Order Nonlinear Coefficient Research Articles

Second order nonlinear properties of monoclinic single crystal BaTeMo2O9

The second order nonlinear optical properties of BaTeMo2O9 were studied by means of Maker fringe technology and the phase matching method. The value and relative sign of the second order nonlinear optical coefficients were obtained, with the largest being d31 = 9.88 pm/V. At 1064 nm, the crystal can support noncritical phase-matching, and the effective nonlinear coefficient is 10.3 pm/V for phase matching II at (90°, 62.8°) in the x0y plane. The relation between the second order nonlinear properties and the crystal structure is also discussed. All the results show that BaTeMo2O9 is a good candidate for nonlinear optical applications.

Electronic states and the resonant optical non-linearity of exciton in a narrow band InSb quantum dot

Binding energy, interband emission energy and the non-linear optical properties of exciton in an InSb/InGa x Sb 1− x quantum dot are computed as functions of dot radius and the Ga content. Optical properties are obtained using the compact density matrix approach. The dependence of non-linear optical processes on the dot sizes is investigated for different Ga concentrations. The linear, third order non-linear optical absorption coefficients, susceptibility values and the refractive index changes of the exciton are calculated for different concentrations of gallium content. It is found that gallium concentration has great influence on the optical properties of InSb/InGa x Sb 1− x dots.

Accurate determination of second order nonlinear optical coefficients from powder crystal monolayers

An accurate procedure for the determination of second harmonic generation (SHG) efficiency from powder crystal monolayers is proposed. The method is based on the analysis of the dependence of the SHG output on the powder particle size. Unlike with conventional powder methods, the amount of material required is very small, and the scattering of the primary beam by the powder particles is negligible, allowing for an accurate analysis of the collected data. The experimental results demonstrate that the proposed method can provide reliable values for the nonlinear optical coefficients, particularly in the case of phase-matchable uniaxial materials, for which simple analytical expressions can be derived.

BROADBAND TERAHERTZ WAVE GENERATION, DETECTION AND COHERENT CONTROL USING TERAHERTZ GAS PHOTONICS

Terahertz (THz) gas photonics uses gas as THz emitter and sensor for time-domain spectroscopy. Unique properties of the gas promise scalable, strong THz wave generation with broad spectral range covering the entire THz gas (0.3 THz to 35 THz). The systematic study of THz wave generation and detection in different gases shows that the generation efficiency is monotonically decreasing with the ionization potential of the gas molecules while the detection efficiency is linearly proportional to the third order nonlinear coefficient of the gas molecules. We also discuss the development of THz wave detection using laser-induced fluorescence and coherent control with THz gas photonics.

Design, synthesis, growth and characterization of 4-methoxy-4′-dimethylamino-benzylidene aniline (MDMABA): A novel third order nonlinear optical material

Synthesis, growth, X-ray crystal structure and characterization of a novel third order nonlinear optical material, 4-methoxy-4′-dimethylamino-benzylidene aniline (MDMABA), are reported for the first time. The asymmetric unit of MDMABA compound contains two crystallographically independent molecules (A and B), and they exist in the E-configuration. The structural perfection of the grown crystal is analyzed by high-resolution X-ray diffraction rocking curve analysis. The functional groups present in MDMABA are investigated by FTIR and FT-Raman spectral analyses. The placement of the protons is determined using HNMR spectrum. The range and percentage of optical transmission were ascertained by recording UV–vis–NIR spectrum. Thermal and mechanical properties are reported. Dielectric study shows that the dielectric constant of the crystal varies with frequency and temperature. The third order nonlinear optical absorption coefficient of the MDMABA crystal is determined by the Z-scan technique.

Design of transmission line driven slot waveguide Mach-Zehnder interferometers and application to analog optical links

Slot waveguides allow joint confinement of the driving electrical radio frequency field and of the optical waveguide mode in a narrow slot, allowing for highly efficient polymer based interferometers. We show that the optical confinement can be simply explained by a perturbation theoretical approach taking into account the continuity of the electric displacement field. We design phase matched transmission lines and show that their impedance and RF losses can be modeled by an equivalent circuit and linked to slot waveguide properties by a simple set of equations, thus allowing optimization of the device without iterative simulations. We optimize the interferometers for analog optical links and predict record performance metrics (V(pi) = 200 mV @ 10 GHz in push-pull configuration) assuming a modest second order nonlinear coefficient (r(33) = 50 pm/V) and slot width (100 nm). Using high performance optical polymers (r(33) = 150 pm/V), noise figures of state of the art analog optical links can be matched while reducing optical power levels by approximately 30 times. With required optical laser power levels predicted at 50 mW, this could be a game changing improvement by bringing high performance optical analog link power requirements in the reach of laser diodes. A modified transmitter architecture allows shot noise limited performance, while reducing power levels in the slot waveguides and enhancing reliability.

