
Name: 
Phone:
(+359 2) 979 XXXX 
Email:
....@ie.bas.bg 
HEAD: 
Assoc. Prof. L. Kovachev, Dr.Sc. 
5915 

RESEARCH SCIENTISTS: 
Assoc. Prof. L. Ivanov, Ph.D. 
5915 

K. Kovachev, Ph.D. 
5915 

A. Dakova 
5915 

RESEARCH ACTIITIES
1. Diffraction of phasemodulated broadband femtosecond pulses
In recent years the linear regime of propagation of optical pulses with broadband spectrum in air and transparent media attracts a considerable attention. The attosecond pulses in UV region as well as femtosecond pulses with time duration 515 fs in optical and IR region admit from one to several optical cycles under their envelopes. For such pulses, as it was pointed in [1], the diffraction is not paraxial and on few diffraction lengths their shape takes parabolic form. In the theory developed in [2, 3] it is shown that the nonparaxiality depends on the spectral width Δκ_{z}=Δω/ν_{gr} of the pulse. Thus, one additional possibility appears: Is it possible to use phasemodulated broadband femtosecond pulses with many cycles under their envelope to obtain Fraunhofer type diffraction? In this paper we will numerically investigate Fraunhofer type diffraction of phasemodulated 25 fs laser pulses which admit at least 10 cycles at level e^{1} of the maximum. This study gives us knowledge about the limits and applicability of paraxiality in the frames of femtosecond optics. The linear scalar nonparaxial amplitude equation, governing the evolution of laser pulses in isotropic dispersive media, is written in Local type coordinates [4]:

(1) 
where A(x,y,τ,z) is the slowly varying amplitude function of the pulse envelope, ν is the group velocity, β=κ_{0}ν^{2}_{gr}κ" is a parameter characterizing the second order of linear dispersion of the medium, z = z and τ=tz/ν.The last two terms in Eq.(1) are called nonparaxial terms, because the rest part gives paraxial spatiotemporal optics. This equation can be solved by using the Fourier method.
We studied the evolution of phasemodulated 25 fs laser pulses with a Gaussian spatiotemporal profile in air. The initial condition for numerical investigation of equation (1) is:

(10) 
where r_{0} is the transverse size (the spot of the pulse), τ_{0} is the temporal size and b=1+ia is a complex number, where a is the linear frequency modulation (chirp of the pulse). Our numerical results have shown that:
 The nonparaxial equation in Local coordinate system (1) gives the correct profile deformation of optical pulses but inverted with respect to the axis Oz;
 The real spatial Fraunhofer diffraction of femtosecond and attosecond laser pulses is obtained when the nonparaxial equation is solved in Galilean or Laboratory coordinate system.
In our investigations we have shown that the Fraunhofer type diffraction is not a characteristic only to attosecond or femtosecond pulses with one or few optical cycles under the envelope. There are different methods to obtain broadband laser pulses with many cycles under the envelope. For examples: nonlinear selfphase modulation, optical grating etc.
We demonstrated that even in the case of phasemodulated femtosecond pulses with many cycles under the envelope Fraunhofer type diffraction can be observed in the experiments.
2. Optimization of the regime of selfcompression for fs pulses in silica and air
One of the main task of modern laser physics is to obtain ultra short laser pulses. There are different optical schemes for selfcompression based on pair diffraction grating or other optical elements during propagation of pulses in linear regime. The shortening of pulse can be obtained also by using nonlinear mechanisms such as phase selfmodulation (PSM), when a pulse reaches critical power for nonlinear regime in dispersion mediums. The most efficient schemes for compression require carful analyse for collection of possibly optical elements, linear and nonlinear effects to obtain maximal compression. We examine by numerical simulations two different mechanisms for selfcompression of femtosecond pulses in fused silica and air. In the first case we consider selfcompression of a laser pulse during its nonlinear propagation in the anomalous dispersion region of a glass. The numerical experiments are performed for pulses with time duration 100 fs at wavelength 800 nm. In the second case we considered compression of initial chirped 25 fs pulse. Our numerical results show, that after only one pass trough optical diffraction grating the chirped pulse selfcompress in nonlinear regime and obtain X wave deformation. Investigated of propagation of phasemodulated femtosecond pulses with the use of the lens as a phase corrector provides substantially different dynamic depending on the dispersion and coefficient of nonlinearity. It appears that during the evolution of the pulse in a medium with normal linear dispersion, initially shows a strong focusing, and is then diffracted at several diffraction lengths. In case of anomalous dispersion the pulse is compressed significantly.
