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Showing papers in "Chinese Optics Letters in 2009"


Journal ArticleDOI
TL;DR: In this article, bends, splitters, and mode converters are introduced for metal-dielectric-metal (MDM) waveguide devices with no additional loss, and optical gain provides a mechanism for on/off switching in MDM waveguides.
Abstract: We review some of the recent advances in the development of subwavelength plasmonic devices for manipulating light at the nanoscale, drawing examples from our own work in metal-dielectric-metal (MDM) plasmonic waveguide devices. We introduce bends, splitters, and mode converters for MDM waveguides with no additional loss. We also demonstrate that optical gain provides a mechanism for on/off switching in MDM plasmonic waveguides. Highly efficient compact couplers between dielectric waveguides and MDM waveguides are also introduced. OCIS codes: 130.2790, 240.6680, 260.2110. doi: 10.3788/COL20090704.0302.

81 citations


Journal ArticleDOI
TL;DR: In this article, the applicability of guided mode resonant structures to tunable optical filtering and sensing is demonstrated using nematic liquid crystals, and the optimum design is achieved by maximizing the evanescent field region in the analyte which maximizes the overlap integral.
Abstract: Applicability of guided mode resonant structures to tunable optical filtering and sensing is demonstrated using nematic liquid crystals. As a sensor, a minimum refractive index detectivity of 10^{-5} is demonstrated while as a tunable filter, tunability range of few tens of nanometers with 2-nm bandwidth is presented. The optimum design is achieved by maximizing the evanescent field region in the analyte which maximizes the overlap integral. The device can be operated in reflection or transmission modes at normal incidence. It can also be operated at a single wavelength by measuring the angular profile of the light beam.

53 citations


Journal ArticleDOI
TL;DR: Recent progresses on the rainbow hologram, the cylindrical holograms, and the disk hologram for 3D display are introduced.
Abstract: We have been studying various types of computer-generated holograms for three-dimensional (3D) displays both for a real-time holographic video display and a hard copy, or a printed hologram. For the hard copy output, we have developed a direct fringe printer, which is achieved to print over 100 gigapixels computer-generated hologram with 0.44-µm pitch. In this paper, we introduce our recent progresses on the rainbow hologram, the cylindrical holograms, and the disk hologram for 3D display.

48 citations


Journal ArticleDOI
TL;DR: In this paper, the authors used multi-frequency phase modulation to generate equal-amplitude spectral lines for stimulated Brillouin scattering (SBS) suppression, and obtained the spectra of three, five, seven, and eleven equal amplitude lines with flatness less than 0.3 dB.
Abstract: The method of generating equal-amplitude spectral lines by multi-frequency phase modulation is used in stimulated Brillouin scattering (SBS) suppression. The spectra of three, five, seven, and eleven equal-amplitude spectral lines are obtained in experiment with flatnesses less than 0.3 dB. Theoretical research on SBS suppression shows that the threshold power after modulation is in reverse proportion to the maximum square of amplitude moduli of fundamental frequency and the nth harmonic wave. The threshold powers of three, five, seven, and eleven equal-amplitude spectral lines are improved by 5.21, 8.36, 9.39, and 10.76 dB, respectively.

44 citations


Journal ArticleDOI
Zhengle Mao1, Lingling Qiao1, Fei He1, Yang Liao1, Chen Wang1, Ya Cheng1 
TL;DR: In this article, a large thermal-induced third-order nonlinear refractive index up to -1.94110?7 cm2/W is obtained from the mixed solution under 488-nm continue wave (CW) laser irradiation, which may result from surface plasmon resonance (SPR) enhancement effect of silver nanoparticles as well as high thermo-optic coefficient and low thermal conductivity of ethanol.
Abstract: The investigation of nonlinear optical characteristics of ethanol solution doped with silver nanoparticles is presented. A large thermal-induced third-order nonlinear refractive index up to -1.94110?7 cm2/W is obtained from the mixed solution under 488-nm continue wave (CW) laser irradiation, which may result from surface plasmon resonance (SPR) enhancement effect of silver nanoparticles as well as high thermo-optic coefficient and low thermal conductivity of ethanol. Obvious spatial self-phase modulation and influence of thermal-induced negative lens effect are observed when a beam propagates through this solution, indicating promising applications such as optical limiting, beam flattening, and so on.

