Unbalanced Michelson Interferometer Research Articles

Phase and frequency noise measurement using passive self-homodyne technique

For single longitudinal-mode lasers, the phase and frequency noises are very important parameters for their applications. The passive self-homodyne technique with an unbalanced Michelson interferometer is demonstrated to measure the phase and frequency noise characteristics. The Michelson interferometer for measurements is composed of a 3×3 optical fiber coupler and two Faraday rotator mirrors. The measurement performance is derived and discussed strictly from the transmission matrix of the coupler. The influence to the demodulation resulting from the asymmetry of the 3×3 optical fiber coupler is eliminated through the derived relationship between the differential phase fluctuation and the interferometer fringes. The technique is utilized to measure the phase and frequency noise features of a distributed feedback fiber laser. Based on the measured frequency noise spectrum, the lineshape, linewidth, and phase-error variance related to the laser coherence are able to be calculated and discussed well.

Distributed fiber optic interferometric geophone system based on draw tower gratings

A distributed fiber optic interferometric geophone array based on draw tower grating (DTG) array is proposed. The DTG geophone array is made by the DTG array fabricated based on a near-contact exposure through a phase mask during the fiber drawing process. A distributed sensing system with 96 identical DTGs in an equal separation of 20 m and an unbalanced Michelson interferometer for vibration measurement has been experimentally validated compared with a moving-coil geophone. The experimental results indicate that the sensing system can linearly demodulate the phase shift. Compared with the moving coil geophone, the fiber optic sensing system based on DTG has higher signal-to-noise ratio at low frequency.

Distributed acoustic sensing with Michelson interferometer demodulation

The distributed acoustic sensing (DAS) has been extensively studied and widely used. A distributed acoustic sensing system based on the unbalanced Michelson interferometer with phase generated carrier (PGC) demodulation was designed and tested. The system could directly obtain the phase, amplitude, frequency response, and location information of sound wave at the same time and measurement at all points along the sensing fiber simultaneously. Experiments showed that the system successfully measured the acoustic signals with a phase-pressure sensitivity about–148 dB (re rad/μPa) and frequency response ripple less than 1.5 dB. The further field experiment showed that the system could measure signals at all points along the sensing fiber simultaneously.

Secondary wavelength stabilization of unbalanced Michelson interferometers for the generation of low-jitter pulse trains.

We present a double unbalanced Michelson interferometer producing up to four output pulses from a single input pulse. The interferometer is stabilized with the Hänsch-Couillaud method using an auxiliary low power continuous wave laser injected into the interferometer, allowing the stabilization of the temporal jitter of the output pulses to 0.02 fs. Such stabilized pulse trains would be suitable for driving multi-pulse laser wakefield accelerators, and the technique could be extended to include amplification in the arms of the interferometer.

Accurate displacement-measuring interferometer with wide range using an I2 frequency-stabilized laser diode based on sinusoidal frequency modulation

We propose the use of the sinusoidal frequency modulation technique to improve both the frequency stability of an external cavity laser diode (ECLD) and the measurement accuracy and range of a displacement-measuring interferometer. The frequency of the ECLD was modulated at 300 kHz by modulating the injection current, and it was locked to the b21 hyperfine component of the transition 6-3, P(33), 127I2 (633 nm) by the null method. A relative frequency stability of 6.5 × 10−11 was achieved at 100 s sampling time. The stabilized ECLD was then utilized as a light source for an unbalanced Michelson interferometer. In the interferometer, the displacement and direction of the target mirror can be determined using a Lissajous diagram based on two consecutive and quadrant-phase harmonics of the interference signal. Generally, the measurement range of the interferometer by the proposed method is limited by the modulation index and the signal-to-noise ratio of the harmonics. To overcome this drawback, suitable consecutive harmonic pairs were selected for the specific measurement ranges to measure the displacement. The displacements determined in the specific ranges by the proposed method were compared with those observed by a commercial capacitive sensor. From the comparison, the proposed method has high precision to determine the displacement. The measurement range was also extended up to 10 m by selecting a suitable modulation index and suitable consecutive pairs of harmonics.