During the evolution of a pulse in a medium with a positive linear dispersion, we initially observe a self  focusing. After the focus of the lens, the paraxiality of the diffraction is preserved and the pulse diffracted in several diffraction lengths without wave front distortion. The propagation in a medium with negative dispersion the initial phase modulation increases the compression of the pulse. Numerical modelling of the optical pulses in a nonlinear regime of propagation with initial phase modulation caused by different optical elements has important application in the modern optical engineering.
PUBLICATIONS
During year 2015, 2014, 2013, 2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003, 2002, 2001.
2015
Daniela A Georgieva and Lubomir M Kovachev,
Energy transfer between two filaments and degenerate fourphoton parametric processes
Laser Physics, 25, 035402 (7pp) (2015). doi:10.1088/1054660X/25/3/035402.IF1.025 (2013).
L M Kovachev, D A Georgieva and A. M. Dakova,
Influence of the fourphoton parametric processes and crossphase modulation on the relative motion of optical filaments
Laser Phys. 25 (2015) 105402 (7pp), doi:10.1088/1054660X/25/10/105402
A. M. Dakova, L. M. Kovachev, K. L. Kovachev, D. Y. Dakova,
Fraunhofer type diffraction of phasemodulated broadband femtosecond pulses
Journal of Physics: Conference Series 594. 012023 (2015), doi: 10.1088/17426596/594/1/012023.
V. Slavchev, L. Kovachev, L.M. Ivanov,
Optimization of the nonlinear regime of selfcompression at femtosecond laser pulses in silica and air
Journal of Physics: Conference Series 594, 012038 (2015), doi: 10.1088/17426596/594/1/012038.
A. Dakova, D. Dakova, L.M. Kovachev
Comparison of soliton solutions of the nonlinear Schrodinger equation and the nonlinear amplitude equation
Proc. of SPIE, V 9447, doi.org/101117/12.2177906
D. A Georgieva, Lubomir M. Kovachev,
Merging and energy exchange between optical filaments
AIP Conference proceedings, V 1684, pp 080005, http://dx.doi.org/10.1063/1.4934316
CONFERENCES:
 NEEDS2015: Nonlinear Evolution Equations and Dynamical Systems, Masrgherita di Pula, Sardinia,
Italy, 24.06.2015  01.07.2015

 Kovachev L.M.
Localized Solutions of the Linear and Nonlinear Wave Equations
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2014
L. M. Kovachev, 2014
The light filament as vector solitary wave
AIP Conference Proceedings 1629, 167; doi: 10.1063/1.4902271.
D. A. Georgieva and L. M. Kovachev,
Fourphoton parametric mixing and interaction between filaments
AIP Conference Proceedings 1629, 146 (2014); doi: 10.1063/1.4902268
D. Georgieva and L. Koachev,
Energy transfer between two filaments and degenerate four  photon parametric processes
Laser Physics, accepted
V. Slavchev, L. Kovachev, L. M. Ivanov,
Optimization of the nonlinear regime of selfcompression of femtosecond pulses in silica and air
submitted in Open Access Journal of Physics: Conference Series (JPCS), accepted
A. Dakova, L. M. Kovachev, K. L. Kovachev, D. Dakova,
λ(3) diffraction of phase modulated broad band laser pulses
submitted in Open Access Journal of Physics: Conference Series (JPCS), accepted.
