Quasi-phase-matched grating characterization using minimum-phase functions

Measurement of the second-harmonic power generated by a quasi-phase-matched (QPM) grating as a function of the frequency detuning parameter yields the Fourier transform (FT) magnitude of the complex nonlinear coefficient profile along the QPM device. This FT magnitude can be measured by tuning either the wavelength of the fundamental laser beam or the temperature of the QPM grating. However, the measured magnitude of the FT cannot be unambiguously inverted without the FT phase to uniquely recover the complex nonlinear coefficient profile of the QPM grating. As we demonstrate in this work, this ambiguity can be completely eliminated by placing a stronger and thinner nonlinear sample against the input or output of the QPM device of interest and measuring the detuning curve of this composite structure. By construction, the nonlinear profile of this assembly has a sharp peak due to the thinner sample, followed by the weaker, broader profile of the QPM grating, which essentially constitutes a minimum-phase function. Therefore, its FT phase can be calculated uniquely from its measured FT magnitude, for example by applying to the FT amplitude the logarithmic Hilbert transform or an iterative error-reduction algorithm. This processing then enables the full recovery of the complex nonlinear coefficient profile of the QPM device from its measured detuning curve. In this paper, we demonstrate with numerical examples that this powerful new technique can accurately recover the period, envelope, and chirp parameters of any QPM grating.     

Theoretical Study on Intra-Cavity Distributed-Bragg-Reflection Quasi-Phase-Matched Second-Harmonic Lasers

The characteristics of intra-cavity distributed Bragg reflector (DBR) quasi-phase-matched (IDQPM) second-harmonic-generation (SHG) lasers are theoretically studied. In the IDQPM-SHG laser, a QPM device and a DBR for feedback are separately fabricated on the same substrate with the QPM device placed between the DBR and a semiconductor laser. The threshold current of the IDQPM-SHG laser depends on the coupling efficiency between the laser diode and the QPM waveguide and the reflectivity of the DBR. The SH output of the IDQPM-SHG laser is strongly dependent on the generalized SHG conversion efficiency, x. This laser has the potential to attain an SH output over a 30-mW using a currently available 50-mW semiconductor laser for the fundamental light source, when highly efficient QPM device (x=2.2 W⁻¹) is used. Its tolerance for various deviations from the initial design and the problems to develop a commercially available IDQPM-SHG laser are also discussed.     

Waveguide second-harmonic generation device with broadened flat quasi-phase-matching response by use of a grating structure with located phase shifts

We report on a theoretical analysis and experiments for bandwidth broadening in quasi-phase-matched (QPM) second-harmonic generation (SHG).We used phase-shifted segments of a periodic grating to obtain a spectrally broadened, nearly flat response simultaneously with high conversion efficiency. We used an x-cut MgO:LiNbO(3) QPM waveguide in our analysis and experiments. The spectral range of the 850-nm fundamental for which SHG conversion exceeded 0.95 of the maximum value broadened from 0.02 to 0.12 nm when a 1-cm-long grating was divided into three segments with optimum phase shift. SHG conversion efficiency was 300%/W for this waveguide. The SHG efficiency and phase-matching characteristics showed good agreement with theoretical results.     

Laser-induced,second-order optical susceptibilities of YAB:Cr3+ single crystals

Complex temperature studies of optically stimulated second harmonic generation (SHG) at 1064?nm for pulsed 10?ns Nd:YAG laser radiation under illumination of two coherent laser beams (at 1064?nm and its 532?nm second harmonic) were carried out by means of the Maker fringe method. The bicolour coherent process allowed detection of some additionally induced non-centrosymmetry. The effect was studied at different temperatures and experimental geometries in YAB:Cr³⁺ single crystals. We found that Cr³⁺ ions play a principal role in the observed effects. The output of optically stimulated SHG was generally non-spherical in the sequence profile, contrary to the traditional non-stimulated SHG. Moreover, we also established that the optimal conditions for obtaining SHG corresponded to the fundamental/writing beam intensities ratio 6:1. A specially performed control of the photo-thermal sample heating showed that the increase of temperature did not exceed 1.2?K, which allowed the influence of photo-thermal heating to be neglected. The optimal input–output laser geometry corresponded to s-p polarisation and to the angle of about 32° between the photo-inducing and fundamental beams. Additionally in the studied temperature range (77–295?K) there was observed an enhancement of the output second-order susceptibilities from 0.72?pm/V up to 1.02?pm/V.     