40 citations


Journal ArticleDOI
TL;DR: In this article, the authors show that the thermal nonlinearity in the microsphere can enhance the ringing phenomenon in silica microspheres, and their measurement results agree very well with the theoretical predictions by the dynamic equation.
Abstract: Whispering gallery modes in silica microspheres are excited by a tunable continuous-wave laser through the fiber taper. Ringing phenomenon can be observed with high frequency sweeping speed. The thermal nonlinearity in the microsphere can enhance this phenomenon. Our measurement results agree very well with the theoretical predictions by the dynamic equation.

33 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of temperature on a surface plasmon resonance (SPR) sensor in Kretschmann configuration are studied experimentally and theoretically, and a detailed theoretical model is provided to analyze the variation of performance with varying temperature of the sensing environment.
Abstract: The effects of temperature on a surface plasmon resonance (SPR) sensor in Kretschmann configuration are studied experimentally and theoretically. SPR experiments are carried out over a temperature range of 278-313 K in steps of 5 K. A detailed theoretical model is provided to analyze the variation of performance with varying temperature of the sensing environment. The temperature dependence of the properties of the metal, dielectric, and analyte are studied, respectively. The numerical results indicate that the predictions of the theoretical model are well consistent with the experiment data.

28 citations


Journal ArticleDOI
Jianhua Shang1, Yan He1, Dan Liu1, Huaguo Zang1, Weibiao Chen1 
TL;DR: Based on the correlation theories of heterodyne detection, a laser Doppler vibrometer (LDV) was developed to detect the sound signal through the vibration of glass as mentioned in this paper.
Abstract: Laser Doppler vibrometer (LDV) has a potential application prospect in remote sensing. Based on the correlation theories of heterodyne detection, a LDV system with a configuration of all fiber and heterodyne techniques is developed to detect the sound signal through the vibration of glass. Experimental results show that the LDV system has an ability to acquire the real-time speech signal 25 m away through glass. While, the system signal-to-noise ratio (SNR) value decreases with the increase of the glass thickness and the detection distance.

28 citations


Journal ArticleDOI
TL;DR: In this article, the deconvolution algorithm is adopted on the fiber Raman distributed temperature sensor (FRDTS) to improve the spatial resolution without reducing the pulse width of the light source.
Abstract: The deconvolution algorithm is adopted on the fiber Raman distributed temperature sensor (FRDTS) to improve the spatial resolution without reducing the pulse width of the light source. Numerical simulation shows that the spatial resolution is enhanced by four times using the frequency-domain deconvolution algorithm with high temperature accuracy. In experiment, a spatial resolution of 15 m is realized using a master oscillator power amplifier light source with 300-ns pulse width. In addition, the dispersion-induced limitation of the minimum spatial resolution achieved by deconvolution algorithm is analyzed. The results indicate that the deconvolution algorithm is a beneficial complement for the FRDTS to realize accurate locating and temperature monitoring for sharp temperature variations.

27 citations


Journal ArticleDOI
TL;DR: In this paper, a numerical model is developed for the calculation of transient temperature field of thin film coating induced by a long-pulsed high power laser beam, where the electric field intensity distribution of HfO2/SiO2 high reflective (HR) film is investigated to calculate the thermal field of the film.
Abstract: A numerical model is developed for the calculation of transient temperature field of thin film coating induced by a long-pulsed high power laser beam. The electric field intensity distribution of HfO2/SiO2 high reflective (HR) film is investigated to calculate the thermal field of the film. The thermal-mechanical relationships are discussed to predict the laser damage area of optical thin film under long pulse high energy laser irradiation.

26 citations


Journal ArticleDOI
TL;DR: In this article, a method for metal coating optical fiber and in-fiber Bragg grating is described in detail, which is based on electroless plating and electroplating method.
Abstract: We present a method for metal coating optical fiber and in-fiber Bragg grating. The technology process which is based on electroless plating and electroplating method is described in detail. The fiber is firstly coated with a thin copper or nickel plate with electroless plating method. Then, a thicker nickel plate is coated on the surface of the conductive layer. Under the optimum conditions, the surfaces of chemical plating and electroplating coatings are all smooth and compact. There is no visible defect found in the cross-section. Using this two-step metallization method, the in-fiber Bragg grating can be well protected and its thermal sensitivity can be enhanced. After the metallization process, the fiber sensor is successfully embedded in the 42CrMo steel by brazing method. Thus a smart metal structure is achieved. The embedding results show that the plating method for metallization protection of in-fiber Bragg grating is effective.

