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Abstract
A method for determining the phase shift of a Mach Zehnder interferometer (MZI) is presented. It is based on switching the wavelength of continuous wave (CW) laser light illuminating the MZI and measuring the interferometer output amplitudes at DC and switching frequency. The method can measure the MZI phase shift unambiguously over the entire phase shift range of 2π. A practical proof of concept demonstration shows that the method can perform real-time measurement with high repeatability and accuracy limited by the optical frequency drift and power fluctuation of the lasers. The method does not require modifications of the sensor or accessing to the laser electronics and also uses simple detection. It is, therefore, suitable for bio and medical sensing applications.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Biosensors have made great impacts in many areas such as health research, medical diagnosis, food safety, security, and environmental monitoring [1]. Biosensors utilise bio-receptors to recognise a specific analyte. The binding events between the analyte and the bioreceptor are converted into readable signals using transducers. Depending on the transducing mechanism, biosensors can be broadly categorised into chemical, electrical, and optical-based sensors [1]. Among them, optical biosensors are one of the most widely used due to their label-free, non-invasive, and non-destructive measurement of the analyte. Optical sensors also offer high specificity, high sensitivity, and low noise [2]. They are also highly compact and compatible with microfluidic technology, enabling full device integration for realising sophisticated lab-on-a-chip applications [3].
In optical biosensors, the analyte-bonded bio-receptor changes the refractive index of the material in the proximity of the optical waveguides [2,3]. This change in refractive index can be precisely measured using resonant or interferometric structures. Resonant structures such as ring resonators change the resonant wavelength in response to the refractive index change [4]. On the other hand, interferometric structures such as Mach Zehnder interferometer (MZI) have one arm exposed to and the other arm protected from the sensing analyte. The refractive index change caused by the analyte is proportional to the phase delay difference between the two arms and therefore the quantity of the sensing analyte can be determined by measuring the phase delay. Although both structures have been used for biosensing, the interferometric structures exhibit the sensitivity that scales with the phase delay and this amount can be deliberately designed to be very large to enhance the detection sensitivity. Therefore, optical biosensors based on interferometric technology offer one of the highest sensitivities in the field [4].
Despite their high sensitivity, the periodic response of interferometric biosensors makes them challenging to read and interpret output [5]. The traditional method for interrogating interferometric sensors is to measure the output intensity and count the number of interference fringes to determine the sensing phase shift [6]. This method is simple but prone to false reading due to output fluctuation with the optical power and temperature variation [7]. Several methods have been investigated to improve the accuracy and reliability of the interferometer phase interrogation. One method uses optical phase modulation and measurement of the modulation harmonics at the sensor output to determine the phase delay [5]. Another method uses the optical frequency comb to sample the frequency response of the interferometer to determine the interferometer spectral response shift to infer the phase delay [4]. The first approach uses laser modulation which causes laser instability and thus impacts the smallest phase change that could be measured accurately compromising the method limit of detection [5]. The second approach although eliminates the disturbance to the laser, it however requires sophisticated optical sources and complex detection equipment and thus increases the system cost [4].
In this paper, we propose and demonstrate a novel phase interrogation scheme for optical MZI-based biosensors that does not disturb the optical source, nor require sophisticated optical frequency comb or complex detection equipment. The method is based on wavelength switching where the two stable optical sources are left undisturbed, and their wavelengths are combined by an external optical switch. The switch creates a “wavelength switching” optical source using a square-wave modulation to select one of the two wavelengths alternately. The wavelength switching optical carrier is then used to interrogate the sensor phase delay. By detecting the DC and the fundamental frequency components of the switching signal at the interferometer output, the sensor phase can be determined accurately and unambiguously. Since the method does not disturb the lasers and uses a simple detector to retrieve the interferometer phase shift, it overcomes the constraints of the existing methods.
This paper is organised into six sections. Section 2 presents the MZI phase interrogating concept and develops the underlined theory. Section 3 presents some rigorous simulations of the concept using VPItransmissionMaker photonic simulation software [8] and shows that the method is reasonably robust to optical wavelength drift and power variation. A practical demonstration of the concept is presented in Section 4. Real-time phase measurements, evaluation of measurement errors and system stability are also studied in this section. Finally, discussions and conclusions are given in Sections 5 and 6 respectively.