Second harmonic generation in SiO 2 sol–gel films functionalized with Ethyl-[4-(4-nitro-phenylazo)-phenyl]-(2-oxiranylmethoxy-ethyl)-amine (ENPMA) molecules

High concentrations of Ethyl-[4-(4-nitro-phenylazo)-phenyl]-(2-oxiranylmethoxy-ethyl)-amine (ENPMA) chromophores were linked covalently to two different kinds of SiO 2 matrices prepared by the sol–gel method. The matrices differed in their reticulation level, determined by the organometallic precursor used during the synthesis. The materials were deposited as films by spin-coating. The chromophores in the films were oriented in a non-centrosymmetric way by a modified Corona poling set-up, and the nonresonant second order non-linear optical coefficient d 33(0) of the films was determined by means of the Maker fringe technique. It was found that there is an optimum concentration of chromophores for attaining the highest d 33(0) value in these materials. Their maximum d 33(0) value was found in the films with the least reticulated matrix, that value was equal to 5.2 ± 0.5 pm/V. Besides, the d 33(0) value was more stable in time in the less reticulated materials.

Enhancement of chaotic carrier bandwidth in a semiconductor laser transmitter using self-phase modulation in an optical fiber external round cavity

A novel method to enhance the bandwidth of a chaotic carrier from a delayed feedback semiconductor laser transmitter is presented using self-phase modulation (SPM) in an optical fiber external round cavity. A physical model of the laser dynamics is established under the condition of optical feedback light with the SPM effect in the fiber path. A formula for frequency detuning of the optical dual-feedback under SPM is theoretically deduced. The results show that the nonlinear phase shift caused by SPM has an impact on the gain and bandwidth enhancement factor of the laser. The second-order nonlinear effect of the fiber enriches the variety of the amplitudes and phases of the laser while the nonlinear phase shift produces a number of new frequencies, which can spread the bandwidth. Numerical results reveal that with the SPM effect, the bandwidth can be enhanced 4 times more than the bandwidth without it, and the relaxation oscillation frequency of the chaotic laser is increased to 2.56 times more than that of the laser without the fiber path. The enhancement of the chaotic bandwidth can be extended by increasing the optical fiber length, the coupling-feedback ratio, the mirror reflectance and the second order nonlinear coefficient affect.

Bandwidth enhancement of a chaotic semiconductor laser transmitter by cross-phase modulation

A novel method of bandwidth enhancement of a chaotic carrier from a semiconductor laser transmitter is studied by cross-phase modulation (XPM). And a physical model of laser dynamics is presented under the condition of XPM effect of optical fiber path. A frequency detuning formula with optical dual-feedback and XPM effect is deduced. The nonlinear phase shift arisen from XPM effect impacts on the gain and bandwidth enhancement factor of the laser. The second order nonlinear effect of the fiber enriches the varieties in the amplitude and the phase of the laser while the nonlinear phase shift produces a lot of new frequencies, which spread the bandwidth. Numerical results reveal that, with XPM effect, the new bandwidth is the quadruple of the bandwidth without XPM effect, and the relaxation oscillation frequency of the chaotic laser is increased to 285 times that of the laser without XPM effect. It is found that the enhancement of the chaotic bandwidth depends evidently on the optical fiber length, the power input into the optical fiber, the mirror reflectance and the second order nonlinear coefficient.

Nonlinear optical properties of a two-dimensional elliptic quantum dot

The linear and third order nonlinear optical absorption coefficient and refractive index changes of an elliptic quantum dot have been investigated, using the compact-density matrix formalism and an iterative method. In this regard, the effect of optical intensity, size and geometry of the dot on the optical absorption coefficient and refractive index changes are investigated. It is found that, not only the light intensity but also the size and the geometry of the dot have a great influence on the optical absorption coefficient and refractive index changes of the system.

