Tunable and broadband microwave frequency combs based on a semiconductor laser with incoherent optical feedback

Based on a semiconductor laser （SL） with incoherent optical feedback, a novel all-optical scheme for generating tunable and broadband microwave frequency combs （MFCs） is proposed and investigated numerically. The results show that, under suitable operation parameters, the SL with incoherent optical feedback can be driven to operate at a regular pulsing state, and the generated MFCs have bandwidths broader than 40 GHz within a 10 dB amplitude variation. For a fixed bias current, the line spacing （or repetition frequency） of the MFCs can be easily tuned by varying the feedback delay time and the feedback strength, and the tuning range of the line spacing increases with the increase in the bias current. The linewidth of the MFCs is sensitive to the variation of the feedback delay time and the feedback strength, and a linewidth of tens of KHz can be achieved through finely adjusting the feedback delay time and the feedback strength. In addition, mappings of amplitude variation, repetition frequency, and linewidth of MFCs in the parameter space of the feedback delay time and the feedback strength are presented.

Optical feedback characteristics in a dual-frequency laser during laser cavity tuning

The optical feedback characteristics in a Zeeman-birefringence dual-frequency laser are studied during the laser cavity tuning in three different kinds of optical feedback conditions： （i） only //-light is fed back; （ii） only ⊥-light is fed back; （iii） both lights are fed back. A compact displacement sensor is designed using the experimental result that there is a nearly 90 degrees phase delay between the two lights＇ cosine optical feedback signals when both lights are fed back into the laser cavity. The priority order that the two lights＇ intensity curves appear can be used for direction discrimination. The resolution of the displacement sensor is at least 79 rim, and the sensor can discriminate the target＇s moving direction easily.

Chaos synchronization in injection-locked semiconductor lasers with optical feedback

Based on the rate equations, we have investigated three types of chaos synchronizations in injection-locked semiconductor lasers with optical feedback. Numerical simulation shows that the synchronization can be realized by the symmetric or asymmetric laser systems. Also, the influence of parameter mismatches on chaos synchronization is investigated, and the results imply that these two lasers can achieve good synchronization, with smaller tolerance of parameter mismatch existing.

Intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level

This paper demonstrates the intensity modulation characters of orthogonally polarized HeNe lasers with different optical feedback level generated by the variable reflectivity of external reflector. The modulation depths of the orthogonally polarized frequencies are increased when the optical feedback level becomes strong. It also observes that the modulation amplitudes are different for different external cavity length. Based on the vectorial extension of Lamb＇s semi-classical theory, it finds that the calculations are consistent with the experimental results.

Mode hopping in single-mode microchip Nd：YAG lasers induced by optical feedback

The mode hopping phenomenon induced by optical feedback in single-mode microchip Nd：YAG lasers is presented. With optical feedback, mode hopping strongly depends on two factors： the ratio of external cavity length to intra-cavity length, and initial gains of the two hopping modes, When external cavity length equals an integral multiple of intracavity length, there is almost no mode hopping. However, if the external cavity length does not equal an integral multiple of intra-cavity length, mode hopping occurs. The ratio of external cavity length to intra-cavity length determines the position of two-mode hopping, The initial gains of the two hopping modes determine the corresponding peak values and oscillating periods of them in the intensity modulation curves.

Anisotropic optical feedback of single frequency intra-cavity He-Ne laser

This paper presents the anisotropic optical feedback of a single frequency intra-cavity He-Ne laser. A novel phenomenon was discovered that the laser output an elliptical polarized frequency instead of the initial linear polarized one. Two intensities with a phase difference were detected, both of which were modulated in the form of cosine wave and a fringe shift corresponds to a λ/2 movement of the feedback mirror. The phase difference can be continuously modulated by the wave plate in the external cavity. Frequency stabilization was used to stabilize the laser frequency so as to enlarge the measuring range and improve the measurement precision. This anisotropic optical feedback system offers a potential displacement measurement technology with the function of subdivision of λ/2 and in-time direction judgment. The three-mirror Fabry Perot cavity model is used to present the experimental results. Given the lack of need of lasing adjustment, this full intra-cavity laser can significantly improve the simplicity and stability of the optical feedback system.

