Laser relaxation-oscillation frequency imaging

Sensing by Dynamics of Lasers with External Optical Feedback: A Review

External optical feedback (EOF) has great impacts on the properties of lasers. It influences the stable operation of lasers. However, various applications based on lasers with EOF have been developed. One typical example is self-mixing interferometry technology, where modulated steady-state laser intensity is utilized for sensing and measurement. Other works show that laser dynamics can also be used for sensing, and the laser in this case is more sensitive to EOF. This paper reviews the sensing technology that uses the dynamics of lasers with EOF. We firstly introduce the basic operating principles of a laser with EOF and discuss the noise properties of and intensity modification in lasers induced by EOF. Then, sensing applications using laser dynamics are categorized and presented, including sensing by frequency-shifted optical feedback, relaxation oscillation frequency, and dynamics with self-mixing interferometry signals and laser optical chaos. Lastly, we present an analysis of the transient response waveform and spectrum of a laser with EOF, showing its potential for sensing.

Influence of feedback optical phase on the relaxation oscillation frequency of a semiconductor laser and its application

Semiconductor lasers (SLs) show relaxation oscillation (RO) due to the cavity damping rate being higher than the carrier damping rate. The presence of RO in SLs contributes to abundant complex dynamics when the laser is perturbed by external optical feedback (EOF). In this work, the influence of feedback optical phase on the relaxation oscillation frequency (ROF) in an SL is investigated both theoretically and experimentally. By numerically solving the well-known Lang Kobayashi equations, the relationship between the ROF and feedback optical phase was obtained, which shows ROF is in a sinusoidal manner with respect to the feedback optical phase under weak feedback strength. A simplified mathematic expression for ROF was derived to describe such a sinusoidal relationship. Potential sensing applications can be developed based on the relationship. As an example, a new method of measuring linewidth enhancement factor of an SL was presented. Finally, an experimental setup was built and experiments were carried out to verify the relationship and the measurement method for linewidth enhancement factor.

Quadrature demodulation based on lock-in amplifier technique for self-mixing interferometry displacement sensor

A new self-mixing interferometry quadrature demodulation method based on a lock-in amplifier technique is proposed. Sinusoidal phase modulation of the beam is obtained by an electro-optic modulator (EOM) in the external cavity. Then the real phase of the external target can be calculated by lock-in amplifier analysis method. In this paper, the validity of the proposed method is confirmed by theoretical analysis and means of simulated signals, and then it is demonstrated by several experimental measurements for target harmonic and arbitrary motion. The results show that the proposed method can get a high-precision measurement, even using a diffusive target.

Displacement sensing using the relaxation oscillation frequency of a laser diode with optical feedback

A laser diode (LD) with external optical feedback can generate undamped relaxation oscillation (RO) under certain operational conditions. The RO frequency can be modified by the external cavity length of the LD and is highly sensitive to the variation of the cavity length (ΔL). This work first investigates the relationship between the RO frequency and ΔL by solving the well-known Lang-Kobayashi (L-K) equations and then verifies the relationship by experiments. Both theory and experiment show that the RO frequency changes in a sawtooth-like quasi-periodic manner with respect to ΔL. The fundamental period is half laser wavelength. This sawtooth feature enables us to achieve period unwrapping and thus extend the measurement range up to a few micrometers. This work shows a possible new solution for achieving high-resolution, large-range displacement measurements.

A microchip laser source with stable intensity and frequency used for self-mixing interferometry

We present a stable 40 × 40 × 30 mm(3) Laser-diode (LD)-pumped-microchip laser (ML) laser source used for self-mixing interferometry which can measure non-cooperative targets. We simplify the coupling process of pump light in order to make its polarization and intensity robust against environmental disturbance. Thermal frequency stabilization technology is used to stabilize the laser frequency of both LD and ML. Frequency stability of about 1 × 10(-7) and short-term intensity fluctuation of 0.1% are achieved. The theoretical long-term displacement accuracy limited by frequency and intensity fluctuation is about 10 nm when the measuring range is 0.1 m. The line-width of this laser is about 25 kHz corresponding to 12 km coherent length and 6 km measurement range for self-mixing interference. The laser source has been equipped to a self-mixing interferometer, and it works very well.

Self-mixing interferometry with mutual independent orthogonal polarized light

A self-mixing interferometry with mutual independent orthogonal polarized light is introduced. Its most important feature is that two mutual independent orthogonal lights are used as measuring and reference light. Frequency shifting and polarization multiplexing technologies are used in the proposed optical system. Phase variation of the two orthogonal polarized beams is simultaneously measured through heterodyne demodulation with a lock-in amplifier. The phase difference of the orthogonal polarized light accurately reflects the target displacement. The target in this system is a non-cooperative object which is different from a traditional Michelson interferometer. The primary experimental results show that this kind of self-mixing interferometry is very feasible. Under typical room conditions, the system's short-term resolution is better than 2 nm.

