A Review of Optical Interferometry Techniques for Quantitative Determination of Optically Active Materials in a Solution

Abstract

Human diet is primarily comprised of optically active ingredients like glucose, sucrose, fructose, amino acids, lactic acid, cholesterol etc. Quality control is one of the most important processes in food industries to test, measure and verify the product for quality control standards. Optical techniques are mostly adopted in these industries for standardization of purity and concentration of optically active ingredients in their products. Quantitative measurements of optically active materials (OAMs) in a solution by interferometry have attracted the intention in present days due to their wide working range, high sensitivity and lower limit of detection. OAMs cause rotation of the angle of polarization when a plane-polarized light passes through them. The angle of rotation is distinct for different materials at different concentrations. For interferometric quantitative determination, the OAMs are generically placed in an arm of the interferometer and their effect on the interference fringe patterns are monitored as a function of their concentrations. Furthermore, the refractive indices of OAMs varies with their concentrations which directly affect the resultant interference pattern. Owing to the vast range of interferometric arrangements and processing techniques, this review assesses the different approaches adopted in detection of concentration of OAMs in a solution by interferometry.

1. Introduction

Optically active materials are the fundamental constituents of the human body and its nutrients. Major part of the daily human diet is comprised of OAMs, and has a strong impact upon wellness and performance of the human body. The monitoring of OAMs in everyday nutrition is of vital importance for being healthy, lean and active. Therefore, a strong check of quality control is always the matter of concern is the industries including food, chemical, pharmaceutical, beverages etc. The OAMs cause the rotation in the angle of polarization of linearly polarized light when it pass through them. The variation in plane of polarization is different for different materials at different concentrations. OAMs are not limited to sugar (glucose, sucrose, fructose, maltose etc.), proteins, acids (tartaric acid, lactic acid etc.), cholesterol, etc.

A number of prescribed analytical techniques have been employed such as Ultra-voilet visible (UV–vis) absorption spectroscopy [1, 2], thin-layer chromatography (TLC) [3], infrared (IR) and Fourier transform infrared (FTIR) spectroscopy [4, 5] and Raman spectroscopy [6, 7]. However, optical techniques such as polarimetry [8, 9], interferometry [10, 11] and refractrometry [12] are commonly used in most of the practical applications for quantitative determination of OAMs due to their rapidity, noninvasiveness and non-destructive nature of their method of analysis.

OAMs are usually comprised of at least one asymmetric atom inside their molecular structure. The list of those atoms include carbon, sulfur, phosphorous, silicon etc. The asymmetric nature of these molecules result in the formation of two different types of isomers. The isomer of the same substance which rotates the plane of polarization of the light clockwise is called dextrorotatory or right-handed. However, those molecules which cause anti clock wise rotation of the polarization is called levorotatory or left-handed. Optical activity is the result of left–right asymmetry around the central carbon atom in the case of amorphous substances. The geometrical shape and chemical composition of both the molecules are same but left-handed isomer is mirror image of right-handed isomer and both of them are called enantiomers, as shown Figure 1 for the D and L configuration of glucose molecule. Both of the enantiomorphs rotate the plane of polarization of light exactly by same magnitude but in opposite directions.

Figure 1.

Dextrorotatory and levorotatory configuration of glucose molecule.

2. Theoretical analysis

2.1 Biot’s law

The foundation of detection of analytes concentration by using optical polarimetry trace back to the observation of Biot’s in early nineteenth century [13]. The mathematical equation for the optical interaction of linearly polarized light with optically active specimen was described as below which is also called Biot’s law;

$${\left[\mathrm{\alpha }\right]}_{\mathrm{\lambda }}^{\mathrm{T}}=\frac{\mathrm{\alpha }}{\mathrm{LC}}$$E1

The term ${\left[\alpha \right]}_{\lambda }^T$ is known as specific rotation of the OAM under consideration for specific wavelength of light (λ) at temperature (T). Where, α is the detected rotation of plane of polarization of light, L is the path length of the sample under test and C is the concentration of sample.

