Group Delay Dispersion Measurements Research Articles

Six-orders-of-magnitude-spanning dispersion measurement via Kalman filtering-aided white-light interferometry.

Dispersion plays a great role in ultrafast laser oscillators, ultrashort pulse amplifiers, and many other nonlinear optical dynamics. Therefore, dispersion measurement is crucial for device characterization, system design and nonlinear dynamics investigation therein. In this work, we demonstrate a versatile approach, i.e., Kalman filtering-aided white-light interferometry, for group delay dispersion (GDD) characterization. Extended Kalman filter is adopted to track the cosine-like interferogram, and to eliminate the unintended bias and the envelope, providing a nearly ideal phase retrieval and GDD estimation. The measurement range could span from tens of fs2 to tens of ps2, with an uncertainty of about 0.1%, enabling precise GDD measurement for diverse optical components, ranging from a millimeter-thick glass slide to highly dispersive chirped fiber Bragg gratings. Benefited by the simplicity, convenient setup, and easy operation as well as relatively low cost, this approach would help photonic device characterization, dispersion management and nonlinear dynamics investigation in the laboratory and work plant.

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.

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.

Fourier-transform spectral interferometry for in situ group delay dispersion monitoring of thin film coating processes.

A fast Fourier-based measurement system to determine phase, group delay, and group delay dispersion during optical coating processes is proposed. The in situ method is based on a Michelson interferometer with a broad band light source and a very fast spectrometer. To our knowledge, group delay dispersion measurements directly on the moving substrates during a deposition process for complex interference coatings have been demonstrated for the first time. Especially for the very precise production of chirped mirrors it is advantageous to get information about the phase properties of the grown layer stack to react on errors and retrieve more information about the coating process.

Group delay dispersion measurements in the mid-infrared spectral range of 2-20 µm.

We present two measurement devices which both allow the direct measurement of the group delay (GD) and group delay dispersion (GDD) of laser optics, covering the near- and mid-infrared (MIR) spectral range from 2 to 20 µm (500-5,000 cm-1). Two different kinds of devices were developed to measure the GDD of multilayer interference coatings. One is a resonant scanning interferometer (RSI) and the other is a white light interferometer (WLI). The WLI is also capable of measuring the GDD in transmission, for instance of bulk material. GDD measurements of a high dispersive mirror for wavelengths from 2.0 to 2.15 µm and one of a multilayer mirror from 8.5 to 12.0 µm are presented. A measurement of a zinc selenide (ZnSe) substrate in transmission was made with the WLI demonstrating the full bandwidth of the device from 1.9 to 20 µm. The comparison of all measurements with their related theoretical values shows a remarkable correspondence.

Low Group Delay Dispersion Optical Coating for Broad Bandwidth High Reflection at 45° Incidence, P Polarization of Femtosecond Pulses with 900 nm Center Wavelength

We describe an optical coating design suitable for broad bandwidth high reflection (BBHR) at 45° angle of incidence (AOI), P polarization (Ppol) of femtosecond (fs) laser pulses whose wavelengths range from 800 to 1000 nm. Our design process is guided by quarter-wave HR coating properties. The design must afford low group delay dispersion (GDD) for reflected light over the broad, 200 nm bandwidth in order to minimize temporal broadening of the fs pulses due to dispersive alteration of relative phases between their frequency components. The design should also be favorable to high laser-induced damage threshold (LIDT). We base the coating on TiO2/SiO2 layer pairs produced by means of e-beam evaporation with ion-assisted deposition, and use OptiLayer Thin Film Software to explore designs starting with TiO2/SiO2 layers having thicknesses in a reverse chirped arrangement. This approach led to a design with R > 99% from 800 to 1000 nm and GDD < 20 fs2 from 843 to 949 nm (45° AOI, Ppol). The design’s GDD behaves in a smooth way, suitable for GDD compensation techniques, and its electric field intensities show promise for high LIDTs. Reflectivity and GDD measurements for the initial test coating indicate good performance of the BBHR design. Subsequent coating runs with improved process calibration produced two coatings whose HR bands satisfactorily meet the design goals. For the sake of completeness, we summarize our previously reported transmission spectra and LIDT test results with 800 ps, 8 ps and 675 fs pulses for these two coatings, and present a table of the LIDT results we have for all of our TiO2/SiO2 BBHR coatings, showing the trends with test laser pulse duration from the ns to sub-ps regimes.

High-precision group-delay dispersion measurements of optical fibers via fingerprint-spectral wavelength-to-time mapping

The group-delay dispersion of an optical fiber was measured with the time-of-flight method, using fingerprint-like characteristic spectra from a mode-locked fiber laser source. To determine the group-delay dispersion up to the fourth order, least-squares fitting was applied to the overall time waveform mapped on the time axis for the fingerprint-spectral broadband pulses through a long optical fiber. The analysis of all 4003 data points reduced statistical uncertainty, and provided second-, third-, and fourth-order dispersion with uncertainties of 0.02%, 0.4%, and 4%, respectively.

