Technique for enhancing the accuracy of the Rayleigh-Sommerfeld convolutional diffraction through the utilization of independent spatial sampling: publisher's note.

This publisher's note contains a correction to Opt. Lett.49, 1385 (2024)10.1364/OL.509688.

Technique for enhancing the accuracy of the Rayleigh-Sommerfeld convolutional diffraction through the utilization of independent spatial sampling.

The Rayleigh-Sommerfeld diffraction integral (RSD) is a rigorous solution that precisely satisfies both Maxwell's equations and Helmholtz's equations. It seamlessly integrates Huygens' principle, providing an accurate description of the coherent light propagation within the entire diffraction field. Therefore, the rapid and precise computation of the RSD is crucial for light transport simulation and optical technology applications based on it. However, the current FFT-based Rayleigh-Sommerfeld integral convolution algorithm (CRSD) exhibits poor performance in the near field, thereby limiting its applicability and impeding further development across various fields. The present study proposes, to our knowledge, a novel approach to enhance the accuracy of the Rayleigh-Sommerfeld convolution algorithm by employing independent sampling techniques in both spatial and frequency domains. The crux of this methodology involves segregating the spatial and frequency domains, followed by autonomous sampling within each domain. The proposed method significantly enhances the accuracy of RSD during the short distance while ensuring computational efficiency.

All-fiber orthogonal-polarized white-noise-modulated laser for short-coherence dynamic interferometry.

An all-fiber orthogonal-polarized white-noise-modulated laser (AOWL) for short-coherence dynamic interferometry is proposed. Short-coherence laser is achieved by current modulating of a laser diode with the band-limited white noise. A pair of orthogonal-polarized lights with adjustable delay for short-coherence dynamic interferometry are output by the all-fiber structure. In the non-common-path interferometry, the AOWL can significantly suppress the interference signal clutter with 73% side lobe suppression ratio, that improves the positioning accuracy of zero optical path difference. The wavefront aberrations of a parallel plate are measured with the AOWL in the common-path dynamic interferometers, avoiding the fringe crosstalk.

Ultrafast two-dimensional imaging for surface defects measurement of mirrors based on a virtually imaged phased-array.

Single-shot measurement of surface defects of mirrors is vital for monitoring the operating states of high power lasers systems. While conventional methods suffer from low speed and small dynamic range. Here, we demonstrate a method for high speed two-dimensional (2D) surface amplitude-type defects measurement based on ultrafast single-pixel imaging assisted by a virtually imaged phased-array. Together with an optical grating, 2D wavelength to space mapping is achieved based on Fraunhofer far field diffraction, and the uniform broad spectrum of a home-made dissipative soliton is uniformly dispersed into the targeted mirror with one-to-one wavelength-to-space mapping. The surface amplitude-type defects are modulated into the intensity variation of the reflected spectrum. Then, we build a dispersive Fourier transform module for wavelength to time mapping, through which modulated spectral information is time stretched into the temporal domain, and recorded by a high speed photodetector together with a real time oscilloscope. Finally, to diminish the distortions induced by nonlinear dispersion during the wavelength-time mapping, we utilize the interpolation, and reconstruct the 2D surface with a frame rate of 7.6 MHz. A two-dimensional image with widths of 1.5 × 2 mm can be obtained within 10 ns, with a y direction spatial resolution of 180 µm and a x direction spatial resolution of 140 µm. This ultrafast 2D surface defects measurement scheme is promising for real-time monitoring of surface defects mirrors with large aperture, which are widely utilized in various high power laser systems.

Problems on polarization aberrations in large aperture dynamic interferometry based on the polarization phase shifting technique.

The polarization based phase shifting method is an effective way for dynamic measurements. However, when this technique is applied to the measurements of large optics, the interferometric results are easily limited by the birefringence of large optics. The birefringence changes the polarization states of reference light and test light, and brings constant polarization aberrations into the measurement results independent of the phase shifting procedure. In this article, the detailed theoretical analysis on the mechanism of polarization aberration is presented. Afterwards, we propose a new interferometric method to determine the birefringence effects by measuring the transmitted wavefronts of the large optics, which are considered as birefringent samples. Theoretical analysis shows that the polarization error in the linearly polarized system can be corrected by two independent measurements with orthogonal polarization states. The phase retardance can be obtained from the wavefront difference of the transmitted wavefronts when switching the polarization states of the incident lights. The birefringence distribution obtained is used to calibrate the polarization aberrations in the measurement result of a homemade large aperture measurement platform and the correction result is compared with the result via the wavelength tuning phase shifting method. The elimination of the polarization aberrations can be observed in the final results.