2.2 Analytical treatment of interference of linearly polarized light beams

Suppose two monochromatic light beams with same frequency originating from single source represented by the electric field vector ${\overrightarrow{\mathrm{E}}}_1\text{and}{\overrightarrow{\mathrm{E}}}_2$ and interfere at the point of observation P. Let the light beams are generalized by the equations below however, physical waves will be represented by their real parts only

$${\overrightarrow{\mathrm{E}}}_1={\overrightarrow{\mathrm{E}}}_{01}{\mathrm{e}}^{-\mathrm{i}\left(\mathrm{\omega t}-{\mathrm{k}}_1.\mathrm{r}-{\mathrm{\varphi }}_1\right)}$$E2

$${\overrightarrow{\mathrm{E}}}_2={\overrightarrow{\mathrm{E}}}_{02}{\mathrm{e}}^{-\mathrm{i}\left(\mathrm{\omega t}-{\mathrm{k}}_2.\mathrm{r}-{\mathrm{\varphi }}_2\right)}$$E3

Where $\mathrm{\omega }$ is the angular frequency of the monochromatic light wave, $\mathrm{r}$ is the position vector of incident point P, ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ are the wave vectors and ${\mathrm{\varphi }}_1$ and ${\mathrm{\varphi }}_2$ are the phase differences of beam 1 and 2, respectively. According to the principle of superposition, the irradiance at point ‘P’ can be calculated as:

$${\mathrm{I}}_{\mathrm{P}}={\overrightarrow{\mathrm{E}}}_1+{\overrightarrow{\mathrm{E}}}_2$$E4

The time averaged irradiance is proportional to the square of the amplitude of the electric field, i.e., for linear, homogeneous, isotropic dielectric medium;

$$\mathrm{I}=\mathrm{ϵ\upsilon }{⟨{\mathrm{E}}^2⟩}_{\mathrm{T}}$$E5

Where $ϵ$ is the permittivity of the medium and $\upsilon$ is the velocity of light in that medium. Considering the relative irradiance within the same medium except for the constant of proportionality, Eq. (4) may be transformed into;

$${\mathrm{I}}_{\mathrm{P}}={\overrightarrow{\mathrm{E}}}_{\mathrm{P}}.{{\overrightarrow{\mathrm{E}}}_{\mathrm{P}}}^{\ast }=\left({\overrightarrow{\mathrm{E}}}_1+{\overrightarrow{\mathrm{E}}}_2\right).{\left({\overrightarrow{\mathrm{E}}}_1+{\overrightarrow{\mathrm{E}}}_2\right)}^{\ast }={\mathrm{I}}_1+{\mathrm{I}}_2+{\mathrm{I}}_{12}$$E6

Where,

$${\mathrm{I}}_1={\overrightarrow{\mathrm{E}}}_1.{{\overrightarrow{\mathrm{E}}}_1}^{\ast }={\mathrm{E}}_{01}^2$$E7

$${\mathrm{I}}_2={\overrightarrow{\mathrm{E}}}_2.{{\overrightarrow{\mathrm{E}}}_2}^{\ast }={\mathrm{E}}_{02}^2$$E8

and

$${\mathrm{I}}_{12}={\overrightarrow{\mathrm{E}}}_1.{{\overrightarrow{\mathrm{E}}}_2}^{\ast }+{\overrightarrow{\mathrm{E}}}_2.{{\overrightarrow{\mathrm{E}}}_1}^{\ast }={\overrightarrow{\mathrm{E}}}_{01}.{\overrightarrow{\mathrm{E}}}_{02}\left({\mathrm{e}}^{\mathrm{i\delta }}+{\mathrm{e}}^{-\mathrm{i\delta }}\right)=2{\overrightarrow{\mathrm{E}}}_{01}.{\overrightarrow{\mathrm{E}}}_{02}cos\mathrm{\delta }$$E9

Where,

$$\mathrm{\delta }=\left({\overrightarrow{k}}_1-{\overrightarrow{k}}_2\right).\overrightarrow{r}+\left({\varphi }_1-{\varphi }_2\right)$$E10

The I₁ and I₂ are the irradiance of the individual beams and I₁₂ represents the interference term. The symbol, $\mathrm{\delta }$ represents the total phase difference between the two waves at the point of interest P. From Eq. (9) it can be observed that maximum inference will occur if both the beams are parallel to each other and no interference will occur if both the vectors are orthogonal to each other. For maximum interference Eq. (9) can be written as;

$${\mathrm{I}}_{12}=2{\mathrm{E}}_{01}{\mathrm{E}}_{02}cos\mathrm{\delta }=2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}cos\mathrm{\delta }$$E11

and total irradiance at point P will become

$${\mathrm{I}}_{\mathrm{P}}={\mathrm{I}}_1+{\mathrm{I}}_2+2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}cos\mathrm{\delta }$$E12

