Gires-Tournois Interferometer Research Articles

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.

Gires-Tournois resonators as ultra-narrowband perfect absorbers for infrared spectroscopic devices.

Ultra-narrowband perfect absorbers and emitters are proposed and realized by engineering multiple-beam interference in Gires-Tournois etalon with the presence of low metallic loss. The absorption mechanism and spectral characteristics of the Gires-Tournois resonators are numerically and experimentally investigated for three configurations: dielectric cavity on metal, metal-dielectric-metal resonator, and distributed Bragg reflector (DBR)-dielectric-metal resonator. Narrowband thermal emitters based on the metal-dielectric-metal cavity and (DBR)-dielectric-metal cavity are experimentally demonstrated with an emissivity of 0.8 and 0.82, and a quality factor of 21 and 85, respectively. A DBR-dielectric-metal resonator-based absorber is directly loaded onto a LiTaO3 film for the first time to constitute an on-chip ultra-narrowband pyroelectric detector with an excellent quality factor of 151 at the absorption band of methane.

Group velocity dispersion analysis of terahertz quantum cascade laser frequency comb

The frequency comb which is characterized by equally-spaced frequency lines with high mode coherence has received much attention since its first demonstration in near-infrared and optical frequency range. In the terahertz frequency range, the electrically-pumped terahertz quantum cascade laser (THz QCL) based on semiconductors is an ideal candidate for achieving frequency comb operation in a frequency range between 1 THz and 5 THz. The group velocity dispersion (GVD) is a key factor for the frequency comb. A higher GVD can pull the frequencies from their equidistant values and limit the comb bandwidth. Therefore the laser dispersion needs to be compensated for in order to make the total GVD sufficiently low and flat, such as using a Gires-Tournois interferometer (GTI) or the double chirped mirror (DCM). However, a successful design still depends on the knowledge of the total GVD in the laser. In this paper, we show how to calculate the GVD in metal-metal waveguide THz QCLs by taking into account the dispersions from the GaAs material, the waveguide, and the laser gain, which conduces to the understanding of the frequency comb behavior. The waveguide loss is modelled by the finite element method. The loss due to intersubband absorption is calculated by Fermi's gold rule. All the losses, i.e., waveguide loss, mirror loss, and intersubband absorption loss, are summed up to calculate the clamped gain. The material loss can be calculated by using the reststrahlen band model. Because of these losses and gain, the refractive index needs to be replaced by a complex refractive index. The real part of the complex refractive index is the refractive index, which can be calculated from the Kramers-Kronig relationship that connects the loss or gain with the refractive index. Then the GVD introduced by the material loss, waveguide loss, and clamped gain can be finally calculated. The results show that the total GVD of THz QCL is approximately –8 × 10<sup>5</sup>~8 × 10<sup>5</sup> fs<sup>2</sup>/mm which is strongly determined by the clamped gain. Finally, the developed numerical model is employed to study the dispersion compensation effect of a GTI mirror which is coupled into a QCL gain cavity. The design of the THz QCL based on GTI structure is more flexible and feasible than that of the DCM. The result shows that by carefully designing the geometry of GTI, the dispersion of a THz QCL can be compensated for, thus achieving the broadband terahertz frequency combs.

Generation of Multi‐Gigahertz Trains of Phase‐Coherent Femtosecond Laser Pulses in Ti:Sapphire Waveguides

AbstractMiniature lasers producing ultrashort phase‐coherent pulses at high repetition rates by stable mode‐locking in ambient conditions can offer unique capabilities in various applications, spanning from microwave photonics to telecom and biological imaging techniques. Here, the operation of graphene mode‐locked lasers based on channel waveguides written by femtosecond and picosecond laser pulses in Ti:sapphire crystals is demonstrated. Trains of pulses of 41.4 fs duration at a 21.25 GHz repetition rate are generated by capitalizing on the formation of solitons in their monolithic resonators through Gires–Tournois interferometers. The latter, allow for effective pulse shaping via tuning of the intracavity group delay dispersion while simultaneously enabling ultralow laser operating thresholds. A number of features of these sources, including their high‐brightness and broad bandwidth, are essential ingredients for achieving high longitudinal resolution and sensitivity, which are the primary performance metrics of the Fourier domain/spectral domain variant of optical coherence tomography systems. A further doubling of the laser repetition rate to 42.5 GHz is achieved by coherent pulse interleaving in optical fiber technology, thereby underlining the potential of the Ti:sapphire waveguide lasers to produce highly stable, wide‐spaced combs of phase‐coherent optical frequency lines.

