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Temporal Kerr Lens


New Approach to Signal Manipulation and Analysis in Ultrafast Optics: Temporal Kerr Lensing

Tech Area / Field

  • INF-SIG/Sensors and Signal Processing/Information and Communications
  • INS-MEA/Measuring Instruments/Instrumentation
  • PHY-OPL/Optics and Lasers/Physics

3 Approved without Funding

Registration date

Leading Institute
Yerevan State University, Armenia, Yerevan


  • Université de Limoges / Institut de Recherche en Communications Optiques et Microondes, France, Limoges\nUniversity of Central Florida / Center for Research and Education in Optics and Lasers (CREOL), USA, FL, Orlando\nLaval University, Canada, QC, Quebec City\nInstitute for Laser Technology, Japan, Osaka\nUniversity of California / Department of Chemistry, USA, CA, Irvine\nIntralase Corporation, USA, CA, Irvine\nDaegu University, Korea, Gyeongsan

Project summary

The recent decade faced the advanced progress of laser physics, which attracts many fields of contemporary science and technology to apply the ultrafast optics methods. Femtosecond laser sources are now widespread in imaging technologies (biology, etc.), non-contact probing of materials, for localized optical alteration of linear and nonlinear optical properties of bulk device, in precision drilling, telecommunication etc. Transition to the new time scale opens new opportunities for investigation of ultrafast processes, and especially, for information transmission and processing (the situation may be compared with the period when the microscope was discovered). E.g., the potential of telecommunication is increased radically in passing to optics, since during the shortest electrical signal one can have a million optical one. Along with it, transition to the new time scale demands the elaboration of new techniques and design of new fast tools for the signal manipulation and analysis (coding and decoding).

The optical amplitude modulation-to-phase modulation and vice versa conversions (AM-PM / PM-AM), soliton-shaping processes had significant impact on development of ultrafast lasers. In 80-s, the fiber-optic pulse compression based on the frequency chirping of relatively long laser pulses in fiber due to Kerr nonlinearity (AM-PM) and subsequent compression in dispersive medium (PM-AM), demonstrated the compression ratios up to ~103, and formation of pulses with the few femtosecond duration. The revealing of Kerr-lens mode-locking regime of Ti:Sapphire laser in 1991 based on the temporal and spatial self-phase modulation (SPM) of radiation in gain medium and next temporal AM in prism compressor allowed direct generation of femtosecond pulses. Transition to the femtosecond time scale stimulated significant development in the areas such as interaction of powerful ultrashort coherent and incoherent pulses with the medium, as well as the control and measurement of their parameters. With recent advances in research of ultrafast processes and coherent control on the time scale of 10-30 fs the need for direct real time characterization and control of laser pulses became evident. Along with the extensive investigation of bright and dark, temporal, spatial, and composite soliton-shaping processes, a new direction of studies of ultrashort pulses self- and cross-phase modulation (SPM/XPM) has been originated.

Our proposing spectral compression – temporal Kerr lensing technique based on the SPM / XPM of initially chirped pulses is a new and promising approach for characterization and control of ultrashort light pulses. This process in the system combining a dispersive delay line and a single-mode fiber is the temporal analog of the diffracted beam collimation in a lens. During the dispersive delay, the pulses are stretched and phase modulated (frequency chirped), in analogy to beam diffraction. The further compensation of the accumulated dispersion phase-shift by means of SPM / XPM in a nonlinear fiber, leads to spectral narrowing: the temporal phase-shift induced by Kerr effect in the fiber, like a temporal lens, “collimates” the radiation in time, and “focuses” the spectrum. Our planning studies in the course of this project will complete the general concept of temporal Kerr-lens by its applications for ultrafast optics and lightwave communication.

The basis for the project are the time and space domain studies by the project team on the optical AM-PM / PM-AM conversion processes in the optical fiber and liquid crystals (LC), respectively. The results of these prior studies, which show the project team competence and its impact in this field, can be grouped in the following way:
· New phenomenon of ultrashort pulses spectral compression is revealed, analyzing reversibility of the fiber-optic pulse compression and spectral-temporal analogy. A compact sub-nanosecond domain dispersive stretcher is designed to elaborate spectral compressor for picosecond pulses. The spectral compression of pico- and femtosecond pulses is demonstrated experimentally.
· Special regime of spectral compression when the radiation noise is suppressed is revealed.
· Nonlinear-optic process of Fourier transformation (FT, time-to-frequency conversion) through spectral compression is proposed. Modified XPM-spectral compressor is proposed, in which the radiation frequency tuning can be implemented, as well.
· Spectral imaging of optical pulse temporal profile is demonstrated experimentally in the picosecond and femtosecond domain.
· Applications of spectral compression for the problems of ultrafast optics and lightwave communication are proposed analyzing the space-time analogy. The new and effective scheme for generation and study of dark solitons is proposed.
· Along with the direct orientational, the orientational-hydrodynamic, and orientational-convective mechanisms of optical nonlinearities in LC are revealed and observed experimentally. The stationary, quasi-stationary (transitional), oscillating and stochastic regimes of the light self-modulation are revealed in studying of temporal instabilities of laser radiation in cylindrical capillary with the radial oriented nematic LC.
· The cholesteric LC under the Bragg-resonance condition as a pulse passive compressor (dispersive delay) is proposed and demonstrated experimentally.
Femtosecond scale joint experiments were conducted in collaboration with our colleagues while visiting their laboratories: IRCOM, Limoges University, France, 1996, 1997; Chemistry Department, University of California, Irvine, US, 1996; COPL, Department of Physics, Laval University, Quebec, Canada, 1999.