The interference is called fully constructive if $cos\delta =2\mathit{n\pi }\mathit{\text{where}}n=0,1,2,\dots$ then Eq. (12) can be written as;

$${\mathrm{I}}_{\mathrm{P}}={\mathrm{I}}_1+{\mathrm{I}}_2+2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}$$E13

Eq. (13) is called the maximum intensity or the maxima of fringes pattern (constructive interference) and can be interpreted as;

$${\mathrm{I}}_{\max }={\left({\mathrm{E}}_{01}+{\mathrm{E}}_{02}\right)}^2$$E14

and I_P will be minimum if the term $2\sqrt{I_1{I}_2}cos\delta$ is negative, i.e., $cos\delta =-1$ which is possible only if $cos\delta =\left(2n+1\right)\pi$ for n = 0,1,2, …, and I_P will be called I_min;

$${\mathrm{I}}_{\min }={\mathrm{I}}_1+{\mathrm{I}}_2-2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}={\left({\mathrm{E}}_{01}-{\mathrm{E}}_{02}\right)}^2$$E15

If the two interfering light waves are mutually coherent then the time averaged value of $cos\delta$ overtime period T should not vanish and a stationary fringe pattern will be obtained in space i.e.,

$${⟨cos\mathrm{\delta }⟩}_{\mathrm{T}}=\frac{1}{\mathrm{T}}{\int }_0^{\mathrm{T}}cos\mathrm{\delta }\mathrm{dt}\ne 0$$E16

At different points of observation ($\overrightarrow{\mathrm{r}}$), different values of ${⟨cos\mathrm{\delta }⟩}_{\mathrm{T}}$ will be obtained and resultantly different intensities will be obtained at different locations in space. Also $\left({\mathrm{\varphi }}_1-{\mathrm{\varphi }}_2\right)$ should not vary in time otherwise $⟨cos\mathrm{\delta }⟩=0$ and no sustained interference fringe pattern will be obtained. The quality of interference fringes is quantitatively described by visibility (V):

$$\mathrm{V}=\frac{{\mathrm{I}}_{\max }-{\mathrm{I}}_{\min }}{{\mathrm{I}}_{\max }+{\mathrm{I}}_{\min }}$$E17

Where I_max and I_min represents the irradiances corresponding to maximum and adjacent minimum in the interference fringes. If one beam is incident with some small angle $\theta$ with respect to the plane of incidence then visibility could be defined as;

$$\mathrm{V}=\frac{2\sqrt{{\mathrm{I}}_1{\mathrm{I}}_2}\text{cosψ}}{{\mathrm{I}}_1+{\mathrm{I}}_2}$$E18

Where, I₁ and I₂ are the irradiances of reference and sample beams respectively and $\mathrm{\psi }$ is the polarization angle of the sample beam of the interferometer [14].

3. Interferometry for OAMs detection

3.1 Mach-Zehnder interferometer

The Mach-Zehnder interferometer is most commonly used for sensing applications and was first introduced by Ludwig Zehnder in 1891 and Ludwig Mach in 1892 independently. In this interferometer, a coherent light beam is split into two using beam splitter and then recombined on another beam splitter with the help of two mirrors to obtain interference pattern. One part of the splitted beam is called reference while other one is called sensing arm. The chiral sample is kept in the sensing arm of the interferometer and its effect on the contrast of the interference fringes is detected. The interference fringes are normally recorded by a camera and analyzed by image processing techniques. MZI has good potential for the detection of OAMs therefore, most of the time exercised in the literature for this purpose.

Calixto et al. proposed a Mach-Zehnder interferometer (MZI) based wavefront division polarimeter for the measurements of chiral solute concentrations in solutions as shown in Figure 2. An optically active solution was kept in a sample chamber in the sensing arm of a MZI. One beam of the polarized light was passed through a liquid sample containing dissolved OAM while the other half of the light was used as reference beam. The plane of polarization of the incident linearly polarized light was rotated when the sample beam propagated through the chiral solutions. As a result, a decrease in the visibility of the interference pattern was observed with increase in the concentration of the OAMs in the solution. Contrast of the interference fringe pattern was maximum when both the sample and reference beams presented a polarization perpendicular to the plane of incidence. However, the visibility of the fringe pattern was deteriorated fully when the polarization of the sample beam is oriented parallel to the plane of incidence. The effect of decrease in the fringes visibility was mainly due to the increase in the refractive index of the solution with increase in the concentration of the OAMs as shown in Figure 3. The following calibration equation was obtained for variation of the visibility of the fringe pattern and concentration of the fructose solution:

Figure 2.

