Gires-Tournois Interferometer Research Articles

Square waves and Bykov T-points in a delay algebraic model for the Kerr-Gires-Tournois interferometer.

We study theoretically the mechanisms of square wave formation of a vertically emitting micro-cavity operated in the Gires-Tournois regime that contains a Kerr medium and that is subjected to strong time-delayed optical feedback and detuned optical injection. We show that in the limit of large delay, square wave solutions of the time-delayed system can be treated as relative homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of square wave solutions. In particular, we unveil the mechanisms behind the collapsed snaking scenario of square waves and explain the formation of complex-shaped multistable square wave solutions through a Bykov T-point. Finally, we relate the position of the T-point to the position of the Maxwell point in the original time-delayed system.

High quality factor unidirectional guided resonances of a silicon-on-lithium niobate photonic crystal slab for a tunable Gires-Tournois interferometer.

High quality (Q) factor, tunable unidirectional guided resonances (UGRs) based on a silicon-on-lithium niobate (Si-on-LN) photonic crystal (PhC) slab are proposed and numerically investigated. The Q factors of UGRs decay quadratically with respect to the distance from the Γ point to the wave vector along the Γ-X direction, and high Q factor UGRs are obtained by moving UGR close to the Γ point. Also, a Gires-Tournois interferometer (GTI) based on a UGR with a Q factor of 9465 is numerically demonstrated, which produces a maximum group delay of 30 ps around 1.55 μm with unitary reflectance. The group delay and operation wavelengths of the GTI can be adjusted effectively by tuning the refractive index of lithium niobate (LN) and the periods of the silicon bars. Our study may find applications in PhC surface-emitting lasers, dispersion compensation, and compression of light pulses.

Design, production, and characterization of a pair of positive and negative high dispersive mirrors for chirped pulse amplification systems.

We report a novel modified Gires-Tournois interferometer (MGTI) starting design for high-dispersive mirrors (HDMs). The MGTI structure combines multi-G-T and conjugate cavities and introduces a large amount of dispersion while covering a wide bandwidth. With this MGTI starting design, a pair of positive (PHDM) and negative highly dispersive mirrors (NHDM) providing group delay dispersions of +1000 fs2 and -1000 fs2 in the spectral range of 750 nm to 850 nm is developed. The pulse stretching and compression capabilities of both HDMs are studied theoretically by simulating the pulse envelopes reflected from the HDMs. A near Fourier Transform Limited pulse is obtained after 50 bounces on each positive and negative HDM, which verifies the excellent matching between the PHDM and NHDM. Moreover, the laser-induced damage properties of the HDMs are studied using laser pulses of 800 nm and 40 fs. The damage thresholds of the PHDM and NHDM are approximately 0.22 J/cm2 and 0.11 J/cm2, respectively. The laser-induced blister structure of the HDMs is observed, the formation and evolution processes of the blister are evaluated.

Sideband-free dispersion-managed Yb-doped mode-locked fiber laser with Gires–Tournois interferometer mirrors

High-order dispersion introduced by Gires–Tournois interferometer mirrors usually causes spectral sidebands in the near-zero dispersion region of mode-locked fiber lasers. Here, we demonstrate a sideband-free Yb-doped mode-locked fiber laser with dispersion-compensating Gires–Tournois interferometer mirrors. Both the simulation and the experiment demonstrate that the wavelength and energy of the sidebands can be tuned by changing the transmission coefficient of the output mirror, the pump power, and the ratio of the net cavity dispersion to the net third-order dispersion in the cavity. By optimizing these three parameters, the laser can generate a sideband-free, Gaussian-shaped spectrum with a 13.56-nm bandwidth at -0.0232 ps2 net cavity dispersion, which corresponds to a 153-fs pulse duration.

90-fs Yb-doped fiber laser using Gires-Tournois interferometers as dispersion compensation

This paper reports a Yb-doped mode-locked femtosecond fiber laser based on a nonlinear amplifying loop mirror (NALM). The improved NALM structure ensures the high repetition rate of 97 MHz and the maximum output power of 126 mW. The Gires-Tournois interferometers (GTI) are used as dispersion compensation devices in laser resonator. The pulse output with full width half maximum (FWHM) of 26 nm and a dechirped pulse duration of 90 fs is obtained. As far as we know, this is the relatively short pulse in an improved NALM mode-locked Yb-doped fiber laser.

