Nonreciprocal Phase Shift Research Articles

Observation of Wavelength Tuning in a Mode-Locked Figure-9 Fiber Laser

We demonstrate an all-PM Er-doped soliton mode-locked fiber oscillator based on the figure-9 configuration with a compact adjustable reflection-type non-reciprocal phase shifter. An analytical model based on the Jones matrix is established to simulate the wavelength tuning phenomenon. Experimentally, it is observed that the increase in pump power results in a significant redshift in the spectrum of output pulses. When the angle of the half-wave plate is rotated in one direction, the output spectrum is redshifted and then blueshifted successively. Good qualitative agreement is presented between the simulations and the experimental results. It is shown that the increase in pump power changes the nonlinear phase shift, which causes the redshift of the transmittance curves at the laser output port. In contrast, the rotation of wave plates not only changes the nonlinear phase shift difference, but also causes variations in linear phase bias and modulation depth. The changes in these parameters lead to the redshift and blueshift of the transmission curves, which enables wavelength tuning.

Polarization-multiplexed dual-comb fiber laser based on an all-polarization-maintaining cavity configuration

In this study, we present a polarization-multiplexed, erbium-doped dual-comb fiber laser based on an all-polarization-maintaining cavity configuration. We observed that the dual-comb fiber laser easily realized the self-starting mode-locking operation due to the non-linear amplifying loop mirror (NALM) with a non-reciprocal phase shifter. Furthermore, owing to the sharing of the NALM part, the two outputs from this laser configuration had similar center wavelengths, with small different repetition rates (∆frep). In the free-running operation, the standard deviation of relative stability for Δfrep of 2.09 kHz was measured to be 1.59 Hz, and the full width at half-maximum of the relative beat note between the two frequency combs in the optical frequency domain was approximately 1 kHz. These results show that the two frequency combs from this laser configuration have high relative stability and mutual coherence.

Environment-stable sub-100 fs Er: fiber laser with a 3 dB bandwidth of 78 nm.

A robust all polarization-maintaining (PM) passively mode-locked Er-doped fiber laser is demonstrated based on the biased nonlinear amplifier loop mirror (NALM). With a π/2 nonreciprocal free-space phase shifter, stable single pulse mode locking can be obtained at the central wavelength of 1565.7 nm with a 3 dB spectral bandwidth of 24.6 nm in the soliton regime. The repetition rate of the pulse train is 98.13 MHz. The direct output pulse duration is 109 fs, which is nearly transform-limited. After the intracavity dispersion management, the robust self-started mode-locking in the stretched-pulse regime is realized at 1564 nm, and the 3 dB spectral bandwidth reaches up to 78 nm. The repetition rate of the pulse train is 199.6 MHz. In particular, the direct output pulse width is only 77 fs with a low integrated relative intensity noise (RIN) of only 0.0044% (integrated from 1 Hz to 1 MHz). To the best of our knowledge, this is the shortest pulse width directly from the all-PM NALM laser oscillator.

Drops deformation influence on the microwaves interaction with a magnetodielectric emulsion

Experimental and theoretical studies of the interaction of microwave radiation with a frequency of 8.2 GHz with magnetodielectric emulsions under the influence of an external magnetic field causing deformation of the emulsion dispersed phase droplets have been carried out. The values of the external magnetic field strength are such that no ferromagnetic resonance is observed in the system at a given radiation frequency. The studies were carried out when a rectangular waveguide was partially filled with a sample cell in the form of a thin plate. It is established that the deformation of magnetic droplets of the emulsion significantly affects the absorption of electromagnetic energy. The value of the droplet concentration at which the maximum response of the system is observed is determined. The features of the phenomenon of nonreciprocal phase shift, which have no analogue in solid-state magnetic materials, are found. To interpret the results obtained, a model of an ensemble of non-interacting isotropic superparamagnetic particles was used.

Low-Noise and Linear Nonmagnetic Circulator by a Temporal Nonreciprocal Phase Shifter

Light may be manipulated not only in space, but also in time. This study uses a nonreciprocal temporal-loop-based phase shifter to construct a low-noise, low-profile, and linear nonmagnetic circulator. In contrast to conventional magnet-based circulators, such a temporal circulator is controllable, compatible with integrated-circuit technology, and suitable for high frequencies. The experimental demonstration at microwave frequencies seems very promising.

1.7 µm figure-9 Tm-doped ultrafast fiber laser.