Efficiency pedestal in quasi-phase-matching devices with random duty-cycle errors

It is shown that random duty-cycle errors in quasi-phase-matching (QPM) nonlinear optical devices enhance the efficiency of processes far from the QPM peak. An analytical theory is shown to agree well with numerical solutions of second-harmonic generation (SHG) in disordered QPM gratings. The measured efficiency of 1550?nm band SHG in a periodically poled lithium niobate (PPLN) waveguide away from the QPM peak agrees with observations of domain disorder in a PPLN wafer by Zygo interferometry. If suppression of parasitic nonlinear interactions is important in a specific application of QPM devices, control of random duty-cycle errors is critical.     

Study of quasi-phase matching wavelength acceptance bandwidth for periodically poled LiNbO3 crystal-based difference-frequency generation

The temperature tuning characteristics of quasi-phase matching (QPM) wavelength acceptance bandwidth in a uniform periodically poled lithium niobate (PPLN) based on difference-frequency generation (DFG) are studied theoretically and experimentally. This paper proposes a PPLN device consisting of several segments of different temperatures to obtain a more desirable performance for the QPM-DFG. The result shows that through the tuning of temperature, the bandwidth can be changed considerably and the method was proved suitable and accurate to calculate QPM wavelength acceptance bandwidth of DFG in a uniform PPLN crystal for temperatures between room temperature and 180 °C and mid-infrared (mid-IR) wavelengths ranging from 2.8 to 4.8 μm.     

Magnetic properties of TmxDy1−xFeO3 single crystals

The magnetic behaviour of Tm_xDy_1?xFeO₃ (x = 0.3; 0.5; 0.7; 1.0) single crystals in the temperature range 90-4.2° K were investigated. The transition from the weak ferromagnetic to antiferromagnetic state was observed at about 9° K for Tm_0.3Dy_0.7FeO₃ single crystal. The reorientation of weak ferromagnetic moment from c- to a-axis was observed for Tm_0.7Dy_0.3FeO₃ single crystal at 35–65° K. The magnetic structure change of iron and rare-earth ions took place when external magnetic field was applied. The thulium and disprosium ion interaction does not essentially influence on the single crystal magnetic properties of the substituted compounds in a low temperature range.     

Widely tunable mid-IR difference-frequency generation based on fiber lasers

A wide tuning technique for mid-IR difference-frequency generation (DFG) with uniform grating periodically poled LiNbO(3) (PPLN) is presented. Based on the dispersion property of the PPLN, the quasi-phase matching (QPM) band for the pump can evolve to two separate bands, and the spacing between them can be increased with the decrease of the crystal temperature. Two such separate QPM bands can be used for increasing the idler tuning range when the crystal temperature is set to adapt the pump tuning. With the technique, an idler tuning range of 690nm is experimentally achieved with fiber laser fundamental lights.     

Microwave power absorbed by and scattered from a multilayered zero-index anisotropic metamaterial-semiconductor cylinder

We present here dependencies of scattered and absorbed powers of incident perpendicularly and parallel polarized microwaves by a multilayered cylinder. We consider here the normal (angle ??=90^°) and oblique (angles ??=60^°,30^°,5^°) incidence of microwave on the cylinder. The one consists of a glass core that is coated by the six anisotropic metamaterial and lossy n-Si semiconductor alternative layers. Characteristics of a cylinder with the semiconductor external layer are presented. The dispersion dependency of n-Si losses was taken into account. The metamaterial is a uniaxial anisotropic medium with the electric and magnetic plasma resonances in the frequency range from 1 until 4?GHz. The anisotropic metamaterial can include the constitutive parameters equal to zero. The multilayered cylinder has the external radius equal to 2?mm. The glass core has a radius equal to 0.5?mm. The thickness of all layers is the same. We have compared the scattered and absorbed power dependencies on the microwave polarization, the angle of microwave incidence (the normal and oblique directions of the incidence to the z-axis), and the n-Si specific resistivity. We discovered specific dependencies of scattered and absorbed powers on the parameters.     

Optical investigation of HoFeO3

The absorption spectra of HoFeO₃ were investigated in the near infrared spectral region at temperatures of 1.2, 4.2, 20 and 77 °K respectively. At every temperatureT≦20 °K all the absorption lines show the same splitting which is attributed to the groundstate; this splitting is (7.2±0.5) cm^?1 at 20 °K and decreases to (4.9±0.8) cm^?1 extrapolated to 0 °K. From these splittings the holmium-iron and the holmiumholmium interactions can be deduced. Measurements with an external magnetic field yield a magnetic moment ofμ=(7.6±0.7)μ _B per holmium ion. The moments are directed at angles of ?28° and ?152° with respect to theb-axis.     

