@article{RaetzelWilkensMenzel2017,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Effect of polarization entanglement in photon-photon scattering},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {95},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {1},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2469-9926},
  doi       = {10.1103/PhysRevA.95.012101},
  pages     = {6},
  year      = {2017},
  abstract  = {It is found that the differential cross section of photon-photon scattering is a function of the degree of polarization entanglement of the two-photon state. A reduced general expression for the differential cross section of photon-photon scattering is derived by applying simple symmetry arguments. An explicit expression is obtained for the example of photon-photon scattering due to virtual electron-positron pairs in quantum electrodynamics. It is shown how the effect in this explicit example can be explained as an effect of quantum interference and that it fits with the idea of distance-dependent forces.},
  language  = {en}
}
@article{MenzelHeuerMilonni2019,
  author    = {Menzel, Ralf and Heuer, Axel and Milonni, Peter W.},
  title     = {Entanglement, Complementarity, and Vacuum Fields in Spontaneous Parametric Down-Conversion},
  series = {Atoms},
  volume    = {7},
  journal   = {Atoms},
  number    = {1},
  publisher = {MDPI},
  address   = {Basel},
  issn      = {2218-2004},
  doi       = {10.3390/atoms7010027},
  pages     = {14},
  year      = {2019},
  abstract  = {Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong-Ou-Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.},
  language  = {en}
}
@article{MenzelMarxPuhlmannetal.2019,
  author    = {Menzel, Ralf and Marx, Robert and Puhlmann, Dirk and Heuer, Axel and Schleich, Wolfgang},
  title     = {The photon},
  series = {Journal of the Optical Society of America : B, Optical physics},
  volume    = {36},
  journal   = {Journal of the Optical Society of America : B, Optical physics},
  number    = {6},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {0740-3224},
  doi       = {10.1364/JOSAB.36.001668},
  pages     = {1668 -- 1675},
  year      = {2019},
  abstract  = {We investigate the role of the spatial mode function in a single-photon experiment designed to demonstrate the principle of complementarity. Our approach employs entangled photons created by spontaneous parametric downconversion from a pump mode in a TEM01 mode together with a double slit. Measuring the interference of the signal photons behind the double slit in coincidence with the entangled idler photons at different positions, we select signal photons of different mode functions. When the signal photons belong to the TEM01-like double-hump mode, we obtain almost perfect visibility of the interference fringes, and no "which slit" information is available in the idler photon detected before the slits. This result is remarkable because the entangled signal and idler photon pairs are created each time in only one of the two intensity humps. However, when we break the symmetry between the two maxima of the signal photon mode structure, the paths through the slits for these additional photons become distinguishable and the visibility vanishes. It is the mode function of the photons selected by the detection system that decides if interference or "which slit" information is accessible in the experiment.},
  language  = {en}
}
@misc{MenzelHeuerMilonni2019,
  author    = {Menzel, Ralf and Heuer, Axel and Milonni, Peter W.},
  title     = {Entanglement, complementarity, and vacuum fields in spontaneous parametric down-conversion},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {1077},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-47354},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-473542},
  pages     = {16},
  year      = {2019},
  abstract  = {Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as the effects of entanglement or equivalently in terms of interfering probability amplitudes and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence counting. For comparison, we show that the Hong-Ou-Mandel dip can be explained by the same approach in which the role of the vacuum signal and idler fields, as opposed to entanglement involving vacuum states, is emphasized. We discuss the fundamental limitations of a theory in which these vacuum fields are treated as classical, stochastic fields.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2017,