2. Topology and operation principle
Figure 1 shows the structure of the proposed biosensing system. Two laser diodes, which generate different-wavelength continuous wave (CW) light, are connected to a 2 × 1 optical switch. The optical switch is driven by a square-wave. Hence, the output of the optical switch alternates between the CW light from the two laser diodes. The wavelength switching optical signal is launched into an MZI, which consists of a sensing arm and a reference arm. The light at the MZI input is split into two portions, which pass through the sensing and reference arms before recombining at the MZI output. The MZI has a free spectral range (FSR) of c/(nΔL) where c is the speed of light in vacuum, n is the waveguide refractive index and ΔL is the length difference between the sensing and reference arms. When a measurand is placed on the sensing arm of the MZI, a time-varying phase shift Δφs(t) is introduced to the light passing through the sensing arm. This causes changes in the MZI output optical signal power given by the below equation:
Fig. 1. Schematic diagram of the proposed wavelength switching MZI based biosensor. OS: optical switch, MZI: Mach Zehnder interferometer, PD: photodetector, LPF: low pass filter.
The MZI output optical signal is detected by a photodetector (PD), which generates a photocurrent that is the product of the PD responsivity ℜ and the power of the optical signal launched into the PD. A low pass filter is connected to the PD output to select the DC and fundamental frequency components while suppressing other higher-order harmonics. The DC component of the photocurrent can be obtained from (4) and it is given by:
Initially, there is no measurand applied to the MZI sensing arm; the sensing phase is 0°. The system output DC voltage is VDC,out,0° = PinℜRo/2. Using (7) and (8) together with VDC,out,0°, the sensing phase Δφs(t) can be calculated as
3. Simulation results
The wavelength switching MZI phase interrogation scheme shown in Fig. 1 was verified using VPItransmissionMaker photonic simulation software [8]. A time delay of 10 ps was introduced to the upper arm of an MZI so that the MZI had an FSR of 100 GHz. The CW light into the MZI was generated by switching between the two laser sources. The two laser sources had the same power but different frequencies of 193.3395 THz and 193.3145 THz, located at -FSR/8 and −3×FSR/8 away from the MZI peak transmission frequency respectively. The output of the MZI was connected to a PD. A low pass filter and a bandpass filter were used at the PD output to select the DC and fundamental frequency components respectively.
Figure 2(a) shows the simulated DC and fundamental frequency components for different sensing phase over a complete phasing range from 0° to 360°. Obviously, the DC and fundamental frequency components vary as sine and cosine functions with respect to the sensing phase as predicted by (7) and (8). Figure 2(b) shows the fundamental frequency waveforms for the two cases of sensing phases of 30° and 120°. Evidently that they are out of phase with respect to each other illustrating the negative amplitude for fundamental frequency component of Fig. 2(a) for the phase range from 90° and 270°. Using (9) together with the values of the DC and fundamental frequency component amplitudes of Fig. 2(a), the sensing phase shift can be determined unambiguously as shown in Fig. 2(c). This verifies the proposed phase interrogation technique.
Fig. 2. (a) DC (blue dots) and fundamental frequency (red squares) component amplitudes versus different phase shifts introduced to the sensing arm of the MZI. (b) System output fundamental frequency waveforms for 30° (blue solid line) and 120° (red dashed line) phase shifts. (c) Calculated phase shift obtained using (9) versus the introduced phase shift.
In practice, the laser stability will nevertheless affect the phase measurement accuracy. We studied the impacts of the laser power variation and the optical frequency drift on the output waveform and the measurement accuracy. Figure 3(a) shows the phase errors when there is ±0.5 GHz variation in one of the laser frequencies. It can be seen from the figure that the phase errors are within ±2.9° for all phase shifts over the entire phasing range. Figure 3(b) shows the phase errors are within ±3.4° when the light powers arrived at the PD for the two wavelengths vary by ±0.2 dB. The result indicates that the maximum phase error occurs when the sensing phase is around 220° and 270° for Figs. 3(a) and (b) respectively. Figure 4 shows the system output waveforms when the system is operated under an ideal situation and when one of the laser sources is experiencing frequency drift or power variation, for the introduced phase shift of 240°, arbitrarily selected in the region of large phase error for both Figs. 3(a) and (b). As can be seen from the figures, the system output waveform retains its sinusoidal shape, but its DC offset and amplitude deviate lightly from those of the ideal cases. Particularly, for a + 0.5 GHz drift in the 193.3395 THz laser frequency, the amplitude of the system output DC and fundamental frequency component reduces by 4 mV and increases by 4 mV respectively; and for a −0.2 dB change in the 193.3395 THz laser power, the amplitude of the system output DC and fundamental frequency component reduces by 7 mV and increases by 9 mV respectively. These slight variations in the system output DC and fundamental frequency component amplitudes result in 2.6° and 2.1° phase measurement errors due to +0.5 GHz laser frequency drift and −0.2 dB laser power variation respectively. It is anticipated that the measurement error will reduce with the improvement of the laser stability. Since modern commercial DFB lasers have a typical power stability of ±0.02 dB and frequency drift of ±2 pm over 8 hours [9], using them as optical sources, the proposed method can provide high phase measurement accuracy.
