Structural and optical properties of waveguides in YbVO4 crystals formed by 3.0 MeV Cu-ions implantation

We report on the structural and optical characterization of waveguides formed in YbVO₄ crystals by Cu²⁺-ion implantation with an energy of 3.0 MeV and doses of 3.0×10¹⁴-1.0×10¹⁵ ions/cm². The damage properties are determined by RBS/Channeling measurements with the help of simulation code RUMP. The m-line method is used to characterize the dark-mode spectroscopy in the planar waveguides. According to the reconstructed refractive index profile of the waveguide cross section, a numerical simulation is carried out to investigate the confinement of the light in the waveguides based on the beam propagation method.     

Reconstruction of extraordinary refractive index profiles of optical planar waveguides with single or double modes fabricated by O ion implantation into lithium niobate

A method named intensity calculation method (ICM), which is based on beam propagation method (BPM) and image processing, was carried out to reconstruct the extraordinary refractive index profile (RIP) of single-mode planar waveguide in lithium niobate (LiNbO₃), which was fabricated by multi-energy megaelectron-volt (MeV) O²⁺ ion implantation. In addition, it has been proved reasonable that the alternation of extraordinary refractive index induced by ion implantation into LiNbO₃ is mainly due to the degradation of polarization and reduction of material physical density. As a result, the possible extraordinary RIP of the double-mode planar waveguide could be reconstructed using BPM according to such a hypothesis and the calculated guiding mode values. The end-fire coupling and m-line arrangements were carried out to obtain the near-field modal patterns and dark-mode spectra of waveguides, respectively.     

Nonlinear optical waveguides fabricated in Mg-doped LiNbO3 by swift heavy ion irradiation: anomalous photorefractive damage behavior

Using swift heavy fluorine ion irradiation, we have successfully fabricated optical waveguides in Mg-doped LiNbO₃ substrates. A systematic characterization of these structures has been carried out including refractive index profiles, propagation losses, nonlinear coefficients, and, specially, photorefractive optical damage. Step-like refractive index profiles with Δn _e ≈ 0.1 and Δn _o ≈ 0.2, propagation losses lower than 0.5 dB/cm and high nonlinear optical coefficients similar to those of the substrate have been obtained. Unexpectedly, the photorefractive damage is only moderately reduced with regard to the one presented in congruent LiNbO₃ waveguides. Specifically, light intensity damage thresholds I _th are only a factor 2 higher at RT and a factor 4 at 90 °C with regard to undoped waveguides. At this latter temperature, a remarkably high I _th = 30.000 W/cm² is reached. A final discussion on the observed anomalous optical damage behavior induced by swift heavy ion irradiation is also included.     

Optical channel waveguides with trapezoidal-shaped cross sections in KTiOPO4 crystal fabricated by ion implantation

Optical channel waveguides were fabricated in KTiOPO₄ crystal by He⁺-ion implantation using photoresist masks with wedged-shaped cross sections. Semi-closed barrier walls with reduced refractive indices inside the crystal constructed the enclosed regions to be channel waveguides with trapezoidal-shaped cross sections. The m-line as well as end-fire coupling arrangements were performed to characterize the waveguides with light at wavelength of 632.8 nm. The propagation loss of the channel waveguides was determined to be as low as ∼2 dB/cm after simple post-irradiation thermal annealing treatment in air.     

Accuracy of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities

A rigorous truncation error analysis of three-point finite difference approximations for optical waveguides with step-wise refractive index discontinuities is given. As the basis for the analysis we use the exact coefficients of the series that expresses the field value at a given finite difference node in terms of the field value and its derivatives at a neighbouring node. This series is applied to develop a rigorous formalism for the truncation error analysis of the three-point finite difference approximations used in the numerical modelling of light propagation in optical waveguides with step-wise discontinuities of the refractive index profile. The results show that the approximations reach O(h²) truncation error only asymptotically for sufficiently small values of the mesh size.     

Analysis of electrooptically induced waveguides in strontium barium niobate and optical modulators

An electrooptically induced optical waveguide can be formed by applying a DC voltage between electrodes fabricated on the surface of a crystal with strong electrooptic coefficients (for example, strontium barium niobate). Calculations of the refractive index profile and the optical mode size for such waveguides are presented. Approximate solutions for the fundamental mode are used to analyse the power coupling between a single-mode step-profile fibre and these waveguides. The power transmission losses in the straight and S-shaped waveguides are estimated by using a finite-difference beam propagation method (FD-BPM). The calculations predict that a new kind of modulator/switch can be realized with the induced waveguides. The important characteristics of these devices are discussed and compared with LiNbO₃ optical waveguide modulators.     

Fabrication of embedded waveguides in lithium-niobate crystals by radiation damage

Irradiation of lithium-niobate crystals (LiNbO₃) with fast, high-energy ³He ions changes the refractive index in the interaction region where the ions speed through the material. Thus an inhomogeneous flux density profile can be used for a tailored modification of the optical properties of LiNbO₃ crystals, without employing ion implantation. A new method to fabricate embedded, polarization sensitive channel waveguides in LiNbO₃ utilizing accelerated ³He ions with an energy of 40 MeV is demonstrated. PACS 78.20; 42.82     

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.     

