A 120° phase difference interferometer technology based on an unbalanced Michelson interferometer composed of a 3 × 3 optical fiber coupler is proposed, and based on this technology, the differential phase of the input laser can be obtained. This technology has many applications. This paper introduced its application in laser phase and frequency noise measurement in detail. The relations and differences of the power spectral density (PSD) of differential phase and frequency fluctuation, instantaneous phase and frequency fluctuation, phase noise, and linewidth are derived strictly and discussed carefully. The noise features of some narrow-linewidth lasers are also obtained conveniently without any specific assumptions or noise models. Finally, the application of this technology in the phase-sensitive optical time domain reflectometer (ϕ-OTDR) is also introduced briefly.
- 120° phase difference
- 3 × 3 optical fiber coupler
- laser noise measurement
- phase-sensitive optical time domain reflectometer
Single-frequency narrow-linewidth lasers are fundamental to a vast array of applications in fields including metrology, optical frequency transfer, coherent optical communications, high-resolution sensing, and light detection and ranging (LIDAR) [1–9]. In these applications, the phase and frequency noise is one of the key factors to affect the system performance. The characterization and measurement of the phase and frequency noise are very important for the applications, and thus have been one of the most attractive subjects of researches in laser and photonics field. The phase and frequency noise of such lasers can be conveniently described either in terms of linewidth or in terms of the power spectral density (PSD) of their phase or frequency noise. The linewidth gives a basic and concise parameter for characterizing laser coherence but lacks detailed information on frequency noise and its Fourier frequency spectrum, which is needed for understanding the noise origins and improving laser performances. Therefore, the measurement of frequency noise PSD is a focus of attention in the field, especially for lasers of very high coherence, whose linewidth is not easy to be measured.
To measure the phase and frequency noise, many methods have been proposed, such as beat note method , recirculating delayed self-heterodyne (DSH) method , DSH technique based on Mach-Zehnder interferometer with 2 × 2 coupler [12, 13], or Michelson interferometer (MI) with 2 × 2 coupler . These methods can obtain good measurement results but need some strict conditions. The beat note method needs a high coherent source as a reference. The recirculating DSH method needs very long fiber delay lines. The DSH interferometers with 2 × 2 coupler need to control the quadrature point by some active feedback methods and accurate calibration.
To overcome these difficulties, we introduce a robust technique that can demodulate directly the laser differential phase accumulated in a delay time and then derive strict mathematical relations between the laser differential phase and the laser phase noise or frequency noise that can describe the complete information on laser phase and frequency noise. Because 3 × 3 optical fiber coupler acts as a 120° optical hybrid, it can demodulate the differential phase of the input light and has been used for DxPSK signal demodulation , optical sensors , optical field reconstruction, and dynamical spectrum measurement . In this chapter, 120° phase difference interference technology based on an unbalanced Michelson interferometer, which is composed of a 3 × 3 optical fiber coupler and two Faraday rotator mirrors, is utilized to demodulate the differential phase of a laser. The structure has the advantage of being polarization insensitive and adjust-free. Especially, it does not need any active controlling operation that is used in the DSH methods with 2 × 2 coupler. Furthermore, based on the differential phase and strict physical and mathematical derivation, the PSD of the differential phase fluctuation and frequency fluctuation, the PSD of the instantaneous phase fluctuation and frequency fluctuation, laser phase noise, and linewidth are completely calculated and discussed.
2. 120° phase difference interference technology
2.1. Symmetric 3 × 3 optical fiber coupler
Figure 1 shows the schematic diagram of the proposed 120° phase difference technology. As we know, the interferometric signals are 180° out of phase because of 2 × 2 optical fiber coupler. In an ideal 3 × 3 optical fiber coupler, there is a 120° phase difference between any two of the three output ports. A symmetric 3 × 3 optical fiber coupler is described by the matrix.
The matrix of the two arms of the Michelson interferometer is given by,
The electric field of input laser is expressed by,
with amplitude |
The measured intensities
2.2. Asymmetric 3 × 3 optical fiber coupler
However, the commercially available 3 × 3 optical fiber coupler is usually asymmetric and lossy. So the transmissivity of 3 × 3 coupler from port
Similarly, the backward transmission matrix of 3 × 3 coupler is then given by,
The output light from the output port
Define an intermediate matrix,
Eq. (16) shows the relation between the differential phase ∆
3. The application in laser noise measurement
3.1. Experimental setup
Based on the 120° phase difference technology, the experimental setup of laser noise measurement is shown in Figure 2 . It consists of a commercially available 3 × 3 optical fiber coupler (OC), a circulator (C), two Faraday rotator mirrors (FRMs), three photodetectors (PDs), a data acquisition board (DAC) or a digital oscilloscope, and a computer. The 120° phase difference Michelson interferometer is composed of the 3 × 3 coupler and the FRMs. On one hand, the FRM will remove the polarization fading caused by external disturbance on the two beam fibers of the interferometer. On the other hand, the length or index of the fiber configuring the interferometric arms would change randomly because of temperature fluctuations, vibration, and other types of environmental disturbances; thus it induces low-frequency random-phase drifts in the interferometric signal. So in the proposed experimental setup, the complete interferometer is housed in an aluminum box enclosed in a polyurethane foam box for thermal and acoustic isolation. Meantime, the two fiber arms of the Michelson interforometer are placed closely in parallel to improve the stability against the perturbation.
