Spectral Talbot phenomena of frequency combs induced by cross-phase modulation in optical fibers

Cross-phase modulation (XPM) of a frequency comb (finite-duration optical pulse sequence) by an intense, long Gaussian pump pulse is theoretically investigated, and new effects, namely, frequency-domain self-imaging phenomena (integer and fractional Talbot effects), are reported. The conditions favorable for observing spectral self-imaging phenomena by XPM are derived and numerically confirmed. The effects of nonidealities in a practical experiment (e.g., group-delay walk-off and dispersion) are also evaluated. One can use spectral self-imaging to tune the free spectral range of a frequency comb (without affecting the shape and bandwidth of the individual passbands) simply by adjusting the pump power in a fiber XPM scheme.     

Frequency shifting of microwave signals by use of a general temporal self-imaging (Talbot) effect in optical fibers

A simple and practical microwave frequency-shifting technique based on a general temporal self-imaging (GTSI) effect in optical fiber is proposed, formulated, and experimentally demonstrated. The proposed technique can be applied to an arbitrary periodic microwave signal (e.g., a microwave tone) and provides unparalleled design flexibility to increase the frequency of the input microwave signal up to the desired value (limited only by the photodetector's bandwidth). For instance, we demonstrate frequency upshifting of microwave tones from approximately 10 to approximately 50 GHz and from approximately 40 to approximately 354 GHz. These results also represent what is to the authors' knowledge the first experimental observation of GTSI phenomena.     

Optical substrate thickness measurement system using hybrid fiber-freespace optics and selective wavelength interferometry

Proposed and demonstrated is a simple few components non-contact thickness measurement system for optical quality semi-transparent samples such as Silicon (Si) and 6H Silicon Carbide (SiC) optical chips used for designing sensors. The instrument exploits a hybrid fiber-freespace optical design that enables self-calibrating measurements via the use of confocal imaging via single mode fiber-optics and a self-imaging type optical fiber collimating lens. Data acquisition for fault-tolerant measurements is accomplished via a sufficiently broadband optical source and a tunable laser and relevant wavelength discriminating optics. Accurate sample thickness processing is achieved using the known material dispersion data for the sample and the few (e.g., 5) accurately measured optical power null wavelengths produced via the sample etalon effect. Thicknesses of 281.1 μm and 296 μm are measured for given SiC and Si optical chips, respectively.     

Self-Imaging Effect Based on Airy Beams with Quadratic Phase Modulation

The self-imaging effect based on Airy beams with quadratic phase modulation (QPM) in 1 + 1 and 2 + 1 dimensions is studied both numerically and analytically. It is demonstrated that, in spite of spatial spectral shape being kept invariant, both the intensity pattern and the accelerating trajectory of this self-imaging effect depend considerably on the QPM. When the QPM parameter is negative, the self-imaging accelerating wave exhibits deceleration and then acceleration, and the self-imaging scope can be expanded. In the opposite case, the self-imaging extent would be narrowed and the self-imaging accelerating wave will only accelerate during propagation. Numerical simulations agree with the theoretical results very well. This study shows the possibility of controlling the self-imaging effect based on 1D and circular Airy beams, by purposely choosing appropriate QPM parameters.     

Investigation of self-imaging based on the field distribution in multimode photonic crystal waveguides

We have investigated the self-imaging phenomena based on the field distribution in two-dimensional multimode photonic crystal waveguides (PCWs) by the finite-difference time-domain (FDTD) method. The new self-imaging conditions are given for the mirrored images and the direct images. The self-imaging distributions in multimode PCWs can be explained by the new self-imaging conditions and the superposition of “sub-images”. The results of numerical simulation show a good agreement with the theoretical predictions.     