The optical properties of planar waveguides in LiB3O5 crystals formed by Cu implantation

A planar optical waveguide has been formed in a LiB₃O₅ crystal using 6.0 MeV Cu⁺-ions with a dose of 1 × 10¹⁵ ions/cm² at room temperature. Possible propagating modes were measured at a wavelength of 633 nm using the prism-coupling method. The refractive index profiles of the waveguide were reconstructed by an effective refractive index method and the beam propagation method was used to investigate the properties of the propagation modes in the formed waveguide. The results suggest that the fundamental TE₀ and TM₀ modes may be well-confined and propagate a longer distance inside the waveguide. The implantation process was also simulated using the transport of ions in matter code (TRIM), which indicates that the nuclear energy deposition may be the main factor for the refractive index change.     

Comparison of gold and silver dispersion laws suitable for FDTD simulations

We report optical planar waveguide formation and modal characterization in β-BaB₂O₄ crystals by Cu²⁺-ion implantation at an energy of 3.0 MeV and doses of ∼ 10¹⁴ ions/cm². The prism-coupling method was used to investigate the dark-mode property at wavelengths of 633 nm and 1539 nm. The refractive-index profile of the waveguide was reconstructed by an effective refractive index method. The modal analysis indicates that the fields of TM modes can be well restricted in the guiding region, which means the formation of a non-leaky waveguide in the crystal. The results show that the β-BaB₂O₄ waveguides may be used in the application of high efficiency frequency conversion. PACS 61.80.Jh; 42.70.Mp; 42.65.Wi     

Buried channel waveguides in neodymium-doped KGd(WO4)2 fabricated by low-repetition-rate femtosecond laser writing

Symmetric buried waveguides were fabricated in neodymium-doped KGd(WO₄)₂ by using femtosecond laser writing in the low-frequency regime. Due to stress-induced index changes in the regions surrounding the focal spot, mode guidance was demonstrated and low propagation losses of ∼0.2 dB/cm were obtained. Based on the comparison of the waveguides fabricated with different parameters, we present further significant analysis to get low-loss waveguides with symmetrical mode profiles. According to the reconstructed index profile, the mode distribution was numerically calculated by the beam propagation method, which showed a reasonable agreement with the experimental results.     

Waveguide structures written in SF57 glass with fs-laser pulses above the critical self-focusing threshold

Waveguide writing with femtosecond (fs) laser pulses in glasses is compromised by uncontrollable non-linear propagation phenomena for powers exceeding a certain threshold, P_cr, which is inversely proportional to the material linear and non-linear refractive indices, n₀ and n₂, respectively. We have studied the behaviour of a commercial glass, Schott SF57, with high values of n₀ and n₂ when it is processed above P_cr with 800 and 1260 nm, 100 fs laser pulses to produce waveguide structures. Two types of structures, longitudinal (l-) and transversal (t-) ones depending on the sample translation, were obtained. In both of them, material damage surrounded by guiding regions was generated. We attribute the formation of the guiding regions of increased refractive index to the high local pressure reached in the focal volume where catastrophic damage occurs. This pressure can be high enough to compress the material nearby thus generating regions with a permanent refractive index increase up to 5 × 10⁻⁴. The efficiency of the guiding region is conditioned by the pulse energy. Mode profile analyses reveal double-sided exponential guided modes in the l-waveguides. As an alternative route to obtain suitable mode shapes and, simultaneously, to increase the coupling efficiency, the use of multiple structures has been investigated. Various l-structures have been written close to each other generating a region of increased refractive index large enough to effectively support a Lorentzian mode at 633 nm.     

基于耦合介质纳米线的深亚波长局域波导

提出了一种基于耦合介质纳米线的深亚波长局域波导,通过两根紧邻的高折射率介质纳米线的耦合,该波导可以将光场有效束缚在纳米线之间的低折射率纳米缝隙中. 计算模拟的结果表明,该波导的有效模场面积达到Λ²₀/200,比单根纳米线波导小一个数量级,这种深亚波长的模场束缚能力可以与表面等离激元混合波导相比拟. 计算模拟的结果还表明,纳米线可能带有的低折射率氧化膜、低折射率衬底的存在、以及纳米线间尺寸存在的一定差异对于该波导结构的实际应用都不会产生很大 关键词： 介质波导 亚波长局域 表面等离激元波导 纳米线     

Secondary-ion-mass spectrometry study on near-stoichiometric LiNbO3 strip waveguide fabricated by vapour transport equilibration and Ti co-diffusion