Journal ArticleDOI
TL;DR: In this paper, a method based on multiple fractional Fourier transform (M-FrFT) for calculating holograms of 3D objects is proposed to suppress zero-order light, conjugate image, and speckle noise.
Abstract: In order to realize holographic display of three-dimensional (3D) objects and suppress zero-order light, conjugate image, and speckle noise, a novel method is proposed based on multiple fractional Fourier transform (M-FrFT) for calculating holograms of 3D objects. A series of kinoforms are generated by adding pseudorandom phase factor (PPF) to object planes in calculating each kinoform, and generating the PPF randomly again in the next kinoform calculation. The reconstructed images from kinoform sequence are superposed together in order to suppress the speckle noise of reconstructed image and improve the contrast and detail resolution of the reconstructed images. The qualities of reconstructed images from single amplitude hologram, single kinoform, and kinoform sequence calculated by M-FrFT are compared. The effects of suppressing speckle noise are analyzed by calculating the speckle index of numerical reconstructed images. The analytical results illustrate that, with the proposed method for 3D holographic display, the zero-order light, conjugate image, and speckle noise can be suppressed, and the qualities of reconstructed images can be improved significantly.

Journal ArticleDOI
TL;DR: In this paper, a combination of analog-to-digital (AD) and photon counting (PC) detection is proposed to improve the accuracy of wind and aerosol measurement in the nonlinear range.
Abstract: Usually, lidar detection systems are optimized for the measurement of the low intensity signal using the photon counting technique, but this approach results in the nonlinear signal response for the higher intensity signal. The problem is successfully solved by the combination of analog-to-digital (AD) and photoncounting (PC) detection. The optimized processing procedure of the signal combination of AD and PC is described, and the corrected result is analyzed and compared with the results by the dead-time correction method. In this way, the accuracy of wind and aerosol measurement in the nonlinear range is improved. In addition, the signal-to-noise ratios (SNRs) of the two detection methods of AD and PC are compared in the overall dynamic range of signal for the performance analysis.

Journal ArticleDOI
TL;DR: In this article, the effect of solution temperature and cooling rate on microstructure and mechanical properties of laser solid forming (LSF) Ti-6Al-4V alloy is investigated.
Abstract: The effect of solution temperature and cooling rate on microstructure and mechanical properties of laser solid forming (LSF) Ti-6Al-4V alloy is investigated. The samples are solutions treated at 900, 950, and 1000 C, followed by water quenching, air cooling, and furnace cooling, respectively. It is found that the cooling rate of solution treatment has a more important effect on the microstructure in comparison with the solution temperature. The martensite \alpha' formed during water quenching results in the higher hardness and tensile strength but lower ductility of samples. With decreasing the cooling rate and increasing the solution temperature, the width of primary \alpha laths increases, and the aspect ratio and volume fraction decrease, which make the hardness and tensile strength decrease and the ductility increase.

Journal ArticleDOI
TL;DR: Based on the scattering properties of nonspherical dust aerosol, a new method was developed for retrieving dust aerosols optical depths of dusty clouds as mentioned in this paper, which is based on transmittance measurements from surface-based instruments multi-filter rotating shadowband radiometer (MFRSR) and cloud parameters from lidar measurements.
Abstract: Based on the scattering properties of nonspherical dust aerosol, a new method is developed for retrieving dust aerosol optical depths of dusty clouds. The dusty clouds are defined as the hybrid system of dust plume and cloud. The new method is based on transmittance measurements from surface-based instruments multi-filter rotating shadowband radiometer (MFRSR) and cloud parameters from lidar measurements. It uses the difference of absorption between dust aerosols and water droplets for distinguishing and estimating the optical properties of dusts and clouds, respectively. This new retrieval method is not sensitive to the retrieval error of cloud properties and the maximum absolute deviations of dust aerosol and total optical depths for thin dusty cloud retrieval algorithm are only 0.056 and 0.1, respectively, for given possible uncertainties. The retrieval error for thick dusty cloud mainly depends on lidar-based total dusty cloud properties.

Journal ArticleDOI
TL;DR: This work tries to exploit the advantages of TOAD-based optical switch to design an integrated all-optical circuit which can perform binary addition and subtraction.
Abstract: An all-optical adder/subtractor (A/S) unit with the help of terahertz optical asymmetric demultiplexer (TOAD) is proposed. The all-optical A/S unit with a set of all-optical full-adders and optical exclusive-ORs (XORs), can be used to perform a fast central processor unit using optical hardware components. We try to exploit the advantages of TOAD-based optical switch to design an integrated all-optical circuit which can perform binary addition and subtraction. With computer simulation results confirming the described methods, conclusions are given.