Photonic Delay Processing With Centralized Etalon Cascade for Radio Beamsteering in Simplified 2 × 5 Phased-Array Radio Heads

The adoption of beam-centric radio communication schemes calls for efficient methods of beamforming with multi-element antennas. We present a delay generation method that employs a shared and centralized cascade of Gires-Tournois etalons for element-by-element radio frequency beamsteering at remote radio heads, thus adding no complexity at the antenna site. We experimentally demonstrate beamsteering of up to 32° in combination with a 2 × 5 phased-array antenna operated at a radio carrier frequency of 3.5 GHz and transmitting 64-ary quadrature amplitude modulated, orthogonal frequency division modulated radio signals. The radio transmission performance over mobile optical fronthaul and free-space radio propagation is evaluated through offline error vector magnitude estimation and real-time transmission of high-definition video traffic. We further show carrier phase switching at 2 kHz using direct emission frequency modulation of the involved optical light sources, proving the proposed concept to support the fast tracking of mobile users.

Robust unbalanced Gires-Tournois mirror for group delay dispersion measurement evaluation by white light interferometer

A robust unbalanced Gires-Tournois interferometer (GTI) mirror for evaluating group delay dispersion (GDD) measurement by scanning white light interferometer is presented, and a novel processing algorithm based on scanning white light interferometer (WLI) is proposed to extract group delay and group delay dispersion characteristics with improved accuracy and low level of noise. The GDD measurement evaluation method is based on error analysis of manufacturing errors and spectral measurement. Spectral measurement is carried out to determine the resonance wavelength of GTI mirror. The sample was prepared by ion beam sputtering deposition. The relative errors of refractive index and layer thickness for the sample are estimated through reverse engineering based on multi-angle transmittance measurements. A novel processing algorithm the extrema searching method (ESM) is proposed that search the positions of multi-order extrema from reconstructed interferogram intensity to exact the GDD characteristics of the sample. GDD measurements performed by WLI with different processing methods are added to comparison including windowed Fourier transform, wavelet transform and time-domain scanning method. The results show that our method is reliable and effective for GDD measurement with a good accuracy and low level of noise.

Research on the Performance of Multimode Optical Chaotic Secure Communication System With Multidimensional Keys and a Complex Entropy Source

In this paper, we design an optical chaotic secure communication system with multi-dimensional keys and a complex entropy source, which can allow secure communication working in different modes such as unicast, multicast, and broadcast. In the proposed scheme, amplified spontaneous emission (ASE) noise of the erbium-doped fiber amplifier (EDFA) with sufficient randomness is used as an entropy source to improve the security of the system. And by using the electro-optic delay feedback loops, the key spaces are introduced and the phase distortion is generated, then the data are masked in both phase and intensity fields. As a frequency-dependent group delay (FDGD) module, Gires-Tournois interferometer (G-T I) in the feedback loop can effectively hide the time delay signature (TDS) and achieve additional 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">36</sup> key spaces. The influence of different key mismatches on decryption function is numerically investigated, and the results indicate that the broadband nature of ASE noise makes the TDS a very sensitive encryption key, which increases the difficulty of illegal third parties stealing information. And with the help of the wavelength converter and wavelength division multiplexer, secure communication in various modes is successfully realized, which greatly improves the communication efficiency and is suitable for various security places.

A normal form for frequency combs and localized states in Kerr-Gires-Tournois interferometers.

We elucidate the mechanisms that underlay the formation of temporal localized states and frequency combs in vertical external-cavity Kerr-Gires-Tournois interferometers. We reduce our first-principles model based upon delay algebraic equations to a minimal pattern formation scenario. It consists in a real cubic Ginzburg-Landau equation modified by high-order effects such as third-order dispersion and nonlinear drift, which are responsible for generating localized states via the locking of domain walls connecting the high and low intensity levels of the injected micro-cavity. We interpret the effective parameters of the normal form in relation with the configuration of the optical setup. Comparing the two models, we observe an excellent agreement close to the onset of bistability.

A diode-pumped femtosecond Pr:YLF laser emitting at the near-infrared 915 nm

Femtosecond pulse generation from diode-pumped praseodymium (Pr) lasers in the near-infrared has been a long pursuit for the optics community. Utilizing the Pr:LiYF4 crystal in a novel dispersion arrangement scheme that includes a set of triple Gires-Tournois interferometer mirrors, mode-locked ultrashort pulses as short as 451 fs at 915 nm have been achieved when the crystal is directly pumped by a blue laser-diode. The pulse energy is 3 nJ and peak power is 7.2 kW at the repetition rate of 85.5 MHz. This is the first demonstration of diode-pumped Pr lasers arriving the femtosecond regime.

Semiconductor saturable absorber mirror mode-locked Yb:YLF laser with pulses of 40 fs.