3.1†kW 1050†nm narrow linewidth pumping-sharing oscillator-amplifier with an optical signal-to-noise ratio of 45.5†dB.

In this paper, the amplified spontaneous emission (ASE) suppression in a 1050 nm fiber laser with a pump-sharing oscillator-amplifier (PSOA) structure is studied theoretically and experimentally. A theoretical model of a fiber laser with a PSOA structure is established. The characteristics of the ASE for the PSOA structure and the pump-independent oscillator-amplifier (PIOA) structure are compared and analyzed. The experimental results show that the ASE can be effectively suppressed by utilizing the PSOA structure, which agree with the simulation results. A 1050 nm high-power narrow-linewidth fiber laser with PSOA structure is demonstrated, in which the gain fiber lengths of the oscillator and amplifier are 1.6 m and 9 m, respectively, to ensure the interconnection of pump power between the oscillator and amplifier. Finally, the maximum output power of 3.1 kW has been achieved, the linewidth is 0.22 nm at 3 dB, the beam quality M2 ≈ 1.33, and the optical signal-to-noise ratio (OSNR) is 45.5 dB.

3.25 kW all-fiberized and polarization-maintained Yb-doped amplifier with a 20 GHz linewidth and near-diffraction-limited beam quality.

In this paper, we demonstrate a high-power, narrow-linewidth, polarization-maintaining fiber amplifier with near-diffraction-limited beam quality. By optimizing the phase modulation signal, a nearly top-hat-shaped spectrum was generated for self-pulsing suppressing. That results in doubling the self-pulsing threshold we got from conventional white noise signal phase modulation with the same optical linewidth. Based on an optimized signal and a high power, polarization-maintaining, counter-pumped fiber amplifier, we obtain a 3.25 kW narrow-linewidth linearly polarized laser output with a linewidth of ∼20GHz, the polarization extinction ratio is about 15 dB, and the M2 is less than 1.22 at the maximum output power. To the best of our knowledge, this is the first demonstration of a narrow-linewidth, linear polarization, all-fiber amplifier with 3.25 kW laser output.

Fast fiber mode decomposition with a lensless fiber-point-diffraction interferometer: publisher's note.

This publisher's note contains corrections to Opt. Lett.46, 2501 (2021)OPLEDP0146-959210.1364/OL.426833.

Fast fiber mode decomposition with a lensless fiber-point-diffraction interferometer.

Recently, the growing interest in few-mode fibers in telecommunications and high-power lasers has stimulated the demand for fiber mode decomposition (MD). Here we present a fast fiber MD method with a lensless fiber-point-diffraction interferometer. The complex amplitude at the fiber end is achieved by the polarization phase-shifting technique and the lensless imaging technique. Then, the eigenmode coefficients are determined by the mode orthogonal operations of the complex amplitude. In the experiment, the SMF-28e fiber containing 10 linear polarized modes at the wavelength of 632.8 nm is studied for MD. The decomposition of the 50 * 50 pixels interferograms takes only 0.0168 s. The similarity of the intensity patterns of the testing light is larger than 97% before and after the MD. This new, to the best of our knowledge, method can achieve fast and accurate 10-mode MD without using any imaging systems.

Stokes light induced modulation instability in high power continuous wave fiber amplifiers.

In this paper, Stokes light induced modulation instability (MI) in high power continuous wave (CW) fiber amplifiers is observed. The investigation shows that the Stokes light generated by inter-modal four wave mixing (IMFWM) and stimulated Raman scattering (SRS) in high power fiber amplifiers can be modulated by the signal light through XPM and cause MI. Then, a sideband will be generated around the second-order Raman frequency shift, which is amplified by SRS and shown as a train of pulses in time domain. It is shown that the frequency shift of the sideband will be influenced by IMFWM and SRS. In addition, the sideband was found to be blue-shifted with the increase of the power, which indicates that the frequency shift of the sideband is mainly depended on MI, while SRS plays the role of amplification.

Dynamic low-coherence interferometry using a double Fizeau cavity.