Schematic diagram of the Mach-Zehnder interferometer and interference fringes pattern recording system [14].

$$V\left(c\right)=0.643-0.31c^2+0.048c^4$$E19

Where, ‘V’ is the visibility of the interference fringe pattern and ‘c’ is the concentration of the chiral materials (Figure 3).

Figure 3.

The effect of concentration on the visibilities of fringes pattern by solutions of (a) fructose and (b) glucose [14].

H.A. Razak et al. proposed an optical sensor based on fiber optic MZI for food composition detection as depicted in Figure 4. The MZI structure was employed as fiber optic sensor in single mode-multimode-single mode (SMS) structural configurations using fusion splicing technique. The interferometer was investigated with 4 cm and 8 cm sensing regions. The sensor response was tested for detection of water, sugar and oil from their respective refractive indices as representative major components of food. A red-shift was seen in the wavelength for increase in the refractive index of the constituent sample. The sensitivity of the sensor was found to be directly dependent on the length of the sensing region.

Figure 4.

(a) Basic block diagram of optical fiber MZ interferometer. (b) Schematic representation of SMS structure. (c) Schematic diagram of liquid concentration detector [15].

A miniature broad-band (BB) MZI was proposed by M. Kitsara et al. for the detection of label-free biochemical OAMs sensing as shown in Figure 5. A theoretical investigation was performed on Si-based MZI with BB input lights in the range 450 nm – 750 nm. They have proved that BB-MZI can be used as a miniaturized optical sensor with enhanced sensitivity, versatile biochemical sensing applications and economical fabrication and operating costs compared to its counterpart single wavelength (SW) MZI. Glucose was used as a representative biomolecular entity because of its relatively small size to demonstrate the designed BB-MZI to detect its concentration in a very diluted solutions with a higher efficiency. The phase changes of the evanescent field at Nd:YAG (532 nm) and He-Ne (633 nm) lasers were studied to evident that an optical setup could be designed where the source of light and MZI chip vary according to application. The theoretical transmission spectra of BB-MZI as a function of the refractive index of the solution were reported for 10 mM, 25 mM, 50 mM and 100 mM glucose concentrations. The recorded peak shifted with concentration of glucose. The performance of the BB-MZI was also observed with a hypothetical protein adlayer over the sensing arm of length 300 μm. An ultra-thin protein adlayer was sensed with recording of the spectral changes or by observing the variation in the integrated intensity. The potential of the designed interferometer was investigated for biomedical applications. It was observed that the performance of the BB-MZI is comparable to the SW-MZI without a requirement of a costly laser system as an input light source.

Figure 5.

Schematic diagram of the prosed BB-MZI for detection of label-free biochemical chiral materials sensing [16].

A. Psarouli et al. also investigated a monolithically integrated BB-MZI for label free detection of biomolecules with high sensitivity as shown in Figure 6. A transducer based on monolithic silicon microphotonic was developed for this purpose. The MZI was fabricated from monomodal silicon nitride waveguides with silicone light emitting diodes (LEDs). BB light was injected into the interferometer setup and were sinusoidal modulated by optically active biomolecules with two different frequencies of the polarization before exiting the sensor. The distinct reporting of the two polarizations and simultaneous investigation of the TE and TM signals were performed by deconvolution in the Fourier transform. The quantitative determination of the binding adlyaers were made possible from their refractive indices by dual polarization analysis over the broad spectral range. The sensor was equipped with power and control electronics, a docking station, an off-chip fluidic circuit, a miniature spectrometer and an optical module. The set of ten interferometers were interrogated with a defined time delay by integrated LEDs which were operated by control electronics. The proposed interferometric sensor was found 60 and 550 times more sensitive than a two-lateral-mode spiral waveguide MZI [18] and polyimide-waveguide MZI [19], respectively.

Figure 6.

(a) Schematic of the biochip showing the monolithic integration of the avalanche-type LED, the MZI, and the silicon nitride rib waveguide. (b) Layout of the 10 MZIs showing the MZI routes as well as the LED positions and metal [17].