A. Dakova, D. Dakova, L. Kovachev,
Comparison of soliton solutions of the nonlinear Schrodinger equation and the nonlinear amplitude equation
18 SPIE, accepted.
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2013
Kovachev L M, Georgieva D A and Serkin V N 2013
Parametric solitons in isotropic media
AIP Conf. Proc. 1561 289
Dakova A M and Dakova D I 2013
Nonlinear regime of propagation of femtosecond optical pulses in a singlemode fiber
Proc. SPIE 8770 87701J
Kovachev L M and Georgieva D A 2013
The long range filament stability: balance between nonparaxial diffraction and thirdorder nonlinearity
Proc. SPIE 8770 87701G
Ivanov L M and Kovachev L M 2013
Improved four photon mixing methods for optical fibre's parameters control
Proc. 5^{th} Int. Sci. Conf. FMNS 2013 3 pp 5764
Kovachev L M, Ivanov L M and Kovachev K L 2013
Broadband laser pulses. Linear and nonlinear regime
Proc. Second Nat. Congress Phys. Sci. (Sept 2011 Sofia Bulgaria) pp 224 225
Dakova A and Dakova D 2013
Propagation of broadband pulses in nonlinear dispersive media
Proc. Second Nat. Congress Phys. Sci. (Sept 2011 Sofia Bulgaria) p 226
Slavchev and Kovachev L 2013
Nonlinear regime of propagation of optical pulses phasemodulated by a doubleconvex lens
Proc. Second Nat. Congress Phys. Sci. (Sept 2011 Sofia Bulgaria) p 230
Kovachev L 2013
Shock wave in EulerHeisenbergKockel nonlinear vacuum
Proc. Second Nat. Congress Phys. Sci. (Sept 2011 Sofia Bulgaria) pp 4534
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2012
Kovachev L M, Georgieva D A and Kovachev K L 2012
Electromagnetic shock wave in nonlinear vacuum: exact solution
Opt. Lett. 37 40479 DOI: 10.1364/ OL.37. 004047
Kovachev L M and Georgieva D A 2012
A class of localized solutions of the linear and nonlinear wave equation
J. Geometry and Symmetry in Physics 27 6782 ISSN: 13125192
Kovachev L M and Georgieva D A 2012
Analytical solution of the linear wave equation with finite energy
AIP Conf. Proc. 1487 264 DOI: 10.1063/1.4758967
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2011
Kovachev L M and Kovachev K 2011
Linear and nonlinear femtosecond optics in isotropic media
Laser System for Applications (InTech. Rijeka) 3/11 20927 ISBN 9789533074290
Belyaeva T L, Serkin V V, Aquero M, HernandezTenorio C and Kovachev L M 2011
Hiden features of the soliton adaptation law to external potentials: optical and matterwave 3D nonautonomous soliton bullets
Laser Phys. 21/1 25863 DOI 10.1134/ S1054660X11010038 ISSN 1054660X
Kovachev L M and Kovachev K L 2011
Ionizationfree filamentation in gases
Proc. SPIE 7751 777512819 DOI 10.1117/12.87921
Belyaeva T L, HernandezTenorio C, PerezTorres R, Kovachev L M and Serkin V N
Enigmas of optical and matterwave nonlinear soliton tunneling effects
Proc. SPIE 7747 77471N ISSN 0277786X ISBN 9780819482372 DOI 10.1117/12.881617
PerezTorres R, Belyaeva T L, HernandezTenorio C, Kovachev L M and Serkin V N 2011
Enhanced soliton spectral tunneling effect of selfcompressing nonautonomous colored femtosecond solitons
Proc. SPIE 7747 77471L ISSN 0277786X ISBN 9780819482372 DOI 10.1117/12.881660
HernandezTenorio C, Belyaeva T L, PerezTorres R, Kovachev L M and Serkin V N
Hidden features of soliton adaptation law to external potentials: Optical and matterwave soliton bullets in nonautonomous and nonlinear systems
Proc. SPIE 7747 77471G ISSN 0277786X ISBN 978 0819482372 DOI 10.1117/12.881663
Belyaeva T L, Hasegawa A, Kovachev L M and Serkin V N 2011
3D solitonlike bullets in nonlinear optics and BoseEinstein condensates
Proc. SPIE 7747 ISSN 0277786X ISBN 9780819482372 DOI 10.1117/12.88901
Kancheva P, Dakova A, Dakova D, Slavchev V and Pavlov L 2011
Three dimensional solutions of a vector type NLS equation with spatial dependence of the nonlinear refractive index
Proc. SPIE 7747 77476L ISSN 0277786X ISBN 9780819482372
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2010
Kovachev L M and Kovachev K L
Ionizationfree filamentation in gases
18^{th} Int. Symp. Gas and Flow Chem. Lasers & High Power Lasers Proc. SPIE 7751
Kovachev K L, Ivanov L M, Serkin V N and Kovachev L M
Propagation of laser pulses in media with nonstationary optical and magnetic response
J. Appl. Electr. 12/2 3036
Kovachev L
A class of localized solutions of the linear and nonlinear amplitude equations governing laser pulse propagation
Proc. 3^{rd} Int. Symp. Filamentation (31 May  05 June, Crete, Greece) pp 115116
Ivanov L M, Serkin V N, Kovachev L M and Ivanov M L
Determination of fiber's parameters by nonlinear optical method
J. Appl. Electr. 12/2 3643
Kovachev L M and Kovachev K L
TH or THz generation in the femtosecond optics?
