Nonreciprocal Phase Shift Research Articles

Non-reciprocal phase shift induced by an effective magnetic flux for light

Photons are neutral particles that do not interact directly with a magnetic field. However, recent theoretical work has shown that an effective magnetic field for photons can exist if the phase of light changes with its direction of propagation. This direction-dependent phase indicates the presence of an effective magnetic field, as shown experimentally for electrons in the Aharonov–Bohm experiment. Here, we replicate this experiment using photons. To create this effective magnetic field we construct an on-chip silicon-based Ramsey-type interferometer. This interferometer has been traditionally used to probe the phase of atomic states and here we apply it to probe the phase of photonic states. We experimentally observe an effective magnetic flux between 0 and 2π corresponding to a non-reciprocal 2π phase shift with an interferometer length of 8.35 mm and an interference-fringe extinction ratio of 2.4 dB. This non-reciprocal phase is comparable to those of common monolithically integrated magneto-optical materials.

Modeling and simulation of polarization errors in Sagnac fiber optic current sensor

Sagnac fiber optic current sensor (S-FOCS) is a kind of optical interferometer based on Sagnac structure, optical polarization states of sensing light wave in Sagnac fiber optic current sensor are limited. However, several factors induce optical polarization error, and non-ideal polarized light waves cause the interference signal crosstalk in sensor, including polarizer, quarter-wave retarder, splice angular, birefringence and so on. With these errors, linearly polarized light wave in PM fiber and circularly polarized light wave in sensing fiber become elliptically polarized light wave, then, nonreciprocal phase shift induced by magnetic field of the current is interrupted by wrong polarization state. To clarify characteristics of optical polarization error in fiber optic current sensor, we analyze the evolution process of random optical polarization state, linear optical polarization state and circular optical polarization state in Sagnac fiber optic current sensor by using Poincare sphere, then, build optical polarization error models by using Jones matrix. Based on models of polarization state in Sagnac fiber optic current sensor, we investigate the influence of several main error factors on optical polarization error characteristics theoretically, including extinction ratio in polarizer, phase delay in quarter-wave retarder, splice angular between quarter-wave retarder and polarization maintaining fiber. Finally, we simulate and quantify nonreciprocal phase shift to be detected in fiber optic current sensor related with optical polarization errors. In the end, we demonstrate S-FOCS in test. The results show that transfer matrix errors are induced by inaccurate polarization properties during polarization state conversion, then, the stability and accuracy of the S-FOCS are affected, and it is important to control the polarization properties at each step of the polarization state conversion precisely.

Accurate vectorial finite element mode solver for magneto-optic and anisotropic waveguides.

In this work, a dielectric waveguide mode solver is presented considering a general nonreciprocal permittivity tensor. The proposed method allows us to investigate important cases of practical interest in the field of integrated optics, such as magneto-optical isolators and anisotropic waveguides. Unlike the earlier developed mode solver, our approach allows for the precise computation of both forward and backward propagating modes in the nonreciprocal case, ensuring high accuracy and computational efficiency. As a result, the nonreciprocal loss/phase shift can be directly computed, avoiding the use of the perturbation method. To compute the electromagnetic modes, the Rayleigh-Ritz functional is derived for the non-self adjoint case, it is discretized using the node-based finite element method and the penalty function is added to remove the spurious solutions. The resulting quadratic eigenvalue problem is linearized and solved in terms of the propagation constant for a given frequency (i.e., γ-formulation). The main benefits of this formulation are that it avoids the time-consuming iterations and preserves the matrix sparsity. Finally, the method is used to study two examples of integrated optical isolators based on nonreciprocal phase shift and nonreciprocal loss effect, respectively. The developed method is then compared with the perturbation approach and its simplified formulation based on semivectorial approximation.

Microwave photonic phase shifter based on a nonreciprocal optical phase shifter inside a Sagnac interferometer

A new microwave photonic phase shifter is presented. It is based on an optical single-sideband modulator and an optical phase shifter inside a Sagnac interferometer. It relies on the use of the novel nonreciprocal optical phase shifter to obtain an optical phase shift, which converts into an RF phase shift. The microwave photonic phase shifter has the advantages of realising a continuous 0–360° phase shift on microwave signals using off-the-shelf components and only requiring a single control. It also has a compact structure and robust performance. Experimental results are presented, which demonstrate 0–360° phase shift of microwave signals over a sub-octave frequency band.

