Optical Parametric Interactions Research Articles

Quantum noise of parametric amplification in a phase-sensitive/insensitive intermediate condition

Phase-sensitive amplification (PSA) is a particular type of optical parametric amplification (OPA) that features a low-noise property such that the quantum-limited noise figure is 0 dB. The PSA operation is typically achieved when the signal and idler spectra are degenerate in optical parametric interactions, i.e., the degenerate OPA condition. However, for a spectrally broadened incident light, these two spectra can be partially degenerate. The present work investigates the noise property of OPA in such conditions in terms of quantum mechanics. The results quantitatively indicate the intermediate properties between PSA and phase-insensitive amplification.

Shared optical parametric generation interactions in square lattice nonlinear photonic crystals

In this work, we investigated common optical parametric generation (OPG) with a 532-nm beam pumped along the x-axis of a square lattice two-dimensional periodically poled lithium tantalate (2D-PPLT). Twin-beam generation are observed with either the signal or the idler beams propagating collinearly to the pump beam due to participation of reciprocal lattice vectors (RLV) of $$\mathbf K _{1,\pm 1}$$ . With both of the signal and the idler beams generated non-collinearly to the pump beam, multi-wavelength dual-beam generation are also observed due to contribution from $$\mathbf K _{1,0}$$ and $$\mathbf K _{1,\pm 1}$$ . Because of mirror symmetry in the domain patterns/structures of the 2D-PPLT, all the OPG processes are doubled with the generated waves spectrally degenerated and spatially separated. By analyzing the spectral and angular distribution of the OPG beams, we confirm that the angular crossing of the $$\mathbf {K_{m,n}}$$ -assisted quasi-phase matching (QPM) spectral tuning curves result in a shared signal or idler wave configuration which leads to intensity enhancement in these parametric beams.

Low-Parametric-Crosstalk Phase-Sensitive Amplifier for Guard-Band-Less DWDM Signal Using PPLN Waveguides

We demonstrated guard-band-less dense wavelength division multiplex signal amplification with a phase sensitive amplifier (PSA). The PSA consists of periodically poled lithium niobate waveguide that employs two-stage nonlinear process, namely second-harmonic generation and optical parametric amplification, which makes it possible to mitigate the crosstalk induced by the optical parametric interaction between DWDM channels. The PSA amplified 16-channel signals simultaneously with a gain of 17 dB over 12-nm wavelength range. We demonstrated a 2.5-dB signal-to-noise-ratio improvement and a low noise figure of 2.1 dB below the 3-dB quantum limit. We achieved the amplification of a 10-Gbaud quadrature phase shift keying signal with phase and amplitude regeneration.

Frohlich Interaction in Compound Semiconductors: A Comparative Study

In polar semiconductor materials, LO phonons produce a macroscopic electric field, which interacts with the electrons. This coupling of long range is known as Frohlich interaction. Due to the interaction of an electron with LO phonons, a quasi-particle is formed known as polaron. The strength of this coupling is expressed by a dimensionless Frohlich coupling constant. Due to the polar coupling to LO phonons, the carriers lose their initial kinetic energy to the lattice by a very efficient relaxation mechanism in III-V bulk semiconductors. Therefore it would be interesting to examine the effect of Frohlich coupling constant on the operational characteristics of optical parametric interaction in compound semiconductor medium. Using hydrodynamic model and coupled mode theory, a theoretical model is developed to determine threshold pump field for the onset of parametric process. For the sake of numerical estimations, data of ZnS and GaAs have been used. These prominent materials are assumed to be shined by a 10.6 μm CO2 laser so that nonlinearity could be induced in the medium. It is found that material having lower coupling constant is beneficial for a cost effective parametric interaction. It is hoped that result of this paper may be useful for various industrial applications.

Frequency-domain nonlinear optics in two-dimensionally patterned quasi-phase-matching media.

Advances in the amplification and manipulation of ultrashort laser pulses have led to revolutions in several areas. Examples include chirped pulse amplification for generating high peak-power lasers, power-scalable amplification techniques, pulse shaping via modulation of spatially-dispersed laser pulses, and efficient frequency-mixing in quasi-phase-matched nonlinear crystals to access new spectral regions. In this work, we introduce and demonstrate a new platform for nonlinear optics which has the potential to combine these separate functionalities (pulse amplification, frequency transfer, and pulse shaping) into a single monolithic device that is bandwidth- and power-scalable. The approach is based on two-dimensional (2D) patterning of quasi-phase-matching (QPM) gratings combined with optical parametric interactions involving spatially dispersed laser pulses. Our proof of principle experiment demonstrates this technique via mid-infrared optical parametric chirped pulse amplification of few-cycle pulses. Additionally, we present a detailed theoretical and numerical analysis of such 2D-QPM devices and how they can be designed.