Fig. 3. (a) Phase error versus introduced phase shifts when there is −0.5 GHz (red square) and +0.5 GHz (blue dot) change in the 193.3395 THz laser frequency. (b) Phase error versus introduced phase shifts when there is −0.2 dB (red square) and +0.2 dB (blue dot) change in the 193.3395 THz laser power.
Fig. 4. System output waveform when the system is operated under an ideal situation (black line). System output waveform (red line) when the 193.3395 THz laser source has (a) + 0.5 GHz frequency drift and (b) −0.2 dB power drift. The introduced phase shift is chosen at 240°.
4. Proof of concept demonstration
An experiment was set up as shown in Fig. 5 to demonstrate the proposed wavelength switching MZI based biosensing system. For the optical sources, two wavelength-tunable lasers (Keysight N7711A and Santec WSL-100) were used to generate CW optical carriers at 193.355 THz and 193.330 THz. The output of each laser source was connected to a variable optical attenuator (VOA) followed by a polarisation controller (PC) before launching into an optical switch (Agiltron CLSW). The power of each CW light from the laser source was adjusted using the VOA so that the power of the CW light into the optical switch was 8 dBm. The PCs were used to minimise the polarisation dependent loss in the optical switch. The optical switch was driven by a 2 kHz square-wave generated by a dual-output arbitrary waveform generator (AWG) (RIGOL DG5101). The output of the optical switch was connected to a Fourier domain optical processor (FD-OP) (Finisar WaveShaper WS-04000A), which was programmed to produce an MZI amplitude response to emulate a practical MZI based optical sensor. The effect of applying a measurand on the sensing arm of the MZI that causes an optical phase shift was emulated by translating the MZI response in frequency. The FSR and the initial peak transmission frequency of the MZI were set to 100 GHz and 193.3678 THz respectively. The optical signal was detected by a PD (Discovery Semiconductor DSC30S-39). The PD output was connected to a 2 kHz low pass filter to select only the DC and fundamental frequency components. This was then followed by an oscilloscope (Keysight DSOX2014A) for measuring the output waveforms.
Fig. 5. Experimental setup of the proposed wavelength switching MZI based biosensing system. VOA: variable optical attenuator, PC: polarisation controller, AWG: arbitrary waveform generator, OS: optical switch, FD-OP: Fourier domain optical processor, PD: photodetector, LPF: low pass filter.
Figure 6(a) shows the normalised amplitude responses of the MZI when the peak transmission frequency is set to 193.3678 THz and 193.3878 THz. This shows the MZI implemented by the FD-OP exhibits an excellent interferometer characteristic with the notch depths exceeding 30 dB for different peak transmission frequencies. The MZI FSR of 100 GHz remains the same as the peak transmission frequency is altered. The frequencies of the two CW light from Laser 1 and Laser 2 are also indicated in the figure using the black arrows, locating at −12.5 GHz and −37.5 GHz away from the MZI transmission peak of 193.3678 THz. Changing the MZI peak transmission frequency shifts the MZI response. This is equivalent to the effect of applying a measurand on the sensing arm of the MZI that causes an optical phase shift. Figure 6(b) shows the relationship between the MZI peak transmission frequency, and the optical phase shift introduced to one arm of the MZI. Since the MZI FSR is 100 GHz, a 100 GHz shift in the MZI transmission peak is equivalent to a 360° phase shift.
Fig. 6. (a) Normalised FD-OP programmed MZI amplitude responses with a peak transmission frequency aligned to 193.3678 THz (blue line) and 193.3878 THz (red line). The two arrows indicate the frequencies of the two CW light generated by the laser sources. (b) Introduced phase shift versus MZI peak transmission frequency.