  author    = {Raetzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Gravitational properties of light: The emission of counter-propagating laser pulses from an atom},
  series = {Physical review : D, Particles, fields, gravitation, and cosmology},
  volume    = {95},
  journal   = {Physical review : D, Particles, fields, gravitation, and cosmology},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0010},
  doi       = {10.1103/PhysRevD.95.084008},
  pages     = {11},
  year      = {2017},
  language  = {en}
}
@article{SandmannGarzMenzel2016,
  author    = {Sandmann, Michael and Garz, Andreas and Menzel, Ralf},
  title     = {Physiological response of two different Chlamydomonas reinhardtii strains to light-dark rhythms},
  series = {Botany},
  volume    = {94},
  journal   = {Botany},
  publisher = {NRC Research Press},
  address   = {Ottawa},
  issn      = {1916-2790},
  doi       = {10.1139/cjb-2015-0144},
  pages     = {53 -- 64},
  year      = {2016},
  abstract  = {Cells of a cell-wall deficient line (cw15-type) of Chlamydomonas reinhardtii and of the corresponding wild type were grown during repetitive light-dark cycles. In a direct comparison, both lines showed approximately the same relative biomass increase during light phase but the cw-line produced significantly more, and smaller, daughter cells. Throughout the light period the average cellular starch content, the cellular chlorophyll content, the cellular rate of dark respiration, and the cellular rate of photosynthesis of the cw-line was lower. Despite this, several non-cell volume related parameters like the development of starch content per cell volume were clearly different over time between the strains. Additionally, the chlorophyll-based photosynthesis rates were 2-fold higher in the mutant than in the wild-type cells, and the ratio of chlorophyll a to chlorophyll b as well as the light-saturation index were also consistently higher in the mutant cells. Differences in the starch content were also confirmed by single cell analyses using a sensitive SHG-based microscopy approach. In summary, the cw15-type mutant deviates from its genetic background in the entire cell physiology. Both lines should be used in further studies in comparative systems biology with focus on the detailed relation between cell volume increase, photosynthesis, starch metabolism, and daughter cell productivity.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2016,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {Gravitational properties of light-the gravitational field of a laser pulse},
  series = {NEW JOURNAL OF PHYSICS},
  volume    = {18},
  journal   = {NEW JOURNAL OF PHYSICS},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/18/2/023009},
  pages     = {16},
  year      = {2016},
  abstract  = {The gravitational field of a laser pulse of finite lifetime, is investigated in the framework of linearized gravity. Although the effects are very small, they may be of fundamental physical interest. It is shown that the gravitational field of a linearly polarized light pulse is modulated as the norm of the corresponding electric field strength, while no modulations arise for circular polarization. In general, the gravitational field is independent of the polarization direction. It is shown that all physical effects are confined to spherical shells expanding with the speed of light, and that these shells are imprints of the spacetime events representing emission and absorption of the pulse. Nearby test particles at rest are attracted towards the pulse trajectory by the gravitational field due to the emission of the pulse, and they are repelled from the pulse trajectory by the gravitational field due to its absorption. Examples are given for the size of the attractive effect. It is recovered that massless test particles do not experience any physical effect if they are co-propagating with the pulse, and that the acceleration of massless test particles counter-propagating with respect to the pulse is four times stronger than for massive particles at rest. The similarities between the gravitational effect of a laser pulse and Newtonian gravity in two dimensions are pointed out. The spacetime curvature close to the pulse is compared to that induced by gravitational waves from astronomical sources.},
  language  = {en}
}
@article{PuhlmannHenkelHeueretal.2016,
  author    = {Puhlmann, Dirk and Henkel, Carsten and Heuer, Axel and Pieplow, Gregor and Menzel, Ralf},
  title     = {Characterization of a remote optical element with bi-photons},