Nonreciprocal phase shift caused by magnetic-thermal coupling of a polarization maintaining fiber optic gyroscope

A theory for nonreciprocal phase shift caused by cross coupling generated in a polarization maintaining (PM) fiber optic gyroscope (FOG) under the combined action of magnetic and temperature fields is proposed. The magnetic-thermal coupling in the FOG originates from the interaction of the magnetic field, fiber twist, birefringence caused by thermal stress, and the intrinsic and bending birefringence of the fiber. The cross coupling changes with temperature. When the PM fiber has a diameter of 250 μm, beat length of 3 mm, length of 500 m, twist rate of 1 rad/m, and optical source wavelength of 1310 nm, the maximum degree of magnetic-thermal coupling generated by a 1 mT radial magnetic field within the temperature range of -20°C to 60°C is -5.47%.

Jumping phase control in interband photonic transition

Indirect interband photonic transition provides a nonmagnetic and linear scheme to achieve optical isolation in integrated photonics. In this paper, we demonstrate that the nonreciprocal transition can be induced through two pathways respectively by different modulation designs. At the end of those pathways, the two final modes have π phaseshift. We call this phenomenon jumping phase control since this approach provides a method to control the mode phase after the conversion. This approach also yields a novel way to generate nonreciprocal phaseshift and may contribute to chip-scale optoelectronic applications.

FERRITE-LOADED HALF MODE SUBSTRATE INTEGRATED WAVEGUIDE PHASE SHIFTER

An X-band ferrite-loaded half mode substrate integrated waveguide (HMSIW) phase shifter is proposed and fabricated in this paper. A full-height E-plane Yttrium Iron Garnet (YIG) ferrite slab is embedded in the HMSIW to construct the non-reciprocal phase shifter. With the application of a magnetic bias fleld on the ferrite slab, the phase of the ferrite-loaded HMSIW can be adjusted and controlled. For a magnetic bias fleld of 1800 Gauss, the insertion loss is less than 3.2dB from 9.7 to 11.0GHz. The return loss is better than 10dB over the same frequency range. The largest difierential phase shift can be up to 337 - . This circuit is easily integrated with other planar components and also has the capability to handle medium power level.

Nonreciprocal Magneto-Plasmonic Waveguide with Compact Metal-Sandwiched Structure

A magneto-optical (MO) metal-sandwiched multilayered structure composed of metal, MO medium and dielectric buffer layers is presented and investigated by finite-element-method-based-mode solver and perturbation theory. The results show that this structure exhibits large nonreciprocal phase shift, strong mode confinement in the narrow buffer layers as well as very low propagation loss. The propagation length with 1 dB loss is much longer than the required length of π/2 nonreciprocal phase shifts in this structure. The modal area is smaller than half of the conventional MO waveguides. This phenomenon can be used to achieve a compact plasmonic isolator based on the Mach—Zehnder interferometer.

Enhancement of nonreciprocal phase shift by using nanoscale air gap: erratum

We correct the calculation method [Opt. Lett.35, 1335 (2010)] of enhancement of nonreciprocal phase shift on the magneto-optical material boundary.

Microwave signal conditioning through non‐reciprocal phase shifting

Two non-reciprocal microwave signal conditioning circuits, a non-reciprocal phase shifter and a quasi-circulator, are proposed as based on the use of active microwave devices. Analytical expressions are derived to demonstrate the principles of operation and prototypes are presented both in hybrid and monolithic form. The hybrid structures operate in the L-band, whereas the monolithic ones are designed for X-band operation, and demonstrate the compactness and performance of the proposed topologies.

