Theory of nonlinear directional couplers

A method is proposed for obtaining exact analytical solutions for the system of nonlinear equations for the propagation of electromagnetic waves in directional couplers with an arbitrary nonlinearity in the propagation constant. The resulting solutions can be used to determine the operating characteristics of nonlinear directional couplers. Zh. Tekh. Fiz. 69, 69–71 (August 1999)     

Semiconductor waveguide directional couplers for coherent receivers

Optical waveguide 3-dB couplers integrated on semicondutors have been studied, designed and fabricated, using both bulk and diluted multi-quantum-well InGaAsP/InP-based materials, grown by MOCVD. The device structure is based on the two-mode interference (TMI) principle and is fully compatible for integration with the optoelectronic and electronic components of a coherent receiver. Bulk material couplers provide an output balanced within 0.05 dB per nanometer and an excess loss of 1.4 dB, compared to a straight guide, while coupling loss to a tapered-lensed single mode fibre is 4 dB.Improved coupling efficiency to single-mode fibres is achieved by use of moderately diluted multi-quantum-well waveguides, which include InGaAsP wells and InP barriers: coupling loss to a tapered-lensed single-mode fibre as low as 0.5 dB and excess loss of 1.8 dB are featured. Couplers fabricated with this waveguide structure have a balance sensitivity of 0.03 to 0.04 dB per nanometer.A moderately diluted multi-quantum-well 3-dB coupler has been permanently pigtailed and butt-coupled to a dual balanced PIN photoreceiver. This hybrid assembly was tested in a coherent transmission system at 155 and 622 Mbits^-1 showing sensitivities, for 10^-9 BER, of about-38.0 dBm and-28.8 dBm, respectively.     

Improved directional couplers for overmoded waveguide systems

The performance of multihole directional couplers can be considerably improved by placing a second hole structure to the existing one. The improvement may be aimed at directivity or at suppression of certain unwanted modes propagating either in forward or backward direction.     

Nonlinear frequency conversion in waveguide directional couplers

Nonlinear optical effects for frequency conversion require a phase-matching condition to efficiently generate a coherent field at the new wavelength. We find that the phase-matching condition can be replaced by a resonance condition when the nonlinear effect takes place in a waveguide directional coupler. We apply this theory to second-harmonic generation and find a theoretical conversion efficiency of 100%, equivalent to the perfect phase-matching condition. An example of the design of such waveguide directional coupler is presented.     

All-optical logic gates using semiconductor-based three-coupled waveguides nonlinear directional coupler

All-optical logic gates with nonlinear optical (NLO) properties of three-coupled identical waveguides have been proposed and designed theoretically in a unique semiconductor-based symmetric structure. The model uses the NLO interactions of the coupled waveguides, like Kerr effect and Two Photon Absorption (TPA). Unlike the previous studies, we take into account higher order NLO effects of semiconductors such as Free Carriers (FC) and loss to control the switching operation. These NLO phenomena lead to high functionality in a simple unique structure. Therefore, in this work, by setting the input intensity of the waveguides, the logic AND, OR, NAND, and NOR gates are designed in a unique structure with different lengths. Our analysis deals with continuous waves (CW) region and the results are valid for the ranges of short optical pulses with time duration longer than FC life time.     

Mode selective directional couplers for overmoded waveguide systems

Two types of directional couplers for transverse electric (TE) modes are described: short and multihole couplers, respectively. They selectively pick one mode out of a mode mixture in an overmoded circular waveguide system. Unwanted modes are either statistically kept at low level or are suppressed by destructive interference in the coupling waveguide. Mode selectivity and directivity in multihole couplers oscillate up and down with an increasing number of holes, finally reaching a minimum of approximately 20 dB, unless there are competing modes with rational fractions of the beat wavelength. A multihole coupler for the TE₀₂ mode (28 GHz, 63.4 mm waveguide diameter, 41 holes) and a length of 1.6 m shows a calculated directivity of 68 dB and suppresses the unwanted modes TE₀₁ with 34 dB (24 dB), TE₂₂ with 37 dB (45 dB), and further modes TE_m (<5, m<6) with 17 dB to 34 dB in forward direction (figures in parentheses are for unwanted modes propagating in backward direction).A short directional coupler for the TE₀₁ mode (28 GHz, 63.4 mm waveguide diameter) with 16 holes and a length of 230 mm shows a directivity of 55 to 100 dB between 27.9 and 28.1 GHz, suppressing the TE₀₂ mode with 35 to 80 dB, the TE₀₃ mode with 30 to 65 dB, and the TE₂₂ mode with 30 to 70 dB.     

Theoretical and experimental research on nonradiative dielectric waveguide directional couplers

A practical design of nonradiative dielectric (NRD) waveguide directional couplers is presented. The dispersion characteristics of coupled NRD-guides and the scattering coefficients of NRD-guide directional couplers are studied as well as the transitions from metal rectangular wave-guide to NRD-guide couplers. Experiments of 3-dB and 10-dB NRD-guide couplers in ka-band show that the couplers are of good performance and promise in millimeter-wave integrated circuits.     

All-optical switching in quadratically nonlinear waveguide arrays

We demonstrate a scheme for efficient switching and routing of low-power signals in waveguide arrays with second-order nonlinearity. With control beams the signal can be switched to different output positions and can be simultaneously converted to another wavelength with low cross talk.     