Structural Color Sensors with Thermal Memory: Measuring Functional Properties of Ti‐Based Nitrides by Eye

AbstractTo ensure safe and reliable operation of materials with high thermal loads, e.g., in turbines or thermal solar collectors, it is key to detect material degradation. Here, a sensor concept providing a direct optical feedback of thermally induced hardness and resistivity changes in transition‐metal‐nitride functional coatings is presented. The sensor concept relies on a lossy Gires–Tournois interferometer configuration using thermally induced detuning of a highly absorbing state in the optical spectrum as feedback. It is demonstrated for the specific case of TiAlN coatings that such detuning is due to a symmetry‐breaking structural phase transition, which is accompanied by the formation of saturated structural colors.

Tunable dispersion compensation of quantum cascade laser frequency combs.

Compensating for group velocity dispersion is an important challenge to achieve stable midinfrared quantum cascade laser (QCL) frequency combs with large spectral coverage. We present a tunable dispersion compensation scheme consisting of a planar mirror placed behind the back facet of the QCL. Dispersion can be either enhanced or decreased depending on the position of the mirror. We demonstrate that the fraction of the comb regime in the dynamic range of the laser increases considerably when the dispersion induced by the Gires-Tournois interferometer compensates the intrinsic dispersion of the laser. Furthermore, it is possible to tune to the offset frequency of the comb with the Gires-Tournois interferometer while the repetition frequency is almost unaffected.

2-GHz carbon nanotube mode-locked Yb:YAG channel waveguide laser.

We demonstrate GHz-repetition rate mode-locked operation of a femtosecond-laser-inscribed Yb:YAG channel waveguide laser using single-walled carbon nanotube saturable absorber mirror (SWCNT-SAM). A 6.3-mm-long, type II Yb:YAG waveguide laser with an extended cavity configuration delivers mode-locked picosecond (ps) pulses at GHz repetition rates. The dispersion of the laser cavity is compensated by the combination of a multi-functional output coupler and the Gires-Tournois interferometer (GTI) effect arising from an air-gap between the facet of the waveguide and the output coupler. The incident beam fluence on the SWNCNT-SAM is controlled by adjusting two intracavity lenses to avoid optical damage on the polymer nanocomposite matrix containing the SWCNTs. The average output power of our mode-locked waveguide laser is 322 mW at a pump power of 3.2 W. Nearly Fourier-limited, stable 2-ps-short pulses are generated at a repetition rate of 2.08 GHz.

Short Terahertz Pulse Generation from a Dispersion Compensated Modelocked Semiconductor Laser

Dispersion compensation is vital for the generation of ultrashort and single cycle pulses from modelocked lasers across the electromagnetic spectrum. It is typically based on addition of an extra dispersive element to the laser cavity that introduces a chromatic dispersion opposite to that of the gain medium. To date, however, no dispersion compensation schemes have been successfully applied to terahertz (THz) quantum cascade lasers for short and stable pulse generation in the THz range. In this work, a monolithic on‐chip compensation scheme is realized for a modelocked QCL, permitting THz pulses to be considerably shortened from 16ps to 4ps. This is based on the realization of a small coupled cavity resonator that acts as an ‘off resonance’ Gires‐Tournois interferometer (GTI), permitting large THz spectral bandwidths to be compensated. This novel application of a GTI opens up a direct and simple route to sub‐picosecond and single cycle pulses in the THz range from a compact semiconductor source.

