Plane wave coupling into single-mode fiber in the presence of random angular jitter

Advanced root mean square propagation with the warm-up algorithm for fiber coupling

Fiber coupling plays an important role in applications such as free-space optical communication (FSOC) and self-referencing interferometry. However, the coupling efficiency is often affected by turbulence and platform vibrations, which requires dynamic coupling with optimization algorithms. In this paper, to further mitigate the effects of sudden disturbances and to expand the effective range of fiber coupling systems, we propose a new method called the advanced root mean square propagation with warm-up (ARW) algorithm. By adaptively adjusting both the gain rate and the perturbation rate with warm-up operations, the ARW algorithm can achieve higher effective range and acceptable steady-state coupling efficiency simultaneously. Simulation and experimental results demonstrate that the proposed method requires only 36.4% of the iterations of the SPGD algorithm to deal with sudden disturbances. Moreover, the effective range of the ARW algorithm is 530.50µrad in the specific coupling platform, which is 20% higher than the effective range of SPGD.

Set of mathematical models for Bessel-Gauss beams coupling into the parabolic-index fiber under the influence of atmospheric turbulence and random jitter

The expression of efficiency for Bessel-Gauss (BG) beams coupling into the parabolic fibers (PF) after passing through the Cassegrain antenna system is first derived. The effects of atmospheric turbulence and random jitter of the coupling lens on the efficiency are also taken into account to improve the practical applicability of our model. This article use a BG beam with a wavelength of 1550 mm and fiber with a core radius R_F of 50 μm and a relative refractive index difference ζ of 0.01 for simulation testing. The optimal parameters of the antenna system are determined: the radius of the primary mirror and the secondary mirror is 8.33 cm and 1.25 cm, respectively. The coupling efficiency of BG beams of different orders reaches above 94% simultaneously when the lens's focal length is 7.8 cm. After taking into account the transmission efficiency of the antenna system, the system's total efficiency for BG beams of different orders averages 76.33%, when the transmission distance is 1 km. The results show that the same degree of turbulence and random jitter have different influences on the coupling efficiency of BG beams of different orders, and lower-order BG beams have better resistance to turbulence and jitter during propagation and coupling. Moreover, the effect of the guided mode field on the coupling efficiency and the resistance to turbulence varies for different values of mode radial index in the fiber p. The guided mode with p = 0 not only enables the BG beams of different orders to achieve the highest transmission efficiency in the coupling system almost simultaneously but also the random jitter and turbulence have less influence on the coupling efficiency of this mode. It means that the BG beams can have higher efficiency when coupled to the mode with p = 0 after long-distance transmission. This property of the fiber mode at p = 0 provides conditions for the simultaneous propagation of multiple BG beams in a parabolic fiber, which provides a theoretical basis for higher transmission capacity. This research work provides a theoretical model for the theoretical study of vortex beams and optical communication, which is beneficial for the design and application of vortex beams and has instructive meaning for practical engineering design.

Efficiency Enhancing Technique for Rod Fiber Picosecond Amplifiers with Optimal Mode Field Matching

A high power and high quality picosecond laser is crucial in MEMS fabrication regarding micromachines. Optimal seed beam coupling is an important precondition to enhance laser efficiency. However, empirical coupling limits its development. In this paper, the physical parameters related to coupling are determined. The relationships among them are established under optical mode matching constraints to satisfy optimal seed beam coupling. According to a theoretical analysis, the focal length cut-off and the optimal coupling position of the coupling lens are acquired. A maximum transmittance of 87.2% is acquired with a 6 W input seed power in the validation experiment. In further power amplification experiments, a diffraction-limited beam quality is achieved, with M²_X = 1.111, M²_Y = 1.017, an optical efficiency of 60.5% and a slope efficiency of 66%, benefiting from the previous theoretical guidance.

Sensitivity Deterioration of Free-Space Optical Coherent/Non-Coherent OOK Modulation Receiver by Ambient Light Noise

In free-space optical (FSO) communication systems, on-off keying (OOK) is a widely used modulation format. Coherent and non-coherent OOK receivers with sensitivities of -54.60 dBm and -51.25 dBm, respectively, were built with a communication rate of 1 Gbit/s and a bit error rate of 10^-3. In an FSO communication system, the parameters must be designed to ensure a sufficient link margin. In contrast to optical fiber systems, FSO systems have ambient light (AL) noise such as sunlight. The efficiency of sunlight coupling in the single-mode fiber (SMF) of the receivers was calculated in this study. For a signal light with AL, the change in the main components of noise and the sensitivity deterioration were theoretically analyzed and experimentally verified in conditions of coherent reception and non-coherent reception with a preamplifier. For coherent reception, the theoretical sensitivity deterioration results are consistent with the experimental results which indicate that coherent reception exhibits better anti-AL noise performance than non-coherent reception when the power spectral density of the AL is the same. Coherent and non-coherent receivers coupled with SMF can work in direct sunlight. When the receiver lens diameter is greater than 4.88 × 10^-4 m, the anti-AL noise performance of the receiver can be improved by increasing the receiver lens diameter.