Fiber Bragg grating dynamic strain sensor using an adaptive reflective semiconductor optical amplifier source.

In this paper, a reflective semiconductor optical amplifier (RSOA) is configured to demodulate dynamic spectral shifts of a fiber Bragg grating (FBG) dynamic strain sensor. The FBG sensor and the RSOA source form an adaptive fiber cavity laser. As the reflective spectrum of the FBG sensor changes due to dynamic strains, the wavelength of the laser output shifts accordingly, which is subsequently converted into a corresponding phase shift and demodulated by an unbalanced Michelson interferometer. Due to the short transition time of the RSOA, the RSOA-FBG cavity can respond to dynamic strains at high frequencies extending to megahertz. A demodulator using a PID controller is used to compensate for low-frequency drifts induced by temperature and large quasi-static strains. As the sensitivity of the demodulator is a function of the optical path difference and the FBG spectral width, optimal parameters to obtain high sensitivity are presented. Multiplexing to demodulate multiple FBG sensors is also discussed.

基于3×3 耦合器的窄线宽单频激光器噪声测量技术

A new delayed self-heterodyne technique using an unbalanced Michelson interferometer (MI) composed of a 3*3 optical fiber coupler is proposed. The principle of the technique to measure the laser phase and frequency noise are analyzed theoretically. The experimental setup is introduced. Also, the technique is used to characterize the phase noise power spectral density (PSD), frequency noise PSD and linewidth of two typical kinds of lasers, distributed feedback (DFB) semiconductor laser (Emcore) and super-narrow linewidth DFB fiber laser (NKT). The results show that the technique can measure the noise characters of different kinds of lasers and it confirms the correction and robustness of the proposed technique.

Laser phase and frequency noise measurement by Michelson interferometer composed of a 3 × 3 optical fiber coupler

A laser phase and frequency noise measurement method by an unbalanced Michelson interferometer composed of a 3 × 3 optical fiber coupler is proposed. The relations and differences of the power spectral density (PSD) of differential phase and frequency fluctuation, PSD of instantaneous phase and frequency fluctuation, phase noise and linewidth are derived strictly and discussed carefully. The method obtains the noise features of a narrow linewidth laser conveniently without any specific assumptions or noise models. The technique is also used to characterize the noise features of a narrow linewidth external-cavity semiconductor laser, which confirms the correction and robustness of the method.

Quantitative reflection phase mesoscopy by remote coherence tuning of phase-shift interference patterns

Conventional low-magnification phase-contrast microscopy is an invaluable, yet a qualitative, imaging tool for the interrogation of transparent objects over a mesoscopic millimeter-scale field-of-view in physical and biological settings. Here, we demonstrate that introducing a compact, unbalanced phase-shifting Michelson interferometer into a standard reflected brightfield microscope equipped with low-power infinity-corrected objectives and white light illumination forms a phase mesoscope that retrieves remotely and quantitatively the reflection phase distribution of thin, transparent, and weakly scattering samples with high temporal (1.38 nm) and spatial (0.87 nm) axial-displacement sensitivity and micrometer lateral resolution (2.3 μm) across a mesoscopic field-of-view (2.25 × 1.19 mm2). Using the system, we evaluate the etch-depth uniformity of a large-area nanometer-thick glass grating and show quantitative mesoscopic maps of the optical thickness of human cancer cells without any area scanning. Furthermore, we provide proof-of-principle of the utility of the system for the quantitative monitoring of fluid dynamics within a wide region.