The optical switch used in the experiment has a typical repetition rate of 2 kHz, which is sufficiently fast for biosensing applications that normally have a response time constant in the order of second or even minute [5]. A 2 kHz square-wave from the arbitrary waveform generator, as shown in Fig. 7(a), was used to drive the optical switch. The square-wave has a peak-to-peak amplitude of 9 V. For a ± 4.5 V driving voltage, the light from Laser 1 and Laser 2 passing through the optical switch has an on/off extinction ratio of ∼50 dB. The spectrum of the 2 kHz square-wave was measured on an electrical signal analyser and shown in Fig. 7(b).
Fig. 7. (a) Switching waveform and (b) electrical spectrum of the optical switch driving signal. The electrical spectrum was attenuated by 38 dB before input to the electrical signal analyser.
Figure 8 shows the system output electrical spectrums when the MZI peak transmission frequency was set to 193.3678, 193.3878, 193.4078 and 193.4528 THz, which are equivalent to introduce a 0°, 72°, 144° and 306° phase shift to the MZI according to Fig. 6(b). Figure 8 shows the second and higher-order harmonics are largely suppressed by the low pass filter. Figure 8(a) shows, when the MZI peak transmission frequency is 193.3678 THz, the power of the system output fundamental frequency at 2 kHz is −28.9 dBm. As the MZI peak transmission frequency increases, i.e., the introduced phase shift increases, the power of the fundamental frequency component reduces as can be seen in Fig. 8(b). The fundamental frequency component power reduces to a minimum value when the phase shift is 90°. Increasing the phase shift from 90° to 180°, the fundamental frequency component power increases from a minimum value to a maximum value. The fundamental frequency component power decreases to a minimum value again when the introduced phase shift is 270°, which agrees to the simulation result of Fig. 2(a). For an MZI peak transmission frequency of 193.4678 THz, which corresponds to a 360° phase shift, the power of the fundamental frequency component is close to that when the MZI peak transmission frequency is 193.3678 THz (0° phase shift).
Fig. 8. System output electrical spectrum when the MZI peak transmission frequency is (a) 193.3678 THz (phase shift = 0°), (b) 193.3878 THz (phase shift = 72°), (c) 193.4078 THz (phase shift = 144°) and (d) 193.4528 THz (phase shift = 306°).
Figure 9 shows the measured output waveforms associated with the four cases of Fig. 8. For reference, a 2 kHz signal synchronised with the square wave driving the optical switch produced by the AWG is also plotted. Evidently that both the amplitude and the DC offset of the output waveform varies with the MZI peak transmission frequency as expected from (9) and Fig. 2(a). Noting from Fig. 9(c) that, when the MZI peak transmission frequency is 193.4078 THz, there is a 180° phase change in the output waveform compared to that when the MZI peak transmission frequency is equal to 193.3678 and 193.3878 THz. This 180° phase change results in a negative fundamental frequency component amplitude as shown in Fig. 2(a).
Fig. 9. System output waveform (red line) when the MZI peak transmission frequency is (a) 193.3678 THz (phase shift = 0°), (b) 193.3878 THz (phase shift = 72°), (c) 193.4078 THz (phase shift = 144°) and (d) 193.4528 THz (phase shift = 306°). The blue line is a 2 kHz reference signal from the arbitrary waveform generator.
Figure 10(a) shows the amplitudes of the DC and fundamental frequency components obtained from the system output waveform measured using an oscilloscope for different introduced phase shifts emulated by changing the MZI peak transmission frequency. As the introduced phase shift increases from 0° to 360°, the DC and fundamental frequency amplitudes behave as the negative-sine and cosine functions respectively; a behaviour that is predicted and agrees excellently with (7) and (8).
Fig. 10. (a) Amplitudes of the system output DC (blue dots) and fundamental frequency (red squares) components versus the introduced phase shift emulated by changing the MZI peak transmission frequency over 360° phasing range. (b) Measured phase shift obtained from the amplitudes of the system output DC and fundamental frequency components using (9) versus the introduced phase shift.
The output DC amplitude for 0° phase shift is 0.028 V. The MZI phase shift can be obtained from the measurement of Fig. 10(a) using (9) and it is presented in Fig. 10(b). The phase error, which is the difference between the measured and introduced phase shifts, is calculated, and is plotted as the blue dots in Fig. 11(a). To confirm the repeatability of the measurement, the measurements were repeated for several times and the results are shown in Fig. 11(a) using the red-square and the green-triangle dots. It can be seen from Fig. 11(a) that the phase errors obtained from the three distinct measurements are within ±3° for the entire phasing range between 0° to 360°. The maximum phase error for this experiment is therefore approximately ±3°.