An asymmetric Mach-Zehnder interferometer (aMZI) was introduced by M. J. Goodwin et al. for interferometric biosensing applications [11]. The device was manufactured using TriPleX technology. The interferometer was fabricated on a chip consist of Si₃N₄ waveguide with silica cladding which made a photonic integrated circuit (PIC). A sensing window was fabricated by locally removing the SiO₂ cladding which given a provision to analyte to make a contact with the waveguide. In the proposed design, the incoming light was split into two arms by the waveguide. One of the arm was exposed to the analyte and the other arm was used as reference. The interference pattern was detected on at the point of recombination of the two arms due to the deliberately induced asymmetry. Subsequent to interaction of the analyte with the evanescent field of the waveguide at the sensing window, a phase shift was introduced due to variation in the refractive index. Performance of the proposed sensor platform in terms of signal-to-noise-ratio (SNR) and absolute response is compared with the commercial quartz crystal microbalance with dissipation (QCM-D). The aMZI proved itself dominated over the QCM-D due to measurement capability streptavidin binding with no need of the added complication of hydrodynamically coupled water which allow the elucidation of absolute protein adsorption. Also the aMZI presented 200 times good SNR and therefore offered a relatively lower limit of detection.

The operation of a versatile and sensitive integrated optical MZI biosensor with three-guide coupler at the output was demonstrated by B. J. Luff et al. as shown in Figure 7. The interferometric devices were designed by Ag⁺–Na⁺ ionexchange in glass substrates. The chemical modification of the waveguide surface of the interferometer made possible the detection of the biochemical species. The waveguide were designed in BGG36 glass with refractive index about 1.6 at 786 nm by Ag⁺–Na⁺ ion-exchange. Photolithographically patterned Ti film was used as the masking material with opening width of 1 μm. The fabricated device was characterized by different concentrations of sucrose solutions to vary the superstrate index. For building up multilayers of protein over the sample surface, a high affinity interaction between vitamin biotin and protein streptavidin base system was used. The refractive index and thickness of the protein multilayer system was calculated reproducibly based on waveguide model.

Figure 7.

(a) Schematic diagram of the biosensor device configuration based on MZI. (b) MZI with three-waveguide coupler [20].

3.2 Fabry–Pérot interferometer

Fabry–Pérot interferometer (FPI) also called etalon is based on an optical cavity made from two parallel reflecting surfaces. The interferometer is named after Charles Fabry and Alfred Perot for their invention in 1899. The parallel reflecting surfaces of the FP cavity is separated by a distance ‘d’ which allows the transmission of infinite number of parallel to each other as shown in Figure 8. A sharp constructive interference can be recorded when these parallel beam superimposed with each other. Free spectral range (FSR) analysis can be used to calculate the separation between the reflective ends of the cavity from refractive index information of a known medium. The spacing between the two reflective surfaces can be calculated from the FSR from refractive index of a known medium, as follow;

Figure 8.

Schematic diagram of the principle of the Fabry-Perot interferometer etalon. Basic structure of cavity [21].

$$\mathrm{FSR}=\mathrm{\Delta \upsilon }={\mathrm{\upsilon }}_{\mathrm{m}+1}-{\mathrm{\upsilon }}_{\mathrm{m}}=\frac{\mathrm{c}}{2\text{ndcosθ}}$$E20

Where, $\mathrm{\upsilon }$ is the frequency at which transmission of maximum intensity occurs, m determines an integral order of transmission peaks, $\mathrm{\theta }$ is the angle of maximum transmission, d is the separation between the end reflective cavity surfaces and n is the index of refraction of a specific medium. FP interferometers are highly sensitive for the detection of OAMs therefore, mostly applied by the researchers in the literature.

The FPI is highly sensitive to any perturbation causing a variation in the optical path length between its two reflective mirrors as presented in Figure 9. Due to its compact size, high sensitivity and fast response, the FPI is applied for different physical parameters sensing, biosensing, gas sensing, current and magnetic field detection etc. [23]. FP etalons based optical sensors provide an efficient label-free biosensing capability with enhanced sensitivity. The biosensing of etalon is measured in terms of absorption or phase shift subsequent to interference between the reflected light beams from the two reflecting surfaces in its cavity [24, 25, 26, 27, 28, 29].

Figure 9.

(a) FP interferometer having reflective surfaces with reflectivity of R₁ and R₂, respectively. Examples of intrinsic and extrinsic FP interferometers. (b) Schematic representation of the FP based experimental setup employed for detection of gaseous biomolecules [22].