Tolerance and tuning properties of the optical parametric processes using periodically poled RbTiOAsO4

The maximal tolerance parameters of poling period and phase-matching, temperature in second harmonic generation (SHG) using periodically poled RbTiOAsO₄(PPRTA) as a function of the fundamental wavelength are investigated theoretically. The tolerance of the poling period ΔΛ of PPRTA is found larger than that of PPLN and PPKTP when the fundamental wavelength is beyond 2 μm, which reaches its maximum ΔΛ_max for PPRTA at a fundamental wavelength of 2.7433 μm. However, the tolerance for the phase-matching temperature ΔT of PPRTA is found smaller than that of PPLN and PPKTP with an exception that PPRTA has a larger tolerance of the temperature or a larger temperature phase-matching bandwidth at fundamental wavelength of 2.2474 μm, where the maximum of ΔT(ΔT_max) is obtained. Furthermore, the tuning characteristics of the optical parametric processes using PPRTA for collinear quasi-phase-matching (CQPM) is analyzed. The combination of temperature tuning and poling period tuning enables a quasi-continuous wavelength tuning range of 1493.2-1593.7 nm for the signal and 3201.8-3699.2 nm for the idler, where poling period of 39 μm, 39.5 μm and 40 μm and a temperature between 20 and 120° have been employed in the corresponding theoretical analysis.     

Theoretical and experimental investigations of the Mid-IR DFG tuning property based on fiber laser fundamental lights

The tuning properties for the mid-IR DFG laser based on uniform grating PPLN have been investigated with tunable YDFL and EDFL fundamental lights. Our results show that, for a fixed crystal temperature, the idler tunable range is less than 10 nm when the EDFL is tuned. Although the pump may be allowed to be tuned in its two QPM acceptance bands, the idler tunable range is still narrow for a fixed temperature. By optimizing the crystal temperature, however, the two pump QPM acceptance bands may be overlapped to form one broadband QPM band, which may be used to increase the idler tunable range to 175 nm near 3.4 μm region. The positions of the single signal and the two separate pump QPM acceptance bands can be continuously moved by adjusting the temperature, which may also be used for enhancing the idler tuning range. By tuning the EDFL while adjusting the temperature, a whole combined idler tuning range between 2.98 and 3.78 μm was experimentally obtained with three fixed pump wavelengths of 1.05, 1.08 and 1.11 μm. By tuning the YDFL in the two separate QPM acceptance bands, a tuning range of 690 nm has been demonstrated with only one fixed signal wavelength of 1.58 μm.     

Second-harmonic generation in periodically poled nonlinear polymer waveguides

We demonstrate quasi-phase-matched (QPM) second-harmonic generation (SHG) at the optical communication wavelengths with side-chain polymer waveguides. A ridge waveguide structure is designed to support fundamental mode guiding at both the pump and the second harmonics, leading to a high field overlap integral of the guided modes. The nonlinearity contrast in the +/0 type QPM waveguide is maximized under a QPM poling electrode width of nearly half the coherence length. Using these configurations, we record a normalized SHG efficiency of 2.2% W(-1) cm(-2) in the polymer waveguide.     

Vector method for studying the second-harmonic-generation light derived from complex periodic ferroelectric domains

In this Letter, in order to overcome the disadvantages of controlling the second-harmonic-generation (SHG) light derived from the traditional one-dimensional (1D) periodic ferroelectric domains we propose a kind of so-called complex periodic ferroelectric structure (CPFS), which unit cell is composed of even layers of positive and negative domains arranged alternatively following aperiodic sequence. It is found that comparing with the traditional periodic structure, CPFS cannot offer more reciprocal vector compensations for the mismatching phase, but CPFS may provide larger effective nonlinear coefficients (ENCs) in high-order quasi-phase-matching (QPM) and possesses advantages of the amplitude modulation for SHG peaks. In this Letter we study CPFS by use of vector method (VM), where the contribution to ENC for each domain or each unit cell will be treated as a vector and the QPM condition for CPFS and the modulation effect of aperiodic unit cells have been obtained. Without any Fourier transformation VM treats the grating function in real space and will be very convenient and intuitive. Both VM and CPFS would possess potential applications in the field of SHG investigations.     