Optimal design of multimode interference couplers using an improved self-imaging theory

Self-imaging theory is widely accepted as a good method in designing 1 × N multimode interference (MMI) couplers, but it is also true that self-imaging theory is not suitable for low-contrast structures. An improved self-imaging theory is proposed in this paper for the optimal design of low-contrast 1 × N MMI couplers. The average effective width of MMI waveguide and the average effective propagation constant of MMI waveguide are used as the basis to modify the conventional self-imaging theory. A direct calculation of the average effective width of low-contrast MMIs is presented. We use this approach in the optimal design of a 1 × 4 silica MMI coupler, and the results show that the improved self-imaging theory is more accurate than conventional self-imaging theory for low-contrast structures, the results also show that if the material parameters and the width of an MMI waveguide are fixed, the average effective width of the MMI waveguide will increase with the decrease of the height of the core layer.     

二维限制多模干涉器自镜像效应分析

采用导模传输分析法对二维限制多模干涉器的自镜像效应进行分析，并用三维作矢量光束传输法对其分析结果作了进一步的验证。分析表明，一维限制多模干涉器的自镜像效应可以完全拓展到二维上。     

Electromagnetically induced self-imaging

We study the self-imaging and image-transforming properties of a probe field in a cold atomic medium with electromagnetically induced transparency (EIT). Due to the similarities between the gradient-index medium and the inhomogeneous index distribution of an EIT medium under the conditions of a negative probe detuning and a Gaussian control field, we find based on analytical investigations that there exists a kind of electromagnetically induced self-imaging phenomenon in cold atomic media. Numerical simulations clearly show that electromagnetically induced self-imaging is observable and controllable.     

Talbot self-image effect in digital holography and its application to spectrometry

For the first time to the authors' knowledge, the Talbot effect has been observed and investigated in digital holography. By numerical reconstruction of holograms, the Talbot self-imaging phenomenon is observed by reconstruction of the amplitude of the image at different distances and (or) wavelengths. A simple spectrometer based on Talbot self-imaging in digital holography is proposed and demonstrated.     

Analysis of optical rib self-imaging multimode interference (MMI) waveguide devices using the discrete spectral index method

We have developed a semianalytical approach to study the propagation characteristics of multimode interference (MMI) waveguide structures. The effect of transverse crosssection geometry on self-imaging length and optical power throughput are investigated. We present results confirming that the nonquadratic modal dispersion encountered in stripe-loaded waveguides impairs self-imaging performance. Results indicate that the image degradation is more predominant for asymmetrically fed MMI waveguides.     

Nonlinear Talbot self-healing in periodically poled LiNbO_3 crystal [Invited]

The nonlinear Talbot effect is a near-field nonlinear diffraction phenomenon in which the self-imaging of periodic objects is formed by the second harmonics of the incident laser beam. We demonstrate the first, to the best of our knowledge, example of nonlinear Talbot self-healing, i.e., the capability of creating defect-free images from faulty nonlinear optical structures. In particular, we employ the tightly focused femtosecond infrared optical pulses to fabricate Li Nb O_3 nonlinear photonic crystals and show that the defects in the form of the missing points of two-dimensional square and hexagonal periodic structures are restored in the second harmonic images at the first nonlinear Talbot plane. The observed nonlinear Talbot self-healing opens up new possibilities for defect-tolerant optical lithography and printing.     

Observation of the Talbot effect for ultrasonic waves

The diffraction of ultrasonic radiation on an amplitude diffraction grating in the near-field area (Fresnel diffraction) has been studied. The effect of self-imaging of the grating (Talbot effect) has been detected for ultrasonic radiation at distances from the grating in the range from z = 0 to z = 2L _T, where L _T is the Talbot length. The fractional Talbot effect, i.e., the ultrasonic image of the grating with the period d/2, has been observed.     

Generation of achromatic and propagation-invariant spot arrays by use of continuously self-imaging gratings

A particular class of Montgomery's self-imaging objects that we call continuously self-imaging gratings (CSIG's) is introduced. When they are illuminated by a plane wave, these objects produce a field whose intensity profile is a propagation- and wavelength-invariant biperiodic array of bright spots. The mathematical construction of these objects and their intrinsic properties are described. On a practical level, CSIG's are compact and achromatic nondiffracting array generators. We show that a good CSIG approximation can be realized by a two-level phase grating that is experimentally tested.     