Fig. 11. Phase measurement error versus the introduced phase shift for the range from (a) 0° to 360° in the step of 36° with three distinct measurements presented using different dots superimposed and (b) 216° to 234° in the minimum step-size of 3.6°.
The MZI peak transmission frequency can only be varied in the step-size of 1 GHz due to the 1-GHz frequency resolution limitation of the FD-OP. This is equivalent to changing the introduced phase shift of the MZI in a step-size of 3.6° for the current experimental setup. Figure 11(b) presents the phase error obtained for an arbitrarily selected phasing range between 216° and 234° using the minimum step-size. It is evident that the measurement phase error is within ±2°. This result indicates that the proposed technique can accurately determine the optical phase shift of an MZI.
To study the system stability, several measurements versus time were obtained for two different phase shifts arbitrarily chosen being at 72° and 234°. For each phase, the measurements were repeated 11 times with a one-minute interval between measurements. Figure 12 presents the phase error for the 11 measurements. It is evident that the measurement variation is less than ±3°, demonstrating the excellent consistency and stability of the method.
Fig. 12. Measured phase error versus time for an introduced phase shift of 72° (blue dots) and 234° (red squares) for 11 measurements at one minute apart.
Real-time phase measurements were also conducted, by varying the MZI peak transmission frequency rapidly while monitoring the system output at DC and fundamental frequency in real-time. For a measurement period of 20 s, the introduced phase shift was varied instantaneously several times. The output waveform consisting of the DC and the fundamental frequency components was captured. Figure 13 presents the output waveform using the red line when the MZI peak transmission frequency abruptly jumps through a sequence of 193.3678, 193.387, 193.4378 and 193.4628 THz, which correspond to changing the introduced phase shift of the MZI through a sequence of 0°, 72°, 252° and 342° respectively. Evidently, the phase shift can still be measured with the phase error within ±3°, which is also consistent with the results of Figs. 11 and 12.
Fig. 13. System output waveform (red line) when the introduced phase shift is jumped through a sequence of 0°, 72°, 252° and 342° values. The blue line is a 2 kHz reference signal from the arbitrary waveform generator.
5. Discussions
The traditional method for MZI based sensor phase shift interrogation often requires a calibration step to determine the association of the output power to the initial optical phase shift, i.e., determine the sensor starting phase [6]. Such calibration step is not required for the technique demonstrated in this paper because the phase can be unambiguously determined from the two measurements of the DC and fundamental frequency components of the MZI output. Additionally, the demonstrated method is also capable of measuring the MZI phase shift instantaneously and continuously as shown in Fig. 13. Such capability may be necessary for observations of the temporal phase change, and it is useful for bio and medical sensing applications where the monitoring of the measurand evolution over time is sometime required.
Generally, any methods based on MZI output power measurement has a drawback of phase determination ambiguity due to the oscillating nature of the power response with the phase and the technique’s inability to distinguish between the two halves of the response oscillation cycle. On the other hand, the wavelength-switching technique utilises two measurements of the MZI output to resolve this ambiguity. The wavelength-switching technique therefore offers unambiguous measurement of the phase shift over the entire phasing range from 0° to 360°.
There are several existing techniques that offers unambiguous phase measurements for MZI based sensors such as the modulation of lasers [5], multiple offsetting outputs [10] and optical frequency comb sampling [4]. The modulation of lasers technique unavoidably disturbs the optical carrier and therefore directly affects the measurement sensitivity, limiting the smallest measurable phase change [5]. The multiple offsetting outputs technique requires non-conventional interferometer design [10], making it less versatile for using with a generic MZI based sensor. The optical frequency comb sampling technique utilises sophisticated and costly optical sources and detection equipment, making its design complex and costly. Conversely, the wavelength-switching method overcomes the above drawbacks, providing a simple solution that minimises disturbance to the lasers, works with any MZI structures and uses simple equipment. The method therefore presents an attractive practical method for interrogating MZI based sensors.
Although the wavelength-switching method does not disturb the laser sources, free-running lasers nevertheless exhibit phase and power instabilities or fluctuations. These fluctuations contribute to the measurement error of the MZI phase using the wavelength-switching technique as explained in Section 3. It was demonstrated that the measurement error can be up to ±3° for the laser frequency drift and power variation of ±0.5 GHz and ±0.2 dB respectively as shown in Fig. 3. Fortunately, modern Distributed Feedback (DFB) lasers have smaller frequency and power variations than these values and thus it is possible to reduce the phase error to less than 3°, illustrating the robustness of the method to the laser wavelength drift and power variation. Further improvement of the measurement accuracy can be achieved by using highly stable lasers such as the mode-locked lasers at the expense of increasing cost. However, it is important to note that this source of measurement error is not unique to the wavelength-switching technique and indeed affects all techniques. Therefore, the methods to minimise this error to enhance the phase interrogation accuracy is a useful topic for future research.