110 W 1678 nm laser based on high-efficiency optical parametric interactions pumped by high-power slab laser.

This Letter presents a high-efficiency optical parametric amplifier pumped by a high-power slab laser with approximate uniform rectangular distribution. By optimizing the overlapping, spectrum matching, and pulse synchronization for the pump and signal lasers, output power of 110.8 W at 1678 nm with corresponding conversion efficiency of 32.3% was achieved in addition to sufficient usage of the effective area in MgO doped periodically poled lithium niobate crystal. It could also provide a designable and tunable wavelength of the amplified laser in a wide infrared region.

Parity-time anti-symmetric parametric amplifier.

We describe the process of parametric amplification in a directional coupler of quadratically nonlinear and lossy waveguides, which belongs to a class of optical systems with spatial parity-time (PT) symmetry in the linear regime. We identify a distinct spectral PT anti-symmetry associated with optical parametric interaction, and show that pump-controlled symmetry breaking can facilitate spectrally selective mode amplification in analogy with PT lasers. We also establish a connection between the breaking of spectral and spatial mode symmetries, revealing the potential to implement unconventional regimes of spatial light switching through ultrafast control of PT breaking by pump pulses.

Characterization of in-situ terahertz detection by optical interaction in a periodically poled stoichiometric lithium tantalate nonlinear crystal

Terahertz waves are generated using a femtosecond laser pulse in a periodically poled stoichiometric lithium tantalate crystal and simultaneously detected via a non-collinear optical parametric interaction inside the same crystal. Real time up-conversion signal between the generated THz and an optic probe pulses is measured depending on the beam overlapped conditions using a general silicon-photodiode for the THz detection. The non-collinear geometry is to facilitate manipulated property of the position-dependent bandwidth at narrow and broad bandwidths of 45 GHz and 3.3 THz, respectively at the one crystal. Furthermore, an aperture effect at the detection part is characterized as the function of size and position owing to the spatial distribution of the frequency conversion signal and it is applied in optimization of the in-situ detection scheme.

Canonical transformations and multipartite coupled parametric processes

A general approach is considered to find wave function and density operator evolution of the systems including the arbitrary number of coupled optical parametric interactions described by the quadratic Hamiltonian. This approach is based on the time-dependent canonical transformations that define the evolution of the system in the Heisenberg picture or in the interaction picture. An application is illustrated with four-frequency entangled light fields, which can be produced at the nonlinear optical interactions in vapors and solid states. The process includes one non-degenerate parametric down-conversion followed by two parametric up-conversions occurring in the field of the same classical pumping wave.

평판 도파로에서의 체렌코프 펌프 형태에 의한 광 매개증폭

평판 도파로에서 pump가 체렌코프 복사(Cerenkov radiation)의 파동인 경우, pump, signal, 그리고 idler 사이의 매개적 상호작용에 의한 signal의 증폭현상을 해석하였다. 결합모드 이론을 사용하여 pump의 고갈(depletion)을 무시할 수 있는 경우, 수치적 계산으로 쉽게 풀 수 있는 1차 결합모드 미분방정식을 유도하였다. 이 미분방정식의 근사해와 수치적 계산 예를 통해서 signal이 매개적으로 증폭될 수 있음을 보였다. We have analyzed the amplification of a signal wave in the optical parametric interactions of the pump, signal, and idler waves in planar waveguides, with the pump wave being Cerenkov radiation. Based on the coupled-mode theory, we have derived the first-order coupled-mode differential equations for no pump depletion. The equations can easily be solved numerically. The approximate analytical and numerical solutions of the equations show that the signal wave can be amplified parametrically.

Classification of angular quasi-phase matching loci in periodically poled uniaxial crystals

We performed an exhaustive determination and classification of all the possible angular quasi-phase matching (AQPM) directions of three-wave nonlinear optical parametric interactions in periodically poled uniaxial crystals. We report 74 classes of AQPM loci depending on the wavelength dispersion of the principal refractive indices, the period of inversion of the sign of the second-order electric susceptibility, and on the eight possible combinations of polarization of the three interacting waves. Their complete classification is summarized in a schematic table providing the topological understanding of AQPM. The cases of second harmonic and difference-frequency generations in 5%MgO:PPLN are detailed.