The evolution of multiphoton microscopy is critically dependent on the development of ultrafast laser technologies. The ultrashort pulse laser source at 1.7 µm waveband is attractive for in-depth three-photon imaging owing to the reduced scattering and absorption effects in biological tissues. Herein, we report on a 1.7 µm passively mode-locked figure-9 Tm-doped fiber laser. The nonreciprocal phase shifter that consists of two quarter-wave plates and a Faraday rotator introduces phase bias between the counter-propagating beams in the nonlinear amplifying loop mirror. The cavity dispersion is compensated to be slightly positive, enabling the proposed 1.7 µm ultrafast fiber laser to deliver the dissipative soliton with a 3-dB bandwidth of 20 nm. Moreover, the mode-locked spectral bandwidth could be flexibly tuned with different phase biases by rotating the wave plates. The demonstration of figure-9 Tm-doped ultrafast fiber laser would pave the way to develop the robust 1.7 µm ultrashort pulse laser sources, which could find important application for three-photon deep-tissue imaging.

Few-photon optical diode in a chiral waveguide.

We study the coherent transport of one or two photons in a one-dimensional waveguide chirally coupled to a nonlinear resonator. Analytic solutions of the one-photon and two-photon scattering is derived. Although the resonator acts as a non-reciprocal phase shifter, light transmission is reciprocal at one-photon level. However, the forward and reverse transmitted probabilities for two photons incident from either the left side or the right side of the nonlinear resonator are nonreciprocal due to the energy redistribution of the two-photon bound state. Hence, the nonlinear resonator acts as an optical diode at two-photon level.

Broadband nonreciprocal spoof plasmonic phase shifter based on transverse Faraday effects.

Spoof surface plasmon polaritons (SSPPs) have aroused widespread concern due to their strong ability in field confinement at low frequencies. For miniaturized integrated circuits, there is a pressing need for nonreciprocal spoof plasmonic platforms that provide diode functionalities. In this letter, we report the realization of nonreciprocal phase shifting in SSPPs using the transverse Faraday effect. A plasmonic coupled line is constructed by flipped stacking two corrugated metallic strips, in order to enhance the mode coupling between evanescent waves that carry opposite transverse spin angular momenta. With a transverse magnetized ferrite cladding, the SSPP mode is split into two circularly-polarized ones that show different propagation constants over a broad band. A nonreciprocal phase shifter compatible to standard microstrips is designed to validate the breaking of time-reversal symmetry in SSPPs. Microwave measurement demonstrates a differential phase shift up to 46.2°/cm from 12 GHz to 15 GHz. Owing to the advantages of strong field confinement and contactless ferrite integration, the proposed method enables an alternative pathway for nonreciprocal spoof interconnects.

Dual-band composite right/left-handed metamaterial lines with dynamically controllable nonreciprocal phase shift proportional to operating frequency.

Dual-band composite right/left-handed transmission lines with the nonreciprocal phase shift approximately proportional to the operating frequency are proposed and demonstrated by using normally magnetized ferrite microstrip lines. The nonreciprocal phase shift can be dynamically controlled by changing the externally applied dc magnetic field. Dynamic change in the nonreciprocal phase gradient along the line enables us to realize dual-band and unidirectional beam-scanning leaky-wave antennas without suffering from frequency-dependent change in the beam direction. A prototype nonreciprocal metamaterial line using polycrystalline yttrium iron garnet was fabricated and measured for verification of our basic concept.

Berry phase with tunable topological charge in Sagnac interferometer

A Sagnac interferometer’s ring structure causes electromagnetic waves traversing it to periodically encounter the same optical elements. Due to this discrete translational symmetry, the frequency spectrum of the clockwise and counter-clockwise modes acquire a band structure with a characteristic band gap. When the interferometer is rotated, an additional non-reciprocal phase shift between the counter propagating modes arises and it results in the loss of time reversal symmetry. While prior understanding of the impact of Sagnac rotation on the band structure exists, the prevalence of topological geometric phase in Sagnac interferometer under rotation has not been prominently discussed. We propose a coupled mode theory with the required time reversal symmetry properties which influences the Berry curvature and we show that it leads to the accumulation of Berry phase with tunable topological charge.

Optical nonreciprocity and nonreciprocal photonic devices with directional four-wave mixing effect.

A scheme for magnetic-free optical nonreciprocity in an ensemble of four-level cold atoms is proposed by exploiting the directional four-wave mixing effect. Using experimentally achievable parameters, the nonreciprocal optical responses of the system can be observed and the conversion on nonreciprocal transmission and nonreciprocal phase shift can be implemented. These nonreciprocal phenomena originate from the directional phase matching, which breaks the time-reversal symmetry and dynamic reciprocity of the cold atomic system. Moreover, by embedding the cold atoms into a Mach-Zehnder interferometer and choosing proper parameters, a two-port optical isolator with an isolation ratio of 79.70 dB and an insertion loss of 0.35 dB and a four-port optical circulator with a fidelity of 0.9985 and a photon survival probability of 0.9278 can be realized, which shows the high performance of isolation and circulation. The proposal may enable a new class of optically controllable cavity-free nonreciprocal devices in optical signal processing at the low light level.