The laser under test (LUT) injects the left port 1 of the 3 × 3 optical fiber coupler through a circulator and then splits into three parts by the coupler. Two of them interfere mutually in the coupler after being reflected by Faraday mirrors and with different delay times, and the third part of them is made reflection-free. Then the interference fringes are obtained from the left port 1, 2, and 3 of the coupler and read by a DAC or a digital oscilloscope.
In the experimental setup, a swept laser source with linewidth of about 2.5 kHz  is used as the broadband light source to show clearly the small free spectral range (FSR) of the MI. The measured interference fringe is shown in the inset figure of Figure 1. On the other hand, all parameters of the devices are considered in the differential phase fluctuation calculation process, so the possible errors from device defects such as imperfect splitting ratio or phase difference are removed, and the requirements for the device performance parameters are also relaxed. In our experimental setup, the final setup parameters are
When the setup parameters are calibrated, the whole setup is in a state of plug-and-play.
To verify the correction of the phase demodulation of the setup, a demodulated test for a preset modulated phase by a LiNbO3 phase modulator is demonstrated. A narrow linewidth laser that is phase-modulated with the LiNbO3 phase modulator is used as LUT. The triangle waveform is selected to the modulation waveform for holding the frequency components as such and much more. Hence, the fact of the interference at the coupler is a subtraction between two triangle waveforms with delay time
3.2. Laser noise theory
Considering the relation between the delay phase
the differential phase variation is from the laser frequency variation in the time interval
Hence, the PSD of differential phase fluctuation Δ
So far, the differential phase fluctuation Δ
Eq. (22) means that, at the low Fourier frequency domain, the PSD of the laser instantaneous phase fluctuation
Eq. (25) means that the PSD of the laser instantaneous frequency fluctuation
3.3. Laser noise measurement results
First, the phase and frequency noise of an external-cavity semiconductor laser (RIO ORIONTM)  with a wavelength of 1551.7 nm and a linewidth of about 2 kHz are measured. The PSD of the differential phase fluctuation is normalized to 1 m delay fiber (
From the PSD of the frequency fluctuation
Second, the noise features of commercial distributed feedback (DFB) semiconductor laser are measured under different operating temperatures (24 and 22.7°C) and different operating currents (71, 91, 111, and 136 mA), shown in Figures 8 and 9. Figure 8 shows that this DFB laser is more suitable for working at 24°C than at 22.7°C. Figure 9 shows that the PSDs of frequency fluctuation
4. The application in phase-sensitive OTDR
The experimental setup is shown in Figure 10 . The light source is a DFB laser with an output power of 20 mW and a wavelength of 1551.72 nm, which is injected into the acoustic-optic modulator (AOM) to generate the pulses with a width of 40 ns and a repetition rate of 100 kHz. Before being injected into the fibre under test (FUT), the pulses would be amplified by the Erbium-doped fiber amplifier 1 (EDFA1). The backward Rayleigh scattering is amplified by the EDFA2 and then launched into the circulator2, and ASE noise of EDFA2 has been filtered by the fibre Bragg grating (FBG). Then the amplified scattering with better signal-to-noise ratio (SNR) is injected into one port of the 3 × 3 coupler through circulator3. There are two ports on the other side of the 3 × 3 coupler connected to FRMs and the other one port made reflection-free. The interferometer with 4 m delay is housed in a sealed box for thermal and acoustic isolation, avoiding disturbance from the environment. The fiber length between PDs and each coupler port is set as equal to guarantee the same optical path. A trichannel digital acquisition (DAQ) card is used to acquire the voltage signal, and a radio frequency driver (RFD) is used to trigger the AOM and DAQ card simultaneously for synchronization. The collected trichannel signals are processed by the software program to demodulate phase information by using Eq. (16).
Phase sensitive optical time domain reflectometer (
A laser phase and frequency noise measurement technique based on a 120° phase difference unbalanced Michelson interferometer composed of a 3 × 3 optical fiber coupler and two Faraday rotator mirrors is proposed. In the method, the laser differential phase fluctuation accumulated by the interferometer delay time is demodulated directly at first and then the phase and frequency noise is calculated by the PSD estimation for the differential phase. Also the concepts and differences of differential phase and frequency fluctuation PSDs, instantaneous phase and frequency fluctuation PSDs, and phase noise are defined strictly and discussed carefully. The method can obtain the noise features of a narrow linewidth laser without any specific assumptions or noise models. Meantime, the technique is used to characterize a narrow linewidth external-cavity semiconductor laser, which confirmed the correction of the method and revealed the fact that the linewidth would increase with the increase of observation time, and the Lorentz fitted linewidth measured by the SDH method only includes the contribution of the white noise components and would be larger than the real value. Moreover, the technique can monitor the state change of commercial DFB semiconductor lasers in different processes of designing, installation, debugging, routine test, and final check test, and it offers suggestions to optimize design and improve its performance. The 120° phase difference technology is also applied to test the phase difference between Rayleigh scattering in phase sensitive optical time domain reflectometer (
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