Strong optical feedback in birefringent dual frequency laser

Strong optical feedback in a birefringent dual frequency He-Ne laser with a high reflectivity feedback mirror has been investigated for the first time. The output characteristics of two orthogonally polarized modes are demonstrated in two different optical feedback cases： one is for both modes being fed back and the other is for only one of the modes being fed back. Strong mode competition can be observed between the two modes with strong optical feedback, And when one mode＇s intensity is near its maximum, the other mode is nearly extinguished. When both modes are fed back into the laser cavity, the mode competition is stronger than when only one mode is fed back, The difference in initial intensity between the two orthogonally polarized modes plays an important role in the mode competition, which has been experimentally and theoretically demonstrated.

Numerical investigation on photonic microwave generation by a sole excited-state emitting quantum dot laser with optical injection and optical feedback

Based on three-level exciton model,the enhanced photonic microwave signal generation by using a sole excited-state(ES)emitting quantum dot(QD)laser under both optical injection and optical feedback is numerically studied.Within the range of period-one(P1)dynamics caused by the optical injection,the variations of microwave frequency and microwave intensity with the parameters of frequency detuning and injection strength are demonstrated.It is found that the microwave frequency can be continuously tuned by adjusting the injection parameters,and the microwave intensity can be enhanced by changing the injection strength.Moreover,considering that the generated microwave has a wide linewidth,an optical feedback loop is further employed to compress the linewidth,and the effect of feedback parameters on the linewidth is investigated.It is found that with the increase of feedback strength or delay time,the linewidth is evidently decreased due to the locking effect.However,for the relatively large feedback strength or delay time,the linewidth compression effect becomes worse due to the gradually destroyed P1 dynamics.Besides,through optimizing the feedback parameters,the linewidth can be reduced by up to more than one order of magnitude for different microwave frequencies.

Optical feedback characteristics in a helium neon laser with a birefringent internal cavity

The output characteristics of optical feedback in a helium neon laser with a birefringent internal cavity are studied systematically in five different regions of the gain curve for the two orthogonally polarized modes. When the laser operates in the two end regions of the laser gain curve, one of the two orthogonally polarized modes will be a leading one in optical feedback. Strong mode competition can be observed. However, when the laser operates in the middle region of the laser gain curve, the two modes can oscillate equally with optical feedback. Besides the intensity of the two polarized lights, the total light intensity is also studied at the same time. M-shaped optical feedback curves are found. Particularly, when the average intensities of the two lights are comparable, the intensity modulation curve of the total light is doubled, which can be used to improve the resolution of an optical feedback system.

Sensitivity to external optical feedback of circular-side hexagonal resonator microcavity laser

The sensitivity to fault reflection is very important for larger dynamic range in fiber fault detection technique.Using time delay signature(TDS)of chaotic laser formed by optical feedback can solve the sensitivity limitation of photodetector in fiber fault detection.The TDS corresponds to the feedback position and the fault reflection can be detected by the laser diode.The sensitivity to feedback level of circular-side hexagonal resonator(CSHR)microcavity laser is numerically simulated and the feedback level boundaries of each output dynamic state are demonstrated.The peak level of TDS is utilized to analyze the sensitivity.The demonstration is presented in two aspects:the minimum feedback level when the TDS emerges and the variation degree of TDS level on feedback level changing.The results show that the CSHR microcavity laser can respond to the feedback level of 0.07%,corresponding to-63-dB feedback strength.Compared to conventional distributed feedback laser,the sensitivity improves almost 20 dB due to the shorter internal cavity length of CSHR microcavity laser.Moreover,1%feedback level changing will induce 1.001 variation on TDS level,and this variation degree can be influenced by other critical internal parameters(active region side length,damping rate,and linewidth enhancement factor).

Analysis of gain distribution in cladding-pumped thulium-doped fiber laser and optical feedback inhibition problem in fiber-bulk laser system

The steady-state gain distribution in cladding pumped thulium-doped fiber laser（TDFL） is analytically and numerically solved based on the rate equations including loss coefficients and cross relaxation effect. With the gain curve, a problem, which is named optical feedback inhibition（OFI） and always occurs in tandem TDFL-Ho：YAG laser system, is analyzed quantitatively. The actual characteristics of output spectra and power basically prove the conclusion of theoretical analysis. Then a simple mirror-deflected L-shaped cavity is employed to restrain the external feedback and simplify the structure of fiber-bulk Ho：YAG laser. Finally, 25 W of 2097-nm laser power and 51.2% of optical-to-optical conversion efficiency are obtained, and the beam quality factor is less than 1.43 obtained by knife-edge method.