Review of integrated magneto-optical isolators with rare-earth iron garnets for polarization diverse and magnet-free isolation in silicon photonics [Invited

Passive optical isolators are needed in silicon photonics but unavailable due to challenges in rare-earth iron garnet processing and integration. Material challenges include incompatibility with silicon and high annealing temperatures, and design challenges include a need for polarization diversity and a preference for no external magnetic bias. These challenges have restricted optical isolation to discrete modules that require physical pick and place of bulk garnet pieces. This review presents developments in the processing of magneto-optical garnets on Si and the enhancement of their Faraday rotation that enables small footprint isolators on silicon waveguide structures. For example, seedlayers and/or new garnet compositions have enabled monolithic Si integration, and in some cases, hybrid integration of garnet-on-garnet or transfer-printed garnet nanosheets enable reduced on-chip thermal processing. Integrated isolators that utilize non-reciprocal phase shift (NRPS) or non-reciprocal mode conversion (NRMC) have been demonstrated to have isolation ratios up to 30 dB, insertion loss as low as 9 dB, polarization diversity and magnet-free operation in the desired telecommunication wavelengths. The advances in materials, processing techniques, and isolator designs shown here will pave the way for on-chip isolators and novel multi-lane photonic architectures.

Analysis and Design of Quasi-Circulating Quadrature Hybrid for Full-Duplex Wireless

This article presents a new electronic device – the four-port quasi-circulating quadrature hybrid (QCQH), which combines desirable features of electronic circulators and quadrature hybrids. The QCQH comprises three quarter-wavelength transmission lines and a 90° non-reciprocal phase shifter (NRPS) and is suitable for inband full duplex applications. We derive the four-port S-parameter matrix of the QCQH and the transfer functions under termination scenarios of interest. The resulting closed-form expressions are compared with the prior art electronic circulator. A 90° transmission line and lumped transformer alternatives are considered for designing a QCQH based on a two-port N-path circuit. TX isolation and transmission expressions are derived and verified against simulations, and a new wideband leakage cancellation approach is proposed. A TSMC 65 nm CMOS N-path chip is integrated on-board with a discrete, lumped, LCL transformer implementation. TX-to-antenna insertion loss of 1.4 dB and an RX NF of 4.7 dB at the frequency of 1 GHz were measured with a primary passive TX-RX isolation of 21 dB. Total isolation of more than 50 dB for an 80 MHz OFDM WiFi TX signal employing digitally equalized active leakage cancellation was achieved along with better than −40 dB TX EVM with SIC ON.

Nonreciprocal-Beam Phased-Array Antennas Based on Transistor-Loaded Phase Shifters

This study presents a nonreciprocal-beam phased-array antenna constituted of phase-gradient patch radiators integrated with transistor-based nonreciprocal phase shifters. Such an antenna exhibits different beams for transmission and reception states. The proposed phased-array antenna provides power amplification for both transmission and reception states, which is of paramount importance in most practical applications. In addition, in contrast to the recently proposed time-modulated antennas, the proposed nonreciprocal-beam phased-array antenna introduces no undesired time harmonics and unwanted frequency conversion, which requires no radio frequency bias signal. Furthermore, the nonreciprocal phased-array antenna is lightweight and is amenable to integrated circuit fabrication. The transmission and reception beam angles, the beam shapes, and the power amplification level may be easily tuned by changing the direct current (dc) bias of the transistors and phase of the passive phase shifters. Such a nonreciprocal-beam phased-array antenna is expected to find military and commercial applications.

Design of ultra-compact TE mode ring optical isolator using a cobalt ferrite film for silicon photonic integrated circuits

In this study, we present the design of an integrated transverse electric mode isolator realized by the epitaxial growth of a cobalt ferrite (CFO) film on a silicon micro-ring resonator structure. Exploiting the large magneto-optical activity of CFO along with the good characteristics of resonator structures, we numerically demonstrated isolator designs with ultra-compact sizes. The use of ring resonator structures with the reduced size is appealing because of lower insertion loss values. The nonreciprocal phase shift was maximized by optimizing the ring cross-section and was further studied in terms of the ring radius employing a transformation optics theory. Finally, we analyzed the optical isolator characteristics in terms of ring size and ring-waveguide power coupling ratio. The computed results pointed out that decreasing the ring size improves the device performance and can ease the device design and fabrication process.