GaInAsP/InP MZI waveguide optical isolator integrated with spot size converter

We fabricated a waveguide optical isolator with a GaInAsP guiding layer integrated with spot size converters (SSCs) for efficient coupling to optical fibers. The isolator is constructed with a Mach-Zehnder interferometer (MZI), which is composed of multi-mode interference (MMI) couplers, as well as nonreciprocal and reciprocal phase shifters. The nonreciprocal phase shifter is constructed with a magneto-optical cladding layer directly bonded to a semiconductor guiding layer. The performance of the GaInAsP waveguide optical isolator was demonstrated with a maximum optical isolation of 28.3 dB at a wavelength of 1558 nm for the TM mode.

Optical Isolator for TE Polarized Light Realized by Adhesive Bonding of Ce:YIG on Silicon-on-Insulator Waveguide Circuits

An optical isolator for transverse electric (TE) polarized light is demonstrated by adhesive bonding of a ferrimagnetic garnet die on top of a 380 nm thick silicon waveguide circuit. Polarization rotators are implemented in the arms of a nonreciprocal Mach-Zehnder interferometer to rotate the polarization to transverse magnetic in the nonreciprocal phase shifter regions. Calculation of the nonreciprocal phase shift (NRPS) as a function of bonding layer thickness experienced by the TM mode in the interferometer arms is presented, together with the simulation of the robustness of the polarization rotator. Experimentally, 32 dB isolation is measured at 1540.5 nm wavelength using a magnetic field transverse to the light propagation directions. This paves the way to the cointegration of laser diodes and optical isolators on a silicon photonics platform.

Presentation and Application of Tunable Reciprocal/Nonreciprocal Metamaterial Transmission Line Based on Edge-Guided Mode

This article proposes a tunable composite right-/left-handed transmission line consisting of a transversely magnetized ferrite substrate periodically loaded by microstrip inductors. The gapless transition between the left- and right-handed bands (balanced response) is the main characteristic of this structure. This composite right-/left-handed transmission line is proposed in both reciprocal and nonreciprocal versions. Based on periodic structure analysis, the dispersion relation is estimated theoretically and validated numerically by the finite-element method in the reciprocal case. Theoretical and numerical results demonstrate the tunability of the proposed structures by changing the DC bias magnetic field applied to the ferrite. To demonstrate the applicability of the proposed structure, a tunable nonreciprocal phase shifter is designed.

Phase in non‐reciprocal gyromagnetic waveguides using multiple ferrite tiles

The non-reciprocal phase shifter in the design of the waveguide differential phase-shift circulator consists of two or four suitably magnetised ferrite tiles on the top and bottom walls of the waveguide. It may be adjusted in terms of a reciprocal condition and a non-reciprocal one. The first condition essentially fixes the geometry of a typical phase-shift section except for the thickness of each ferrite tile; the second determines the connection between the split-phase constants and the thickness of the tiles for parametric values of gyrotropy. The purpose here is to satisfy the first requirement of the two-tile geometry using a calculation and to meet the second one by having recourse to measurements. It includes some preliminary experimental data on new four- and eight-stacked ferrite tile structures. It is likely to prove of value in the design of large continuous wave power devices.

Integrated TE and TM optical circulators on ultra-low-loss silicon nitride platform

In this paper, we present two four-port optical circulators for TE and TM modes, respectively. Exploiting the recent technological development concerning Ce:YIG pulse laser deposition on silicon nitride platform, we design two integrated circulators, which can be used to implement several functions in integrated optics, such as de-interleavers, input/output amplifier isolators and output laser isolators. The proposed devices combine the benefit of low loss silicon nitride waveguides with the non-reciprocal properties of magneto-optical materials. The ring cross-section has been optimized in order to maximize the non-reciprocal phase shift and finally the scattering coefficients have been computed using the transfer matrix method. The material stability and refractive index regularity of silicon nitride, the small micro-ring footprint, and the high wavelength selectivity make these devices particularly attractive.

On-chip optical isolation via unidirectional Bloch oscillations in a waveguide array

We propose to use the unidirectionality of the optical Bloch oscillation phenomenon achievable in a magneto-optic asymmetric waveguide array to achieve optical isolation. At the 1.55 μm telecommunication wavelength, our isolator design exhibits an isolation ratio of 36 dB between forward- and backward-propagating waves. The proposed design consists of a waveguide array made in a silicon-on-insulator substrate with a magnetic garnet cover layer. A key role is played by the transverse-magnetic mode nonreciprocal phase shift effect.