Polarization switching in a quasi-isotropic microchip Nd:YAG laser induced by optical feedback

This paper demonstrates the influence of external optical feedback on the polarization state of longitudinal modes in quasi-isotropic microchip Nd：YAG lasers. Under optical feedback, the polarization state of longitudinal modes in quasi-isotropic lasers relies strongly on the intracavity anisotropy loss and mode competition. When the intracavity anisotropy loss is small, external optical feedback can cause polarization switching and strong mode competition between two orthogonal linearly polarized eigenstates of one laser longitudinal mode, which leads to the distortion of laser intensity modulation waveform. The polarization switching is independent of the initial external cavity length. By increasing the intracavity anisotropy loss, one polarization eigenstate can be suppressed and the laser works in single-polarization state. A theoretical analysis based on the compound cavity model is presented, which is in good agreement with the experimental results. The results offer guidance to the development of laser feedback interferometers.

Intensity tuning characteristics of double-mode He-Ne laser with optical feedback

This paper investigates the intensity tuning characteristics of a double longitudinal modes HeiNe laser subjected to optical feedback. The intensity undulations of the total light and the two modes are observed for different external cavity length. Two modulations of the internal cavity length are performed. One is only for the internal cavity length being modulated and the other is for both the internal and the external cavity length being modulated. The undulation frequency of the total light is found to be determined by the ratio of external cavity length to internal cavity length in both modulations. When the external cavity length is integral times of the internal cavity length, the fringe frequency of the total light could be seven or even more times of that in conventional optical feedback. A simple theoretical analysis is presented, which is in good agreement with the experimental results. The potential use of the experimental results is also discussed.

External Optical Feedback Induced Noise in DFB Fiber Laser Sensor System

External optical feedback effects due to reflection, Rayleigh backscattering and coherent Rayleigh backseattering in fiber distributed feedback （DFB） fiber laser sensor system have been investigated. If the feedback intensity exceeds critical amount, excess noise would be induced in the demodulator. The maximum tolerable intensity back-reflection coefficient Rc and backscattering coefficient Sc into a fiber DFB laser with lead fiber length from I m to 37.5 km before the onset of instabilities are shown. Rc is found to decrease with increasing lead fiber length while Sc was relatively invariable with varying fiber length. The coherent Rayleigh backscattering （CRBS） would induce neglectable noise with a lead fiber exceeding 13.5 kin. To eliminate these noises, one or two isolators should be incorporated in the system.

Distortion of optical feedback signals in microchip Nd:YAG lasers subjected to external multi-beam interference feedback

This paper proposes a theoretical analysis for the characteristics of an external cavity Nd：YAG laser with feedback of multiple-beam interference, which is induced by the multi-reentrance of the light from the external Fabry-Perot cavity. The theoretical model considers the multiple beam interference of the external Fabry-Perot cavity. It is found that the optical feedback signals are distorted to pulse waveforms instead of the sinusoidal ones in conventional feedback. The experimental results are in good agreement with the theoretical analysis. The obtained theoretical and experimental results can advance the development of a laser feedback interferometer.

Time-Domain Traveling Wave Model of Single-Section Quantum Dot Mode-Locked Lasers with Optical Feedback

The optical feedback modulations of a passively mode-locked semiconductor laser with quantum dot structure were investigated in this study. The delay-induced dynamics of QD MLL under the condition of optical feedback have been studied by exploiting a time domain traveling wave(TDTW) model. The conventional TDTW model was improved to make it suitable for studying optical feedback system, especially the system with long external cavity structure. Combing the TDTW model with optical feedback and carrier rate equations, the pulse variation of a single section QD MLL was studied. This new model shows good agreement with the published experimental data. The roundtrip time and local light intensity modulation to the pulse evolution of QD MLL were studied. The results show that when the time for a light to go to and return from external cavity is equal to the integral times of the period of laser pulse without external feedback, resonance will be formed, and the period of pulse sequence is the shortest. The results also show that the stronger the local light intensity modulation is, the shorter the pulse period is.

