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.     

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.     

Second-mode cutoff in rectangular-core couplers using the Fourier decomposition method

By transforming the infinitex-y plane onto the unit square and using two-dimensional Fourier series expansions, the modal fields and propagation constants of dielectric waveguides can be accurately determined within the scalar (weak-guidance) regime. In particular, the method gives cutoffV-values directly. By applying the technique to symmetric and asymmetric rectangular-core couplers, the second-mode cutoffV-value is determined numerically as a function of both the centre-to-centre core separation and the core aspect ratios. Approximate analytical expressions are derived from the exact numerical data which give the cutoff values to within 2.5%.     

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.     

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.     

Sensor properties of planar waveguide structures with grating couplers

The paper presents the results of theoretical analysis as well as the results of experimental research involving planar sensor structures with input grating couplers of the period Λ = 800 nm. In the theoretical part of the paper we discussed the influence of the parameters of a sensor structure on it sensitivities. The experimental part of the work presents the results of experimental research involving the influence of refractive index of the cover on the coupling characteristics of sensor structures with grating couplers. The full widths at half maximum (FWHM) were from 0.023° to 0.029°. For the investigated structures we estimated detection thresholds for the changes of refractive index of the cover and the changes of sensitive film thickness. It has been demonstrated that by the application of the elaborated structures we can detect minimal changes of the refractive index (Δn_c)_min = 2.1×10⁻⁶ when the refractive index of the cover n_c = 1.333 and (Δn_c)_min = 1.0×10⁻⁶ when n_c = 1515. For sensitive films of the thickness w < 100 nm, by using the elaborated structures, we can detect mean changes of the thickness along the values lower than 10⁻³ nm.     

Spectral properties of asymmetrical optical directional couplers with periodic structures

A comparison is made of co- and contradirectional couplers with periodic structures, with a view to their suitability as WDM devices for integrated optical systems. Expressions are obtained for the spectral response within the framework of a coupled-mode theory. It is shown that the competition between direct Bragg, Bragg-exchange and codirectional coupling in the contradirectional coupler leads to shifting and constriction of the stop bands. Calculations are made for a codirectional coupler with a new type of meander structure and for the contradirectional coupler.     

All-optical limiting using nonlinear directional couplers composed of a self-focusing and a self-defocusing waveguide

We numerically demonstrate the all-optical limiting features in a mismatched nonlinear directional coupler (NLDC) composed of a self-focusing and a self-defocusing waveguide for both continuous wave and pulse cases. The working conditions required are analyzed. To obtain the limiting feature, the propagation constant of the self-focusing waveguide should not be larger than that of the self-defocusing waveguide. Cascaded asymmetric NLDCs are investigated to improve the limiting characteristics. The limiting threshold and the limiting output power can be adjusted by varying the coupler length or the ratio of the nonlinearity coefficients of the self-defocusing and self-focusing waveguides. Analytical solutions are presented in the case of a continuous wave. For the pulse case, numerical solutions show that the top part of the output pulse, if it exceeds the limiting threshold, will be tailored, while the rising and falling edges of the output pulse are almost the same as the input pulse. There is almost no pulse breakup. The influence of the second order dispersion and the intermodal dispersion on the limiting characteristics are analyzed. PACS 42.79.Gn; 42.79.Ta     

Optical sensing by silicon slot-based directional couplers

A theoretical investigation of an optical liquid sensor, based on asymmetric directional coupler employing slot optical waveguides, is carried out. The sensing principle is based on the shift in the waveguide transmitted spectrum induced by analyte refractive index change. Silicon-on-insulator technology has been assumed in sensor design, and sensor modelling is carried out by using the coupled modes theory and the finite element method. The influence of geometrical parameters on the sensor characteristics has been investigated. A minimum detectable refractive index change of the order of 10^?6 can be theoretically predicted.     