Compact Mach–Zehnder Interferometer Ce:YIG/SOI Optical Isolators

We demonstrate an optical isolator integrated with a silicon-on-insulator waveguide platform realized by the adhesive bonding of a Ce:YIG/SGGG die on top of a Mach-Zehnder interferometer (MZI). The design is based on the different nonreciprocal phase shifts (NRPS) experienced by both arms of the interferometer, which have different waveguide widths. Simulation of NRPS versus silicon waveguide width is shown for a few different benzocyclobutene bonding layer thicknesses for a particular silicon waveguide thickness and Ce:YIG/SGGG stack. Variations of NRPS as a function of MZI arm lengths with bonded stack on top of MZI are measured. Optical isolation of 11 dB is experimentally obtained for a device with a footprint of 1.5 mm × 4 μm.

Self-Biased Nonreciprocal Microstrip Phase Shifter on Magnetic Nanowired Substrate Suitable for Gyrator Applications

Magnetic nanowired substrates (MNWS) have been used for the fabrication of a planar nonreciprocal microstrip device. It shows a differential phase shift of 300 degrees cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> at K a -band without requiring the application of a dc bias magnetic field, and making it suitable for miniaturized gyrator applications. The nonreciprocal operation is achieved by loading the device with nanowires of different ferromagnetic materials. This allows to control the phase velocity of the microwave signal passing through the device by virtue of the spatial variation of the MNWS permeability. The measured microwave performances of the device have been reproduced with excellent accuracy using a proposed analytical model based on an effective medium theory and useful for the prediction of further tunable capabilities.

Phase Shifter Operation of the Azimuthally Magnetized Coaxial Ferrite Waveguide

The terms for operation of the coaxial waveguide, entirely lled with azimuthally magnetized latching ferrite, as a digital nonreciprocal phase shifter for the normal TE01 mode, are found. They are classi ed as physical, mathematical and functional ones. The physical prerequisites are drawn from the phase curves of the structure and specify the boundaries of the interval in which it produces di erential phase shift for a given numerical equivalent of the modulus of o -diagonal ferrite permeability tensor element. The mathematical condition brings the parameters of con guration together with certain roots of its characteristic equation, derived in terms of complex Kummer and Tricomi con uent hypergeometric functions and with the related to them positive real L2(c, ρ, n) numbers (c = 3, 0 < ρ < 1, n = 1). The functional criteria determine the borders of the domain of phase shifter operation of the geometry. These are functions, de ned for a xed central conductor thickness which express in normalized form the impact of the guide radius on the phase shift at the cut-o frequencies and at the envelopes, denoting the termination of the phase curves for negative ferrite magnetization from the side of higher frequencies. The same are reckoned, employing iterative methods, consisting in a repeated numerical solution of the equation mentioned, followed by a computation of the guide radius and phase constant of the wave and are plotted graphically. The in uence of the parameters of transmission line on the area referred to is analyzed.

Direct Wafer Bonding and Its Application to Waveguide Optical Isolators.

This paper reviews the direct bonding technique focusing on the waveguide optical isolator application. A surface activated direct bonding technique is a powerful tool to realize a tight contact between dissimilar materials. This technique has the potential advantage that dissimilar materials are bonded at low temperature, which enables one to avoid the issue associated with the difference in thermal expansion. Using this technique, a magneto-optic garnet is successfully bonded on silicon, III-V compound semiconductors and LiNbO3. As an application of this technique, waveguide optical isolators are investigated including an interferometric waveguide optical isolator and a semileaky waveguide optical isolator. The interferometric waveguide optical isolator that uses nonreciprocal phase shift is applicable to a variety of waveguide platforms. The low refractive index of buried oxide layer in a silicon-on-insulator (SOI) waveguide enhances the magneto-optic phase shift, which contributes to the size reduction of the isolator. A semileaky waveguide optical isolator has the advantage of large fabrication-tolerance as well as a wide operation wavelength range.