Proceedings of LFNM 2002. 4th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Cat. No.02EX549)
Modal behavior of a 2D (square lattice geometry) antiguided vertical cavity surface emitting lase... more Modal behavior of a 2D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by the 3D bidirectional beam propagation method. Above-threshold operation of leaky modes was simulated using multiple iterations. In addition, a method based on functions of Krylov's subspace was developed to find the number of array optical modes in a VCSEL array with gain and index distributions established by the oscillating mode. In calculations, both Fourier and space variable descriptions of beam propagation were combined. Analysis of an effective-index approximation is made, and explicit expressions are derived for the effective index and blue shift of the laser frequency. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality. The 2D antiguided array results from shifting the cavity resonance between the element and interelement regions and is fabricated by selective chemical etching and two-step metalorganic chemical vapor deposition (MOCVD) growth. In-phase and out-of-phase array mode operation is observed from top-emitting rectangular arrays as large as 400 elements, depending on the interelement width, in good agreement with theory. The experimentally realized set of laser arrays of variable size was studied numerically.
The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003.
The in-phase mode emission in coupled VCSELs and 2D 4×4 VCSEL arrays has been reported using anti... more The in-phase mode emission in coupled VCSELs and 2D 4×4 VCSEL arrays has been reported using antiguided VCSEL elements. Two-step metalorganic chemical vapor deposition (MOCVD) is used for the growth of the antiguided VCSEL array structure. Here we demonstrate that in-phase mode operation can be achieved from very large aperture (up to 20×20) rectangular and triangular antiguided VCSEL arrays in
CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, 2009
ABSTRACT Single spatial mode operation of a fiber laser leads to perfect output beam quality, whi... more ABSTRACT Single spatial mode operation of a fiber laser leads to perfect output beam quality, which is important for industry. Increasing of the effective mode area allows for achieving higher laser power at the wave field intensity lower than the limit imposed by non-linear effects. However, the large mode area (LMA) fiber lasers are open to higher order mode (HOM) appearance. This paper considers a novel approach to realize the flattened fundamental mode in an all-glass design of an Yb-doped fiber laser by special profiling of the refractive index. In particular, large-diameter core rimmed by circular chain of round waveguides was simulated numerically to find optimal geometry for stable single-mode operation. Paraxial and scalar approximations are used for wave field modelling in combination with Rigrod's approximation for the gain.
ABSTRACT A vertical cavity surface emitting laser (VCSEL) containing a resonant heterostructure o... more ABSTRACT A vertical cavity surface emitting laser (VCSEL) containing a resonant heterostructure of an array of quantum wells (QW) is considered. The set of QW separated by barriers represents a periodical structure with period equal to a laser wavelength. Bragg reflectors serve as the laser mirrors. In the first stage we study ldquocoldrdquo cavity properties neglecting change of material characteristics induced by the electromagnetic field. The eigenvalue problem to determine the resonator modes is solved numerically. Complex eigenvalues found define the wavelength shifts relative to reference value and threshold gains. The next stage of study relates to a case of a loaded cavity when self-consistent solving of a wave field equation and material equations is required. The charge carrier distributions in each of QW obey non-linear diffusion equation. We have developed the special iteration procedure for round-trip operator evaluation, which is applicable for a set of QW of any size and has computational costs growing linearly with number of QW. The results of calculations for a cylindrical VCSEL with e-beam pumping will be reported.
ABSTRACT Three-dimensional numerical calculations made of the radiation parameters of a cw CO2 am... more ABSTRACT Three-dimensional numerical calculations made of the radiation parameters of a cw CO2 amplifier with a circulating active medium. An analysis was carried out of the amplification of Gaussian and annular-profile beams. The calculated energy characteristics of the output radiation showed a satisfactory agreement with the experimental data. The angular divergence of the output beam was 1.5–2 times greater than the diffraction limit because of local temperature inhomogeneities. As a result of self-interaction of the radiation, splitting of the amplified laser beam was possible in the far-field zone. Under selected conditions the upstream angular shift of the output beam did not exceed its divergence.