  series = {Physica scripta : an international journal for experimental and theoretical physics},
  volume    = {91},
  journal   = {Physica scripta : an international journal for experimental and theoretical physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {0031-8949},
  doi       = {10.1088/0031-8949/91/2/023006},
  pages     = {113 -- 114},
  year      = {2016},
  abstract  = {We present a simple setup that exploits the interference of entangled photon pairs. 'Signal' photons are sent through a Mach-Zehnder-like interferometer, while 'idlers' are detected in a variable polarization state. Two-photon interference (in coincidence detection) is observed with very high contrast and for significant time delays between signal and idler detection events. This is explained by quantum erasure of the polarization tag and a delayed choice protocol involving a non-local virtual polarizer. The phase of the two-photon fringes is scanned by varying the path length in the signal beam or by rotating a birefringent crystal in the idler beam. We exploit this to characterize one beam splitter of the signal photon interferometer (reflection and transmission amplitudes including losses), using only information about coincidences and control parameters in the idler path. This is possible because our bi-photon state saturates the Greenberger-Yelin-Englert inequality between contrast and predictability.},
  language  = {en}
}
@article{RaetzelWilkensMenzel2016,
  author    = {R{\"a}tzel, Dennis and Wilkens, Martin and Menzel, Ralf},
  title     = {The effect of entanglement in gravitational photon-photon scattering},
  series = {epl : a letters journal exploring the frontiers of physics},
  volume    = {115},
  journal   = {epl : a letters journal exploring the frontiers of physics},
  publisher = {EDP Sciences},
  address   = {Mulhouse},
  issn      = {0295-5075},
  doi       = {10.1209/0295-5075/115/51002},
  pages     = {S12 -- S13},
  year      = {2016},
  abstract  = {The differential cross-section for gravitational photon-photon scattering calculated in perturbative quantum gravity is shown to depend on the degree of polarization entanglement of the two photons. The interaction between photons in the symmetric Bell state is stronger than between not entangled photons. In contrast, the interaction between photons in the anti-symmetric Bell state is weaker than between not entangled photons. The results are interpreted in terms of quantum interference, and it is shown how they fit into the idea of distance-dependent forces. Copyright (C) EPLA, 2016},
  language  = {en}
}
@misc{MenzelPuhlmannHeuer2017,
  author    = {Menzel, Ralf and Puhlmann, Dirk and Heuer, Axel},
  title     = {Complementarity in single photon interference - the role of the mode function and vacuum fields},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-395210},
  pages     = {7},
  year      = {2017},
  abstract  = {Background In earlier experiments the role of the vacuum fields could be demonstrated as the source of complementarity with respect to the temporal properties (Heuer et al., Phys. Rev. Lett. 114:053601, 2015). Methods Single photon first order interferences of spatially separated regions from the cone structure of spontaneous parametric down conversion allow for analyzing the role of the mode function in quantum optics regarding the complementarity principle. Results Here the spatial coherence properties of these vacuum fields are demonstrated as the physical reason for complementarity in these single photon quantum optical experiments. These results are directly connected to the mode picture in classical optics. Conclusion The properties of the involved vacuum fields selected via the measurement process are the physical background of the complementarity principle in quantum optics.},
  language  = {en}
}
@article{MenzelPuhlmannHeuer2017,
  author    = {Menzel, Ralf and Puhlmann, Dirk and Heuer, Axel},
  title     = {Complementarity in single photon interference - the role of the mode function and vacuum fields},
  series = {Journal of the European Optical Society-Rapid},
  volume    = {13},
  journal   = {Journal of the European Optical Society-Rapid},
  publisher = {Springer},
  issn      = {1990-2573},
  doi       = {10.1186/s41476-017-0036-x},
  pages     = {7},
  year      = {2017},