Full-duplex reflective beamsteering metasurface featuring magnetless nonreciprocal amplification

Nonreciprocal radiation refers to electromagnetic wave radiation in which a structure provides different responses under the change of the direction of the incident field. Modern wireless telecommunication systems demand versatile apparatuses which are capable of full-duplex nonreciprocal wave processing and amplification, especially in the reflective state. To realize such a functionality, we propose an architecture in which a chain of series cascaded radiating patches are integrated with nonreciprocal phase shifters, providing an original and efficient apparatus for full-duplex reflective beamsteering. Such an ultrathin reflective metasurface can provide directive and diverse radiation beams, large wave amplification, steerable beams by simply changing the bias of the gradient active nonmagnetic nonreciprocal phase shifters, and is immune to undesired time harmonics. Having accomplished all these functionalities in the reflective state, the metasurface represents a conspicuous apparatus for efficient, controllable and programmable wave engineering.

Terahertz magneto-optical response of bismuth-gadolinium-substituted rare-earth garnet film.

We report the magneto-optical Faraday response of bismuth-gadolinium-substituted rare-earth iron garnet at terahertz frequencies ranging from 100 GHz to 1.2 THz. The maximum transmittance of ±45° component is about 60% near the frequency point of 0.63 THz. When the external magnetic field change from -100 mT to +100 mT, the Faraday rotation angle is between -6° and +7.5°. The overall change of ellipticity is relatively small. The maximum value of the Verdet constant is about 260 °/mm/T at 0.1 THz and then gradually decreases to 80 °/mm/T at 1.2 THz. Within the considered frequency range, the thick film exhibits magnetically tunable, non-reciprocal characters and a strong magneto-optical effect within a small external magnetic field at room temperature, which will be widely used for the terahertz isolators, circulators, nonreciprocal phase shifters, and magneto-optical modulators.

Exceptional point magneto-optic isolators

We show that operating magneto-optic coupled ring isolators near an exceptional point (EP) fundamentally improves their tradeoff between isolation bandwidth and insertion loss. In analogy to EP sensors, operating a coupled ring isolator at an EP causes its isolation bandwidth to depend on the square root of the nonreciprocal phase shift (NRPS) instead of the usual linear dependence, thereby enhancing the bandwidth when the NRPS is small. In cases of practical interest, this behavior enables more than a 50% increase in 20 dB isolation bandwidth at 3 dB insertion loss for a given pair of rings. The advantage of EP operation grows in the vicinity of magneto-optic material resonances and should extend to other types of on-chip isolators that rely on similarly weak nonreciprocal perturbations.

Theoretical analysis of the non-reciprocal phase shifts due to birefringence and topology in fiber ring interferometers

The non-reciprocal phase shifts in fiber ring interferometers due to the fiber birefringence and the path topology are investigated for the first time. It is shown that the resultant birefringence of the fiber, which is the combination of the linear birefringence intrinsic to the fiber and the circular birefringence induced by the twisting in the fiber coiling, is not reciprocal for both rays in the bidirectional propagation due to the path topology confined by the coiled fiber. Our model indicates that the performance of fiber ring interferometers periodically depends on both the linear and the circular birefringence of the coiled fiber, and the bias error can be reduced by the typical fabrication process of the fiber ring interferometers.

Phase Nonreciprocity of Microwave‐Frequency Surface Acoustic Waves in Hybrid Heterostructures with Magnetoelastic Coupling

AbstractMagnetoelastic coupling is considered as one of the most reliable method to induce nonreciprocity of propagation losses of microwave‐frequency surface acoustic waves (SAW) and other acoustic modes propagating in nonmagnetic‐ferromagnetic heterostructures. Here, it is demonstrated theoretically that magnetoelastic coupling can also induce phase nonreciprocity of SAW, which is necessary for the development of SAW circulators and other nonreciprocal solid‐state‐acoustic devices. In contrast to previous studies, induction of the phase nonreciprocity requires the coupling of SAW to a strongly nonreciprocal spin wave (SW), having the nonreciprocal splitting of the SW spectrum much larger than the strength of the magnetoelastic coupling, which, in turn, should be much larger than the geometric mean of the SW and SAW damping rates. In this case, the hybridized SAW in the spectral region between the magnetoelastic gaps demonstrate significant phase nonreciprocity, retaining, at the same time, propagation losses that are close to those of unhybridized SAW. Possible practical realization of nonreciprocal SAW phase shifters and SAW‐ring‐based circulators based on hybridized waves in acoustic crystal and synthetic antiferromagnetic heterostructures is discussed.