrahigh sensitive cell concentration detection

is experimentally demonstrated by exploiting a special physical

mechanism of the ROTE. By using PS particles as the model,

the ROTE sensor has been calibrated to have a sensitivity of

19,000 nm/RIU and a Q value of 620. The experiments with

hepatoma cells have shown that the detection limit of the

concentration resolution is as low as 1.2 × 105 cells/ml, which

is comparable to the best results obtained by other optical cell

sensors. The ROTE sensor will be particularly useful for drug

screening, environment protection and drinking water safety.

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