  abstract  = {Background In earlier experiments the role of the vacuum fields could be demonstrated as the source of complementarity with respect to the temporal properties (Heuer et al., Phys. Rev. Lett. 114:053601, 2015). Methods Single photon first order interferences of spatially separated regions from the cone structure of spontaneous parametric down conversion allow for analyzing the role of the mode function in quantum optics regarding the complementarity principle. Results Here the spatial coherence properties of these vacuum fields are demonstrated as the physical reason for complementarity in these single photon quantum optical experiments. These results are directly connected to the mode picture in classical optics. Conclusion The properties of the involved vacuum fields selected via the measurement process are the physical background of the complementarity principle in quantum optics.},
  language  = {en}
}
@article{NiebuhrZinkJechowetal.2015,
  author    = {Niebuhr, Mario and Zink, Christof and Jechow, Andreas and Heuer, Axel and Glebov, Leonid B. and Menzel, Ralf},
  title     = {Mode stabilization of a laterally structured broad area diode laser using an external volume Bragg grating},
  series = {Optics express : the international electronic journal of optics},
  volume    = {23},
  journal   = {Optics express : the international electronic journal of optics},
  number    = {9},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {1094-4087},
  doi       = {10.1364/OE.23.012394},
  pages     = {12394 -- 12400},
  year      = {2015},
  abstract  = {An external volume Bragg grating (VBG) is used for transverse and longitudinal mode stabilization of a broad area diode laser (BAL) with an on-chip transverse Bragg resonance (TBR) grating. The internal TBR grating defines a transverse low-loss mode at a specific propagation angle inside the BAL. Selection of the TBR mode was realized via the angular geometry of an external resonator assembly consisting of the TBR BAL and a feedback element. A feedback mirror provides near diffraction limited and spectral narrow output in the TBR mode albeit requiring an intricate alignment procedure. If feedback is provided via a VBG, adjustment proves to be far less critical and higher output powers were achieved. Moreover, additional modulation in the far field distribution became discernible allowing for a better study of the TBR concept. (C) 2015 Optical Society of America},
  language  = {en}
}
@article{ElsnerPuhlmannPieplowetal.2015,
  author    = {Elsner, Robert and Puhlmann, Dirk and Pieplow, Gregor and Heuer, Axel and Menzel, Ralf},
  title     = {Transverse distinguishability of entangled photons with arbitrarily shaped spatial near- and far-field distributions},
  series = {Journal of the Optical Society of America : B, Optical physics},
  volume    = {32},
  journal   = {Journal of the Optical Society of America : B, Optical physics},
  number    = {9},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {0740-3224},
  doi       = {10.1364/JOSAB.32.001910},
  pages     = {1910 -- 1919},
  year      = {2015},
  abstract  = {Entangled photons generated by spontaneous parametric downconversion are ubiquitous in quantum optics. In general, they exhibit a complex spatial photon count distribution. This spatial structure is responsible for seemingly surprising results concerning, e.g., complementarity such as the apparent simultaneous observation of interference fringes V and which-way information D at a double slit, as recently reported by Menzel et al. [Proc. Natl. Acad. Sci. USA 109, 9314 (2012)]. We implement a complete quantitative model of the SPDC interaction that fully incorporates the effects of crystal anisotropies, phase matching, and the pump beam structure and allows for arbitrary manipulations of the SPDC light in the near and far fields. This enables us to establish an upper bound D-2 + V-2 <= 1.47 for the experimental parameters reported by Menzel et al. We report new experimental results that agree excellently with these theoretical predictions. The new model enables a detailed quantitative analysis of this surprising result and the fair sampling interpretation of biphotons passing a double slit. (C) 2015 Optical Society of America},
  language  = {en}
}
@article{HeuerMenzelMilonni2015,
  author    = {Heuer, Axel and Menzel, Ralf and Milonni, P. W.},
  title     = {Complementarity in biphoton generation with stimulated or induced coherence},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {92},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1050-2947},
  doi       = {10.1103/PhysRevA.92.033834},