In comparison with the phase modulation method using temperature tuning of the laser frequency [5], the wavelength switching method does not disturb the laser; it is therefore anticipated that the stability of the optical carrier is improved, leading to the enhancement of the measurement accuracy, directly impacting the measurement sensitivity which is the smallest phase change that can be detected, i.e., the limit of detection. Demonstrating this impact is however, beyond the scope of this paper and thus, the investigation will be reported elsewhere.
In terms of complexity, the wavelength-switching method has similar complexity to the traditional power measurement method [6] and phase modulation method [5] but obviously, it is much simpler than the optical frequency sampling method [4]. Despite its simplicity, it still can deliver all advantages of all other methods such as low cost, high accuracy, rapid sensing, real-time, and stable phase measurement. It is therefore proposed to be an improved interrogation technique for MZI based sensors.
The proof-of-concept demonstration presented in Section 4 utilises a FD-OP programmed to emulate a practical MZI response. Characterisation of the FD-OP for different MZI phase shift settings showed that the response matches excellently to the expected response of a practical MZI as evident in Fig. 6. The concept therefore readily translates to a practical MZI based sensor.
In the current demonstration, a moderate optical power level was used to achieve a strong signal at detection. The output signal-to-noise ratio is excellent as evident by the high-quality output waveforms of Fig. 9. It is anticipated that the method will continue to perform well at a much lower optical power level. However, the investigation of the system performance versus optical power level is outside the scope of the current study and thus it was not included. Further improvement to the signal-to-noise ratio can be achieved by using low noise electrical amplification at the detector output. In the extreme cases, a lock-in amplifier can also be used to measure only the signals that are synchronised to the switching waveform to improve noise rejection. These approaches are obviously relevant when the limit of detection of the wavelength-switching method is investigated, and it is proposed for future investigation.
The MZI-based sensor exhibits a sinusoidal response with respect to the sensing phase shift. The slope of the response varies continuously with the phase shift where the greatest and zero slopes occur at the quadrature and π or 2π phase shift points respectively. Since the response slope indicates the sensor’s detection sensitivity, it is desirable to eliminate the zero slope from the sensor response. Several approaches can be investigated to overcome this loss of sensitivity including the use of offsetting sensor responses [11] or orthogonal responses such that when one response is at the zero slope, other responses will be at the non-zero slope or even at the maximum slope so that the overall response will be optimised. Such investigations are useful for improving sensing sensitivity and therefore they are also suggested for future studies.
6. Conclusion
A novel method for measuring the phase shift of an MZI based sensor has been presented. It is based on wavelength-switching of CW light illuminating the sensor. The frequency difference between the two CW light is chosen to be a quarter of the MZI’s FSR. The sensor output is analysed at both DC and the switching fundamental frequency. The DC and the switching fundamental frequency components are proportional to the sine and the cosine of the MZI phase shift. The phase shift can, therefore, be determined unambiguously. Simulation study shows that the method works as predicted by the theory and it is quite robust to the laser wavelength drift and optical power variation, producing phase measurement error within ±3° for optical frequency and power variation up to ±0.5 GHz and ±0.2 dB respectively. Since the stability of modern DFB lasers are better than the above values, it is anticipated using these lasers, the phase measurement error would be less. A practical demonstration of the concept has been presented using a FD-OP to emulate a real MZI-based sensor. The practical results, which agree excellently with the theory, provide the proof-of-concept demonstration for the technique. The wavelength-switching method is unsophisticated and label-free. It does not require any modifications to the sensor, nor accessing to the laser electronics. The detection is simple and does not require any specialised or expensive instruments. The output waveform can be simply captured using a typical oscilloscope or a simple analog to digital converter (ADC) device for real-time measurement and analysis. The entire system can be designed and implemented using low-cost off-the-shelf components. The method is therefore suitable for realising sensing systems from the sophisticated high-end bench-top analyser for laboratory uses to the simple and low-cost hand-held device for field testing. The method is also compatible with the lab on a chip technology [12] and can be readily applied for bio and medical sensing applications.
Funding
Central Queensland University (RSH4150).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon request.
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