Nonlinear frequency conversion in 2D χ (2) photonic crystals and novel nonlinear double-circle construction

The analytic solution to the wave equation for small-signal sum-frequency process is derived in 2D χ ⁽²⁾ photonic crystals with use of the Green function method. It is predicted that the sum-frequency electrical field at quasi-phase matching (QPM) resonance is proportional to the angle-dependent effective crystal length. This implies that multiple wavelength QPM frequency conversion with controllable intensity output can be realized in a single 2D χ ⁽²⁾ photonic crystal. It is revealed that efficient frequency conversion requires both the QPM and the proper structure matching. A novel double-circle construction, different from the conventional Ewald construction, is presented to reflect important QPM processes. It is also shown that the QPM resonance tuning of second-harmonic generation can operate over the whole transparent wavelength range of crystals. Received 19 April 2001     

Second-harmonic generation with a high-index-clad waveguide

Theoretical and experimental analyses of second-harmonic generation (SHG) with a high-index-clad waveguide are reported. It was found that confinement of the propagation modes and the overlap between the fields of fundamental and second-harmonic waves could be increased in this waveguide. This structure was achieved in an x-cut MgO:LiNbO (3) quasi-phase-matched (QPM) waveguide by use of Nb(2)O(5) as a cladding layer. With the QPM SHG device, harmonic blue light of 5.5 mW at the 434-nm wavelength was generated with a normalized conversion efficiency of 1200%/W cm(2).     

Channelingeffekte bei der Lichtausbeute von Anthrazen-, Naphthalin- undp-Terphenylkristallen bei Anregung mit α-Teilchen

The scintillation light yield of anthracene atT=300 °K andT=80 °K and of naphthalene andp-terphenyl atT=80 °K was investigated for impact directions in the (a, c)-plane. The light yield was measured for welldefined integration times. The relative depth of the channeling-minimum observed for impact directions parallel to thec-axis of anthracene is found to increase with increasing integration times. For the first time channeling-minima of the light yield were observed at impact directions parallel to thec- and the [102]-axis of naphthalene and thec- and [¯102]-axis ofp-terphenyl. The [¯102]-axis ofp-terphenyl shows a more pronounced effect than thec-axis.     

Widely tunable difference frequency generation around 3.4 μm using index dispersion property of PPLN

In this paper, the wide difference frequency generation (DFG) tuning characteristics around 3.4 μm are investigated by using the index dispersion property of PPLN. With a ytterbium doped fiber laser (YDFL) and an erbium doped fiber laser (EDFL) as the fundamental light sources, our simulation results show that the quasi-phase matching (QPM) wavelength acceptance bandwidth (BW) for the pump is much larger than that for the signal. Although the positions of the broadened QPM pump bands vary with the poling period and the signal wavelength, the corresponding idler tuning ranges center around 3.4 μm. With a signal wavelength of 1.57 μm, an idler tuning range of greater than 170 nm is experimentally obtained in the 30 uniform grating PPLN. When the signal wavelength and the poling period are respectively changed to 1.55 and 29.50 μm, wide DFG tuning operations around 3.4 μm are also achieved with the crystal temperature adjusted to adapt the change.     

Intracavity second-harmonic generation of 1.06 μm in GdCa4O(BO3)3 crystals

The characteristics of intracavity second-harmonic generation (SHG) at 1.06 μm in GdCa₄O(BO₃)₃ (GdCOB) crystals cut for different type I phase-matching (PM) directions of (θ,φ)=(66.8°, 132.3°); (19.4°, 0°); (90°, 46°) have been investigated. It was found that the intracavity SHG was significantly efficient in the PM direction of (66.8°, 132.3°), and that the intrinsic lower effective nonlinear coefficient (d_eff) was responsible for the less-efficient SHG in the other two directions. A maximum CW SHG output power of 2.81 W was obtained with an optical conversion efficiency of 18.7%, while the corresponding effective intracavity SHG efficiency was determined to be 41.3%. The intracavity SHG efficiency of GdCOB has been found to reach two-thirds of that obtained with type II phase-matching KTiOPO₄ (KTP). Received: 26 April 2000 / Revised version: 3 July 2000 / Published online: 5 October 2000     

Structures responsible for quasisynchronism in second-harmonic generation in BaTiO3:Fe

Second harmonic generation (SHG) of light in iron-doped BaTiO₃ crystals occurs primarily at an angle of about 7° to incident λ=1.06 μm radiation. It is shown that the quasisynchronism is accounted for by a 90° domain structure with a spatial wave vector q∥[011] and a spatial period of about 3 μm. This result may serve as a basis for interpretation of the anomalous SHG enhancement near the phase transition. Fiz. Tverd. Tela (St. Petersburg) 41, 1076–1079 (June 1999)