Journal ArticleDOI
TL;DR: The experimental results suggest that silver nanoparticles may serve as slow-release drug carriers, which is important in antitumor drug delivery.
Abstract: Optical methods and MTT method are used to characterize the antiproliferation effect of antitumor drug 9-aminoacridine (9AA) with and without silver nanoparticles. Intracellular surface enhanced Raman scattering (SERS) spectra and fluorescent spectra of 9AA indicate the form of 9AA adsorbed on the surface of silver nanoparticles. Although both silver nanoparticles and antitumor drug can inhibit the growth of Hela cells, silver nanoparticles can slow down the antiproliferation effect on Hela cells at low concentration of antitumor drugs. Our experimental results suggest that silver nanoparticles may serve as slow-release drug carriers, which is important in antitumor drug delivery.

Journal ArticleDOI
TL;DR: The weighting spatial deconvolution algorithm is presented based on the non-periodic matrix model, which avoids solving morbidity resulting from the noise induced by measurement error and can satisfy the solving requirement of actual dwell time.
Abstract: Theoretical and experimental research on the deconvolution algorithm of dwell time in the technology of computer controlled optical surfacing (CCOS) formation is made to get an ultra-smooth surface of space optical element. Based on the Preston equation, the convolution model of CCOS is deduced. Considering the morbidity problem of deconvolution algorithm and the actual situation of CCOS technology, the weighting spatial deconvolution algorithm is presented based on the non-periodic matrix model, which avoids solving morbidity resulting from the noise induced by measurement error. The discrete convolution equation is solved using conjugate gradient iterative method and the workload of iterative calculation in spatial domain is reduced effectively. Considering the edge effect of convolution algorithm, the method adopts a marginal factor to control the edge precision and attains a good effect. The simulated processing test shows that the convergence ratio of processed surface shape error reaches 80%. This algorithm is further verified through an experiment on a numerical control bonnet polishing machine, and an ultra-smooth glass surface with the root-mean-square (RMS) error of 0.0088 \mum is achieved. The simulation and experimental results indicate that this algorithm is steady, convergent, and precise, and it can satisfy the solving requirement of actual dwell time.

Journal ArticleDOI
Meng Wang1, Lixia Yi1, Liyan Zhang1, Guonian Wang1, Lili Hu1, Junjie Zhang1 
TL;DR: In this article, thermal stability and 2-µm fluorescence of high and low Al(PO3)3 content of fluorophosphate glasses are investigated and 2.04 to 1.57 µm peak intensity ratios are calculated.
Abstract: Thermal stability and 2-µm fluorescence of high and low Al(PO3)3 content of fluorophosphate glasses are investigated. Thermal stability of high Al(PO3)3 content of fluorophosphate glass is better than low Al(PO3)3 content of fluorophosphate glass. However, 2.04-µm fluorescence intensity of high Al(PO3)3 content of fluorophosphate glass is only 48.2, lower than low Al(PO3)3 content of fluorophosphate glass. Raman spectroscopy is employed to investigate the difference in thermal stability and 2-µm fluorescence. Moreover, fluorescence peak intensity ratios of 2.04 to 1.81 µm and 2.04 to 1.57 µm are calculated, which indicate that Er-Tm-Ho doped fluorophosphate glasses are suitable materials in 2-µm applications.

Journal ArticleDOI
TL;DR: In this paper, a lensless in-line digital holographic microscopy is presented for dynamic metrology of micro-electro-mechanical systems devices, which can relax the spatial resolution requirement on charge-coupled device sensors for digital recording of holograms.
Abstract: In-line digital holography helps to relax the spatial resolution requirement on charge-coupled device sensors for digital recording of holograms and to utilize the full sensing area for image reconstruction which provides larger field of view and better imaging resolution. In this letter, a lensless in-line digital holographic microscopy is presented for dynamic metrology of micro-electro-mechanical systems devices. The methodologies of interferometry and time-averaged in-line digital holography are presented for dynamic measurements, which are also useful for simultaneous suppression of in-line waves from real image wave. The experimental results are presented for dynamic thermal characterization of microheater and vibration analysis of cantilevers.