Group Delay Dispersion Measurement From a Spectral Interferogram Based on the Cubic Phase Function

A novel group delay dispersion (GDD) measurement from a spectral interferogram is presented. Based on the cubic phase function (CPF) of the interference term, the GDD can be directly read from the ridge of CPF without phase retrieval and numerical differentiation operation. The proposed method is applied to measure the GDD and chromatic dispersion difference (CDD) of a polarization-maintaining fiber. The experimental results are unambiguous and insensitive to the filter choice of interference term calculation. GDD measurement can reach a resolution of 1 $\hbox{fs}^{2}$ , with a processing time of 25 s for 1001 wavelength points, and CDD measuring deviation is less than 0.5 $\hbox{fs}/(\hbox{km}\cdot\hbox{nm})$ around the center wavelength. The method is expected to be suitable for processing all spectral interferograms with polynomial phases.

Measurements of the group delay and the group delay dispersion with resonance scanning interferometer

We developed a method for group delay and group delay dispersion measurements, based on location of interference resonance peaks. Such resonance peaks can be observed in transmittance or in reflectance when two mirrors are placed parallel to each other and separated by a thin air spacer. By using a novel approach, based on simultaneous processing of the data acquired for different spacer distances we obtained reliable results with high resolution. Measurements were performed both in transmittance and reflectance layouts depending on the reflectivity of the mirror to be measured. The developed method allows dispersion measurements of ultraviolet mirrors and ultra-broadband mirrors spanning more than one optical octave to be performed.

Direct measurement of group delay dispersion in metamagnetics for ultrafast pulse shaping

In this paper, we explore the use of magnetic resonant metamaterials, so called metamagnetics, as dispersive elements for optical pulse shaping. We measure both positive and negative group delay dispersion (GDD) values in a metamagnetic material using the multiphoton interference phase scan (MIIPS) technique and show pulse temporal profiles numerically. The results are compared with finite element models. These GDD properties of metamagnetics, along with previously shown tunability and loss control with gain media, enable their use in ultrashort pulse optical applications.

基于白光干涉测量色散补偿薄膜的群延迟色散

基于白光干涉测量色散补偿薄膜的群延迟色散

Group delay dispersion measurement of a dispersive mirror by spectral interferometry: comparison of different signal processing algorithms

We built a dispersive white-light spectral interferometer for precisely measuring the dispersion properties of a multilayer thin-film structure. A novel algorithm with improved robustness to measurement errors is presented by combining a windowed Fourier transformation with wavelet-based differentiation. Compared with previously published algorithms, this method shows substantial resistance to measurement errors. The group delay dispersion properties of bulk materials and a homemade chirped mirror are measured by our apparatus, and the measurement result manifests considerable accuracy and robustness. The technique shows reasonable potential for the characterization of ultrabroadband chirped mirrors.

Group delay dispersion measurement of Yb 3+:YAl 3(BO 3) 4 crystal with white-light interferometry

We report the group delay dispersion of Yb 3+:YAl 3(BO 3) 4 (Yb:YAB) crystal measured by a white-light interferometer, and compare with that calculated from the Sellmeier formulae provided by the crystal supplier, over the wavelength range from 1000 nm to 1080 nm. The data should be useful for the dispersion compensation for femtosecond pulse generation in Yb:YAB lasers.

Group delay dispersion measurement of Yb:Gd_2SiO_5, Yb:GdYSiO_5 and Yb:LuYSiO_5crystal with white-light interferometry

We report the measured group delay dispersion (GDD) of new crystals Yb:Gd(2)SiO,(5)(Yb:GSO), Yb:GdYSiO(5) (Yb:GYSO) and Yb:LuYSiO(5) (Yb:LYSO) over wavelengths from 1000nm to 1200nm, with a white-light interferometer. Those GDD data should be useful for the dispersion compensation for femtosecond pulse generation in the lasers with these new crystals as the gain media.

Complete characterization of a broadband high-finesse cavity using an optical frequency comb

We demonstrate a new method to simultaneously measure spectrally resolved dispersion and losses (finesse) of a passive optical cavity over the entire bandwidth of an optical frequency comb. To this end, we record and analyze the spectral Moiré pattern between the perfectly equidistant frequency comb emitted from a Ti:Sapphire laser and the longitudinal modes of the passive cavity as a function of the laser's carrier-envelope-offset phase slippage (ø)CE. In the group-delay dispersion measurement of additionally introduced optical elements we verify a 2fs(2) accuracy in a 2THz resolution bandwidth and find good agreement of the measured performance and the target design of a high reflectance dielectric mirror. The sensitivity of the method is essentially equivalent to a cavity ring down technique allowing us also to readily observe signatures of atmospheric gas species.

Measurement of group delay dispersion of high numerical aperture objective lenses using two-photon excited fluorescence

We determined the group-delay dispersion (GDD) of five microscope objectives by measuring the second-order autocorrelation at the focal points of the objectives with two-photon excited fluorescence as the power square sensor. We found that typical microscope lens systems introduce significant GDD (2000-6500 fs(2)). The third-order dispersion determined for these objectives limits the minimum obtainable pulse width at the focal point of an objective to 20-30 fs if not compensated. No significant chromatic aberration or higher-order dispersion effects were found for any of the optical components measured within the wavelength range of 700-780 nm and for pulse widths greater than 50-60 fs.