A diffractive study of optical parametric interactions in nonlinear photonic crystals

We report a general description of quasi-phase-matched parametric process in nonlinear photonic crystals (NLPC) by extending the conventional X-ray diffraction theory in solids. Under the virtual wave approximation, phase-matching resonance is equivalent to the diffraction of the scattered virtual wave. Hence a modified NLPC Ewald construction can be built up, which illustrates the nature of the accident for the diffraction of the virtual wave in NLPC and further reveals the complete set of diffractions of the virtual wave for both of the air-dielectric and dielectric-dielectric contacts. We show the two basic linear sequences, the anti-stacking and para-stacking linear sequences, in one-dimension (1D) NLPC and present a general rule for multiple phase-matching resonances in 1D NLPC. The parameters affecting the NLPC structure factor are investigated, which indicate that not only the Ewald construction but also the relative NLPC atom size together determine whether a diffraction of the virtual wave can occur in 2D NLPC. The results also show that 1D NLPC is a better choice than 2D NLPC for a single parametric process.

Substantial gain enhancement for optical parametric amplification and oscillation in two-dimensional χ^(2) nonlinear photonic crystals

We have analyzed optical parametric interaction in a 2D NPC. While in general the nonlinear coefficient is small compared to a 1D NPC, we show that at numerous orientations a multitude of reciprocal vectors contribute additively to enhance the gain in optical parametric amplification and oscillation in a 2D patterned crystal. In particular, we have derived the effective nonlinear coefficients for common-signal amplification and common-idler amplification for a tetragonal inverted domain pattern. We show that in the specific case of signal amplification with QPM by both G(10) and G(11), symmetry of the crystal results in coupled interaction with the corresponding signal amplification by G(10) and G(1,-1). As a consequence, this coupled utilization of all three reciprocal vectors leads to a substantial increase in parametric gain. Using PPLN we demonstrate numerically that a gain that comes close to that of a 1D QPM crystal could be realized in a 2D NPC with an inverted tetragonal domain pattern. This special mechanism produces two pairs of identical signal and idler beams propagating in mirror-imaged forward directions. In conjunction with this gain enhancement and multiple beams output we predict that there is a large pulling effect on the output wavelength due to dynamic signal build-up in the intrinsic noncollinear geometry of a 2D NPC OPO.

Triple-photon generation: comparison between theory and experiment

We conceived an optical generator leading to the production of 3×1013 triple photons per pulse with a full-width duration of 88ps at 1/e2, by using a third-order optical parametric interaction phase-matched in a KTP crystal and pumped at 532 nm. The triple photon generation is stimulated by two photons orthogonally polarized emitted by a homemade optical parametric oscillator emitting at 1665 nm. The energy generated at 1474 nm is well modelized by an analytical model based on Jacobi elliptic functions. These results open the way to new quantum measurement relative to Greenberger-Horne-Zeilinger state of light.

Widely phase-matched tunable difference-frequency generation in periodically poled LiNbO3 crystal

We report on the development of a laser source in the mid-infrared spectral region based on difference-frequency generation (DFG) in a periodically poled LiNbO3 (PPLN) crystal. Continuously tunable coherent radiation from 2.75 to 4.78μm was produced by optical parametric interaction between a diode-pumped monolithic continuous-wave (CW) Nd:YAG laser operating at 1.064μm and a CW Ti:Sapphire laser tunable from 767 to 871nm. Temperature-dependent quasi-phase-matched DFG wavelength acceptance bandwidth was studied and characterized. An empiric formula is given to estimate the phase-matched wavelength acceptance bandwidth as a function of the crystal temperature at Λ=22.5μm. A large frequency scan of 128cm−1 (about 78cm−1 above 1μW) near 4.2μm was achieved. The whole absorption spectrum of the P and R branches of the ν3 band of atmospheric carbon dioxide has been recorded with a single phase-matched frequency scan.

