Spectral Interference Fringes Research Articles

Simultaneous measurement of thickness and group refractive index in birefringent crystals

In order to measure the group refractive index and thickness of birefringent crystals simultaneously, a method based on spectral-domain interferometry is proposed. The optical path of each reflection layer of birefringent crystal is converted into spectral interference fringe of corresponding frequency by the principle of spectral-domain interferometry, and the accurate optical path calculation is realized by fast Fourier transform and Hanning-windowed energy centrobaric method. A two-step measurement method was designed to measure the crystal thickness and group refractive index of ordinary ( o ) and extraordinary ( e ) light synchronously by comparing the changes of the optical path before and after the insertion of the sample. The comparison between experimental and theoretical results of LiNbO3 crystals shows that the accuracy of the thickness measured by this system is better than 1 μm and the relative error of the group refractive index is better than 0.15%. The measurement method is simple to implement and has high precision, which is of practical significance for realizing the rapid and high-precision measurement of optical parameters of birefringent crystals.

One-shot three-dimensional imaging using a two-dimensional spectrometer with a fiber bundle

Using spectral interference from a chirped optical frequency comb, we developed a one-shot three-dimensional (3D) imaging method. We formed a two-dimensional spectrometer using fiber bundles made up of single-mode and multi-mode fibers to detect the spectral interference fringe images. The proposed method demonstrated one-shot 3D imaging of reflective targets with sub-µm level depth uncertainty and a wide dynamic range of 6 digits. Furthermore, by developing a method to remove the speckle noise caused by multi-mode fibers, we succeeded in capturing 3D profiles with sub-µm uncertainty in a one-shot with 299 times higher efficiency than single-mode fibers using a large numerical aperture.

Phase interrogation surface plasmon resonance hyperspectral imaging sensor for multi-channel high-throughput detection.

Phase interrogation surface plasmon resonance (SPR) imaging is, in principle, suitable in multiple samples and high-throughput detection, but the refractive index difference of various samples can be largely varied, while the dynamic range of phase interrogation SPR is narrow. So it is difficult to perform multi-sample detection in phase interrogation mode. In this paper, we successfully designed a multi-channel phase interrogation detection SPR imaging sensing scheme based on a common optical interference path between p- and s-polarized light without using any mechanical moving components. The fixed optical path difference between p- and s-polarized light is introduced by a birefringence crystal to produce sinusoidal spectral interference fringes. We adopted a time-division-multiplexing peak-finding algorithm to track the resonance wavelength so that the detection range can cover every channel. The phase values which carry the high sensitivity signal of the corresponding samples are calculated by the iterative parameter scanning cross-correlation algorithm.

Measurement of glass thickness and refractive index based on spectral interference technology.

A non-contact glass thickness and refractive index measurement method based on spectral interferometry is proposed. The method uses the Michelson interference principle to calculate the interference signal obtained by the spectrometer using the Fourier transform algorithm to obtain the modulation period of the spectral interference fringes. The geometrical thickness and refractive index of a glass sample can be calculated from the optical path difference between the reflected light of the reference arm and that of the front and back surfaces of the glass sample before and after being placed in the measuring arm. The linear interpolation method is used to resample the interference pattern in the frequency domain to ensure uniform sampling. It also adopts an improved phase extraction algorithm in the Fourier domain, which improves the anti-interference ability of the measurement system, and it exhibits a fast detection speed and high signal-to-noise ratio. To verify the accuracy of the measurement results of this method, a high-precision coordinate measuring machine is used for comparative experiments, and the characteristics of the tested object are analyzed. The experimental results show that the measurement accuracy of the system is in good agreement with that of a high-precision coordinate measuring machine.

Polarization modeling and predictions for DKIST, part 8: calibration polarizer spatial variation impacts

Astronomical spectropolarimeters require high accuracy polarizers with large aperture and stringent uniformity requirements. In solar applications, wire grid polarizers are often used as performance is maintained under high heat loads and temperatures over 200°C. DKIST is the NSF’s new 4-m aperture solar telescope designed to deliver accurate spectropolarimetric solar data across a wide wavelength range, covering a large field of view simultaneously using multiple facility instruments. Polarizers at 120 mm diameter are used to calibrate DKIST instruments but vary spatially in transmission, extinction ratio, and orientation of maximum extinction. We combine new spatial and spectral metrology for polarizers and retarders to simulate the accuracy losses with field angle and wavelength caused simultaneously by spatial variation of several optical parameters including beam decenter from misalignments. We also present testing of a new crystal sapphire substrate polarizer designed and fabricated to improve DKIST long wavelength calibrations. We assess spatial thickness variation of sapphire and fused silica wafer substrates using spectral interference fringes.