G. Allison et al. investigated an efficient FP cavity coupled surface plasmon photodiode for electrical label-free biomolecular sensing [30]. The surface plasmonic sensor was developed inside a photovoltaic cell. The information of solutions containing biomolecules was extracted from its refractive indices in the form of electronic signal generated subsequent to incident light. The resultant photocurrent was enhanced due to surface plasmon mode coupling with the FP modes inside the photovoltaic cell due to its absorbing layer. An optically transparent substrate with special ability for surface plasmon resonance (SPR) was replaced by a silicone layer of semi-transparent optical nature. With the help of this mechanism, an absorbing layers was sandwiched between a metallic layer and an optically transparent conducting electrode. Photocurrent was caused as a result of incident light due to built-in potential of fabricated device in a similar nature to that of photovoltaic cell. The surface plasmon was excited in the metal layer and generated the photocurrent simultaneously by illuminating a thin silicon layer by a visible light with single wavelength at a resonant angle. The photocurrent was reduced drastically by surface plasmon due to disruption of the distribution of electric field in the silicone layer. The mechanism were further enhanced by the silicone layer as an optical FP cavity to produce the FP modes which were coupled with the plasmon mode. The mechanism was confirmed by the simulation of the distribution of electric field which was further confirmed experimentally by electric detection of mode and resultantly the variations in the refractive index and the protein – protein interactions were measured.

A microfluidic optical sensor integrated with FP etalon geometry was investigated for detection of concentrations of different biochemical species in solution by K. E. You et al.. The concentration information were extracted in terms of the refractive index variation with concentration with high accuracy and sensitivity. The FP cavity was fabricated from a liquid channel with two partially reflected Ag/SiO₂ reflective surfaces. The refractive index dependent interference peaks were achieved in the transmission spectra subsequent to transmission of light through the fluid channel. Concentrations of different biomolecules, i.e., glucose, potassium chloride and sodium chloride were calculated from their refractive indices in terms of a shift in the position of maxima of wavelength of the interference peaks in the transmission spectra. The devised optical sensor shown a linear response with good accuracy. Sensitivities of 10⁻³, 1.4x10⁻³ and 1.8x10⁻³ refractive indices per percent of glucose, KCl and NaCl, respectively were obtained. Schematic diagram of the investigated FP cavity based optical sensor and its response to the optically active glucose sample was shown in Figure 10.

Figure 10.

Schematic diagram of the devised modified microfluidic Fabry-Perot etalon (a) 2D view, (b) simulation (c) refractive index vs. glucose concentration (%) [21].

A micro Fabri-Pérot interferometer (MFPI) was designed and developed for quantitative determination of sugar in a transparent solutions by G. Chavez et al. as shown in Figure 11(a). The MFPI was developed in the form of a micro bubble made of a hollow core photonic crystal fiber (PCF) as shown in Figure 11(b). The cavity was fabricated by splicing of a segment of PCF to a single mode fiber (SMF) by a conventional arc fusion splicer which form an air MFPI. The fabricated MFPI then acted like an optical cavity having two reflecting surface of different refractive indices separated by a distance d. The erbium doped fiber (EDF) was illuminated by 200 mW laser diode with 980 nm wavelength with the help of wavelength division multiplexer (WDM). Output light from EDF was incident on the MFPI subsequent to passing through a three-port circulator. The reflection from MPI was guided towards optical spectrum analyzer (OSA) by port three of the circulator. The MFPI was immersed inside a sugar solution filled cuvette and the reflected interference patterns were recorded at different concentrations of sugar solution in the range 0–30.88 g/100 ml. The contrast of the interference fringes decreases with increased in the sugar concentration in solution as illustrated in Figure 11(d). The predicted results from simulation were also experimentally confirmed with good agreement. The reflected optical power was directly decreased with increase in the concentration and resultant refractive index of solution with sensitivity of −0.0123 dBm/(g/100 ml) at 1538.27 nm wavelength.

Figure 11.

(a) Schematic diagram of the experimental setup for MFPI based sugar concentration sensing, (b) schematic view of the fabricated MFPI, (c) reflected energy and the refractive index of the exit medium at λ = 1538.27 nm as a function of the sugar concentration (d) measured reflected power spectra for different sugar concentrations and (e) enlarged view of the spectra [31].

J. Martini et al. also proposed a glucose concentration sensor in interstitial fluids based on a small size double-chamber FP etalon. One of the FP chamber of the proposed sensor was used as reference to overcome the effect of ambient temperature variations. The 400 μm etalon cavity was filled with water – glucose solution which had FSR of 680 pm in response to the normal incident light of wavelength 850 nm. A wavelength shift of ∼1 pm was produces per 1 mg/dl of the optically active analyte (glucose). The light beam from an SM vertical cavity surface emitting laser (VCSEL, 850 nm) was guided towards 50/50 beam splitter and was incident on one of the FP chamber subsequent to proper collimation. The perpendicular half of the beam was redirected into the other FP chamber with the help of a prism. The transmitted light signal from FP chamber were recorded by PIN photodiodes with two active segments as shown in Figure 12. Difference in the refractive indices of the two etalon chambers produced a phases in the transmitted optical signals. The proposed optical sensor was studied in the range 0–700 mg/dl of glucose concentration with precision of ±2.5 mg/dl. The temperature compensation was confirmed in the range 32–42°C.