2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, 2007
ABSTRACT The fiber laser containing 7-core hexagonal structure doped by Yb was suggested and expe... more ABSTRACT The fiber laser containing 7-core hexagonal structure doped by Yb was suggested and experimentally studied in ref. [1]. It was observed that the pattern in the far field at more than 100 W laser power looks like that of the in-phase mode of the structure. Numerical simulations based on 3D Beam Propagation Method (BPM) in have demonstrated that the effect observed in is associated with filtering by spatial configuration of gain in the cores.
2007 Conference on Lasers and Electro-Optics (CLEO), 2007
It is numerically revealed and properly interpreted a phenomenon of predominant amplification of ... more It is numerically revealed and properly interpreted a phenomenon of predominant amplification of an optical mode with lower modal gain in 7-core fiber laser. Mode beating is a key factor responsible for this effect.
ABSTRACT Coherent laser beam combining is potentially attractive way to increase the output beam ... more ABSTRACT Coherent laser beam combining is potentially attractive way to increase the output beam brightness beyond the limits imposed on single-mode lasers by technological problems. Passive phase locking does not need complex external management. A specific feature of fiber amplifiers and lasers is that they possess optical path differences of many wavelengths magnitude. Cold-cavity theory of coherent laser beam combining predicts in this case rather low efficiency of beam combining even for an array of 8 lasers. Experiments, in contrast, demonstrated in such systems that high degree of phasing takes place for up to 20 lasers in an array. Possible explanation of this discrepancy may be associated with a number of factors. These factors are: gain saturation, intensity-dependent index, laser wavelength self-adjustment within the gain bandwidth. Besides, high degree of phase-locking can be established in self-sustained pulse periodic or spiky regime. Our approach takes injection controlled laser as a base unit of an ensemble. Beams from the neighboring lasers are injected into the reference laser in the array. Then a relationship between reference laser characteristics and whole wave field parameters can be found. As an example, fiber laser array with global coupling is numerically simulated with laser wavelength scanned within the gain bandwidth. Non-linear index is found to improve essentially passive phasing efficiency independent of the non-linearity sign.
The vertical external cavity surface emitting laser (VECSEL) as a typical example of laser with m... more The vertical external cavity surface emitting laser (VECSEL) as a typical example of laser with multilayer active medium is considered. The round-trip operator technique is presented in the given paper based on the bidirectional beam propagation method (BiBPM). Similarly to traditional Fox-Li technique our method not requires explicit calculation of matrix of the round-trip operator and suits perfectly to Krylov subspace methods of linear algebra. The presented method is extended in natural way to non-linear case taking into account light-medium interaction. The results of modeling of a VECSEL with a resonant array of quantum wells are presented.
Coherent laser beam combining potentially provides an opportunity to achieve extremely high brigh... more Coherent laser beam combining potentially provides an opportunity to achieve extremely high brightness of the output beam, permitting high on-target power density. All passive phasing techniques are limited by existence of optical path differences of individual fiber amplifiers. Cold-cavity theory predicts fast decrease in efficiency of coherent fiber laser beam combining with number of lasers. Experiments demonstrated in such systems that high degree of phasing takes place for laser array of up to 16 lasers. Origins of this illusory contradiction will be analyzed in the paper. Effects of laser wavelength self-adjustment and non-linearity of gain will be discussed.
Fiber Lasers III: Technology, Systems, and Applications, 2006
Along with rapid progress in characteristics of single-fiber lasers much attention is paid these ... more Along with rapid progress in characteristics of single-fiber lasers much attention is paid these days to the problem of phase locking of multi-core fiber lasers. It is known that only strong-coupled system has a chance to be phase locked despite non-identity of channels. In case of the strong inter-channel coupling the traditional theoretical approach based on expansion over modes of
ABSTRACT Three-dimensional (3-D) above-threshold analyses have been performed on laterally antigu... more ABSTRACT Three-dimensional (3-D) above-threshold analyses have been performed on laterally antiguided laser structures operated on leaky modes and twin-waveguide structures operated on guided modes for generating watt-range CW powers in a single, stable spatial mode. The 3-D numerical code takes into account carrier diffusion in the quantum well, thermooptic effects as well as edge radiation losses. Additionally, higher-order optical modes on a 'frozen background' provided by the fundamental mode operation are computed by the Arnoldi algorithm. Approaching the threshold for a competing higher-order mode puts a limit on the range for stable, single-mode operation. The modal structure and stability for both device types are studied over a wide range of the active core width and widths of the buried waveguides bordering the low-index device core. The numerical analyses results indicate an essential role of thermal lensing in transformations of optical-modes shapes and in mode stability loss with the drive current increase. The CW operation in a stable, single spatial mode to powers as high as 2 W is predicted for 2-mm length lasers operated on leaky modes. The maximum CW power in single-guided-mode is predicted as high as 2.46 W for 2-mm length and 3.4 W for 3-mm length devices.