Evolutions of versatile wavelength-dependent bound solitons

Versatile structures of wavelength-dependent bound solitons are obtained based on nonlinear polarization rotation (NPR) mode-locked technology in an anomalous-dispersion fiber laser. After optimizing the intra-cavity birefringence and finely adjusting the operating wavelength of the laser, both the conventional soliton and loosely bound-state soliton pairs can be generated and switched under different operating wavelengths. With the evolution of bound state, the spectral interference fringes show significant changes and the temporal separation between bound solitons varies accordingly. Altering initial settings of laser parameters, wavelength-dependent multiple-soliton bound states are also found experimentally. Moreover, the formation and evolution mechanism of the bound states are explored and analyzed in this work.

Power spectral density analysis of relative comb-line phase jitter in a twin-soliton molecule

Investigation on the relative phase evolution between two bounded optical solitons is essential for its potential applications in development of larger telecommunication capacity of optical fiber transmission lines, resolution improvement in advancing ultrafast characterization approaches and development of all-optical information storage. Here we characterized relative comb-line phase jitter power spectral density (PSD) of a soliton molecule pair generated from a passively mode-locked Er:fiber laser. Through tracking the intensity difference between two selected wavelengths in one certain spectral interference fringe, the relative comb-line phase noise PSD is measured by balanced detection. The estimated measurement resolution is at 10−14 rad2/Hz level and the estimated integrated phase noise from 10 MHz to 100 Hz is 2.04 mrad. The estimated relative linewidth is far below 1 mHz. Comparison between phase noise PSD and intensity noise PSD indicates that AM–PM conversion plays an important role in relative phase jitter dynamics between the two solitons. Our spectral interference fringe tracking technique is attractive for its simplicity and shows potential in ultra-high resolution in phase noise measurement, providing an ultra-sensitive alternative approach for relative phase noise stabilization of optical soliton molecules, two independent mode-locked lasers and optical length stabilization of interferometers.

Analysis of loose bunches of soliton molecules in passive mode-locked fibre laser using time-stretching technology

Loose bunches of soliton molecules (SMs) in a passive mode-locked fiber laser with a WTe2 saturable absorber are observed using the photonic time-stretching (TS) technique. Due to the large temporal separations between the SMs, the TS profiles of the loose bunches appear as the intensity superposition of the spectral interference fringes of the adjacent SMs. The bandwidth limitations and the electronic system sampling rate contribute to the loss of phase information between adjacent SMs and the formation of the intensity overlap profiles. The phase difference and pulse width are estimated using a simulated annealing algorithm.

Phase interrogation SPR sensing based on white light polarized interference for wide dynamic detection range.

A phase surface plasmon resonance (SPR) sensing technology based on white light polarized interference in common-path geometry is reported. A halogen lamp is used as the excitation source of the SPR sensor. The fixed optical path difference (OPD) between p- and s-polarized light is introduced by a birefringence crystal to produce sinusoidal spectral interference fringes. The SPR phase is accurately extracted from the interference fringes using a novel iterative parameter-scanning cross-correlation algorithm. The dynamic detection range is expanded by tracking the best SPR wavelength, which is identified using a window Fourier algorithm. The experimental results show that the sensitivity of this SPR system was 1.3 × 10-7 RIU, and the dynamic detection range was 0.029 RIU. This sensor, not only simple to implement and cost efficient, requires no modulators.

基于光谱干涉技术的玻璃厚度及折射率测量方法

Based on spectral interference technique, a method for simultaneously measuring the thickness and refractive index of a glass was proposed. This method used the Michelson optical path to solve the interference signal received by the spectrometer through a Fourier transform algorithm to obtain the modulation period of the spectral interference fringe. The modulation period was determined according to the optical path difference formed between the measuring arm and the reference arm before and after the glass sample to be tested was placed in the measuring arm, and the geometric thickness and refractive index of the glass sample can be obtained. The method did not need mechanical scanning delay line and adopted the improved phase extraction algorithm in the Fourier domain, which improved the anti-interference ability of the measurement system and the detection speed was fast. The experimental results show that the thickness measurement accuracy of the glass sample is better than±1μm, and the refractive index measurement accuracy is ±5×10-4.

High-resolution 3D imaging method using chirped optical frequency combs based on convolution analysis of the spectral interference fringe

We applied an imaging optical system and convolution analysis to a one-shot 3D imaging method with a chirped optical frequency comb to greatly improve the transverse spatial resolution and depth accuracy. We obtained the high contrast spectral interference of a diffusive surface using the designed lens system and developed a simple and robust analysis technique using convolution of an obtained the interference fringe. The developed method was demonstrated to realize submicron-level uncertainty for the depth measurement. When applied to the surface structure of a coin, it demonstrated a transverse spatial resolution of 8.98 lp/mm and depth resolution of 0.35 µm.