Figure 12.

(a) Schematic diagram of the experimental setup of the double-chamber FP etalon (b) spectral position of FP modes for two different refractive indices (c) calibration curve of the refractive index with varied concentration of glucose [32].

3.3 Sagnac interferometer

In the Sagnac interferometer, the light beam is split to follow the same optical path but in opposite directions in the form of a closed loop. The beams get interference upon returning back to the point of entry. In the case of optical fiber Sagnac interferometer, a section of birefringent fiber is splices to the loop which causes interference between the counter propagating light beams.

A Sagnac interferometer based optical sensor system was designed, developed and demonstrated by T. Kumagai et al. for quantitative analysis of glucose in a solution. The optical rotation proportion to concentration of glucose concentration was measured in a Sagnac loop from a phase difference introduced between the clockwise (CW) and counter clockwise circularly polarized light. The proposed optical sensor was composed of a Sagnac interferometer made from a polarization maintaining fiber (PMF) and other optical components to avoid the unwanted sources of noise due to different reasons. A coherent light of wavelength 840 nm from a super luminescent diode was transmitted in the sensor system. Two orthogonal mode of polarizations with a minor difference in their propagations constants were transmitted in the interferometer. The ambient sources of noise those were temperature variations and external vibrations may vary the zero level of the output signal which were controlled by fabricating the interferometer from PMF. A quarter-wave retarder was used to convert the linearly polarized light into circularly polarized light which was subsequently passed through a low birefringence span SMF or in free space. The interference signal achieved from recombination of CCW and CW lights was confirmed from the output of a preamplifier and was physically observed on an oscilloscope. The polarization measurement system (polarimeter) was checked by measuring the phase difference with the help of Faraday effect optical rotation measurement setup. In this regard, current was applied to a 1300-turn copper coil and a span fiber was a wounded around the coil. Concentration of glucose was measured from the degree of optical rotation using Biot’s law as shown in Eq. (1). The phase difference analysis was performed in a I dm long measurement cell. The specific rotation of +51.6 and − 91.2 were measured for glucose and fructose respectively which were close to their physical properties. To make the sensor suitable for practical applications, the active length of the measurement cell was reduced to about 2 mm and the resolution of the sensor was monitored. A trial based noninvasive measurement with human body was performed by skin webbing between fingers. The resultant interference between CCW and CW lights was investigated. The skin webbing caused a bias in the interference signal which was observed in the form of noise due to a phase difference between CCW and CW light. A resolution of 1 mg/dl was achieved for glucose concentration and 0.5 mdeg resolution of optical rotation was detected for the devised sensor (Figure 13).

Figure 13.

(a) Configuration of optical rotation measurement system with a Sagnac interferometer. (b) Concentration dependent optical rotation of sugar samples [33].

An optical polarimetry based Sagnac interferometry technique was investigated for noninvasive glucose sensing by A. M. Winkler et al. [34]. A phase sift in the interference fringes of the Sagnac interferometer was detected in a glucose solution as a representative OAM. The proposed method was linked with the sugar detection from the aqueous humor of human eye. The interferometer was simulated such that the counter propagating beams in which one of them passed through an optically active sample caused a difference in the optical path traversing. The effect was due to a difference in the refractive indices of the left and right circularly polarized beams.

A compact PCF Sagnac interferometer based glucose sensor was introduced by G. Ann et al. [35]. A light signal from a broadband light source was launched in a 3 dB coupler and split into two beams.. A Saganac loop was mainly comprised of a polarization controller and PCF spliced with an SMF. The splitted beams counter propagated and interfered with an accumulated phase difference when passed through the PCF. The interference signal was effected greatly by the phase difference between the two orthogonal guided modes of PCF. A similar trend of phase birefringence was observed when the wavelength was varied in the range 1000–2000 nm with a gradual decrease in the maxima of the curve with increase in the glucose concentration. The nature of the devised sensor was analyzed between 15 cm to 40 cm. It was observed that the response of the sensor was highly sensitive to the PCF length. A prominent interference peaks were observed between 1050 nm to 2000 nm. The interference signatures becomes highly sensitive with good SNR for 20 cm PCF length. An average sensitivity of 0.76 mg/dL of glucose solution in water was recorded which is lower than 70 mg/dl of hypoglycemia episodes. The sensor was designed for effective sensing of glucose level in the patients with hypoglycemia.