The influence of a phase shift in a channel coupling two unstable-resonator CO 2 lasers on the ba... more The influence of a phase shift in a channel coupling two unstable-resonator CO 2 lasers on the band width of stable phase locking of the laser fields was studied experimentally for the first time. The fraction of the radiation effecting the optical coupling was determined experimentally and found to vary in the range 10 ~~3-10 ~2 for different coupling apertures. The maximum mismatch of the resonator lengths which did not disrupt the coherence amounted to ΔΖ, χλ /20. A method developed for calculating the diffraction made it possible to determine numerically the stable phase locking range of the output radiation from two lasers with unstable resonators. The calculated and experimental parametric dependences of the phase-locking band width were in qualitative agreement.
Dual metal gate transistors with high-k gate dielectrics have been investigated for low-power met... more Dual metal gate transistors with high-k gate dielectrics have been investigated for low-power metal oxide semiconductor (MOS) devices in 45 nm nodes and beyond. Using high-quality HfSiO gate dielectrics, using TiN and Ta for the gate electrode, and minimizing process damage, we have succeeded in markedly improving device performance. Effective work functions of 4.9 eV for TiN and 4.3 eV for Ta on HfSiO were obtained for the first time. Symmetrical threshold voltages of AE0:5 V were realized for these work functions. Small hysteresis and low interface trap densities for both TiN and Ta were obtained, which are almost the same as those of poly-Si/HfSiON transistors. No degradation in electron mobility was achieved for the first time for Ta-NMOS transistors at an effective field of 1.0 MV/cm. The gate leakage current at an equivalent electrical oxide thickness in an inversion of 1.7 nm was suppressed to 1 mA/cm À2 at a gate bias of Vth þ 0:6 V.
ABSTRACT The round-trip operator technique is widely used for dispersionless optical resonators b... more ABSTRACT The round-trip operator technique is widely used for dispersionless optical resonators beginning from pioneering studies of Fox and Li. The resonator modes are determined as eigenfunctions of the round-trip operator and may be calculated by means of numerical linear algebra. Corresponding complex eigenvalues determine the wavelength shifts relative to reference value and threshold gains. Dispersion elements, for example, Bragg mirrors in a vertical cavity surface emitting laser (VCSEL) cause a dependence of the propagation operator on the wavelength and threshold gain. We can determine the round-trip operator in this case also, but the unknown values of the wavelength and threshold gain enter into the operator in a complicated manner. Trial-and-error method for determination of the wavelength shifts and the threshold gains is possible but it is rather time consuming method. The proposed approximate numerical method for calculation of resonator modes is based on the solution of linear eigenvalue problem for the round-trip operator with reference wavelength and zero attenuation. The wavelength shifts and threshold gains can be calculated by simple formulae using the eigenvalues obtained and the computed effective length of the resonator. Calculations for a cylindrical antiresonant-reflecting optical waveguide (ARROW) VCSEL are performed for verification of the model.
Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting las... more Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by 3-D bi-directional beam propagation method. Above threshold operation of leaky modes was simulated using multiple iterations. Besides, a method based on functions of Krylov"s subspace, was developed to find a number of array optical modes in a VCSEL array with gain
Proceedings of LFNM 2002. 4th International Workshop on Laser and Fiber-Optical Networks Modeling (IEEE Cat. No.02EX549)
Modal behavior of a 2D (square lattice geometry) antiguided vertical cavity surface emitting lase... more Modal behavior of a 2D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by the 3D bidirectional beam propagation method. Above-threshold operation of leaky modes was simulated using multiple iterations. In addition, a method based on functions of Krylov's subspace was developed to find the number of array optical modes in a VCSEL array with gain and index distributions established by the oscillating mode. In calculations, both Fourier and space variable descriptions of beam propagation were combined. Analysis of an effective-index approximation is made, and explicit expressions are derived for the effective index and blue shift of the laser frequency. Conditions are found for favorable lasing of the in-phase mode providing high laser beam quality. The 2D antiguided array results from shifting the cavity resonance between the element and interelement regions and is fabricated by selective chemical etching and two-step metalorganic chemical vapor deposition (MOCVD) growth. In-phase and out-of-phase array mode operation is observed from top-emitting rectangular arrays as large as 400 elements, depending on the interelement width, in good agreement with theory. The experimentally realized set of laser arrays of variable size was studied numerically.
The 16th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2003. LEOS 2003.
The in-phase mode emission in coupled VCSELs and 2D 4×4 VCSEL arrays has been reported using anti... more The in-phase mode emission in coupled VCSELs and 2D 4×4 VCSEL arrays has been reported using antiguided VCSEL elements. Two-step metalorganic chemical vapor deposition (MOCVD) is used for the growth of the antiguided VCSEL array structure. Here we demonstrate that in-phase mode operation can be achieved from very large aperture (up to 20×20) rectangular and triangular antiguided VCSEL arrays in
CLEO/Europe - EQEC 2009 - European Conference on Lasers and Electro-Optics and the European Quantum Electronics Conference, 2009
ABSTRACT Single spatial mode operation of a fiber laser leads to perfect output beam quality, whi... more ABSTRACT Single spatial mode operation of a fiber laser leads to perfect output beam quality, which is important for industry. Increasing of the effective mode area allows for achieving higher laser power at the wave field intensity lower than the limit imposed by non-linear effects. However, the large mode area (LMA) fiber lasers are open to higher order mode (HOM) appearance. This paper considers a novel approach to realize the flattened fundamental mode in an all-glass design of an Yb-doped fiber laser by special profiling of the refractive index. In particular, large-diameter core rimmed by circular chain of round waveguides was simulated numerically to find optimal geometry for stable single-mode operation. Paraxial and scalar approximations are used for wave field modelling in combination with Rigrod's approximation for the gain.
ABSTRACT A vertical cavity surface emitting laser (VCSEL) containing a resonant heterostructure o... more ABSTRACT A vertical cavity surface emitting laser (VCSEL) containing a resonant heterostructure of an array of quantum wells (QW) is considered. The set of QW separated by barriers represents a periodical structure with period equal to a laser wavelength. Bragg reflectors serve as the laser mirrors. In the first stage we study ldquocoldrdquo cavity properties neglecting change of material characteristics induced by the electromagnetic field. The eigenvalue problem to determine the resonator modes is solved numerically. Complex eigenvalues found define the wavelength shifts relative to reference value and threshold gains. The next stage of study relates to a case of a loaded cavity when self-consistent solving of a wave field equation and material equations is required. The charge carrier distributions in each of QW obey non-linear diffusion equation. We have developed the special iteration procedure for round-trip operator evaluation, which is applicable for a set of QW of any size and has computational costs growing linearly with number of QW. The results of calculations for a cylindrical VCSEL with e-beam pumping will be reported.
ABSTRACT Three-dimensional numerical calculations made of the radiation parameters of a cw CO2 am... more ABSTRACT Three-dimensional numerical calculations made of the radiation parameters of a cw CO2 amplifier with a circulating active medium. An analysis was carried out of the amplification of Gaussian and annular-profile beams. The calculated energy characteristics of the output radiation showed a satisfactory agreement with the experimental data. The angular divergence of the output beam was 1.5–2 times greater than the diffraction limit because of local temperature inhomogeneities. As a result of self-interaction of the radiation, splitting of the amplified laser beam was possible in the far-field zone. Under selected conditions the upstream angular shift of the output beam did not exceed its divergence.