  pages     = {8},
  year      = {2015},
  abstract  = {Coherence can be induced or stimulated in parametric down-conversion using two or three crystals when, for example, the idler modes of the crystals are aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114, 053601 (2015)] focused on which-path information and the role of vacuum fields in realizing complementarity via reduced visibility in single-photon interference. Here we describe experiments comparing induced and stimulated coherence. Different single-photon interference experiments were performed by blocking one of the pump beams in a three-crystal setup. Each counted photon is emitted from one of two crystals and which-way information may or not be available, depending on the setup. Distinctly different results are obtained in the induced and stimulated cases, especially when a variable transmission filter is inserted between the crystals. A simplified theoretical model accounts for all the experimental results and is also used to address the question of whether the phases of the signal and idler fields in parametric down-conversion are correlated.},
  language  = {en}
}
@article{ZinkWernerJechowetal.2014,
  author    = {Zink, Christof and Werner, Nils and Jechow, Andreas and Heuer, Axel and Menzel, Ralf},
  title     = {Multi-wavelength operation of a single broad area diode laser by spectral beam combining},
  series = {IEEE photonics technology letters},
  volume    = {26},
  journal   = {IEEE photonics technology letters},
  number    = {3},
  publisher = {Inst. of Electr. and Electronics Engineers},
  address   = {Piscataway},
  issn      = {1041-1135},
  doi       = {10.1109/LPT.2013.2291963},
  pages     = {253 -- 256},
  year      = {2014},
  abstract  = {Stabilized multi-wavelength emission from a single emitter broad area diode laser (BAL) is realized by utilizing an external cavity with a spectral beam combining architecture. Self-organized emitters that are equidistantly spaced across the slow axis are enforced by the spatially distributed wavelength selectivity of the external cavity. This resulted in an array like near-field emission although the BAL is physically a single emitter without any epitaxial sub-structuring and only one electrical contact. Each of the self-organized emitters is operated at a different wavelength and the emission is multiplexed into one spatial mode with near-diffraction limited beam quality. With this setup, multi-line emission of 31 individual spectral lines centered around and a total spectral width of 3.6 nm is realized with a 1000 mu m wide BAL just above threshold. To the best of our knowledge, this is the first demonstration of such a self-organization of emitters by optical feedback utilizing a spectral beam combining architecture.},
  language  = {en}
}
@article{ZinkNiebuhrJechowetal.2014,
  author    = {Zink, Christof and Niebuhr, Mario and Jechow, Andreas and Heuer, Axel and Menzel, Ralf},
  title     = {Broad area diode laser with on-chip transverse Bragg grating stabilized in an off-axis external cavity},
  series = {Optics express : the international electronic journal of optics},
  volume    = {22},
  journal   = {Optics express : the international electronic journal of optics},
  number    = {12},
  publisher = {Optical Society of America},
  address   = {Washington},
  issn      = {1094-4087},
  doi       = {10.1364/OE.22.014108},
  pages     = {14108 -- 14113},
  year      = {2014},
  abstract  = {The emission characteristics of a novel, specially designed broad area diode laser (BAL) with on-chip transversal Bragg resonance (TBR) grating in lateral direction were investigated in an off-axis external cavity setup. The internal TBR grating defines a low loss transversal mode at a specific angle of incidence and a certain wavelength. By providing feedback at this specific angle with an external mirror, it is possible to select this low loss transverse mode and stabilize the BAL. Near diffraction limited emission with an almost single lobed far field pattern could be realized, in contrast to the double lobed far field pattern of similar setups using standard BALs or phase-locked diode laser arrays. Furthermore, we could achieve a narrow bandwidth emission with a simplified setup without external frequency selective elements. (C) 2014 Optical Society of America},
  language  = {en}
}
@article{SchwarzeGarzTeuchneretal.2014,
  author    = {Schwarze, Thomas and Garz, Andreas and Teuchner, Klaus and Menzel, Ralf and Holdt, Hans-J{\"u}rgen},
