When periodic structures are illuminated by a monochromatic continuous light source, the exact images of themselves at
certain distances can be observed in the Fresnel diffraction region, and this is the so-called Talbot effect. The Talbot
effect has attracted more and more attention because of its wide ranging applications in fields which include optical
measurement, optical array illumination, and optical interconnections. Following the rapid development in the techniques
of ultrashort laser, therefore, it is necessary to study behaviors of the Talbot effect under ultrashort laser pulses
illumination. In this paper, the Talbot effect under illuminated by ultrashort laser pulses with complex spectral
distribution has been studied. By using a Michelson interferometer, ultrashort laser pulses with complex spectral
distribution can be generated based on the spectral interference of ultrashort laser pulses. In experiments, the Talbot
images of a grating under illuminated by ultrashort laser pulses with different complex spectral distributions are obtained.
Experimental results are in good agreement with the theoretical analysis. We believed that the behaviors of the Talbot
effect should have potential applications in optical measurement.
A method for measurement of the absolute phase by using femtosecond laser spectral interference technique has been
reported. Theoretical simulation indicates that the interference fringes of double femtosecond laser pulses are
significantly different when phase difference between the double femtosecond laser pulses is different. An experimental
apparatus based on a Michelson interferometer devices is built, in which one femtosecond laser pulse is split into two
pulses in half by a beam splitter (BS), each pulse is reflected by mirrors and the two pulses are then reunited. The double
femtosecond laser pulses interfere with each other and are focused on a spectrometer to record the spectral interference
fringes. By applying Fourier transformation to the recorded spectral interference signal, we retrieve the absolute phase
between the double femtosecond laser pulses. Theory analysis and experiment results show that this method is
reasonable and efficient, which present a new application of femtosecond laser interference. We believe that the method
reported in this paper provides a useful approach for measuring the absolute phase which should have applications in
determining thickness and measuring refractive index of optical samples.
Hexagonal array structure is not only a nature-preferred basic structure widely exists in nature, but also is an important
pattern that has been widely used in optoelectronics field. Talbot effect and fractional Talbot effect is one of the most
basic optical phenomena that has received extensive investigations both because it is a fundamental Fresnel diffraction
effect and also because of its wide applications. As one of the most application of the Talbot effect, Talbot array
illuminators have been extensively studied since Lohmann and Thomas put forward for the first time. One-dimensional
and two-dimensional orthogonal Talbot array illuminators are in-depth investigated and can be designed and
manufactured based on the theory of the fractional Talbot effect. A hexagonal array is a periodic nonorthogonal array
that cannot be represented by orthogonal array. Thus, it is difficult to analyze the diffraction field of hexagonal arrays at
fractional Talbot planes. Previous studies have shown that light distribution at Talbot distance can be considered multiple
copies of the original aperture by shifting and superimposing. In this paper, qualitative analysis of a hexagonal array is
carried out at fractional Talbot planes based on the fractional Talbot theory. Theory and experiment analysis show that
diffraction patterns at 1/6 and 1/3 Talbot distance are consist of nine equally spaced copies of the original aperture, and
each copy is shifted by 2a and a (a represent the side length of the hexagon) from another copy, respectively.
Experimental results are in good agreement with the theoretical analysis.
In this paper, it is discussed relationship between the beam quality factor and high order mode in fiber laser, and the relationship between the divergence angle and the beam quality factor. An aperture with adapted diameter in cavity could introduce low loss for the fundament mode but high loss for high order modes. In this method, it is easy to realized mode-selection. By using this method, experiment demonstrated that 23.4W output from a single fiber laser with 1.20 of M<sup>2</sup> is obtained.
The Talbot effect under illumination of double femtosecond laser pulses has been reported. Spectrums of double
femtosecond laser pulses with phase differences are quite different from that of one single femtosecond laser pulse.
Therefore, the Talbot images of the double femtosecond laser pulses with phase differences are different from that of one
single femtosecond laser pulse. Specifically, for the phase difference corresponding to π, the Talbot image shows the
largest difference from that of one single pulse. Experimental results are in good agreement with the theoretical analysis.