Proc. 3^{rd} Int. Symp. Filamentation (31 May  05 June, Crete, Greece) pp 126127
Ivanov L M, Kovachev L M, Kovachev K L and Ivanov M L
Optical quartz fibers as nonlinear media
Int. workshop on innovative approaches to physical investigations INRNE Blagoevgrad Bulgaria Paradigma Publishing Sofia ISBN 9899543261239
Kovachev K L, Ivanov L M, Kovachev L M and Tunchev I
Localized solutions of the linear and nonlinear amplitude equations governing laser pulse propagation regime
Int. workshop on innovative approaches to physical investigations INRNE Blagoevgrad Bulgaria Paradigma Publishing Sofia ISBN 9899543261239
CONFERENCES
Kovachev L M,
3^{rd} Int. Symp. Filamentation, 31 May  05 June, Crete, Greece.
Kovachev L M,
18^{th} Int. Symp. Gas and Flow Chemical Lasers & High Power Lasers, Sofia, Bulgaria, 30 Aug.  3 Sept. 2010.
Kovachev L M,
Conf. Appl. of Mathematics in Technical and Natural Sci., Sozopol, Bulgaria, June 2010, keynote lecture.
Kovachev L M,
16^{th} ISQE Laser Physics and Applications, Nesebar, Bulgaria, 2010.
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2009
Kovachev L M
New mechanism for THz oscillation of the nonlinear refractive index in air: particlelike solutions
J. Modern Optics 56/16 17971803
Serkin V N, Belyaeva T L, Khawaja U Al and Kovachev L M
Soliton bullets of compressing Bose Einstein condensates
J. Nanosci. Moletron. 6/2 123346
Serkin V N, Belyaeva T L, Viligran E V, Morales L C, Kovachev L M, Pena R M and Gorro G H
Derivation de la ecuacion no lineal de Schrodinger para el modelo de DNA
J. Nanosci. Moletron. 6/2 126372
Serkin V N, Belyaeva T L, Hernandez C T, Kovachev L M, Pena R M, Morales L C and Gorro G H
Posibilidad de generation de balas solitonicasen un laser atomico: Illuctration de analogia entre laser optica y laser atomico
J. Nanosci. Moletron 6/2 128190
Kovachev L M
Groupphase velocity difference and THz oscillation of the nonlinear refractive index: particlelike solutions
1^{st} Int. Conf. Appl. Mathematics in Techn. Natural Sci. (Sozopol, Bulgaria) AIP Proc. 1186 6981 ISBN: 9780735407527
Kovachev L M, Kovachev K L and Tunchev I
Femtosecond pulses in air: linear and nonlinear regime
Int. Conf. Ultrafast and Nonlinear Optics (Sept. 2009 Bourgas Bulgaria) Proc. SPIE 7501 75010E DOI: 10.1117/12.849380
Ivanov L M
Nonlinear optical method for measurement of fibre parameters
Proc. Third Int. Sci. Conf. FMNS 2009 211620
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2008
Kovachev L M,
Beyond the spatiotemporal model in femtosecond optics,
J Modern Optics 2008;55/17:297581.
Kovachev L M, Kovachev K L,
Diffraction of femtosecond pulses: nonparaxial regime,
J Opt Soc Am A 2008;25/9:223243.
Kovachev L M; Kovachev K L,
Diffraction of femtosecond pulses. Nonparaxial regime: erratum,
J Opt Soc Am A 2008;25/12:30978.