2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference, 2007
ABSTRACT The fiber laser containing 7-core hexagonal structure doped by Yb was suggested and expe... more ABSTRACT The fiber laser containing 7-core hexagonal structure doped by Yb was suggested and experimentally studied in ref. [1]. It was observed that the pattern in the far field at more than 100 W laser power looks like that of the in-phase mode of the structure. Numerical simulations based on 3D Beam Propagation Method (BPM) in have demonstrated that the effect observed in is associated with filtering by spatial configuration of gain in the cores.
2007 Conference on Lasers and Electro-Optics (CLEO), 2007
It is numerically revealed and properly interpreted a phenomenon of predominant amplification of ... more It is numerically revealed and properly interpreted a phenomenon of predominant amplification of an optical mode with lower modal gain in 7-core fiber laser. Mode beating is a key factor responsible for this effect.
ABSTRACT Coherent laser beam combining is potentially attractive way to increase the output beam ... more ABSTRACT Coherent laser beam combining is potentially attractive way to increase the output beam brightness beyond the limits imposed on single-mode lasers by technological problems. Passive phase locking does not need complex external management. A specific feature of fiber amplifiers and lasers is that they possess optical path differences of many wavelengths magnitude. Cold-cavity theory of coherent laser beam combining predicts in this case rather low efficiency of beam combining even for an array of 8 lasers. Experiments, in contrast, demonstrated in such systems that high degree of phasing takes place for up to 20 lasers in an array. Possible explanation of this discrepancy may be associated with a number of factors. These factors are: gain saturation, intensity-dependent index, laser wavelength self-adjustment within the gain bandwidth. Besides, high degree of phase-locking can be established in self-sustained pulse periodic or spiky regime. Our approach takes injection controlled laser as a base unit of an ensemble. Beams from the neighboring lasers are injected into the reference laser in the array. Then a relationship between reference laser characteristics and whole wave field parameters can be found. As an example, fiber laser array with global coupling is numerically simulated with laser wavelength scanned within the gain bandwidth. Non-linear index is found to improve essentially passive phasing efficiency independent of the non-linearity sign.
The vertical external cavity surface emitting laser (VECSEL) as a typical example of laser with m... more The vertical external cavity surface emitting laser (VECSEL) as a typical example of laser with multilayer active medium is considered. The round-trip operator technique is presented in the given paper based on the bidirectional beam propagation method (BiBPM). Similarly to traditional Fox-Li technique our method not requires explicit calculation of matrix of the round-trip operator and suits perfectly to Krylov subspace methods of linear algebra. The presented method is extended in natural way to non-linear case taking into account light-medium interaction. The results of modeling of a VECSEL with a resonant array of quantum wells are presented.
Coherent laser beam combining potentially provides an opportunity to achieve extremely high brigh... more Coherent laser beam combining potentially provides an opportunity to achieve extremely high brightness of the output beam, permitting high on-target power density. All passive phasing techniques are limited by existence of optical path differences of individual fiber amplifiers. Cold-cavity theory predicts fast decrease in efficiency of coherent fiber laser beam combining with number of lasers. Experiments demonstrated in such systems that high degree of phasing takes place for laser array of up to 16 lasers. Origins of this illusory contradiction will be analyzed in the paper. Effects of laser wavelength self-adjustment and non-linearity of gain will be discussed.
Fiber Lasers III: Technology, Systems, and Applications, 2006
Along with rapid progress in characteristics of single-fiber lasers much attention is paid these ... more Along with rapid progress in characteristics of single-fiber lasers much attention is paid these days to the problem of phase locking of multi-core fiber lasers. It is known that only strong-coupled system has a chance to be phase locked despite non-identity of channels. In case of the strong inter-channel coupling the traditional theoretical approach based on expansion over modes of
ABSTRACT Three-dimensional (3-D) above-threshold analyses have been performed on laterally antigu... more ABSTRACT Three-dimensional (3-D) above-threshold analyses have been performed on laterally antiguided laser structures operated on leaky modes and twin-waveguide structures operated on guided modes for generating watt-range CW powers in a single, stable spatial mode. The 3-D numerical code takes into account carrier diffusion in the quantum well, thermooptic effects as well as edge radiation losses. Additionally, higher-order optical modes on a 'frozen background' provided by the fundamental mode operation are computed by the Arnoldi algorithm. Approaching the threshold for a competing higher-order mode puts a limit on the range for stable, single-mode operation. The modal structure and stability for both device types are studied over a wide range of the active core width and widths of the buried waveguides bordering the low-index device core. The numerical analyses results indicate an essential role of thermal lensing in transformations of optical-modes shapes and in mode stability loss with the drive current increase. The CW operation in a stable, single spatial mode to powers as high as 2 W is predicted for 2-mm length lasers operated on leaky modes. The maximum CW power in single-guided-mode is predicted as high as 2.46 W for 2-mm length and 3.4 W for 3-mm length devices.
