Measurement Of Free Spectral Range Research Articles

Free spectral range measurement based on a multi-longitudinal mode laser self-mixing ellipse fitting degree detection technique.

A method by detecting the ellipse fitting degree of the trajectory equation formed by two self-mixing (SM) signals in the multi-longitudinal mode laser SM system with a Wollaston prism is presented to test the free spectral range (FSR) of the laser. By utilizing the orthogonal vector and phase-shift characteristics between adjacent longitudinal modes, the fluctuations in multi-mode SM effects caused by changes in the external cavity length are transformed into alterations in the trajectory composed of two orthogonal SM signals. The FSR is calculated by detecting the difference in external cavity lengths between the two positions, where the trajectory of the two SM signals best fits an ellipse. To achieve an automatic FSR measurement, the ellipse fitting degree is proposed as the criterion for positioning the external cavity mode. Experimental results indicate that the FSR of the laser diode is measured to be 85.23 GHz with a resolution of 0.48 GHz, while the corresponding external cavity resolution is 10 µm, and the resolution of the ellipse fitting degree is less than 1. The compact and straightforward design, coupled with high sensitivity, automated measurements, and immunity to optical feedback, holds significant promise as a robust tool for measuring FSR and assessing laser performance.

Fabry-Perot parallel type high sensitivity fiber optic temperature sensor based on vernier effect beyond free spectral range measurement

Accurate detection of temperature is crucial in industry, agriculture, the military, etc. In our paper, using the vernier effect of fiber optic interference, we demonstrate a temperature sensoru, in parallel with a grating, to improve the sensitivity of the probe while expanding the measurement range. The probe consists of a combination of a temperature-sensitive polymer Fabry-Perot interferometer (SFPI) and a temperature-insensitive 3D printed reference Fabry-Perot interferometer (RFPI). The innovative combination of femtosecond-induced two-photon polymerization provides a reference cavity with determinable cavity length for vernier effects. Innovative use of fiber Bragg grating (FBG) for vernier effect to determine the temperature interval and extend the range. This experiment concluded that the average sensitivity of the parallel probe reached −22.52 nm/°C in the temperature detection interval of 31°C to 37°C, a 16.8-fold increase in sensitivity, based on which the temperature outside the six free spectral ranges (FSR) can be measured in the interval of 31°C to 51°C using the FBG.

Real-time free spectral range measurement based on a correlated resonance-tracking technology.

In this paper, we present a real-time measurement technology for the free spectral range (FSR) of an ultrahigh-aspect-ratio silicon nitride (Si3N4) waveguide ring resonator (WRR). Two different correlated resonant modes were tracked by two optical single-sideband frequency-shifted lights to eliminate interference noise in the Pound-Drever-Hall error signals. A relative precision of 0.1474 ppm was achieved for a 35 mm WRR with FSR = 1,844,944.5 kHz and finesse (F) = 13.2. Furthermore, a cross-correlation of 0.913 between FSR-calculated and thermistor-measured temperatures indicated a high correlation between the real-time FSR and room temperature. We believe this technology is currently the best way to realize low-finesse (F < 50) real-time FSR measurements in the GHz range.

Design of Real-Time Free Spectral Range Measurement Based on HOPLL Technique

A real-time free spectral range (FSR) measurement system based on heterodyne optical phase-locked loop (HOPLL) is proposed for the first time to test the FSR of a fiber resonator. In this system, HOPLL is used to lock phase between the master and slave lasers, so that the frequency difference between them reach one FSR. In addition, PDH technique is used to establish a resonant tracking loop. By setting the loop control parameters, the master and slave lasers are respectively locked on two adjacent resonance peaks of the cavity. If the ambient temperature changes, the cavity length of the resonant cavity will change accordingly. Then the real-time change of FSR of the resonant cavity can be measured by detecting feedback change of the loop. The experimental results show that the linewidth of beat signal of the master and slave lasers after phase-locking is less than 10Hz, and also the frequency noise of the 10Hz bandwidth is 0.0154Hz which is 60dB lower than that before phase-locking. The researchers find that the FSR coefficient of thermal expansion is −210.35 ± 0.15Hz/°C, which is consistent with theoretical results. The relative measurement accuracy of $1.5\times 10 ^{-9}$ is achieved in this loop. Therefore, the experimental results effectively verify the actual application performance of the real-time FSR measurement based on HOPLL technique.