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2007
Kovachev L M, Tunchev I,
Dynamics of femtosecond laser pulses in air and in vacuum,
Proc SPIE 2007;6604:66041G.
Kovachev L M,
Collapse arrest and waveguiding of femtosecond pulses,
Optics Express 2007;15/16:1031823.
Kovachev L M,
Nonparaxial evolution of femtosecond optical pulses,
Proc SPIE 2007;6582.
Serkin V N, Kovachev L M, Belyaeva T L,
Exactly inferable models for optical solitons amplifications: analytical and computational studies,
Proc SPIE 2007;6604:6604IV.
Serkin V N, Hasegawa A, Kovachev L M, Pena R, Morales L,
La posibilidad degeneracion de las balas solitonicas en un laser atomico,
Proc V Foro Int de Investigacion Nanotron'2007, 2930 (2007, Puebla, Mexico).
Vargas V, Serkin V N, Kovachev L M, Pena R, Morales L,
Derivacion de la ecuacion nolineal de Schrodinger para el modelo de ADN,
Proc V Foro Int de Investigacion Nanotron'2007, (2007, Puebla, Mexico).
Serkin V N, Hasegawa A, Kovachev L M, Belyaeva T L,
Optical soliton amplification in fiber optics systems with varying dispersion,
Proc IEEE Int Conf Cerma'2007, (2007, Cuernavaca, Mexico).
Kovachev L M, Ivanov L, Tunchev I,
Ultrashort optical pulses in media with nonstationary optical and magnetic response,
Proc SPIE 2007;6604:66041H.
Pavlov L I, Kovachev L M, Dakova D Y, Naboko S V, Stoimenova D V, Pavlov R L, Pavlova S I; Tabanliyski I Y, Penchev S P,
Effect of parametric processes on the stimulated Raman scattering in fibers,
Proc SPIE 2007;6604:66041R.
Arabadjiev T, Uzunov I M,
Modulation instability of stochastic optical waves in nonlinear media with anomalous dispersion,
Proc SPIE 2007;6604:66041L.
Kovachev K, Ivanov L, Serkin V, Tunchev I, Kovachev L,
Nonlinear dynamics of femtosecond pulses with one or few optical cycles in media with non stationary optical and magnetic response,
Proc Int Conf FMNS'2007 (2007, Blagoevgrad, Bulgaria) pp8792.
Kovachev L, Ivanov L, Serkin V, Tunchev I, Kovachev K,
Slowlyvarying equation of amplitudes in media with non stationary optical and magnetic response. Negative group velocity,
Proc Int Conf FMNS'2007 (2007, Blagoevgrad, Bulgaria) pp938.
Arabadzhiev TN, Uzunov IM,
Amplification of solitary optical waves in fibers with positive group velocity dispersion,
Central European J Phys 2007;5/1:6268.
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2006
Kovachev LM, Pavlov LI, Ivanov LM, Dakova DY,
Optical filaments and optical bullets in dispersive nonlinear media,
J Russian Laser Research, 2006;27:185203.
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2005
Kovachev LM, Pavlov LI, Ivanov LM, Dakova DY,
Relative linear stability of light bullets,
Proc 4^{th} Int Symp Laser Technol and Lasers, October 2005, Plovdiv, Bulgaria, pp 184193.
Kovachev LM, Ivanov LM,
Vortex solitons in dispersive nonlinear Kerr type media,
Proc SPIE, Nonlinear Optics Applications, 2005;5949/07:112.
Pulov V, Uzunov IM, Chakarov E,
Two light modes propagation in nonlinear media with negative crossphase modulation via Lie group analysis,
Proc SPIE, Laser Physics and Applications, 2005;5830:100104.
Pulov V, Uzunov IM, Chakarov E,
Symmetry properties of nonlinear pulse propagation in nonlinear birefringent optical fibers with Stimulated Raman scattering,
Proc SPIE, Laser Physics and Applications;2005;5830:105109.
Kovachev LM, Ivanov LM,
Vortex solitons,
Los Allamos Email Lab., 2005; 1: Paper arXin:nlin.PS/0504020.