The influence of a phase shift in a channel coupling two unstable-resonator CO 2 lasers on the ba... more The influence of a phase shift in a channel coupling two unstable-resonator CO 2 lasers on the band width of stable phase locking of the laser fields was studied experimentally for the first time. The fraction of the radiation effecting the optical coupling was determined experimentally and found to vary in the range 10 ~~3-10 ~2 for different coupling apertures. The maximum mismatch of the resonator lengths which did not disrupt the coherence amounted to ΔΖ, χλ /20. A method developed for calculating the diffraction made it possible to determine numerically the stable phase locking range of the output radiation from two lasers with unstable resonators. The calculated and experimental parametric dependences of the phase-locking band width were in qualitative agreement.
Dual metal gate transistors with high-k gate dielectrics have been investigated for low-power met... more Dual metal gate transistors with high-k gate dielectrics have been investigated for low-power metal oxide semiconductor (MOS) devices in 45 nm nodes and beyond. Using high-quality HfSiO gate dielectrics, using TiN and Ta for the gate electrode, and minimizing process damage, we have succeeded in markedly improving device performance. Effective work functions of 4.9 eV for TiN and 4.3 eV for Ta on HfSiO were obtained for the first time. Symmetrical threshold voltages of AE0:5 V were realized for these work functions. Small hysteresis and low interface trap densities for both TiN and Ta were obtained, which are almost the same as those of poly-Si/HfSiON transistors. No degradation in electron mobility was achieved for the first time for Ta-NMOS transistors at an effective field of 1.0 MV/cm. The gate leakage current at an equivalent electrical oxide thickness in an inversion of 1.7 nm was suppressed to 1 mA/cm À2 at a gate bias of Vth þ 0:6 V.
ABSTRACT The round-trip operator technique is widely used for dispersionless optical resonators b... more ABSTRACT The round-trip operator technique is widely used for dispersionless optical resonators beginning from pioneering studies of Fox and Li. The resonator modes are determined as eigenfunctions of the round-trip operator and may be calculated by means of numerical linear algebra. Corresponding complex eigenvalues determine the wavelength shifts relative to reference value and threshold gains. Dispersion elements, for example, Bragg mirrors in a vertical cavity surface emitting laser (VCSEL) cause a dependence of the propagation operator on the wavelength and threshold gain. We can determine the round-trip operator in this case also, but the unknown values of the wavelength and threshold gain enter into the operator in a complicated manner. Trial-and-error method for determination of the wavelength shifts and the threshold gains is possible but it is rather time consuming method. The proposed approximate numerical method for calculation of resonator modes is based on the solution of linear eigenvalue problem for the round-trip operator with reference wavelength and zero attenuation. The wavelength shifts and threshold gains can be calculated by simple formulae using the eigenvalues obtained and the computed effective length of the resonator. Calculations for a cylindrical antiresonant-reflecting optical waveguide (ARROW) VCSEL are performed for verification of the model.
Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting las... more Modal behavior of a 2-D (square lattice geometry) antiguided vertical cavity surface emitting laser (VCSEL) array was studied by 3-D bi-directional beam propagation method. Above threshold operation of leaky modes was simulated using multiple iterations. Besides, a method based on functions of Krylov"s subspace, was developed to find a number of array optical modes in a VCSEL array with gain
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Papers by Nikolay Elkin