The behaviors of Talbot images under double femtosecond laser pulses illumination cannot be obtained under one
femtosecond laser pulse, monochromatic or polychromatic light illumination. Therefore, it is a new interesting optical
phenomenon for the Talbot effect which should have potential applications.
Based on the frustrated total internal reflection theory, a leaky large-mode-area double clad fiber is
designed. The propagation constants and leakage loss of the fundamental mode LP<sub>01</sub> and sub-low order
mode LP<sub>11</sub> is investigated by using of the matrix method. Results show that the designed fiber can
operate with single-mode.
Talbot self-imaging effect and fractional Talbot effect of a grating under illumination of monochromatic continuous wave is an important basic diffraction phenomenon, and has been extensively studied. In this paper, we studied the Talbot self-imaging effect of gratings that was illuminated by femtosecond pulse. Femtosecond laser beam is not monochromatic but includes a broad range of spectrum distribution. In this case, observed optical field in the output plane can be regarded as a coherent superposition of the contribution from each frequency component. Based on this assumption, we study diffractive characteristic of femtosecond pulse, and we theoretical analyse the intensity distributions with Fresnel diffraction formula behind a grating under illumination of a femtosecond pulse laser. Intensity distribution on the Talbot imaging planes are obtained, which show that Talbot images of femtosecond pulse are not the same as that under continuous wave illumination. At the same time, experimental results are in good agreement with the theoretical analysis. Rectangular amplitude gratings with different periods (200 μm and 80 μm respectively) were illuminated by an expanded femtosecond pulse laser, and the Talbot images are obtained by using a CCD camera at different Talbot distances. Experimental results demonstrate that the femtosecond pulse laser can cause a large distortion of Talbot images (including the contrast of imaging and the decrease of diffraction efficiency), compared with that under continuous wave illumination. In addition, increasing of the Talbot distance can also result in distortion of a Talbot image. The theoretical and experimental results are helpful for further applications of the Talbot effects under femtosecond pulse illumination.
The Talbot effect is one of the most basic optical phenomena that has received extensive investigations both because its new results provide us more understanding of the fundamental Fresnel diffraction and also because of its wide applications. We summarize our recent results on this subject. Symmetry of the Talbot effect, which was reported in Optics Communications in 1995, is now realized as the key to reveal other rules for explanation of the Talbot effect for array illumination. The regularly rearranged-neighboring-phase-differences (RRNPD) rule, a completely new set of analytic phase equations (Applied Optics, 1999), and the prime-number decomposing rule (Applied Optics, 2001) are the newly obtained results that reflect the symmetry of the Talbot effect in essence. We also reported our results on the applications of the Talbot effect. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages. Furthermore, a novel two-layered multifunctional computer-generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters, 2003). We believe that these new results should bring us more new understanding of the Talbot effect and help us to design novel optical devices that should benefit practical applications.
Array illuminator based on Talbot effect is an important optical element that has wide applications in optical interconnection, optical communication, and optical computing. This paper summarizes our recent results on this subject. Symmetry of the Talbot effect, that was reported in Optics Communication 115, 40 (1995), is now realized as the first step to revealing other rules for explanation of the Talbot effect for array illumination. The prime-number decomposing rule (Applied Optics 40, 607 (2001)) shows that the number of phase level of a Talbot array illuminator is related with the prime number. Along with the study of the characteristics of the Talbot array illuminator, the applications of the Talbot effect are also in progress. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages over the previous Fresnel encoding method. Furthermore, the hexagonal array illumination based on the Talbot effect was reported in Optics Letters 27, 228 (2002). Recently, a novel two-layered multifunctional computer generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters 28, 1513 (2003)), which can be multifunctional for potential use in secure system technology. We believe that the results reported in this paper should be useful tools for further exploration of the Talbot effect and design of novel optical devices that should benefit the practical applications.