Method for 10 Gbps near-ground quasi-static free-space laser transmission by nutation mutual coupling

This study proposes a method to reduce link loss in near-ground space laser communication with fiber-nutation-based mutual coupling. We designed a transmit-receive coaxial laser terminal with a 50 mm aperture and implemented beam acquisition tracking and nutation coupling using a single-detector and single-actuator. Following an indoor experiment and a 1 km field test, the single-ended nutation coupling and the two-way nutation mutual coupling theories were compared and analyzed. In conclusion, the proposed method could significantly increase the reception efficiency by ∼8 dB. The bit error rate of 10 Gbps pseudo-random code transmission was 2.478E-9. We also demonstrated video transmission.

Fiber coupling efficiency of a Bessel-Gaussian beam received by a Cassegrain antenna under atmospheric turbulence

A coupling efficiency calculation method for a Bessel-Gaussian (BG) beam in a free space optical communication system received by a parabolic Cassegrain antenna and coupled into a few-mode fiber is proposed. The system of the antenna and the coupling lens is approximate to a ring-shaped lens. The effect of the antenna in the coupling system is analyzed, and maximum coupling efficiency is increased by 76.25% on average by applying the antenna. With the application of the antenna, the configurations to generate the maximum point of coupling efficiency among BG beams of different topological charges are restricted to being almost the same, which is useful for the simultaneous propagation of multiple BG beams. The effects of radial displacement and atmospheric turbulence on coupling efficiency are researched as well. Coupling efficiency becomes more sensitive to radial displacement, while the influence of turbulence on coupling efficiency remains almost the same after applying the antenna. Our calculation method has an average absolute error of only 0.6625% while increasing the calculation speed greatly, which is practical for further studies of vortex beams.

Theoretical and Experimental Analysis on Statistical Properties of Coupling Efficiency for Single-Mode Fiber in Free-Space Optical Communication Link Based on Non-Kolmogorov Turbulence

Non-Kolmogorov turbulence has been widely observed in free-space optical communication links and should be used to evaluate the system performance. We calculated the wavefront residual variance in the condition of the non-Kolmogorov turbulence model and deduced the mathematical expression of the probability density function (PDF) for the coupling efficiency (CE) of a single-mode fiber (SMF). The PDF was simulated, and the results showed its robustness and rationality. Moreover, an experiment was set up to verify the PDF with experimental distribution. The correlation coefficients are above 0.95 in all cases, which means the statistical model of the CE fitted the experimental distribution well.

Diffraction-based overlay metrology using angular-multiplexed acquisition of dark-field digital holograms

In semiconductor device manufacturing, optical overlay metrology measures pattern placement between two layers in a chip with sub-nm precision. Continuous improvements in overlay metrology are needed to keep up with shrinking device dimensions in modern chips. We present first overlay metrology results using a novel off-axis dark-field digital holographic microscopy concept that acquires multiple holograms in parallel by angular multiplexing. We show that this concept reduces the impact of source intensity fluctuations on the noise in the measured overlay. With our setup we achieved an overlay reproducibility of 0.13 nm and measurements on overlay targets with known programmed overlay values showed good linearity of R²= 0.9993. Our data show potential for significant improvement and that digital holographic microscopy is a promising technique for future overlay metrology tools.

The Effect of Spatial Mode Distribution on Coupling Efficiency of Single-Mode Fiber: Theoretical Analysis and Experimental Verification

In this study, Zernike polynomials and optical fiber field theory are applied to build a mathematical model of coupling efficiency (CE) and spatial mode of aberrations. The theory built in this paper can be used to quickly calculate the CE affected by a single aberration as well as the aberrations caused by atmospheric turbulence. The aberrations are classified based on Zernike polynomials and the effects of aberrations on CE of different types and different spatial frequencies are analyzed. The influence of the effects of AO system residual errors is also analyzed. Adaptive optics (AO) equipment is applied to build a system on which the proposed theory was tested; the experimental results validate the theoretical analysis.

Intensity-based adaptive optics with sequential optimization for laser communications

Wavefront distortions of optical waves propagating through the turbulent atmosphere are responsible for phase and amplitude fluctuations, causing random fading in the signal coupled into single-mode optical fibers. Wavefront aberrations can be confronted, in principle, with adaptive optics technology that compensates the incoming optical signal by the phase conjugation principle and mitigates the likeliness of fading. However, real-time adaptive optics requires phase wavefront measurements, which are generally difficult under typical propagation conditions for communication scenarios. As an alternative to the conventional adaptive optics approach, here, we discuss a novel phase-retrieval technique that indirectly determines the unknown phase wavefront from focal-plane intensity measurements. The adaptation approach is based on sequential optimization of the speckle pattern in the focal plane and works by iteratively updating the phases of individual speckles to maximize the received power. We found in our analysis that this technique can compensate the distorted phasefront and increase the signal coupled with a significant reduction in the required number of iterations, resulting in a loop bandwidth utilization well within the capacity of commercially available deformable mirrors.

Statistical model of the efficiency for spatial light coupling into a single-mode fiber in the presence of atmospheric turbulence

The average efficiency of spatial light coupling into a single-mode optical fiber is widely used but cannot estimate the signal-to-noise ratio (SNR) and bit error rate (BER) in free-space optical communication. We provide a statistical model for coupling efficiency and derive the exact expression of the probability density function (PDF). The simulation results confirm that the model is reasonable in the condition of different turbulence intensities and wavefront compensation terms, which is also consistent with our outdoor experiment. We also estimate the average SNR and BER using the PDF. The model is quite useful in a satellite-to-ground laser communication downlink.