The coexistence of anti-vibration and a common optical path is difficult to realize in dynamic Fizeau interferometry. To address this problem, we propose a dynamic low-coherence interferometry (DLI) using a double Fizeau cavity. The DLI method is a new optical model that creatively renders both surfaces of the RM to interfere with the test surface, utilizing a low-coherence source and optical path matching to construct the common-path p-polarized Fizeau cavity (p-FC) and carrier-frequency s-polarized Fizeau cavity (s-FC). The relative tilt phases of the s-FC are calculated using the carrier frequency interferograms; then the final phase is retrieved with the relative tilt phases and p-FC interferograms. The experimental results demonstrate that the DLI method can provide high-precision phase measurement in a vibration environment.

High-efficiency full-surface defects detection for an ICF capsule based on a null interferometric microscope.

Laser inertial confinement fusion (ICF) triggers a nuclear fusion reaction via the evenly compressed capsule containing deuterium tritium fuel with a high-power laser. However, isolated defects on the surface of the capsules reduce the probability of ignition. In this paper, we present a full-surface defects detection method based on a null interferometric microscope (NIM) to achieve high-precision, high-efficiency, and full-surface defects detection on ICF capsules. A dynamic phase-shifting module is applied to the NIM to achieve a single-shot measurement in a single subaperture. With the capsule controlling system, the capsule is rotated and scanned along a planned lattice to get all subapertures measured. The eccentricity error can be measured from wavefront aberrations and compensated online to guarantee the measurement accuracy during the scanning process. After the scanning process, all of the surface defects are identified on the full-surface map. Theories and experimental results indicate that for the capsule with 875-µm-diameter, the lateral resolution could reach 0.7 µm and the measurement time is less than 1 h. The number of sampling points can reach about 50 million. To the best of our knowledge, our proposed system is the first to achieve full-surface defects detection of ICF capsules with such high efficiency and high resolution at the same time.

A flexible numerical calculation method of angular spectrum based on matrix product.

Fast Fourier transform (FFT) is the most commonly used mathematical method in numerical calculation, and the FFT-based angular spectrum method (ASM) is also used widely in diffraction calculation. However, the frequency and spatial sampling rules in FFT limit the effective propagation distance and the observation window range of ASM. A novel method for calculating the angular spectrum based on the matrix product is proposed in this Letter. This method realizes the fast calculation of discrete Fourier transform (DFT) based on the matrix product, in which the sampling matrix is orthogonally decomposed into two vectors. Instead of FFT, angular spectrum diffraction calculation is carried out based on the matrix product, which is named the matrix product ASM. The method in this Letter uses a simple mathematical transformation to achieve maximum compression of the sampling interval in the frequency domain, which significantly increases the effective propagation distance of the angular spectrum. Additionally, the size of the observation window can be enlarged to obtain a wider calculation range by changing the spatial sampling of the output plane.

Modelling and correction for polarization errors of a 600†mm aperture dynamic Fizeau interferometer.

The polarization errors of large aperture dynamic interferometers based on the polarization phase shifting method are mainly coming from the effects of imperfect polarized elements and birefringence of large elements. Using the Lissajous ellipse fitting algorithm to correct the influence of the polarized device can effectively eliminate single and double frequency print through errors. We develop a wave plate model for analyzing the birefringence effect, and on this basis, we establish the relationship between the calculated phase and the ideal phase distribution. Experiments are carried out on a 600mm aperture Fizeau interferometer and then compared with the result acquired through the wavelength tuning method. The difference between PV is only 0.002λ.

System design and error correction for 300 mm aperture vertical Fizeau spatial-temporal phase-shifting interferometer.

With the development of high-power lasers for aerospace, electronics, etc., the demand for large-aperture planar optical elements has become more urgent, along with the demand for measurement methods. In this paper, the design of a 300 mm aperture vertical Fizeau spatial-temporal phase-shifting interferometer is discussed. Based on position difference between laser sources, the spatial phase-shifting technique is achieved by generating a laser source array on the focal plane of the collimation lens, and four pairs of coherent beams with different phase shifts are integrated in a vertical Fizeau interference system. Combined with a tunable laser diode, a temporal phase-shifting technique can be realized in any pair of coherent beams through wavelength tuning. The key techniques, which include laser duplication to introduce different phase shifts, conjugate imaging, and separation for interferograms, and assembly for a transmission flat, are demonstrated. The systematic error and position mismatch error of interferograms are eliminated. Comparison experiments are conducted between spatial and temporal phase-shifting techniques. A dynamic water surface is also measured to verify its capacity for detecting dynamic objects.