The progress, applications, and unsolved problems of the contemporary ultrafast optics and laser techniques as well as the project team competence determine the subjects and objectives of this project. The objectives of our project are the development and introduction (innovation) of new and effective methods for optical signal characterization and control at pico-femtosecond time scale. The subjects of our proposing applied research are related with the optical spatial and temporal AM-PM and PM-AM conversions, soliton-shaping type phenomena: SPM / XPM, generation and interaction of spatial and temporal solitons, temporal Kerr-lensing – spectral compression, and nonlinear-optic FT. The specific goal of the project is the design of an optical oscilloscope / decoder of subpetahertz service band for applications in ultrafast optics and lightwave communication: a spectroscopic tool of femtosecond temporal resolution based on spectral imaging of pulse temporal profile.

In the proposing applied research directed to development, we plan to push the studies from the basic step of theoretical predictions and experimental demonstrations to the phase of quantitative analysis, work out practical recommendations, elaborate the novel methods and design the laboratory versions of the equipment. The methodology of the research in the course of this project is based on our time and space prior studies in the optical fiber and LC, respectively. Planning theoretical studies include the following steps:
· Construction of physical models and adequate mathematical description of the studying nonlinear-optic processes. Although the nature and mechanisms of the radiation self-interaction in the single-mode fiber and LC is principally different, the process description in both cases leads to the Nonlinear Scrodinger Equation (time and space domain, receptively), according to spatial-temporal analogy. Consideration of the physical factors variety is reduced to generalization of the Equation by the corresponding terms.
· Elaboration of effective algorithms. Here our approach is based on the split-step method using the fast Fourier transform algorithm. Consideration of the radiation regular and random modulation is reduced to choosing of relevant initial conditions to Equation.
· Numerical modeling and quantitative analysis of physical processes to work out practical recommendations and comments for experiment.
For the proposing detailed experiments, we plan to refresh the technical basis of our YSU laboratory. Particularly, we plan to obtain a commercial Argon-ion cw laser, which will serve as a pump for an home-made KLM Ti:Sapphire femtosecond laser, as well as use it directly – for the studies in LC. The planning experimental studies involve:
· The time domain, pico- and femtosecond scale experiments on the project objectives, developing our methodology processed and used in the prior studies.
· Space domain experiments on nonlinear-optic processes in LC. These studies, along with the basic and applied interest, will serve for experimental modeling of the time domain processes.
· Engineering / technical issues on the applications of elaborated methods aimed to design the industrial tools.

The expected results of the project are the following new and effective methods for the problems of optical signal manipulation and analysis in result of our applied research:
· Nonlinear optic FT – conversion of temporal information to the spectral domain for both the intensity and the phase: the temporal lens, as an spatial one, serves as a Fourier transformer. Elaboration of this method will have applications for both of the signal control and characterization problems.
· Direct, real-time, pico/femtosecond scale temporal measurements though nonlinear-optic FT. The temporal lens with a spectrometer serves as an optical oscilloscope, and the problem of pico/femtosecond scale measurements is reduced to standard spectrometry. High resolution of measurements demands the detailed studies of the temporal Kerr-lens “aberrations” caused by the high order dispersive and nonlinear physical factors.
· Spectral control – fine frequency tuning of radiation, along with spectral narrowing, for the problems of resonant spectroscopy. The temporal lens serves as a time-to-frequency converter, in which the temporal delay of the signal pulse with respect to reference one in XPM-spectral compressor causes the frequency shift.
· Formation of dark temporal pulses and generation of dark solitons in spectral compressor. The impact of group velocity dispersion, and high order dispersive and nonlinear physical factors, which are secondary for picosecond domain, become essential for spectral compression of femtosecond pulses and interesting, particularly, in view of the solitary wave formation, and their interaction. We plan to study the generation of spatial solitons in LC as well. The slow and giant nonlinearity, along with the opportunity of external control (e.g. via temperature or electric field) makes LC attractive for studying of the onset and interaction mechanisms of stable and robust solitary waves, and so for modeling of the analogous temporal processes.
· Reorientation of LC director under the action of various external signals, such as elastic / acoustic waves, static electric / magnetic fields, light, temperature gradient, low viscous fluid flow, etc.
· Nonlinear-optic suppression and filtering of the radiation noise through Kerr lensing. Spatial implementation of this method in LC can be effective for correction of beam structure. Temporal analog in the fiber – is of interest for the problems of lightwave communication.

The key expected product of the project is a laboratory version of the femtosecond optical oscilloscope / decoder based on spectral imaging of pulse temporal profile. In contrast to most powerful contemporary techniques of FROG / TROG- and SPIDER, requiring numerical data processing (iterative or noniterative), our method provides the pulse direct, real-time measurement in a standard spectrometer, exceeding, so, the bandwidth of the existing electronic oscilloscopes and streak-cameras by several orders of magnitude. The elaborated new methods can be applied as well to innovate and introduce the new and effective ultrafast fiber-optic tools for all optical networks, such as the decoder, demultiplexer, analog-to-digital converter, router, nonlinear-optic noise filter, etc. The results of space domain studies can lead to design of the acoustic field visualizer, LC seismometer; IR LC-detector, thermo-sensor, LC detector of airflow.

The project will regulate, expand, and develop the scientific contacts between the project collaborators and YSU party making the existing collaboration significantly effective and productive. We plan to conduct a series of joint experiments and seminars through mutual visits between the collaborating parties. We envisage to attract the M. Sc. / Ph. D. students, engineers, and scientists previously engaged in the defence topics, to integrate them in the international scientific community, and thus to promote the open society building and progress, and so, meet the ISTC goals.


The International Science and Technology Center (ISTC) is an intergovernmental organization connecting scientists from Kazakhstan, Armenia, Tajikistan, Kyrgyzstan, and Georgia with their peers and research organizations in the EU, Japan, Republic of Korea, Norway and the United States.


ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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