Journal ArticleDOI
TL;DR: In this paper, the authors study the high numerical aperture focusing properties and typical applications of axially-symmetric polarized beams (ASPBs) with high polarization orders, and calculate the field distribution near focus of an aplanatic system for incident ASPBs with different polarization orders and initial azimuthal angles, and based on the simulation results, they find some unique focusing properties of the beams, such as ever on-axis energy null, strong longitudinal field, and flowerlike intensity distribution at focus.
Abstract: We study the high numerical aperture focusing properties and typical applications of axially-symmetric polarized beams (ASPBs) with high polarization orders. We calculate the field distribution near focus of an aplanatic system for incident ASPBs with different polarization orders and initial azimuthal angles, and based on the simulation results, we find some unique focusing properties of the beams, such as ever on-axis energy null, strong longitudinal field, and flowerlike intensity distribution at focus. In addition, we can manipulate the three-dimensional (3D) focused field distribution flexibly by use of diffractive optical elements (DOEs), which will give rise to some interesting applications, and we also discuss possible applications and present an example of a 3D optical chain at last.

PatentDOI
TL;DR: In this paper, a high sensitive fiber Bragg grating strain sensor with automatic temperature compensation, comprising a FBG (1), a stick (2)axially connected with the FBG, and two flanges (5) that fix the free ends of both FBG and the stick to the object to measure the strain change of the measured object, is presented.
Abstract: A high sensitive fiber Bragg grating strain sensor with automatic temperature compensation, comprising a FBG (1), a stick (2)axially connected with the FBG (1), and two flanges (5) that fix the free ends of both the FBG and the stick to the object (4) to be measured, specialized in the shift of the resonance Bragg wavelength of the FBG Δλ B = λ B (1 — P e )(d + L) / d * Ae m , where P e is the photo-elastic constant, d is the distance between two mounting points of FBG, L is the length of the stick, Δe m is the strain change of the measured object.

Journal ArticleDOI
TL;DR: In this article, a fiber Bragg grating temperature sensor with controllable sensitivity and variable measurement range was demonstrated using bimetal configuration, achieving sensitivities of -51.2, -86.4, and -520 pm/K.
Abstract: At cryogenic temperature, a fiber Bragg grating (FBG) temperature sensor with controllable sensitivity and variable measurement range is demonstrated by using bimetal configuration. In experiments, sensitivities of -51.2, -86.4, and -520 pm/K are achieved by varying the lengths of the metals. Measurement ranges of 293-290.5, 283-280.5, and 259-256.5 K are achieved by shortening the distance of the gap among the metals.

Journal ArticleDOI
TL;DR: A three-dimensional object reconstruction technique that uses pure-phase computer-generated holograms (CGHs) and a phase-only spatial light modulator (SLM) to reconstruct the 3D diffusive objects without considering the reference wave is proposed.
Abstract: A three-dimensional (3D) object reconstruction technique that uses pure-phase computer-generated holograms (CGHs) and a phase-only spatial light modulator (SLM) is proposed. The full parallax CGHs are generated by the point source method and the wave-oriented method without paraxial approximation. Different from conventional CGHs, the pure-phase information on the hologram plane is loaded on the SLM to reconstruct the 3D diffusive objects without considering the reference wave. This technique is more efficient in its utilization of the space-bandwidth product of the SLMs. Numerical simulations and experiments are performed, and the results show that our proposed method can reconstruct 3D diffusive objects successfully.

Journal ArticleDOI
TL;DR: In this paper, the color appearance of the samples with different inks on glossy substrates, five kinds of paper with different gloss levels were assessed using spectrophotometers under different illuminating/viewing geometries and visually estimated using the psychophysical method of magnitude estimation.
Abstract: We assess the color appearance of the samples with different inks on glossy substrates, five kinds of paper with different gloss levels The color samples are measured using spectrophotometers under different illuminating/viewing geometries and visually estimated using the psychophysical method of magnitude estimation The results of the two approaches are compared through the color appearance model of CIECAM02 The experimental data analysis indicates that the 0/45 and 15/0 geometries can be used to describe the two major aspects of gloss effect, the enlargement of color gamut, and the reduction of lightness The agreement for hue attribute between instrumental measurement and visual assessment is better than those for colorfulness and lightness