Ultrafast Switching Time and Third Order Nonlinear Coefficients of Microwave Treated Single Walled Carbon Nanotube Suspensions

Microwave treated water soluble and amide functionalized single walled carbon nanotubes have been investigated using femtosecond degenerate pump-probe and nonlinear transmission experiments. The time resolved differential transmission using 75 femtosecond pulse with the central wavelength of 790 nm shows a bi-exponential ultrafast photo-bleaching with time constants of 160 fs (130 fs) and 920 fs (300 fs) for water soluble (amide functionalized) nanotubes. Open and closed aperture z-scans show saturation absorption and positive (negative) nonlinear refraction for water soluble (amide functionalized) nanotubes. Two photon absorption coefficient, beta0 approximately 250 cm/GW (650 cm/GW) and nonlinear index, gamma approximately 15 cm2/pW (-30 cm2/pW) are obtained from the theoretical fit in the saturation limit to the data for two types of nanotubes.

Determination of third order elastic constants in a complex solid applying coda wave interferometry

In this letter we describe the development of coda wave interferometry to determine acoustoelastically derived third order nonlinear coefficients of a highly complex material, concrete. Concrete, a structurally heterogeneous and volumetrically mechanically damaged material, is an example of a class of materials that exhibit strong multiple scattering as well as significant elastic nonlinear response. We show that intense scattering can be applied to robustly determine velocity changes at progressively increasing applied stress using coda wave interferometry, and thereby extract nonlinear coefficients.

Effects of main chains on the second order nonlinear optical susceptibility of poled poly(dipropargyloxybenzoates) containing 2-[4-(2-chloro-4-nitrophenylazo)- N-ethyl-phenylamino]ethanol ( Disperse Red 13)

A series of isomeric polymers containing hexa-2,4-diynylene-1,6-dioxybenzoate group as the main chain and a polar azo dye ( Disperse Red 13) as in the side chain were synthesized, and their second order nonlinear optical responses were studied. The second order nonlinear coefficients, d 33 were found to be in the range of 50–90 pm/V. The nonlinear response ( d 33) with respect to the positions of main chain was found to be in the order; 3,5-( meta) > 3,4-( ortho) > 2,5- ( para) > 2,4-( meta), but the order of values d 33/ d 31 was 3,5-( meta) > 2,4-( meta) > 2,5- ( para) > 3,4 ( ortho). The higher response of the 3,5-polymer may be attributed to the symmetric substitution on the benzene ring, permitting the main chain conformation with less flexibility, as well as a higher Tg.

Nonlinear responses and optical limiting behavior of fast green FCF dye under a low power CW He–Ne laser irradiation

The nonlinear responses and optical limiting performance of a dye type acid, called fast green FCF, are investigated under irradiation of 35mW continuous wave He–Ne Laser. The second order refractive index and nonlinear absorption coefficient are measured by use of z-Scan technique. The optical limiting behavior is investigated by transmission measurement through the sample. Linear absorption coefficient (α), nonlinear absorption coefficient (β) and second order refractive index (n2) of fast green FCF are measured at different concentrations.

Blue second harmonic generation from aluminum nitride films deposited onto silicon by sputtering technique

We studied the second order optical nonlinearity of aluminum nitride films grown by sputtering onto silicon substrates. The crystalline properties of the films were investigated by x-ray diffraction measurements. Preliminary linear optical characterization of the films was carried out by spectrophotometric optical reflectance measurements at different incidence angles; thus the dispersion laws for both ordinary and extraordinary refractive indices were retrieved. Finally, second harmonic generation measurements in reflection mode were performed at a fixed angle from a fundamental beam provided by a picosecond Ti:sapphire laser system at λ=800nm. In the experiments a high blue light conversion efficiency was found for samples 1.5 and 2μm thick, and the second order nonlinear coefficient d33=11±1pm∕V was found.

Second harmonic generation of a new nonlinear optical material: urea L-malic acid

Second harmonic generation (SHG) of a new organic optical crystal-urea L-malic acid (ULMA) was studied. A comparison of SHG efficiency of ULMA and KDP at a fundamental wavelength of 1064 nm using the Kurtz powder method demonstrated that the second order nonlinear coefficient of ULMA is 1.57 times of that of KDP, and the damage threshold of ULMA is relatively higher. Finally, both Type I and Type II phase match angles of the biaxial crystal ULMA were calculated.