Free spectral range measurement using homologous heterodyne optical phase-locked loop based on acousto-optic modulation.

We demonstrate a homologous heterodyne optical phase-locked loop for free spectral range measurement of a fiber ring resonator. In this loop, the frequency noise within the 10Hz bandwidth is reduced by more than 40dB from 147.350 to 0.014Hz, and the power spectral density of the frequency noise reaches 7.69×10-8 Hz2/Hz at 10Hz. Finally, the relative measurement accuracy of 1.39×10-9 is achieved by this loop and the free spectral range coefficient of thermal expansion is measured as -174.1±0.2 Hz/°C with a cavity finesse of 26.65. This work provides a method to measure free spectral range by tracking the resonance modes of the resonator and reducing frequency noise, especially for two signals with frequency offset.

Real-time free spectral range measurement based on optical single-sideband technique.

We demonstrate a real-time scheme for measuring the free spectral range (FSR) of a high-aspect-ratio Si3N4 waveguide ring resonator with a fiber-based hybrid unbalanced Mach-Zehnder modulator (MZM) using an optical single-sideband technique. Resonance-tracking loops were established with the Pound-Drever-Hall technique for locking resonance modes. A relative precision of 3.25 × 10-6 was achieved for a 35-mm waveguide ring resonator with FSR = 1,844,628 kHz and Q = 3.211 × 106. Furthermore, the Si3N4 resonator FSR coefficient of thermal expansion was measured as -16.735±0.002 kHz/°C. This method will provide a flexible photonic interface for realizing advanced photonic systems.

Technique for in situ measurement of free spectral range and transverse mode spacing of optical cavities

Length and g-factor are fundamental parameters that characterize optical cavities. We developed a technique to measure these parameters in situ by determining the frequency spacing between the resonances of fundamental and spatial modes of an optical cavity. Two laser beams are injected into the cavity, and their relative frequency is scanned by a phase-lock loop, while the cavity is locked to either laser. The measurement of the amplitude of their beat note in transmission reveals the resonances of the longitudinal and the transverse modes of the cavity and their spacing. This method proves particularly useful to characterize complex optical systems, including very long and/or coupled optical cavities, as in gravitational-wave interferometers. This technique and the results of its application to the coupled cavities of a 40 m-long gravitational-wave interferometer prototype are presented here.

Free spectral range measurement of fabry-perot cavity using frequency modulation

In this paper, we propose a novel method to measure the free spectral range (FSR) of a Fabry-Perot cavity (FPC) using single-frequency modulation (FM) with one electric optical modulator (EOM) and the null method. A laser beam modulated by the EOM, to which a cosine-wave signal is supplied from a radio frequency (RF) oscillator, is incident on the FPC. The transmission light from the FPC is observed and converted to an RF signal by a highspeed photodetector, and the RF signal is synchronously demodulated with a lock-in amplifier (LIA) by referring to the oscillator. We theoretically and experimentally demonstrate that the LIA signal become null with a steep slope, when the modulation frequency equals the FSR under the condition that the carrier frequency is slightly detuned from the resonance of the FPC. The experimental results show that the proposed method has the capability to determine the FSR by the null method with a small measurement uncertainty.

Free spectral range measurement of a fiberized Fabry–Perot etalon with sub-Hz accuracy

In this work a narrow linewidth (1 kHz) laser source is used to measure the free spectral range of a fiberized Fabry-Perot etalon with sub-Hz accuracy (10(-8)). A previously demonstrated technique based on the Pound-Drever-Hall error signal is improved in accuracy by the use of a narrow linewidth laser swept in frequency via an acousto-optic modulator, or single sideband generation. The sub-Hz (10(-8)) accuracy attained enables the characterization of both the long-term drift and the polarization dependence of the free spectral range of the fiberized etalon.

Modified Pound-Drever-Hall scheme for high-precision free spectral range measurement of Fabry-Perot etalon

Improvement of two orders of magnitude of the Pound-Drever-Hall based free spectral range (FSR) measurement method is reported. The improved technique results in 1 part in 10 6 precision. This is believed to be the most precise measurement of FSR.

High-precision measurement of free spectral range of etalon

A novel measurement technique to determine the free spectral range of an etalon utilising a modified Pound-Drever-Hall technique is demonstrated with better than 1 part in 104 precision.