Dependence of output power in modulated optical fiber ring resonator on nonlinear refractive index

Nonlinear dynamics in optical fiber ring resonators (OFRRs) can be applied to the estimation of the nonlinear refractive index of optical fibers. The output power of the OFRR becomes convergent, periodic, and chaotic with an increase in the input power. In this study, the dependence of the output power on the nonlinear refractive index is analyzed numerically. The critical input power at which the convergent state changes to the periodic state decreases smaller as the nonlinear refractive index increases. In addition, the maximum oscillation width of the output power decreases monotonically with the nonlinear refractive index. These dependences are sensitive to the parameters of the OFRR. The estimation of the nonlinear refractive index can be realized effectively using the maximum or minimum critical input power, and the maximum oscillation width of the output power even under a subtle fluctuation in the optical fiber ring length.     

Thermal nonlinear refraction properties of Ag2S semiconductor nanocrystals with its application as a low power optical limiter

In this work, nonlinear refraction properties of 3 nm sized silver sulfide (Ag₂S) semiconductor nanocrystals dispersed in the dimethyl sulfoxide with varying concentrations are reported. Observation of the colloids far-field diffraction ring patterns indicates of large induced thermal nonlinear refraction in the medium. The thermally induced effective nonlinear refractive index due to nonlocal heat effect is characterized by Z-scan technique with a low power CW laser irradiation at 532 nm. This allows us to measure thermo-optic coefficient and effective nonlinear refractive index up to −1.52 × 10⁻⁷ cm²/W in the tested samples. Low power optical limiting, with low limiting thresholds is obtained in the samples based on thermal defocusing and self diffraction. The limiting thresholds of colloids at different Ag₂S nanocrystals concentrations are also reported.     

Nonlinear Refractive Index of Er3+-Doped Fiber and Its Application to Nonlinear Fiber Coupler

A large change in the refractive index originating in the transition absorption of erbium ions is induced in an Er³⁺-doped fiber. It is shown that the Er³⁺-doped fiber exhibits the nonlinear refractive index of n₂=7.4 × 10⁻¹⁵ m²/W, which is 10⁵−10⁶ times larger than that caused by the optical Kerr effect in a usual silica fiber at the pumping, wavelength of 514.5 nm. The large nonlinear refractive index occurred in a fiber directional coupler fabricated with the Er³⁺-doped fiber optically changes the coupling condition. The coupling ratio changes up to 0.16 by increasing the pumping power up to 0.7 mW.     

Nonlinear optical properties of periodic gold nanoparticle arrays

Periodic Au nanoparticle arrays were fabricated on silica substrates using nanosphere lithography. The identical single-layer masks were prepared by self-assembly of polystyrene nanospheres with radius R = 350 nm. The structural characterization of nanosphere masks and periodic particle arrays was investigated by atomic force microscopy. The nonlinear optical properties of the Au nanoparticle arrays were determined using a single beam z-scan method at a wavelength of 532 nm with laser duration of 55 ps. The results show that periodic Au nanoparticle arrays exhibit a fast third-order nonlinear optical response with the nonlinear refractive index and nonlinear absorption coefficient being n₂ = 6.09 × 10⁻⁶ cm²/kW and β = −1.87 × 10⁻⁶ m/W, respectively.     

Phase contribution to dynamic gratings recorded in Er-doped fiber with saturable absorption

Experimental observation of phase (i.e. refractive index) component in the dynamic gratings recorded in erbium-doped optical fiber with saturation of optical absorption is reported. We utilized configuration of transient two-wave mixing with rectangular phase modulation of one of counterpropagating recording waves, where unshifted phase grating resulted in a transient energy exchange. The reported experiments were performed with heavily doped (≈5400 ppm erbium) fibers in a wide spectral range of Er³⁺ fundamental absorption at selected laser wavelengths 1492, 1526, 1549, and 1568 nm. Relative contribution of phase grating was especially large (up to ≈100% of the maximal amplitude component) at the opposite sides of the investigated spectral range and was significantly lower in its central part. The amplitude grating was found especially strong at short wavelength side of the spectrum (i.e. at 1492 nm), where the grating amplitude proved to be only two times lower than the theoretically predicted from consideration of two-level model.     