Optimal design of coupling waveguide structure for adiabatic optical directional full couplers weighted by sin-square and raised-cosine functions

The optimal design of coupling waveguide structure for adiabatic optical directional full couplers (AODFC) based on weighted sin-square function (SSF) and raised-cosine function (RCF) are investigated in this paper. The coupling lengths with a crosstalk smaller than −30 dB at the operating wavelength of 1.57 μm resulted in a value of 3.0 and 2.4 mm for the SSF and RCF cases, respectively. Under the same level of crosstalk, the wavelength ranges obtained by weighted SSF and RCF could be varied about 1.33-1.70 μm and 1.27-1.70 μm with coupler lengths of 6.0 and 5.5 mm, respectively. Clearly, the AODFC weighted by RCF has the superior performances of both short coupling length and broad wavelength ranges.     

Phase sensitivity of directional couplers

Directional couplers of various design have been treated widely, both theoretically and experimentally. However, in most cases directional couplers are designed as 1 to 2 port circuits. If both input ports are used, the phase of the guided waves has to be taken into account. The influence of the phase term on the switching behaviour of Δβ-reversal couplers is discussed as an example. It is shown that the phase difference of two waves coupled to both coupler input ports will not affect crossover and straight-through states, but all states in between. Therefore electrical controlled 2 to 2 port switches will become very sensitive, if low crosstalk is required. This effect can be used to design an all optical working switch or optical logic.     

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)     

Effective index method for planar lightwave circuits containing directional couplers

A simple and intuitive effective index method for planar lightwave circuits containing directional couplers is proposed. The optimal cladding refractive index of the effective two-dimensional planar waveguide is found according to the coupling length of the directional coupler involved. Numerical examples indicate that this proposed effective index method gives accurate results while saving significant computation time in simulation and design of planar lightwave circuits containing directional couplers.     

Crosstalks of two-waveguide and three-waveguide directional couplers

Crosstalks of two-waveguide and three-waveguide directional couplers are analyzed mathematically based on the relationship between the coupled mode and the normal mode. Numerical techniques such as the finite-difference method and the beam propagation method are employed to confirm the validity of the derived expressions. The calculation results show that two-waveguide directional coupler is superior to any type of three-waveguide couplers from the practical viewpoint of the crosstalk and the coupling length.     

Analysis of directional emission in square resonator lasers with an output waveguide

Square microcavity laser with an output waveguide is proposed and analyzed by the finite-difference time-domain (FDTD) technique. For a square resonator with refractive index of 3.2, side length of 4 μm, and output waveguide of 0.4-μm width, we have got the quality factors (Q factors) of 6.7 × 102 and 7.3 × 103 for the fundamental and first-order transverse magnetic (TM) mode near the wavelength of 1.5 μm, respectively. The simulated intensity distribution for the first-order TM mode shows that the coupling efficiency in the waveguide reaches 53%. The numerical simulation shows that the first-order transverse modes have fairly high Q factor and high coupling efficiency to the output waveguide. Therefore the square resonator with an output waveguide is a promising candidate to realize single-mode directional emission microcavity lasers.     

Numerical simulation of quantum directional couplers

 A numerical analysis of a quantum directional coupler based on Π-shaped electron waveguides is presented with use of the scattering-matrix method. After the optimization of the device parameters, uniform output for the two output ports and high directivity are obtained within a wide range of the electron momenta. The electron transfer in the device is found more efficient than that in the previously proposed structures. The study of the shape-dependence of transmission for the device shows that the device structure with smooth boundaries exhibits a much better performance. Received: 4 July 1996/Accepted: 9 September 1996     

Radiation properties of ICRF waveguide couplers

The radiation spectra of a dielectric-filled waveguide (DWG) and a folded waveguide (FWG) antenna in the ion cyclotron range of frequencies are evaluated for tokamaks with the waveguide codes, which model the coupling of the waveguide modes to the plasma waves with outward radiating boundary conditions. The codes provide a self-consistent calculation of the fields across the waveguide apertures for various antenna phasings taking into account a complete set of waveguide eigenmodes including the reflected modes and, in the case of DWG, an arbitrary orientation of the antenna to the plasma magnetic field. In the studied cases, the spectra are found to be well described by a model which is based on a simplified wave field pattern determined by the antenna aperture geometry. Comparison to the corresponding loop antenna is carried out