We have generated pulses as short as 40 fs with an average power of 265 mW from a semiconductor saturable absorber mirror (SESAM) mode-locked Yb:YLF oscillator employing a 1% transmitting output coupler (OC). The room-temperature laser is pumped by a low-cost 960 nm single-emitter multimode diode and dispersion compensation is provided via double chirped mirrors (DCMs). The 40-fs pulses are centered around 1050 nm with a width of 34 nm at a repetition rate of 87.3 MHz. By increasing the output coupling to 5% and by using Gires-Tournois interferometer (GTI) mirrors for dispersion compensation, we have also demonstrated 380-fs pulses with 1.85 W of average power around 1025 nm at a repetition rate of 190.4 MHz. Using an intracavity off-surface optic axis birefringent filter, the central wavelength of the pulses could be tuned in the 1020-1025 nm and 1019-1047 nm ranges for the 5% and 1% transmitting OCs, respectively. To the best of our knowledge, these are the shortest pulses and highest average and peak powers generated from room-temperature Yb:YLF lasers to date.

Control of the Phase of Reflected Spin Waves From Magnonic Gires–Tournois Interferometer of Subwavelength Width

The phase is one of the fundamental properties of a wave that allows to control interference effects and can be used to efficiently encode information. We examine numerically a magnonic resonator of the Gires-Tournois interferometer type, which enables the control of the phase of spin waves reflected from the edges of the ferromagnetic film. The considered interferometer consists of a Py thin film and a thin, narrow Py stripe placed above its edge, both coupled magnetostatically. We show that the resonances and the phase of the reflected spin waves are sensitive for a variation of the geometrical parameters of this bi-layerd part of the system. The high sensitivity to film, stripe, and non-magnetic spacer thicknesses, offers a prospect for developing magnonic metasurfaces and sensors.

Yb-doped polarization-maintaining femtosecond fiber laser using Gires–Tournois interferometers for dispersion management

We demonstrate an ultrashort pulsed Yb-doped polarization-maintaining fiber laser which uses Gires–Tournois interferometers (GTI) for managing dispersion. The GTI placed in the oscillator cavity aims to compress the pulse. Resulting in a pulse with a duration of 78 fs. The fact that the laser does not require additional de-chirp makes it more compact and avoids the insertion loss of additional components. Experiments with different dispersion confirm the excellent dispersion-managed performance of GTI. As far as we know, the duration of 78 fs is the shortest pulse obtained by using intracavity GTI dispersion management in fiber lasers.

Integrated Gires-Tournois interferometers based on evanescently coupled ridge resonators.

We propose integrated Gires-Tournois interferometers (GTIs) for guided modes of dielectric slab waveguides. The proposed GTIs consist of one or several dielectric ridge resonators separated by subwavelength-width grooves patterned into an abruptly terminated slab waveguide and operate at oblique incidence of the fundamental transverse-electric-polarized mode. The grooves act as partially reflective mirrors, whereas the end facet of the last ridge works in the total internal reflection regime and reflects all the incident radiation. We show that the single-ridge structure provides a nonlinear staircase-like phase response characteristic for GTIs. By using several properly arranged ridges, one can engineer group delay or group delay dispersion in a required spectral range. As an example, we design a three-ridge GTI providing an almost constant group delay dispersion in a 50-nm-wide wavelength range. The proposed planar GTIs may find application in integrated optical circuits for introducing or compensating for chromatic dispersion.

Measuring the spatial deformation of a liquid-crystal on silicon display with a self-interference effect.

We present a simple technique to characterize the spatial non-uniformity of a liquid-crystal on silicon (LCOS) spatial light modulator (SLM). It is based on illuminating the display with a wavelength out of the operation range, so there is a significant reflection at the output surface. As a consequence, a Gires-Tournois interferometer is directly created, without any alignment requirement and insensitive to vibrations. The beam reflected at the output surface is the reference beam, while the beam reflected at the silicon backplane is modulated with the addressed gray level in order to quantitatively derive its deformation. We provide an experimental demonstration using a LCOS-SLM designed to operate in the near-infrared range but illuminated with visible light.

Gires–Tournois interferometer based on the self-collimation effect in a two-dimensional photonic crystal

A photonic crystal Gires–Tournois interferometer (PCGTI) based on the self-collimation effect in two-dimensional photonic crystal (PC) is proposed and numerically investigated using finite-difference time-domain (FDTD) simulations. The PCGTI is composed of two 100% reflecting mirrors, a partially reflecting mirror and a beam splitter. Both of hole-type and rod-type PCGTIs have rectangular-shaped transmission spectra. So, they can work as bandpass/bandstop filters with appropriate structure parameters. If the central normalized frequency corresponds to 1550 nm, the TE bandpass and bandstop bandwidths for the hole-type PCGTI are 15 nm and 18 nm respectively, while the TM bandpass and bandstop bandwidths for the rod-type PCGTI are both 20 nm. As its size is on the order of 10 micrometers, the PCGTI may have potential applications in the future photonic integrated circuits.