Synthesis and investigation of nonlinear optical properties of semiconductor ZnS nanoparticles

ZnS nanoparticles were prepared by a simple chemical method and using PVP (poly vinylpyrrolidone) as capping agent. The sample was characterized by UV-vis spectrophotometer, X-ray diffraction (XRD) and Z-scan technique. XRD pattern showed that the ZnS nanoparticles had zinc blende structure with an average size of about 2.18 nm. The value of band gap of these nanoparticles was measured to be 4.20 eV. The nonlinear optical properties of ZnS nanoparticles in aqueous solution were studied by Z-scan technique using CW He-Ne laser at 632.8 nm. The nonlinear absorption coefficient (β) was estimated to be as high as 3.2×10⁻³ cm/W and the nonlinear refractive index (n₂) was in order of 10⁻⁸ cm²/W. The sign of the nonlinear refractive index obtained negative that indicated this material exhibits self-defocusing optical nonlinearity.     

Supercontinuum generation at 1.55μm using highly nonlinear photonic crystal fiber for telecommunication and medical applications

In this paper, we present a theoretical calculation of a highly nonlinear germanium (Ge) doped photonic crystal fiber with all-normal group velocity dispersion to design a supercontinuum (SC) light source at 1.55 μm. By doping 3% higher refractive index Ge inside the host silica, the nonlinear coefficient is increased to a value as large as 60.5 W^?1 km^?1 at 1.55 μm. A 10 dB bandwidth of a 120 nm SC spectrum for a 2.5 ps input optical pulse and a 10 dB bandwidth of a 190 nm SC spectrum for a 1.0 ps input optical pulse have been found using the same fiber length of 200m and input optical power of 18 W. The coherent lengths of the generated SC light sources are found to be 8.8 μm for a 2.5 ps input optical pulse and 5.6 μm for a 1.0 ps input optical pulse. Therefore, the highest longitudinal resolution at 1.55 μm is found to be about 4.0 μm for biological tissues.     

Z-scan measurements of optical nonlinearity in acid blue 29 dye

The third order nonlinear optical properties of acid blue 29 solutions have been studied using Z-scan technique. Experiments are performed using a CW He–Ne laser at 632.8 nm wavelength and 3 mW power. The linear absorption coefficient α₀, nonlinear absorption coefficient β, nonlinear refractive index n₂, Re χ³, and Im χ³ are measured at three different concentrations. Our results show that higher concentration gives better nonlinear optical properties. Also, it was found that there is an increasing trend in the value of the nonlinear refractive index n₂ as the concentration increases.     

Investigation of third-order nonlinear optical properties of conjugated benzodioxal derivatives

An investigation of third-order nonlinear optical characterization of newly synthesized conjugated benzodioxal derivatives has been done by using nanosecond Z-scan technique at 532 nm. The molecules demonstrate self-defocusing effect with intensity dependent refractive index (n₂) of the order of 10⁻¹⁴ cm²/W. The measured molecular TPA cross-section is ranging from 2.47 ×10⁻⁴⁷ cm⁴ s/photon to 6.00 cm⁴ s/photon. Their input-output curves indicate that there is a clear optical power limiting behavior with the limiting threshold in the range 125-181 μJ. The main factor to exhibit the observed nonlinearity in these molecules is the presence of charge donor and acceptor groups. The increased conjugation length increases the nonlinear refraction and increased electron density enhances the nonlinear absorption. The molecules exhibit good nonlinear optical properties, comparable to those of regular azoaromatic compounds. Therefore, the molecules investigated here are promising candidates for optical power limiting devices.     

A simple reflection-type two-dimensional refractive index profile measurement technique for optical waveguides

We report a new configuration of a reflection-type confocal scanning optical microscope system for measuring the refractive index profile of an optical waveguide. Several improvements on the earlier design are proposed; a light emitting diode at 650 nm wavelength instead of a laser diode or He-Ne laser is used as a light source for better index precision, and a simple longitudinal linear scanning and a curve fitting techniques are adapted instead of a servo control for maintaining an optical confocal arrangement. We have obtained spatial resolution of 800 nm and an index precision of 2 × 10⁻⁴. To verify the system’s capability, the refractive index profiles of a conventional multimode fiber and a home-made four-mode fiber were examined with our proposed measurement method.     

Z-scan measurement for the nonlinear absorption and the nonlinear refraction of poly1,4-diazophenylene-bridged-tris(8-hydroxy-quinoline) aluminum (PDPAlq3)

The nonlinear optical properties of the poly1,4-diazophenylene-bridged-tris(8-hydroxy-quinoline) aluminum (PDPAlq₃) solution were studied using single beam Z-scan technique with a continuous-wave Diode laser radiation at 657.2 nm with 10 Hz repetition rate. The results show that the solution of PDPAlq₃ exhibits large nonlinear refractive index (n₂ = −1.7642 × 10⁻¹² m²/W) and nonlinear absorption coefficient (β = 1.12 × 10⁻⁶ m/W). The negative sign of the nonlinear refractive index n₂ indicates that the material exhibits self-defocusing optical nonlinearity. The evaluation of the figure of merit (W = 1.8) shows that the solution of PDPAlq₃ is sufficient for application in all-optical switching technology. These results show that the solution of PDPAlq₃ have potential application in nonlinear optics.     