Ultrashort Gaussian pulse-width expansion and shape deformation induced by group velocity dispersion

Pulse-width expansion and pulse-shape deformation of an ultrashort Gaussian pulse induced by both low and high order group velocity dispersion were theoretically analyzed in terms of energy conservation and coupled equations for three wave radiations. As an example, the optical parametric interaction processes in a negative uniaxial crystal of CsLiB6O10 with 50 fs of ultrashort Gaussian pulse were simulated. The results indicate that the degree of the pulse expansion induced by low and high order group velocity dispersion is determined by both the wavelength of the incident wave and the crystal length. A pulse could be expanded to 1.41 times its initial value as a crystal length equals the dispersion length and further heavily expanded with decreasing wave-length and increasing crystal length. The pulse expansion induced by high order group velocity dispersion using an incident wavelength of 213 nm is 1.6 times that when using 532 nm in a 50 fs pulse width without chirp modulation, and the symmetry deformation and the frequency pushing phenomena of the ultrashort pulse shape are also found.

Coupling of reciprocal vectors and corresponding degeneracy effect in a dual-periodic optical superlattice

A dual-periodic structure for quasi-phase matching cascaded optical parametric interactions is proposed. Due to the coupling of reciprocal vectors between the original and imposed periodic sequence, the reciprocal vectors and the corresponding effective nonlinear coefficients is no longer the simple combination of two periodic structures. The new analytical expression of the effective nonlinear coefficients is deduced and given. The degeneracy phenomena and the novel extinction rule resulting from the coupling of reciprocal vectors are found and investigated. The corresponding physical nature is also discussed.

OPTICAL PARAMETRIC INTERACTIONS IN DISTRIBUTED MAGNETO-OPTICAL BRAGG GRATINGS

We analyze optical parametric interactions in nonlinear magneto-optical media simultaneously possessing a second-order nonlinearity and a spatial modulation of its linear optical properties. An analytic solution for the conversion efficiency of energy transfer from an optical pump to a signal wave is presented, and we discuss the possibility of tunability that is added to the parametric process.

A general solution for the dynamics of a generalized non-degenerate optical parametric down-conversion interaction by virtue of the Lewis–Riesenfeld invariant theory

The dynamics of a generalized non-degenerate optical parametric down-conversion interaction whose Hamiltonian includes an arbitrary time-dependent driving part and a two-mode coupled part is studied by adopting the Lewis–Riesenfeld invariant theory. The closed formulae for the evolution of the quantum states and the evolution operators of the system are obtained. It is shown that various generalized squeezed states arise naturally in the process, and the two-mode squeezed effect is independent of the driving part. An explicitly analytical solution of the Schrodinger equation is further derived as the classical generalized force acting on each mode and the coupling of the two modes both have harmonic time dependences. This solution is found to be in agreement with previous research in special cases.

Specific properties of cubic optical parametric interactions compared to quadratic interactions

This paper is devoted to the phase matching and parametric gain properties of the ${\ensuremath{\chi}}^{(3)}$ mixing, and points out several specific behaviors whenever compared to ${\ensuremath{\chi}}^{(2)}$ interactions. For a given pulsation ${\ensuremath{\omega}}_{4}$ and a fixed direction of propagation, phase matching simultaneously exists for numerous sets $({\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2},{\ensuremath{\omega}}_{3}).$ Two combinations of the interacting pulsations exist: ${\ensuremath{\omega}}_{4}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}+{\ensuremath{\omega}}_{3}$ and ${\ensuremath{\omega}}_{4}+{\ensuremath{\omega}}_{1}={\ensuremath{\omega}}_{2}+{\ensuremath{\omega}}_{3},$ both with ${\ensuremath{\omega}}_{4}>{\ensuremath{\omega}}_{1},{\ensuremath{\omega}}_{2},{\ensuremath{\omega}}_{3}.$ The second scheme has no equivalent among the three-wave processes; in this scheme, phase matching exists for all configurations of polarizations. It is then possible to make use of the largest elements of the ${\ensuremath{\chi}}^{(3)}$ tensor. Furthermore, in noncentrosymmetric crystals, solutions exist where nonzero ${\ensuremath{\chi}}^{(3)}$ nonlinear effective coefficient is associated with a zero ${\ensuremath{\chi}}^{(2)}$ nonlinear effective coefficient. Concerning the gain of ${\ensuremath{\chi}}^{(3)}$ parametric amplification, the conversion efficiency is analytically calculated for the most general case: it is nonzero only if at least three fields are incident on the crystal. The calculated gain allows us to deduce the oscillation threshold of a ${\ensuremath{\chi}}^{(3)}$ optical parametric oscillator and the effect of the pulse duration: the threshold is not independent of the parametric fluorescence field, so that it can only be calculated analytically for an injection-seeded optical parametric oscillator.