Research of a double fiber Bragg gratings vibration sensor with temperature and cross axis insensitive

A novel double fiber Bragg gratings (FBGs) vibration sensor with temperature and cross axis insensitive is developed. In order to eliminate the influences of the temperature drift, the symmetrical pull–push structure is adopted. The sensor head is based on two elastic material cylinders, into which two matching FBGs are embedded respectively, loaded with a seismic mass. Closed-form analytical formulas describing the resonant frequency and sensitivity of the FBG vibration sensor are provided which may be utilized to tailor the sensor performance to specific applications. The phase generation carrier (PGC) interrogation technique based on the unbalanced Michelson interferometer is studied. Experimental results of a prototype vibration sensor show that the acceleration sensitivity of the FBG vibration sensor reaches 450pm/g in the frequency range of 5–100Hz. The resonant frequency of the FBG vibration sensor is 210Hz. For a temperature change from 0°C to 50°C, the wavelength shift of the sensor is almost 0 without any temperature compensation schemes. The noise floor of the FBG vibration sensor is obviously improved and reaches −100dB/Hz1/2 over the range of 40–100Hz. The experimental results prove the good performance of the FBG vibration sensor.

Phase-Sensitive Optical Time Domain Reflectometer Based on Phase-Generated Carrier Algorithm

We propose a novel approach to generate distributed fiber sensing system based on phase-sensitive optical time domain reflectometer (Φ-OTDR) and phase-generated carrier demodulation algorithm. An unbalanced Michelson interferometer is introduced at the receiving end of the system. The back Rayleigh scattering light from a certain position along the sensing fiber would interfere to generate interference light signal versus time, whose phase carries the sensing information. Phase-generated carrier demodulation algorithm is proposed and carried out to recover the phase information. A single frequency vibration event is applied to a certain position along the sensing fiber and we realize to demodulate it correctly. The noise level of the phase sensitive OTDR system is about 3 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> rad/VHz and a signal to noise ratio about 30.45 dB is achieved. The maximum sensing length and the spatial resolution of the Φ-OTDR system are 10 km and 6 m with pulse repetition rate at 10 kHz and 6 m fiber delay in MI with interrogating pulse width of 30 ns.

Frequency noise suppression of a single mode laser with an unbalanced fiber interferometer for subnanometer interferometry.

We present a method of noise suppression of laser diodes by an unbalanced Michelson fiber interferometer. The unstabilized laser source is represented by compact planar waveguide external cavity laser module, ORIONTM (Redfern Integrated Optics, Inc.), working at 1540.57 nm with a 1.5-kHz linewidth. We built up the unbalanced Michelson interferometer with a 2.09 km-long arm based on the standard telecommunication single-mode fiber (SMF-28) spool to suppress the frequency noise by the servo-loop control by 20 dB to 40 dB within the Fourier frequency range, remaining the tuning range of the laser frequency.

Observation of mode instability and coherence collapse in a single-frequency polarization-maintaining fiber ring laser

Mode instability acts as a common feature in single-frequency fiber ring lasers. The mechanism of coherence collapse by mode instability is theoretically analyzed and demonstrated with an unbalanced fiber Michelson interferometer utilizing phase modulation, which is illuminated by a single-frequency erbium-doped fiber ring laser. Multiform mode instability phenomena accompanied with coherence collapse are observed and discussed in detail by tracing the dynamics of the interference fringe visibility. The results show that mode instability would introduce extra phase noises like a false alarm to interferometric fiber optic sensing systems.

Bragg grating–based fiber laser vibration sensing system with novel phase detection

We characterized the dynamic response of a Bragg grating-based fiber laser sensing system. The sensing system comprises of a narrow line width fiber laser based on π -phase-shifted fiber Bragg grating formed in an active fiber, an unbalanced fiber Michelson interferometer (FMI), which performs wavelength-to-phase mapping, and a phase detection algorithm, which acquires the phase change from the interferometric output signal. The novel phase detection algorithm is developed based on the combination of the two traditional phase generated carrier algorithms: differential-cross-multiplying and arctangent algorithms, and possesses the advantages of the two algorithms. The modulation depth fluctuation of the carrier does not affect the performance of the sensing system. A relatively high side mode suppression ratio of above 50 dB has been achieved within a wide range of carrier amplitude from 1.6 to 5.0 V which correspond to the modulation depth from 1.314 to 4.106 rad. The linearity is 99.082% for the relationship between the power spectral density (dBm/Hz ) of the detected signal and the amplitude (mv) of the test signal. The unbalanced FMI is used to eliminate the polarization effect.