All-optical flip-flop by nonlinear coupling of microring and waveguide

Careful studies of coupling show that transmittance power between microring and waveguide is dependant to field intensity. Also more researches show that optical multistable behavior of microring had been affected by nonlinear power coupling efficiency in high field intensities. Operation of microring in nonlinear regions can be so useful in designing all optical switches and control techniques. In this paper has been proposed an all-optical flip-flop based on nonlinear treatment of microring.     

Photonic crystal waveguide directional couplers as wavelength selective optical filters

Waveguide directional couplers, formed by two closely spaced linear defect waveguides in a two-dimensional photonic crystal of air holes in a semiconductor matrix, are numerically studied using plane wave expansion and finite difference time domain methods. The coupling lengths are on a wavelength scale and show a strong wavelength dependence, allowing for the design of compact wavelength selective optical filters. Applications as a channel interleaver for the 1.55 μm wavelength range and as a micrometer sized 1.31/1.55 μm wavelength demultiplexer are presented.     

Analysis of rectangular-core waveguide structures and directional couplers by an iterated moment method

Using an iterated moment method (weighted index method), formulae are derived for the accurate calculation of the dispersion characteristics and field distributions of guided modes in strip dielectric waveguides and strip-loaded waveguides, and for the calculation of the coupling length of rectangular-core dual-channel directional couplers. The formulae are simple and the results obtained by the present analysis agree well with computer-aided exact numerical analysis. This method can be readily extended to the analysis of other dielectric waveguide structures.     

Split-step time-domain analysis of optical waveguide devices composed of a directional coupler and gratings

An extended split-step time-domain model for composite coupling structures is reported. Time-dependent coupled-wave equations are solved by splitting of the operators for phase accumulation, forward directional coupling, and reverse Bragg reflection. Through an analysis of an add-drop filter based on a grating-written directional-coupler structure, the proposed modeling method is shown to be an order of magnitude more efficient than the previous methods.     

All-optical switching of solitons in an active nonlinear directional coupler

A numerical study of the all-optical switching properties of an active nonlinear directional coupler is presented. The switching power is reduced for both CW and soliton inputs because of the gain. The switching properties of the coupler are enhanced for solitons, which switch nearly completely. For ultrashort pulses, the effects of the bandwidth of the gain medium are considered by using a general form for the gain band. The gain spectrum of erbium is also considered as a specific example.     

Modeling of racetrack-resonator add-drop filters with arbitrary nonlinear directional couplers

In this Letter we employ the general coupled-mode equations of the nonlinear directional coupler and demonstrate that the switching characteristics of prototypical nonlinear racetrack-resonator structures may differ considerably from those obtained when the standard, generally incorrect, coupled-mode equations are used.     

Conntinuous wave and pulse propagation in three-core fibre nonlinear directional couplers

A numerical study of continuous-wave and pulse propagation in three-core fibre nonlinear directional couplers is presented. Intensity dependent demultiplexing is illustrated; in particular, novel nonlinear behaviour where a very small change in peak input intensity alters the core from which a pulse emerges.     

Theory of self-focusing in a hollow waveguide

We present a theoretical investigation of self-focusing in a hollow waveguide filled with noble gas. Our analysis was performed for a laser pulse that was predominantly in the fundamental mode and revealed the physical processes involved in self-focusing in a hollow waveguide. A critical power for self-focusing was obtained that was found to be substantially higher than the critical power for self-focusing in a bulk medium. Useful design criteria for pulse-compression systems are presented. We identify the parameter range for which the transverse variation of the pulse phase introduced by the Kerr nonlinearity is small.     

All-optical flip-flop composed of a single nonlinear passive microring coupled to two straight waveguides

Microrings can have different hysteresis characteristics at their different resonance frequencies. They can be used as a multi-hysteresis optical component. In this paper an optical D-flip-flop circuit composed of a single nonlinear passive microring coupled to two straight waveguide based on the Kerr effect is proposed. The proposed circuit can operate as an optical digital circuit which synchronizes input DATA with the CLOCK of the circuit. A simple analytical model for hysteresis design and the transient analysis of the proposed D-flip-flop are presented. According to our model, the switching time of the flip-flop is in the order of 10 ps.     

Electro-optically tunable self-focusing and self-defocusing in KTP crystals by a cascaded second-order process

We report the transformation of a linear electro-optically tunable non-phase-matched second-order nonlinear process into a cascaded second-order nonlinear process in a bulk KTP crystal to generate the effect of electrooptically tunable Kerr-type nonlinearity. By applying an electric field on the x–y plane, parallel to the z-axis of the crystal, phase mismatch is created, which introduces a nonlinear phase shift between the launched and reconverted fundamental waves from the generated second harmonic wave. Due to the nonuniform radial intensity distribution of a Gaussian beam, a curvature will be introduced into the fundamental wavefront, which focuses or defocuses the incident beam while propagating through the crystal.     

Determination and stability analysis of the supermodes in nonlinear directional couplers through a variational approach

The even and the odd supermodes of nonlinear directional couplers are determined by means of a variational approach; both slab and channel nonlinear couplers are considered. The validity of the solutions given by the analytical method and their stability properties are analysed through numerical integration of the governing equations. It is shown that channel nonlinear directional couplers improve the stability of the eigenmodes.     

Effects of third-order dispersion on soliton switching in fiber nonlinear directional couplers

The split-step Fourier method is used to study the energy switching characteristics of fiber nonlinear directional couplers with the third-order dispersion. The effects of the third-order dispersion increases with the third-order dispersion coefficient and input power and result in pulse shift and energy decreases. Adding high-order nonlinear can partly overcomes these effects.