Suppressing stimulated Raman scattering in kW-level continuous-wave MOPA fiber laser based on long-period fiber gratings.

Two long-period fiber gratings (LPFGs) used to separately suppress the stimulated-Raman-scattering (SRS) in the seed and amplifier of kW-level continuous-wave (CW) MOPA fiber laser are developed in this paper. A process that combines constant-low-temperature and dynamic-high-temperature annealing was employed to reduce the thermal slopes of 10/130 µm (diameter of core/cladding fiber) and 14/250 LPFGs, used in the seed and amplifier respectively, from 0.48 °C/W to 0.04 °C/W and from 0.53 °C/W to 0.038 °C/W. We also proposed a reduced-sensitivity packaging method to effectively reduce the influence of axial-stress, bending, and environmental temperature on LPFGs. Further, we established a kW-level CW MOPA system to test SRS suppression performance of the LPFGs. Experimental results demonstrated that the SRS suppression ratios of the 10/130 and 14/250 LPFGs exceed 97.0% and 99.6%, respectively.

1.5 kW polarization-maintained Yb-doped amplifier with 13 GHz linewidth by suppressing the self-pulsing and stimulated Brillouin scattering.

In this work, we study the characteristics of self-pulsing in a polarization-maintained fiber amplifier operated with different linewidths based on white noise source phase modulation. It indicates that the self-pulsing is almost simultaneous with the stimulated Brillouin scattering process, and its threshold is increasing near-linearly with the linewidth. By optimizing the laser structure, the threshold of self-pulsing increases by a factor of 1.5. We demonstrate a high-power linear polarization and all-fiberized amplifier with narrow linewidth and near-diffraction-limited beam quality. The output power scales to 1.5 kW with the pumping efficiency of 83%. The full width at half-maximum linewidth was measured to be 13 GHz. The polarization extinction ratio was larger than 13 dB. The beam quality M2 was about 1.14 at the maximum laser power.

Theoretical and experimental study on the thermally dependent transient response of the high power continuous wave Yb-doped fiber laser.

In this paper, transient thermal effects of the Yb-doped fiber and the laser diode (LD) in high power Yb-doped fiber lasers (YDFLs) are studied theoretically to analyze the transient response of the fiber laser. Based on the transient heat conduction equation, we simulated the temperature variation of the YDF and LD. It is found that the transient response of the laser is mainly affected by the thermally induced wavelength shifting of LDs. We modified the rate equations of the fiber laser according to the temperature variation of the LD. To improve the transient response speed of the fiber laser, we present three methods: (a) raising the cooling temperature, (b) increasing the length of gain fiber, and (c) using the YDF with high doping. Finally, experiments were carried out to verify the theory, and the results are in good agreement.

Dynamic phase-deforming interferometry: suppression of errors from vibration and air turbulence.

In this Letter, dynamic phase-deforming interferometry (PDI) is proposed to solve the impact of environmental vibration and air turbulence on the measurement accuracy. Two interference passes, namely, the measurement pass (MP) and carrier-frequency pass (CP), are constructed, utilizing one detector to acquire the fringe patterns of the two passes simultaneously. The relative deformation phases of the CP fringe patterns are calculated with the Fourier transform method; then the phase extraction of the MP is performed via the least squares method to obtain the final phase distribution. The optical layout and phase-extraction algorithm of the PDI method are investigated, and the principle simulation and measurement experiments are performed. The experimental results show that the PDI can provide not only high-precision phase measurement under the influence of environmental vibration and air turbulence, but also has low system complexity and fast measurement speed.

Optical homogeneity measurement of parallel plates by wavelength-tuning interferometry using nonuniform fast Fourier transform.

Wavelength-tuning interferometry is commonly employed to measure the optical homogeneity of parallel plates. However, the nonlinearity of phase shifts caused by wavelength tuning errors and environmental vibration leads to a spatially uniform error in the calculated phase distribution. Herein, a wavelength-tuning interferometry method based on nonuniform fast Fourier transform (WTI-NUFFT) was developed, which solves the spectral aliasing resulting from the spatially uniform error. The characteristics of the WTI-NUFFT method were estimated through comparison with the FFT method. Both the simulated and experimental results showed that the WTI-NUFFT method can improve the accuracy of the optical homogeneity measurement of parallel plates.