自成像魏格纳函数分析

在空域-频域空间,基于魏格纳变换和魏格纳分布函数,分析讨论了一维物体的自成像及其形成过程.从成像过程中各衍射频谱分量的光程差,给出了Talbot效应和Montgomery效应的统一解释.对于周期物的Talbot效应,得到了用杨氏双缝干涉解释自成像现象的理论依据.周期物的自成像是物平面上间距为两倍周期、光程差为波长的整数平方倍的各衍射频谱分量同相相干迭加的结果.Montgomery效应是物平面上间距为抛物线关系、光程差为波长整数倍的各衍射频谱分量同相相干迭加的结果.     

Self-collimation and self-imaging effects in modulated waveguide arrays

Self-collimation and self-imaging are comparatively investigated for discretized light in engineered modulated arrays of optical waveguides. It is shown that self-imaging is a rather extraordinary effect related to a fortuitous band collapse and it is thus rather distinct from self-collimation.     

Detailed investigation of self-imaging in multimode photonic crystal waveguides for applications in power and polarization beam splitters

Properties of the self-imaging effect based on multimode interference (MMI) in multimode photonic crystal waveguides (PCWs) are investigated and analyzed in detail. By combining photonic band gap (PBG) and total internal reflection (TIR) effects in PCWs, self-imaging phenomena are achieved for both TE and TM polarizations. To observe the images reproduced by this self-imaging phenomenon, finite-difference time-domain (FDTD) simulations are performed on a multi-mode PCW. From these numerical simulations the reproduced images are identified and their positions along the propagation axis are described. We also, present the design and simulation of novel polarization-insensitive power splitter and polarization splitter. The simulation results show that the optimized devices have excellent transmission efficiencies as well as wide operating frequency bandwidths and small structure size. So, the proposed devices are promising and may play an important role in high-density photonic integrated circuits in the future.     

Spectral self-imaging effect by time-domain multilevel phase modulation of a periodic pulse train

We propose and analyze a novel (to our knowledge) approach to implement the spectral self-imaging effect of optical frequency combs. The technique is based on time-domain multilevel phase-only modulation of a periodic optical pulse train. The method admits both infinite- and finite-duration periodic pulse sequences. We show that the fractional spectral self-imaging effect allows one to reduce by an integer factor the comb frequency spacing. Numerical simulation results support our theoretical analysis.     

Talbot imaging with increased spatial frequency: a technique for replicating truncated self-imaging objects

The Talbot effect in the presence of a convergent beam of coherent light yields a demagnified image of a self-imaging object. In fact, the object does not even have to fulfill the self-imaging condition; the object with truncated self-imaging feature is sufficient to yield an image that is sufficiently accurate for many practical purposes. We have taken this approach to fabricating circular gratings with a reduced period compared to the period of the mask. Using a simple experimental setup and a concentric circular grating mask, we have created images whose periods are either one-half or one-third of the mask's period. Demagnified Talbot imaging of fully or truncated self-imaging objects provides an attractive approach to photolithographic fabrication of structures whose periods are somewhat greater than the wavelength of the light source.     

高斯光束照射下的近似Talbot自成像效应及其两种新应用

本文讨论了高斯光束照明下的Talbot近似自成像的性质.提出了利用Talbot自成像测量高斯光束发散角的简便方法;也提出在满足一定条件下,可得到自成像的超高倍放大率.     

Ray aberrations of two-dimensional oblique lattices on the self-image plane

We extend the geometrical theory of aberration for a self-imaging system to the case of two-dimensional oblique lattices. In our approach, the fundamental translation vectors of the lattice are not restricted in both length and orientation. Evaluating the disturbance of light through the oblique lattice under coherent illumination, we find the conditions of constraint which limit the self-imaging of the oblique lattice. Various types of oblique lattices are shown to obey the self-imaging conditions. We derive the equations to trace the optical paths of self-imaging rays and then analyze the ray aberrations which arise from the difference between the optical paths of a self-imaging ray and of the corresponding actual ray. The ray aberrations are shown to disappear when the periods of the lattice are large compared with the wavelength of light. We find that the ray aberrations carried by self-imaged oblique lattices are totally undercorrected and the aberrated image patches are displaced along the direction tangent vector of a chief ray.