Kovachev LM, Ivanov LM,
Propagation of ultra short optical pulses in dispersive Kerr type media with nostationary response,
Proc First Int Conf FMNS, Blagoevgrad, Bulgaria, 2005, pp 198205.
Uzunov IM, Pulov V,
Vector solitary wave solutions to coupled nonlinerar Schrodinger equations with Raman terms,
Proc Second Int Congress Mechanical and Electrical Engineering and Marine Industry (MEEMI2005), 2005;3:187190.
Pulov V, Uzunov IM, Chakarov E, Lyutskanov V,
Lie group symmetry reduction of two coupled nonlinear Schrodinger equations,
Proc Second Int Congress Mechanical and Electrical Engineering and Marine Industry (MEEMI2005), 2005;3:191195.
Uzunov IM,
Optical fiber communication systems,
Proc ÕÕÕIII National Conf Physics and Information and Communication Technologies, Varna, Bulgaria, 2005, pp 1825 (in Bulgarian).
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2004
Kovachev L,
Optical vortices in dispersive nonlinear Kerr type media,
Int J Mathematics and Mathematical Sciences 2004;18:949967.
Kovachev L,
Optical leptons,
Int J Mathematics and Mathematical Sciences 2004;27:14031422.
Kovachev L,
Vortex solutions of the nonlinear optical MaxwellDirac equations,
Physica DNonlinear Phenomena 2004;190:7892.
Kovachev L, Kaymakanova N, Dakova D, Pavlov L, Rousev R, Donev S, Pavlov R,
Threedimensional solutions in media with spatial dependence of the nonlinear refractive index,
Journal of Physical Studies 2004;8:137140.
Kovachev L, Ivanov L, Simeonov D, Arabadzhiev T,
Stability of optical vortices with integer spin,
Proc Int Conf Nonlinear waveguide phenomena, Toronto, Canada 2004;TuC27:13.
Kovachev L,
Nonlinear amplitude MaxwellDirac equations. Optical leptons,
Proc 5^{th} Int Conf Symmetry in Nonlinear Mathematical Physics, Kyiv, Ukraine 2004;2:843850.
Arabadzhiev T, Uzunov I,
Frequency characteristics of stationary optical pulses in lightwave communication systems with periodical gain created by semiconductor amplifiers,
Optical Fiber Technology 2004;10:171186.
Uzunov I, Arabadzhiev T,
Frequency conversion by means of semiconductor optical amplifiers with gain modulation and fourwave mixing,
Å+Å 2004;34:2632 (in Bulgarian).
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2003
Arabadziev T, Uzunov I,
Stable optical pulse propagation in fiber optics transmission line with semiconductor optical amplifiers,
Proc SPIE 2003;5226:8993.
Arabadziev T, Uzunov I,
Amplification of an optical pulses sequence in semiconductor optical amplifiers,
Proc. SPIE 2003;5226:8488.
Arabadziev T, Uzunov I, Ferdinandov E,
Stationary optical pulses in fiber optic communication systems using semiconductor amplifiers for periodic amplification,
Electrical Engineering and Electronics (Å+Å) 2003;56:2026.
Arabadziev T, Uzunov I, Ferdinandov E,
Frequency characteristics of Stationary optical pulses in fiber optic communication systems using semiconductor amplifiers for periodic amplification,
Electrical Engineering and Electronics (Å+Å) 2003;1012:4046.
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2002
R. Andersen, L.M. Kovachev,
Interaction of coupled optical vortices,
JOSA B 2002, 19, pp. 376384.
23. D.R. Andersen, L.M. Kovachev,
Interaction of coupled vector optical vortices
JOSA B, 2, (2002), pp. 1501.
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2001
I.M. Uzunov,
Stable optical pulse propagation in a dissipative nonlinear medium
Eleventh Internationl school on quantum electronics, 1922, September 2000, Varna , Bulgaria., Proc. SPIE , 4397, (2001), pp.171175.
ONGOING RESEARCH PROJECTS:
Financed by the Bulgarian Academy of Sciences
 Propagation of ultrashort optical pulses in media with nonstationary optical and magnetic response (20142016).
LECTURE COURSES:
 L.M. Ivanov,
 Fiber Optic Communication Systems; Optics; Electricity and Magnetism;
 SouthWestern University, Blagoevgrad, Bulgaria.