3.4 Michelson interferometer

In this type of interferometer, a coherent light beam is split into two by a beam splitter. Each of the two beams are reflected back and recombines at the same beam splitter to get interference pattern. Although, the Michelson interferometer has good potential for the detection of OAMs but rarely applied due to its relatively complex optical arranges. L. K. Chin reported a droplet Michelson interferometer for biochemical and protein detection. The interferometer was fabricated in the form of on-chip liquid grating as schematically shown in Figure 14(a). A branch of the interferometer was spared for injection of two immiscible liquids. A T-junction was developed for the formation of the liquid grating. The other branch with microchannel was filled with immersion oil which caused a phase shift due to optical path difference produced in the paths of light transmitted through the core and the cladding. A buffer solution was injected in the third branch to measure its refractive index. An optical fiber was aligned with one end of the microchannel for input/output light detection and the other end was coated with a gold film to use it as end mirror. The light was coupled from core to the cladding with the help of liquid grating. In the interferometer, the second and third branches of the microchannel was used to propagate the light which was reflected back by the gold layer which caused an optical path difference. An interference pattern was observed with attenuation band when both the light signals recombines in the core subsequent to passing through the liquid grating as shown in Figure 14(b). The microchip was fabricated in polydimethylsiloxane (PDMS) using lithography. Sputtering technique was applied to coat the sidewall of the PDMS edge. The PDMS slab with the pattern was attached with the unpatented PDMS slab using plasma bonding. The broadband light was coupled by an optical circulator with the optofluidic chip. The reflection from the optofluidic interferometer was detected by an OSA. The immersion oil and glycerol with refractive indices 1.462 and 1.420, respectively were used as carrier and dispersed flow, respectively. Reflection from the devised interferometer for different buffers with distinct refractive indices was recorded by the spectrum analyzer as shown in Figure 14(c). Two distinct attenuation peaks were observed in the overall attenuation band at slightly different positions and intensities.

Figure 14.

Schematic illustrations of (a) the droplet Michelson interferometer and (b) the physics model of Michelson interferometer (c) reflection spectra of liquid grating Michelson interferometer [36].

4. Conclusion

In this study, different interferometric optical sensors employed for the detection and quantification of OAMs are briefly reviewed (Table 1). The working principle, design and the important performance parameters including working range, sensitivity, and limit of detection were discussed in detail. Different materials analyzed in the sensors were outlined with special focus on sugar and protein being a representative OAMs. Two different interferometric arrangements, i.e., free space and optical fiber based optical sensors were discussed. It was concluded that optical fiber based interferometry has mind blowing potential for highly precise sensing of OAMs with good sensitivity and can be applied in industrial and research and development applications.

Interferometer	Characterized material	Dynamic range	Sensitivity	Limit of detection	Reference
Mach-Zehnder	Protein	50–1000 nm	2000 nm/RIU	—	[11]
	Glucose	625 mg/ml	−2.36^o/ml	25.5 mg/ml	[14]
	Fructose	922 mg/ml	−1.31^o/ml	37.5 mg/ml
	Sucrose	—	4.413 nm/RUI	—	[15]
	Glucose/protein	—	—	10 mM	[18]
	Protein	—	0.4 rads/ng/mm^2	2 pg/mm^2	[20]
	Glucose	0–25%	0.001 RUI/%	10-5 RUI	[21]
Fabry–Pérot	glycerol	0–50%	1.5 μA/mRIU	10 pg/ml	[30]
	Sugar	0–30.88 g/100 ml	−0.0123 dBm/(g/100 ml)	—	[31]
	Glucose	0–700 mg/dl	2.5 mg/dl		[32]
Sagnac	Glucose	0–0.6 g/dl	0.5156 deg/(g/dl)	1 mg∕dl	[33]
	Fructose	0–0.6 g/dl	0.9120 deg/(g/dl)	—
	Glucose	0–500 mg/dl	—	—	[34]
	Glucose	0–120 g/l	2.63 nm/g/l	0.76 mg/dl	[35]

Table 1.

Comparison of different OAMs analyzed by different interferometric arrangements.