Bound states in the continuum and strong phase resonances in integrated Gires-Tournois interferometer

Abstract Photonic bound states in the continuum (BICs) are eigenmodes with an infinite lifetime, which coexist with a continuous spectrum of radiating waves. BICs are not only of great theoretical interest but also have a wide range of practical applications, e.g. in the design of optical resonators. Here, we study this phenomenon in a new integrated nanophotonic element consisting of a single dielectric ridge terminating an abruptly ended slab waveguide. This structure can be considered as an on-chip analog of the Gires-Tournois interferometer (GTI). We demonstrate that the proposed integrated structure supports high-Q phase resonances and robust BICs. We develop a simple but extremely accurate coupled-wave model that clarifies the physics of BIC formation and enables predicting BIC locations. The developed model shows that the studied BICs are topologically protected and describes the strong phase resonance effect that occurs when two BICs with opposite topological charges annihilate.

Tunable Kerr frequency combs and temporal localized states in time-delayed Gires-Tournois interferometers.

In this Letter, we study theoretically a new setup allowing for the generation of temporal localized states (TLSs) and frequency combs. The setup is compact (a few centimeters) and can be implemented using established technologies, while offering tunable repetition rates and potentially high power operation. It consists of a vertically emitting micro-cavity, operated in the Gires-Tournois regime, containing a Kerr medium strong time-delayed optical feedback, and detuned optical injection. We disclose sets of multistable dark and bright TLSs coexisting on their respective bistable homogeneous backgrounds.

Thin film-based Gires–Tournois Resonator (GTR) as quasi-optical analogue of the Thomas rotation angle effect in special relativity

We present an unconventional approach to generate an optical analogue of the Thomas rotation angle found in Special Relativity (SR) by using a thin-film–based Gires–TournoisResonator (GTR). At first glance, the phase response of the GTR seems to fail as an optical analogue for the Thomas rotation angle in the phase domain but we demonstrate that an analogue can be successfully constructed in the intensity domain by combining the GTR with a Michelson interferometer (MI), thus forming an interferometer known as the Michelson–Gires–Tournois Interferometer (MGTI). Thomas rotation angle is a spatial rotation of the reference frame due to the Einstein velocity addition (EVA) law of two successive relativistic velocities travelling in non-collinear directions, whereas, the GTR is a thin-film based asymmetric Fabry–Perot resonator (FPR) with a partially reflecting front mirror, and a 100% rear-reflecting mirror. We investigate in detail, both analytically and numerically, the Thomas rotation angle’s full behaviour under various parameter conditions. This approach offers the following advantages: (i) it leads to a simpler overall configuration, (ii) it measures the Thomas rotation angle directly requiring only a single optical parameter instead of multiple parameters compared with other methods, and (iii) it requires no sophisticated multilayer thin film design.

Tunable and compact dispersion compensation of broadband THz quantum cascade laser frequency combs.

Miniaturized frequency combs (FCs) can be self-generated at terahertz (THz) frequencies through four-wave mixing in the cavity of a quantum cascade laser (QCL). To date, however, stable comb operation is only observed over a small operational current range in which the bias-depended chromatic dispersion is compensated. As most dispersion compensation techniques in the THz range are not tunable, this limits the spectral coverage of the comb and the emitted output power, restricting potential applications in, for example, metrology and ultrashort THz pulse generation. Here, we demonstrate an alternative architecture that provides a tunable, lithographically independent, control of the free-running coherence properties of THz QCL FCs. This is achieved by integrating an on-chip tightly coupled mirror with the QCL cavity, providing an external cavity and hence a tunable Gires Tournois interferometer (GTI). By finely adjusting the gap between the GTI and the back-facet of an ultra-broadband, high dynamic range QCL, we attain wide dispersion compensation regions, where stable and narrow (~3 kHz linewidth) single beatnotes extend over an operation range that is significantly larger than that of dispersion-dominated bare laser cavity counterparts. Significant reduction of the phase noise is registered over the whole QCL spectral bandwidth (1.35 THz). This agile accommodation of a tunable dispersion compensator will help enable uptake of QCL-combs for metrological, spectroscopic and quantum technology-oriented applications.