  title     = {Two-photon probes for metal ions based on phenylaza[18]crown-6 ethers and 1,2,3-triazoles as pi-linkers},
  series = {ChemPhysChem : a European journal of chemical physics and physical chemistry},
  volume    = {15},
  journal   = {ChemPhysChem : a European journal of chemical physics and physical chemistry},
  number    = {12},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {1439-4235},
  doi       = {10.1002/cphc.201402232},
  pages     = {2436 -- 2439},
  year      = {2014},
  language  = {en}
}
@article{HeuerRaabeMenzel2014,
  author    = {Heuer, Axel and Raabe, S. and Menzel, Ralf},
  title     = {Phase memory across two single-photon interferometers including wavelength conversion},
  series = {Physical review : A, Atomic, molecular, and optical physics},
  volume    = {90},
  journal   = {Physical review : A, Atomic, molecular, and optical physics},
  number    = {4},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {1050-2947},
  doi       = {10.1103/PhysRevA.90.045803},
  pages     = {4},
  year      = {2014},
  abstract  = {Spontaneous parametric down-conversion (SPDC) in a nonlinear crystal generates two single photons (signal and idler) with random phases. Thus, no first-order interference between them occurs. However, coherence can be induced in a cascaded setup of two crystals if, e.g., the idler modes of both crystals are aligned to be indistinguishable. Due to the effect of phase memory it is found that the first-order interference of the signal beams can be controlled by the phase delay between the pump beams. Even for pump photon delays much larger than the coherence length of the SPDC photons, the visibility is above 90\%. The high visibilities reported here prove an almost perfect phase memory effect across the two interferometers for the pump and the signal photon modes.},
  language  = {en}
}
@article{HeuerSagahtiJechowetal.2012,
  author    = {Heuer, Axel and Sagahti, A. and Jechow, Andreas and Skoczowsky, D. and Menzel, Ralf},
  title     = {Multi-wavelength, high spatial brightness operation of a phase-locked stripe-array diode laser},
  series = {Laser physics},
  volume    = {22},
  journal   = {Laser physics},
  number    = {1},
  publisher = {Pleiades Publ.},
  address   = {New York},
  issn      = {1054-660X},
  doi       = {10.1134/S1054660X12010057},
  pages     = {160 -- 164},
  year      = {2012},
  abstract  = {Stable continuous wave multi-wavelength operation of a stripe-array diode laser with an externalcavity spectral beam combining geometry is presented. In this setup each emitter of the stripe-array is forced to operate at a different wavelength, which leads to a decoupling between the usually phase-locked emitters. With a reflective diffraction grating with a period of 300 lines per mm, 33 equidistant laser lines around a center wavelength of 978 nm were realized, spanning a spectral range of 26 nm. With this novel approach near-diffraction limited emission with a beam quality of M (2) < 1.2 and an output power of 450 mW was achieved. This laser light source can be used for applications requiring low temporal but high spatial coherence.},
  language  = {en}
}
@article{ElsnerUllmannHeueretal.2012,
  author    = {Elsner, Robert and Ullmann, Roland and Heuer, Axel and Menzel, Ralf and Ostermeyer, Martin},
  title     = {Two-dimensional modeling of transient gain gratings in saturable gain media},
  series = {OPTICS EXPRESS},
  volume    = {20},
  journal   = {OPTICS EXPRESS},
  number    = {7},
  publisher = {OPTICAL SOC AMER},
  address   = {WASHINGTON},
  issn      = {1094-4087},
  doi       = {10.1364/OE.20.006887},
  pages     = {6887 -- 6896},
  year      = {2012},
  abstract  = {A transient two-dimensional model describing degenerate four-wave mixing inside saturable gain media is presented. The new model is compared to existing one-dimensional models with their qualitative results confirmed. Large quantitative differences with respect to peak reflectivity and optimum pump fluence are observed. Furthermore, the influence of the beam focus size, the transverse position and the crossing angle on the reflectivity of the grating is investigated using the improved model. It is demonstrated that the phase conjugate reflectivity depends sensitively on the transverse features of the interacting beams with a transverse shift in the position of the pump beams yielding a threefold improvement in reflectivity. (C) 2012 Optical Society of America},
  language  = {en}
}