Journal ArticleDOI
TL;DR: Yb-Er codoped Na2O-Al2O3-P2O5-xSiO2 glasses containing 0-20 mol% SiO2 were prepared successfully as mentioned in this paper.
Abstract: Yb-Er codoped Na2O-Al2O3-P2O5-xSiO2 glasses containing 0-20 mol% SiO2 were prepared successfully. The addition of SiO2 to the phosphate glass not only lengthens the bond between P^{5+} and non-bridging oxygen but also reduces the number of P=O bond. In contrast with silicate glass in which there is only four-fold coordinated Si^{4+}, most probably there coexist [SiO4 tetrahedron and [SiO6] octahedron in our glasses. Within the range of 0-20 mol% SiO2 addition, the stimulated emission cross-section of Er^{3+} ion only decreases no more than 10%. The Judd-Ofelt intensity parameters of Er^{3+}, \Omega_{2} does not change greatly, but \Omega_{4} and \Omega_{6} decrease obviously with increasing SiO2 addition, because the bond between Er^{3+} and O^{2-} is more strongly covalently bonded.

Journal ArticleDOI
TL;DR: It is found that the proposed approach can be used to highlight the edge area of an infrared image to make anrared image more suitable for observation by human eyes.
Abstract: Infrared images are firstly analyzed using the multifractal theory so that the singularity of each pixel can be extracted from the images. The multifractal spectrum is then estimated, which can reflect overall characteristic of an infrared image. Thus the edge and texture of an infrared image can be accurately extracted based on the singularity of each pixel and the multifractal spectrum. Finally the edge pixels are classified and enhanced in accordance with the sensitivity of human visual system to the edge profile of an infrared image. The experimental results obtained by this approach are compared with those obtained by other methods. It is found that the proposed approach can be used to highlight the edge area of an infrared image to make an infrared image more suitable for observation by human eyes.

Journal ArticleDOI
TL;DR: In this article, a mobile molecular Doppler wind lidar at an eye-safe wavelength of 355 nm based on double-edge technique is being built in Hefei (China) for wind measurement from 10-to 40-km altitude.
Abstract: A mobile molecular Doppler wind lidar at an eye-safe wavelength of 355 nm based on double-edge technique is being built in Hefei (China) for wind measurement from 10-to 40-km altitude. The structure of this lidar system is described. A triple Fabry-Perot etalon is employed as a frequency discriminator whose parameters are optimized. The receiver system is designed to achieve compactness and stability by putting in a standard 19-inch socket bench. Simulation results show that within the wind speed dynamic range of +-100 m/s, the horizontal wind errors due to noise are less than 1 m/s below 20-km altitude for 100-m vertical resolution, and less than 5.5 m/s from 20 km up to 40 km for 500-m vertical resolution with 400-mJ laser energy, 30-min temporal resolution, and a 45-cm aperture telescope.

Journal ArticleDOI
TL;DR: In this article, the authors report experimental results and discuss the possibility of designing mono-mode and (nearly) polarization independent SOI ring and racetrack resonators with the free spectral range (FSR) in excess of 30 nm.
Abstract: Channel dropping waveguide filters based on single and multiple resonators in silicon-on-insulator (SOI) technology are of great interest due to their compactness and high wavelength selectivity, which is a desirable feature for photonic modulators, detectors, and other optically integrated components in telecommunication systems, in particular for wavelength division multiplexing (WDM) systems. Particular advantage of these filters is that they are capable of producing relatively large free spectral range (FSR) as well as narrow 3-dB bandwidth of the filter resonances. Herein we report experimental results and discuss the possibility of designing mono-mode and (nearly) polarization independent SOI ring and racetrack resonators with the FSR in excess of 30 nm.

Journal ArticleDOI
TL;DR: In this article, the effect of tilt error on coherent combining of fiber laser arrays is studied in detail, where the complex amplitude distribution in the far field for the Gaussian beam with tilt angle is obtained by a novel coordinate transform method.
Abstract: Limited by the precision of optical machining and assembling, the optical axes of lasers in an array cannot be strictly parallel to each other, which will result in the beam quality degradation of the combined beam. The tolerance on tilt error for coherent combining of fiber lasers is studied in detail. The complex amplitude distribution in the far field for the Gaussian beam with tilt angle is obtained by a novel coordinate transform method. Effect of tilt error on coherent combining is modelled analytically. Beam propagation factor is used to evaluate the effect of coherent combining. Numerical results show that for ring-distributed fiber laser array with central wavelength \lambda and geometry size D, if the root-mean-square (RMS) value of the tilt error is smaller than 0.72\lambda/D, the energy encircled in the diffraction-limited bucket can be ensured to be more than 50% of the value when there is no tilt error. The results are helpful to the designing and manufacturing of fiber array for coherent combining.