Parallel multiplex laser feedback interferometry

We present a parallel multiplex laser feedback interferometer based on spatial multiplexing which avoids the signal crosstalk in the former feedback interferometer. The interferometer outputs two close parallel laser beams, whose frequencies are shifted by two acousto-optic modulators by 2Ω simultaneously. A static reference mirror is inserted into one of the optical paths as the reference optical path. The other beam impinges on the target as the measurement optical path. Phase variations of the two feedback laser beams are simultaneously measured through heterodyne demodulation with two different detectors. Their subtraction accurately reflects the target displacement. Under typical room conditions, experimental results show a resolution of 1.6 nm and accuracy of 7.8 nm within the range of 100 μm.

Multidimensional subwavelength position sensing using a semiconductor laser with optical feedback

We demonstrate experimentally how to harness quasi-periodic dynamics in a semiconductor laser with dual optical feedback for measuring subwavelength changes in each arm of the cavity simultaneously. We exploit the multifrequency spectrum of quasi-periodic dynamics and show that independent frequency shifts are mapped uniquely to two-dimensional displacements of the arms in the external cavity. Considering a laser diode operating at telecommunication wavelength λ≈1550 nm, we achieve an average nanoscale resolution of approximately 9.8 nm (~λ/160).

Self-mixing thin-slice solid-state laser metrology

This paper reviews the dynamic effect of thin-slice solid-state lasers subjected to frequency-shifted optical feedback, which led to the discovery of the self-mixing modulation effect, and its applications to quantum-noise-limited versatile laser metrology systems with extreme optical sensitivity.

Influence of external cavity length on multimode hopping in microchip Nd:YAG lasers

The influence of external cavity length on multimode hopping in microchip Nd:YAG lasers is investigated experimentally. With an optical feedback loop, the threshold gain of different longitudinal modes are all modulated by changing the external cavity length; a lambda/2 change in the external cavity length causes a one-period oscillation. The longitudinal modes can be divided into groups according to different initial threshold gain variations and modulation trends corresponding to different external cavity phases. Because of the initial gain difference, only one mode in each group is the dominant potential lasing mode, while others are suppressed. During the 2 pi change of the external cavity phase, mode hopping occurs among these potential lasing modes from different groups. Both the intensity waveforms and the number of hopping modes strongly depend on the external cavity length. Experimental results agree well with the theoretical analysis of the phenomenon of multimode hopping subjected to optical feedback in microchip Nd:YAG lasers.

Quasi-common-path laser feedback interferometry based on frequency shifting and multiplexing

We present a quasi-common-path laser feedback interferometer based on frequency shifting and multiplexing. The interferometer uses two acousto-optic modulators to shift the frequency of the target-generated feedback light by 2 Omega. A properly aligned mirror is inserted into the feedback path to generate a feedback light frequency shifted by Omega. Phase variations of the two quasi-common-path feedback light beams are simultaneously measured through heterodyne demodulation with two different reference signals. Their subtraction accurately reflects the target displacement. Under typical room conditions, the system's short-period resolution is better than 2 nm, and its 3 min displacement accuracy is 8 nm.

Absolute distance measurement with heterodyne optical feedback on a Yb:Er glass laser

Absolute distance measurement based on optical feedback using a single-frequency Yb:Er glass laser is demonstrated via the combination of heterodyne detection and frequency sweep. The technique allows for the enhancement of the sensitivity of the laser response to self-mixing thanks to resonant excitation close to the relaxation-oscillation frequency peak. The experimental results on noncooperative targets are in good agreement with the theory, and the shape of the resulting signal is analyzed in both the temporal and the frequency domains considering the specific dynamic of the class B solid-state laser. Suggestions are provided for further improvements on the signal processing.

Frequency-shifted optical feedback in a pumping laser diode dynamically amplified by a microchip laser

Compared with conventional optical heterodyne detection, laser optical feedback imaging (LOFI) allows for a several orders of magnitude higher intensity modulation contrast. The maximum contrast amplification is typically 10(3) for a diode laser in the gigahertz range and 10(6) for a microchip laser in the megahertz range. To take advantage of the wavelength tunability of a laser diode and of the lower resonant detection frequency of a microchip laser, we used LOFI modulation induced by the frequency-shifted optical feedback in a laser diode as a modulated pumping power for a microchip laser for resonant dynamic amplification. In this way, we were able to transfer the optical feedback sensitivity of the laser diode to the megahertz range. Application to telemetry is also reported.

External cavity modes of semiconductor lasers with phase-conjugate feedback

External cavity modes (ECMs) of a semiconductor laser with phase-conjugate feedback are defined as time-periodic pulsating intensity solutions exhibiting a frequency close to an integer multiple of the external cavity frequency. As the feedback rate progressively increases from zero, they sequentially appear as stable attractors in the bifurcation diagram. We construct a simple analytical approximation of these pulsating intensity solutions and determine their frequencies. We show that branches of ECMs are isolated. Finally, the validity of our approximation is tested by comparing numerical bifurcation diagrams obtained by simulation and continuation techniques with our analytical results.