Laser Feedback Technique for Precise Retardation Measurements

A simple and precise retardation measurement based on laser feedback is demonstrated. The measurement principle is based on polarization flipping induced by optical feedback from an external birefringence cavity. The measured wave plate is located in the external cavity. When the length of the external cavity is tuned, the polarization states of laser will flip between two eigenstates, and the position of polarization flipping in one period of intensity modulation will vary with retardation of the wave plate. The duty ratio of two eigenstates is used to determine the retardation. Main advantages of the technique are that it is compact, low cost, fast and flexible. Especially, it is insensitive to a fluctuation of laser intensity and is suitable for on-line measurement. The experimental results have shown that the measurement uncertainty is better than 0.03° in the range 30°-150°.

Cavity-Mode Properties of Semiconductor Lasers Operating in Strong-Feedback Regime

This paper investigates the modal properties of semiconductor lasers operating in the strong-feedback regime. Analytical expressions are developed based on an iterative travelling-wave model, which enable a complete and quantitative description of a compound cavity mode in its steady state. Additional information is provided about the physical inside into a compound laser system, such as a bifurcation diagram of the compound cavity modes for full variation range （from 0 to 1） of the external reflection coefficient and a more general shape for the diagram of photon density versus mode phase - this latter will reduce to the classical ＂ellipse＂ in the weak-feedback regime. It is shown that in the strong-feedback regime, a feedback laser is characterized by a small mode number and a high density of photons. This behavior confirms previous experimental observations, showing that beyond the coherence-collapse regime, the compound laser system could be re-stabilized, and that as a result power-enhanced low-noise stable laser operation with quasi-uniform pulsation is possible with external-mirror reflectivity close to 1. Moreover, it is also shown that for a compound system operating in the strong-feedback regime, an anti-reflection treatment of a laser can significantly reduce its current threshold, and that in the absence of this treatment excitation of a minimum-linewidth mode with higher output power would be possible inside such a system. Finally, it is shown that in the weak-feedback regime except for a phase shift the iterative travelling-wave model will reduce to the Lang-Kobayashi model in cases where the product of the feedback rate and the internal round-trip time is much less than unity （that would mean in situations of as-cleaved lasers）.

A sensitive method of determining optic axis azimuth based on laser feedback

A sensitive method to determine the optic axis azimuth of the birefringence element is presented, which is based on laser feedback. The phase difference between the two intensities in birefringence feedback changes with the angle between the optic axis of the birefringence element and laser original polarization. The phase difference is highly sensitive to the relative position of the optic axis and the laser original polarization. This method is used to highly precisely determine the optic axis azimuth, and is able to distinguish between the fast axis and the slow axis of the birefringence element. Theoretical analysis and experimental results are both demonstrated.

Parallel generation of low-correlation wideband complex chaotic signals using CW laser and external-cavity laser with self-phase-modulated injection

A novel scheme for generating optical chaos is proposed and experimentally demonstrated,which supports to simultaneously produce two low-correlation chaotic signals with wideband spectrum and suppressed time-delay-signature(TDS).In the proposed scheme,we use the output of an external-cavity semiconductor laser(ECSL)as the driving signal of a phase modulator to modulate the output of a CW laser.Then the phase-modulated continuous-wave(CW)light is split into two parts,one is injected back into the ECSL that outputs one chaotic signal,while the other part is passed through a dispersion module for generating another chaotic signal simultaneously.The experimental results prove that the proposed scheme has three merits.Firstly,it can improve the bandwidth of ECSL-based chaos by several times,and simultaneously generate another wideband flat-spectrum chaotic signal.Secondly,the undesired TDS characteristics of the simultaneously-generated chaotic signals can be efficiently suppressed to an indistinguishable level within a wide parameter range,as such the complexities of the chaotic signals are considerably high.Thirdly,the correlation coefficient between these two simultaneously-generated chaotic signals is smaller than 0.1.The proposed scheme provides an attractive solution for parallel multiple chaos generation,and shows great potential for multiple channel chaos communications and multiple random bit generations.