Optimization of group delay dispersion measurement by Gires–Tournois interferometer

In this paper the group delay dispersion (GDD) of some laser mirrors is measured by a Gires–Tournois interferometer (GTI). The GTI is constructed with a partially reflective non-dispersive mirror and a highly reflective dispersive mirror. The GDD of the dispersive mirrors is calculated by determining the spectral position of the minima in the reflection light of the GTI. The previous GDD measurement equation is modified by introducing a correction coefficient. An appropriate level of accuracy is obtained by optimizing the Gires–Tournois mirror distances in our simple and inexpensive practical setup.

Highly efficient and high-power diode-pumped femtosecond Yb:LYSO laser

A diode-pumped high-power femtosecond Yb:LYSO laser with high efficiency is demonstrated. With a semiconductor saturable absorber mirror for passive mode-locking and a Gires–Tournois interferometer mirror for intracavity dispersion compensation, stable mode-locking pulses of 297 fs duration at 1042 nm were obtained. The maximum average power of 3.07 W was realized under 5.17 W absorbed pump power, corresponding to as high as 59.4% opt–opt efficiency. The single pulse energy and peak power are about 35.5 nJ and 119.5 kW, respectively.

Modulation instability of wave packets in a Gires–Tournois interferometer

We study the specific features of the perturbation dynamics of a wave packet in a Gires–Tournois interferometer. We obtain a dispersion relationship that relates the perturbation parameters to the parameters of the structure and pump wave, the analytical expressions for the gain increment of a harmonic perturbation and other important characteristics that determine the dynamics of the modulation instability of the reflected wave. Based on numerical simulation, we plot the dependences of the dispersion and nonlinearity parameters and the gain increment on the spacing between the interferometer mirrors, the angle of incidence of the radiation onto the mirrors, and the radiation intensity.

Dispersion engineering of quantum cascade laser frequency combs

Quantum cascade laser (QCL) frequency combs offer the potential for building ultra-compact broadband spectrometers operating in the mid-infrared spectral region, where many light molecules have their fundamental absorption bands. However, key characteristics must be improved for correctly addressing frequency comb spectroscopy applications. In this work, we investigate how the device dispersion influences the comb operation of QCLs. We measure the group delay dispersion of such a device while in operation just below threshold. We then show that by implementing a dispersion compensation scheme based on a Gires–Tournois interferometer integrated into the QCL, the comb operation regime is dramatically improved. In particular, the formation of high-phase-noise regimes is prevented. The continuous-wave output power of these combs can be as high as 150 mW with optical spectra centered at 1330 cm−1 (7.52 μm) with up to 70 cm−1 of optical bandwidth, demonstrating that QCLs are ideal sources for chip-based frequency comb spectroscopy systems.

11-GHz waveguide Nd:YAG laser CW mode-locked with single-layer graphene.

We report stable, passive, continuous-wave (CW) mode-locking of a compact diode-pumped waveguide Nd:YAG laser with a single-layer graphene saturable absorber. The depressed cladding waveguide in the Nd:YAG crystal is fabricated with an ultrafast laser inscription method. The saturable absorber is formed by direct deposition of CVD single-layer graphene on the output coupler. The few millimeter-long cavity provides generation of 16-ps pulses with repetition rates in the GHz range (up to 11.3 GHz) and 12 mW average power. Stable CW mode-locking operation is achieved by controlling the group delay dispersion in the laser cavity with a Gires–Tournois interferometer.

Condition for unity absorption in an ultrathin and highly lossy film in a Gires–Tournois interferometer configuration

We present a condition for unity absorption for a Gires-Tournois interferometer configuration constructed from an ultrathin and highly lossy film on top of metallic mirror. From the impedance matching condition in the transmission line theory, we identify a solution space for the required complex refractive index of the lossy film in various film thickness and dielectric constants of the metallic mirror. It is shown that strong absorption requires the imaginary part of the refractive index of the ultrathin lossy film be larger than 0.64, and the physical origin of this condition is elucidated. The proposed method is useful in identifying candidate semiconductor materials that can be used as the lossy film in a unity-absorption Gires-Tournois interferometer configuration and designing the thickness of this film to maximize absorption.