Effect of concentration and particle size on nonlinearity of Au nano-fluid prepared by γ (Co) radiation

Nonlinear properties of Au nano-fluid prepared by γ-radiation method at different concentrations were investigated. Measurements of nonlinear refractive index and nonlinear absorption coefficient were carried out using a single beam Z-scan technique. A green CW laser beam operated at 532 nm was used as excitation source. The Au nano-fluid shows a good third order nonlinear response. The sign of the nonlinear refractive index is found to be negative and the magnitude is in the order of 10⁻⁷ cm²/W. This nonlinear effect increases as the concentration increases from 3.119 × 10⁻⁴ to 2.354 × 10⁻³ M which correspond to particle sizes of 4.0-30.5 nm, respectively. A good linear relationship was obtained between nonlinear refractive index and concentration. However the relationship between nonlinear refractive index and particle size was nonlinear behavior.     

Photophysical and nonlinear optical properties of zincphthalocyanines with peripheral substitutions

Photophysical and nonlinear optical properties of zinc phthalocyanines (ZnPc) bearing peripheral phenoxy substituents containing different functionalized groups were studied. Fluorescence spectra corresponding to the optical transition S₁ → S₀ are found to be appeared at 684 or 686.4 nm. Z-scan technique reveals large nonlinearities, where the absorptive and refractive effects are separately evaluated. Saturation absorption of ZnPc-1 was observed at 632.8 nm, with a very large nonlinear absorption coefficient β = −1.36 × 10⁻² cm/W. However a strong nonlinear refractive effect was found in all ZnPcs (1-4). Transmitted versus incident irradiance measurements carried out on ZnPc-1 and ZnPc-2, showed a very clear optical limiting behavior with irradiance thresholds around be 44 W/cm² and 90 W/cm² respectively.     

Determination of nonlinear coefficient and group-velocity-dispersion of bismuth-based high nonlinear optical fiber by four-wave-mixing

Nonlinear coefficient and group-velocity-dispersion of bismuth-based nonlinear fibers were determined by four-wave-mixing measurements. The wavelength dependence of refractive index of bulk bismuth-based glasses was also measured to estimate the material dispersion and waveguide dispersion. A newly developed bi-directional four-wave-mixing configuration enabled us to determine all fiber parameters simultaneously. The obtained fiber nonlinearity γ ∼ 1000 W⁻¹ km⁻¹ of bismuth-based nonlinear fiber is the highest one in the step-index fiber made of oxide glasses as expected from a high refractive index at 1550 nm. Dispersion analysis reveals that the both material dispersion and waveguide dispersion affect to the large group-velocity-dispersion of bismuth-based nonlinear fiber.     

Nonlinear refraction and photoinduced birefringence in chlorophosphonazo I doped polymer thin films

The nonlinear refraction and photoinduced birefringence of chlorophosphonazo I (CPA I ) doped PVA thin films were investigated. The single-beam Z-scan measurement showed that CPA I doped PVA thin film possessed a large value of nonlinear refractive index (n₂=1.82×10⁻¹² cm²/W) under a pulse 532 nm excitation, and the mechanism accounting for the process of nonlinear refraction was discussed in term of resonant electronic effect. Moreover, fast and stable molecular reorientation was observed when investigating the photoinduced birefringence of CPA I doped PVA thin film with a CW 532 nm laser as pump light and a CW 650 nm laser as probe light.     

Single beam Z-scan measurement of the third order optical nonlinearities of styryl7 dye

The optical nonlinearity of styryl7 dye in ethanol solution at different concentrations has been studied using pulsed Nd:YAG laser at 532 nm as the source of excitation. The optical responses were characterized by measuring the intensity dependent refractive index (n₂) of the medium using the Z-scan technique. The open aperture Z-scan trace of the dye in solution displayed saturable absorption. The closed aperture Z-scan trace of the dye exhibited a negative nonlinearity. The styryl7 dye at 1 mM concentration exhibited nonlinear refractive co-efficient n₂ = −1.24 × 10⁻⁸ cm²/W, nonlinear absorption coefficient β = − 3.9 × 10⁻⁴ cm/W and real and imaginary parts of third-order nonlinear optical susceptibility χ³ = 3.26 × 10⁻⁶ esu in ethanol. These results showed that the dye has potential application in nonlinear optics.     

Nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer

The nonlinear optical properties and photoinduced anisotropy of an azobenzene ionic liquid-crystalline polymer were investigated. The single beam Z-scan measurement showed the polymer film possessed a value of nonlinear refractive index n₂ = −1.07 × 10⁻⁹ cm²/W under a picosecond 532 nm excitation. Photoinduced anisotropy in the polymer was studied through dichroism and photoinduced birefringence. A photoinduced birefringence value Δn ∼ 10⁻² was achieved in the polymer film. The mechanism for the nonlinear optical response and the physical process of photoinduced anisotropy in the polymer were discussed.     

Full investigation of the backscattering in resonator fiber optic gyro

Resonator Fiber optic gyro (RFOG) is a high accuracy inertial rotation sensor based on the Sagnac effect. The optical fiber ring resonator (OFRR) is the key rotation sensing element. The backscattering characteristics of the OFRR are fully investigated. The Rayleigh backscattering dominates the backscattering spectrum with the input power below the threshold. High carrier suppression is crucial to reduce this Rayleigh backscattering error. Being different from the intrinsic Rayleigh scattering of the fiber, the stimulated Brillouin scattering (SBS) in the OFRR should be avoided. This is because the finesse and the resonance notch depth of the OFRR decrease for the pump depletion through the SBS process. The shot noise limited sensitivity (SLS) of the RFOG is improved by increasing the input power. Through analysis, it is found that the threshold input power is improved after phase modulation. The SLS of the RFOG is analyzed at different modulation parameters and its relevant SBS threshold. Accordingly, the optimized modulation frequency and the corresponding maximum input power are all obtained. A simple method of testing the frequency shift in the SBS is also proposed. In this method, the central frequency of the laser source is locked to the resonance frequency of the OFRR in one direction. A steady SBS light is observed and its frequency shift is measured together.     

Priority-based parameter optimization strategy for reducing the effects of four-wave mixing on WDM system

In order to meet the ultra high speed and ultra long-haul transmission distance in wavelength division multiplexing (WDM) systems, the nonlinear impairment affecting the overall spectral efficiency and system performance should be minimized. This paper proposes a strategy to mitigate the four-wave mixing (FWM) effect in WDM system. The strategy determines the effect of both single and combined effects of second, third, and fourth optimization priority parameters such as fiber length, input power, dispersion, channel spacing, and effective area on FWM power. A comparison study was made under different types of optical fiber such as single-mode fiber (SMF), dispersion shifted fiber, non-zero dispersion fiber, and non-zero dispersion shifted fiber. In addition, the system performance in term of bit-error-rate was calculated in the case of single priority (impact of effective area) and combined priority (impact of effective area, input power, fiber length and channel spacing). The results show that the FWM effect was reduced based on the transmission parameters order of optimization, i.e., priority selection proposed. Moreover, the results indicated that increasing sequentially the effective area, fiber length; channel spacing and decreasing the input power provide the most significant sequence in suppressing the effects of FWM. This priority sequence brought the suppression ratio to approximately 26.3% in SMF, which suppressed the FWM effects up to −50 dBm. In term of BER; the combined priority introduces improvement in BER of 2.31 × 10⁻²⁵ in comparison with single priority that has value of BER 4 × 10⁻¹⁴. Finally, this work suggests that the proposed priority-based parameter optimization strategy is an ideal solution for optimum performance of WDM system.     

Analysis of non-linear refractive index influences on four-wave mixing conversion efficiency in semiconductor optical amplifiers

In this paper, we have analyzed the influences of non-linear refractive index on the four-wave mixing (FWM) characteristics in semiconductor optical amplifiers (SOAs). It has been shown that the generated FWM signal characteristics can be modified due to the variation of non-linear refractive index of the SOA's medium. The wave propagation in the SOA has been modeled using the nonlinear propagation equation taking into account gain spectrum dynamics, gain saturation, which depends on carrier depletion, carrier heating, spectral hole-burning, group velocity dispersion, self-phase modulation and two photon absorption. Simulation of optical wave evolution in the SOA has been carried out using the finite-difference beam propagation method (FD-BPM) both in time and spectral domains. Our simulation results confirm that higher FWM conversion efficiency and lower time bandwidth product are achieved for higher absolute values of non-linear refractive index. Moreover, non-linear refractive index is more efficacious for high power propagated waves in SOAs. Finally, we have studied the modification of waveguide refractive index due to the propagation of optical pulses. We have also shown that when |n₂|=1 cm²/TW, refractive index variation is in the order of 10^?4 to 10^?7 for high and low power input pulses, respectively.