Chirp Control of an Electroabsorption Modulator to be used for Regeneration and Wavelength Conversion at 40 Gbit/s in All-Optical Networking

Chirp control to produce low or negative values of chirp at the output of an electroabsorption modulator (EAM) is an important mechanism for reducing the signal degradation due to chromatic dispersion in high-speed transmission over standard single-mode fibre. An analytical model for the chirp performance of an EAM capable of optical regeneration and simultaneous wavelength conversion operating at 40 Gbit/s is derived. A chirp control approach is identified using this model by exploring the tradeoff between the α-parameter describing the chirp factor (based on the nonlinear absorption coefficients) and bias voltage requirements of an EAM. In particular, an optimum range of bias voltage is determined to ensure reduced chirp operation when a two-tone signal (i.e., comprised of bias and modulating voltages) is applied to the EAM. It is also demonstrated for large signal operation at 40 Gbit/s that the optimum range of reverse bias voltage is between 0 and 2 V to obtain low values for the chirp factor (between +1 and −2) in order to facilitate the necessary chirp control in all-optical networking. In addition, it is identified that at 40 Gbit/s higher positive values of the second- and third- order nonlinear coefficients of chirp must be avoided when operating at reverse bias voltages less than 1 V.

Nonlinear optical coefficients and phase-matching conditions in Sn<sub>2</sub>P<sub>2</sub>S<sub>6</sub>

Phase matching conditions and second and third order nonlinear optical coefficients of Sn2P2S6 crystals are reported. The coefficients for second harmonic generation (SHG) are given at lambda = 1542 nm and 1907 nm at room temperature. The largest coefficients at these wavelengths are d111 = 17+/-1.5pm/V and d111 = 12+/-1.5pm/V, respectively. The third-order subsceptibilities chi(3) 1111 = (17 +/- 6) . 10-20m2/V2 and chi(3) 2222 = (9 +/- 3) . 10-20m2/V2 were determined at lambda = 1907 nm. All measurements were performed by the Maker-Fringe technique. Based on the recently determined refractive indices, we analyze the phase-matching conditions for second harmonic generation, sum- and difference-frequency generation and parametric oscillation at room temperature. Phase-matching curves as a function of wavelength and propagation direction are given. Experimental phase-matched type I SHG at 1907 nm has been demonstrated. The results agree very well with the calculations. It is shown that phase-matched optical parametrical oscillation is possible in the whole transparency range up to 8 microm with an effective nonlinear coefficient deff approximately 4pm/V.

Effects of Li + and Nb 5+ cationic sites on macroscopic properties of lithium niobate crystals

A comprehensive study on the role of Li + and Nb 5+ sites in a lithium niobate (LiNbO 3) crystallographic frame using Pauling's rules, Abrahams' empirical model, the bond valence sum model and chemical bond method, is briefly summarized in the present paper. Some physical properties of LiNbO 3 crystals such as calculated dielectric responses (including refractive indices and second order nonlinear optical coefficients), experimental ferroelectric Curie temperature T c, and calculated spontaneous polarization P s, are discussed in this connection. Our results clearly show that Li + site can produce much stronger effects on these physical properties than Nb 5+ site, which is helpful to the further development of various properties of LiNbO 3 crystals.

Wavelength dependence of the third order non‐linear coefficient in hydrothermally grown ZnO crystals

In this work, the dispersion of the third order nonlinear coefficients χ3xxxx and χ3zzzz of ZnO single crystals is determined. For this purpose, the third harmonic generation (THG) technique is employed. Tunable laser source has been used for the fundamental beam, spanning the optical range between 1.05 and 1.5 microns so that the generated third harmonic signal is made to cover a range (from 500 nm up to 350 nm) which encompasses both the transparency and the one photon absorption region above the fundamental bandgap. The determined data in the transparency region (with the THG signal at 500 nm) are 2.2x10−12 esu for both coefficients. These values are about significantly larger than previously reported ones. In the high absorption range the exciton contribution to the dispersion of the nonlinear coefficients is evidenced. For the first time the dispersion of χ3xxxx and χ3zzzz is studied in ZnO single crystals. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)