Flat focusing in reflection from a chirped dielectric mirror with a defect layer

Recently, the principle of flat focusing based on one-dimensionally chirped dielectric mirrors has been proposed and experimentally demonstrated. The flat chirped mirror causes anomalous diffraction of the beam during reflection, opposite to the normal diffraction in free space propagation. The anomalous diffraction compensates the normal diffraction of the beam resulting in focusing after reflection. For a better focusing performance and for a larger near-field focal distance, a stronger anomalous diffraction is required. We show that the anomalous diffraction can be enhanced by introducing a defect layer in the chirped mirror, as the structure becomes similar to a Gires–Tournois interferometer. The focal distance can be substantially increased due to the defect layer. In our specific structure, the focal distance shows an increase from 19 to 39 μm, numerically.

Graphene oxide mode-locked Yb:GAGG bulk laser operating in the femtosecond regime

High-quality graphene oxide saturable absorber (SA) is successfully fabricated with 1–2 layer graphene oxide. By employing this SA, we have demonstrated femtosecond pulse generation from a graphene oxide passively mode locked bulk laser for the first time to our best knowledge. With two Gires–Tournois interferometer mirrors for dispersion compensation, pulses as short as 493fs with an average power of 500mW are obtained at the central wavelength of 1035.5nm. These results presented here indicate the great potential of GO for generating femtosecond mode-locked pulses in the bulk laser.

Adjustable dispersion reduction in low-coherent techniques by a system of tilted metallic mirrors with dielectric coating

In this paper a new method for adjustable reduction of a dispersive drop in axial resolution during low-coherent measurements is presented. This method is based on multiple reflections of a light beam from dielectric coated metallic mirrors and is intended for reducing dispersion in full-field systems. The tilted metallic mirror with a dielectric coating works like an adjustable Gires–Tournois interferometer. The concept of adjustability is based on a polarization dependent phase shift upon reflection from metallic surfaces at incidence angles different from θi=0°. The dispersion compensation was simulated numerically with the use of Fresnel equations for a silver mirror based compensator. The possibility of dispersion reduction was then verified experimentally in a Twyman–Green interferometer showing over 40% improvement in the axial resolution.

Design and Analysis Gires-Tournois-Interferometer Mirrors

We report the implementation and operation of GTI with high-reflectivity negative-dispersion dielectric mirrors for use in tunable ultrafast laser systems. The mirror structure is divided into two distinct regions: an underlying high-reflectivity dielectric quarter-wavelength stack and an overlying negative-dispersion section consisting of only a few layers and forming simple multiple Gires–Tournois interferometers. The example that we present was designed two structures with different spacers for operation from 670-860 nmand680-840nm has a near-constant group-delay dispersion of ±3000fs 2 and a peak reflectivity greater than 98%. We can usingand application of these mirrors in a mode-locked Ti: Sapphire laser.

Diode-pumped passively mode-locked femtosecond Yb:CTGG laser

A diode-pumped passively mode-locked Yb:CTGG disordered crystal laser has been demonstrated for the first time to our knowledge. With a semiconductor saturable absorber mirror for passive mode locking and two Gires–Tournois interferometer mirrors for dispersion compensation, pulses as short as 389 fs at a repetition rate of 45 MHz were obtained at the central wavelength of 1,037.8 nm. The maximum average power was 420 mW, corresponding to pulse energy of 9.3 nJ and peak power of 24 kW.

Design of Optical Notch Filters Based on Equivalent Relations

The transfer functions of optical notch filters based on all fiber unbalanced Mach-Zehnder interferometer with fiber ring coupled structure and Michelson Gires–Tournois interferometer structure are presented based on z-transform method respectively. On this basis, the structural parameters between the two kinds of notch filters are revealed to have some certain equivalent relations. With this equivalent relationship, the structural parameters for designing one of the two kinds of notch filter can be conveniently obtained by that of the other of the two kinds of notch filters. A design example of a two notch point notch filter using the method is given in detail in the paper.