Secondary-ion-mass spectrometry was applied to study Ti-concentration profiles in the depth direction and on the surface of near-stoichiometric (NS) Ti:LiNbO₃ strip waveguides fabricated using vapour transport equilibration (VTE) and co-diffusion of Ti-metal strips. Results show that the profile of Ti concentration along the width direction on the waveguide surface can be well fitted by a sum of two error functions, while, in the depth direction, the Ti concentration follows either a complementary error function or a generalized Gaussian function. Surface Ti concentration, 1/e width and depth, mean diffusivities along the width and depth directions of the guide are, respectively, 1.04?×?10²¹?cm^–3, 8.5?µm, 6.3?µm, 0.18 and 0.1?µm²/h. Two-dimensional refractive index profile in the NS waveguides is indirectly constructed by assuming linearity between Ti-induced index change and Ti concentration. The surface refractive index increments at 1545?nm, Δn_o and Δn_e , are evaluated to be 3.132?×?10^–3 and 1.186?×?10^–2, respectively. All of the above-mentioned diffusion and optical parameters are compared with the corresponding data of the common congruent Ti:LiNbO₃ waveguide or NS waveguide fabricated starting from a NS substrate. The rationality of the assumed linear relationship between the index change and the Ti concentration is discussed. The results show that the assumed linearity remains controversial, and all expressions and data with regard to the refractive index are the approximate results and need to be verified by direct measurement on refractive index.     

Property study of Si + -ion-implanted Nd:YVO 4 waveguides

Planar waveguides were formed in Nd:YVO₄ crystals by 3.0-MeV Si⁺-ion implantation at doses of 1×10¹³–1.5×10¹⁵ ions/cm² at room temperature. The effective refractive indices of the waveguide propagation modes were measured by using a prism-coupling method. It was found that the number of the propagation modes is dependent on the doses for the waveguides in Nd:YVO₄. The atom displacement in the near-surface region (about 2 μm beneath the surface) of the Nd:YVO₄ crystal induced by the implantation was simulated by using the TRIM 98 (transport and range of ions in matter) code. The possible reasons for the waveguide formation are discussed in a primary way. Received: 17 July 2002 / Revised version: 20 September 2002 / Published online: 11 December 2002 RID="*" ID="*"Corresponding author. Fax: +86-531-8565167, E-mail: drfchen@sdu.edu.cn     

Fabrication and characterization of double-diffused waveguides

An experimental study of two-step Ag⁺/Na⁺ ion exchange in BK-7 glass substrates in molten solutions consisting of AgNO₃/NaNO₃ mixtures is presented. This paper describes a method for evaluating the measured mode index spectra and the index profile of double-diffused semiburied waveguides. They are first diffused at 320°C in 2% melt and are then converted to semiburied waveguides by a second diffusion step consisting of a short-time reimmersion in a 0.25% melt.     

Liquid-core/liquid-cladding integrated silicon ARROW waveguides

The fabrication and characterization of a liquid-core/liquid-cladding integrated antiresonant reflecting optical waveguide (L²-ARROW) is presented. In this waveguide, the light is confined vertically by the ARROW mechanism, whereas the lateral confinement is obtained by using liquid-core/liquid-cladding (L² waveguides) with different refractive indexes. This approach permits to realize L² waveguides with very low refractive index core (n ≈ 1.333) and represents a new solution to solve the difficulty to reduce the optical losses in 2D-ARROWs due to the TM polarization in lateral direction. The device has been fabricated with standard silicon technology. The results show that the optical properties can be tuned by changing the type and the flow velocity of the core and the cladding liquids.     

Optical waveguide with homogeneous refractive index profile in LiNbO3 by double-low-energy Oxygen ion implantation

We report on the formation of the planar waveguide by 550 keV O ion followed by 250 keV O ion implantation in lithium niobate (LiNbO₃), at fluences of 6 × 10¹⁴ ions/cm² and 3 × 10¹⁴ ions/cm², respectively. The Rutherford backscattering/channeling spectra have shown the atomic displacements in the damage region before and after annealing. A broad and nearly homogeneous damage layer has been formed by double-energy ion implantation after annealing. Both the dark mode spectra and the data of refractive index profile verified that the extraordinary refractive index was enhanced in the ion implanted region of LiNbO₃. A homogeneous near-field intensity profile was obtained by double-low-energy ion implantation. There is a reasonable agreement between the simulated modal intensity profile and the experimental data. The estimated propagation loss is about 0.5 dB/cm.     

Femtosecond laser embedded grating micromachining of flexible PDMS plates

We report on the femtosecond laser micromachining of photo-induced embedded diffraction grating in flexible Poly (Dimethly Siloxane) (PDMS) plates using a high-intensity femtosecond (130 fs) Ti: sapphire laser (λ_p = 800 nm). The refractive index modifications with diameters ranging from 2 μm to 5 μm were photo-induced after the irradiation with peak intensities of more than 1 × 10¹¹ W/cm². The graded refractive index profile was fabricated to be a symmetric around from the center of the point at which femtosecond laser was focused. The maximum refractive index change (Δn) was estimated to be 2 × 10⁻³. By the X-Y-Z scanning of sample, the embedded diffraction grating in PDMS plate was fabricated successfully using a femtosecond laser.