Time-reversed two-photon interferometry for phase superresolution

We observed two-photon phase super-resolution in an unbalanced Michelson interferometer with classical Gaussian laser pulses. Our work is a time-reversed version of a two-photon interference experiment using an unbalanced Michelson interferometer. A measured interferogram exhibits two-photon phase super-resolution with a high visibility of 97.9% \pm 0.4%. Its coherence length is about 22 times longer than that of the input laser pulses. It is a classical analogue to the large difference between the one- and two-photon coherence lengths of entangled photon pairs.

Theory of interferometric photon-correlation measurements: Differentiating coherent from chaotic light

Interferometric photon-correlation measurements, which correspond to the second-order intensity cross correlations between the two output ports of an unbalanced Michelson (or Mach-Zehnder) interferometer, are sensitive to both amplitude and phase fluctuations of an incoming beam of light. Here, we present the theoretical framework behind these measurements and show that they can be used to unambiguously differentiate a coherent wave undergoing dynamical amplitude and phase fluctuations from a chaotic state of light. This technique may thus be used to characterize the output of nanolasers and monitor the onset of coherent emission.

Unequivocal Differentiation of Coherent and Chaotic Light through Interferometric Photon Correlation Measurements

We present a novel experimental technique that can differentiate unequivocally between chaotic light and coherent light with amplitude fluctuations, and thus permits us to characterize unambiguously the output of a laser. This technique consists of measuring the second-order intensity cross correlation at the outputs of an unbalanced Michelson interferometer. It is applied to a chaotic light source and to the output of a semiconductor nanolaser whose "standard" intensity correlation function above threshold displays values compatible with a mixture of coherent and chaotic light. Our experimental results demonstrate that the output of such lasers is not partially chaotic but is indeed a coherent state with amplitude fluctuations.

Phase noise characteristics of narrow-linewidth f iber laser and laser diode in unbalanced interferometers

The phase noises of two narrow-linewidth fiber laser and laser diode are measured by using unbalanced Michelson interferometers with various optical path differences (OPDs). The measured results indicate that the phase noises of the two lasers do not change linearly with the OPD over the range from 1 to 100 m. The laser diode exhibits phase noise levels higher than that of the fiber laser at OPDs longer than 10 m. However, the laser diode outperforms the fiber laser at OPDs shorter than 10 m. The results obtained can assess laser performance and determine the suitable laser for use in a particular application.

Detecting mode hopping in single-longitudinal-mode fiber ring lasers based on an unbalanced fiber Michelson interferometer

A method of detecting mode hopping for single-longitudinal-mode (SLM) fiber ring lasers has been proposed and experimentally demonstrated. The method that is based on an unbalanced Michelson interferometer (MI) utilizing phase generated carrier modulation instantly transforms mode-hopping dynamics into steep phase changes of the interferometer. Multiform mode hops in an SLM erbium-doped fiber ring laser with an 18.6 MHz mode spacing have been detected exactly in real-time domain and discussed in detail. Numerical results show that the MI-based method has a high testing sensitivity for identifying mode hopping, which will play a significant role in evaluating the output stability of SLM fiber lasers.

A new method for high-accuracy gauge block measurement using 2 GHz repetition mode of a mode-locked fiber laser

We developed a Fabry–Perot etalon to select high-frequency parts of repetition-frequency modes of a short pulsed, mode-locked fiber laser at the wavelength of 1.55 µm. The 2 GHz repetition-modified laser is transmitted to an unbalanced Michelson interferometer with gauge blocks wrung on a platen. Two interference fringes were generated from the gauge block and platen at different positions. The interference fringes have a temporal coherence pattern and can make positioning in space easy. The length of the gauge block was directly determined from different positions of the two interference fringes, without using the excess fractions method.