Spectral calibration for spectral domain optical coherence tomography based on B-scan Doppler shift with tissue images

We propose a simple method of linearizing spectral interference fringes of spectral domain optical coherence tomography based on B-scan Doppler frequency shift (DFS), which can be obtained by offsetting the laser beam from the pivot of a scanning mirror. We show that DFS is proportional to wavenumber. A DFS based calibration curve can be then extracted from either a single mirror image or multiple tissue images. By examining the convergence of the nonlinear coefficients of the DFS curve fitted with a polynomial equation, tissue images themselves can be used to linearize the wavenumber without requiring mirror images or additional hardware. The method is verified with both ex vivo and in vivo tissue images. Using B-scan Doppler shift, we also demonstrate significantly improved imaging quality by combining complex conjugate ambiguity removal, speckle reduction, and spectral calibration with tissue images.

Interferometric Refractive Index Sensing with Terahertz Spoof Surface Plasmons

Near field interference of spoof surface plasmons propagating on two opposing faces of a thin metal sheet waveguide perforated by a periodic array of tapered holes has been investigated by time-domain terahertz spectroscopy. Closely spaced, chirped spectral interference fringes are observed in the output near the field as a result of the different nonlinear dispersion of the two surface modes. Results illustrating the potential of such a structure for interferometric refractive index sensing of nanolitres of analytes are presented.

Polarimetric Sensitivity to Torsion in Spun Highly Birefringent Fibers.

We report on experimental studies of polarimetric sensitivity to torsion in spun highly birefringent fibers. Two classes of spun fibers were examined, namely spun side-hole fibers and birefringent microstructured fibers with different birefringence dispersion, spin pitches, and spin directions. The polarimetric sensitivity to torsion was determined by monitoring a displacement of the spectral interference fringes arising in the output signal because of interference of polarization modes and induced by an additional fiber twist. Both the experimental results and the analytical predictions showed that the sensitivity to torsion normalized to the fringe width in the spun highly birefringent fibers increased asymptotically with the twist rate to the value of 1/ π rad−1. We have also studied the polarimetric response to temperature in the spun side-hole fibers. We have found that, in contrast to the torsional sensitivity, the temperature sensitivity decays asymptotically to zero with increasing fiber twist rate. Therefore, the spun fibers with short spin pitches are especially well suited for torsion measurements because the torsional sensitivity and the range of linear response are both enhanced in such fibers, while at the same time, the cross-sensitivity to temperature is reduced.

Method of synchronization measurement via spatial–spectral interference in coherent combination of multi-channel ultra-short pulses

Spatial–spectral interference fringes contain information on the time delay between pulses. By extracting the slope of the equiphase line in the spatial–spectral interference fringes, a large range and high-precision detection of the time delay is realized. Theoretical analysis is given. An experiment demonstrates the fundamental process for obtaining the time delay between two femtosecond pulses. In the current experiment the measurement range is from 0.4 fs to hundreds of fs. This method was first proposed for synchronization measurement of coherent combination of ultra-short pulses in a multi-channel system. The method can be applied at large scales in an ultra-short pulse laser facility.

Multiscale control and rapid scanning of time delays ranging from picosecond to millisecond.

Femtosecond amplifiers seeded by two independent femtosecond oscillators normally produce amplified pulse pairs with a timing jitter equal to the oscillator period, which is typically around 12 ns for Titanium:Sapphire lasers. Combining Arbitrary-Detuning Asynchronous Optical Sampling (AD-ASOPS) with an appropriate selection of amplified pulses, we demonstrate that the time-delay distribution can be narrowed down to a 25-ps time window, allowing to produce spectral interference fringes for each amplified pulse pair. Subsequent AD-ASOPS determination of the actual time delay with subpicosecond accuracy allows to tailor the delay distribution with an electronic control all the way to the repetition period of the amplifiers. We thus demonstrate rapid scanning of the time delays up to nearly 1 ms with a sub-picosecond accuracy, which makes this method an ideal tool for multiscale pump-probe spectroscopy.

Spectral interference fringes in chirped large-mode-area fiber Bragg gratings

Abstract Spectral interference fringes were experimentally observed in chirped large mode area fiber Bragg grating (CFBG) in the overlapping region of the reflected spectrum of fiber modes by a high resolution spectrometer. It was demonstrated that the interference is due to optical path difference of the reflected modes in slight chirped FBGs. By assuming chirped fiber Bragg gratings as a Fabry–Perot (FP) cavity, free spectral range (FSR) of FP was calculated 0.08 nm which is matched with measurement very well. Furthermore, the experiments show that axial tension and temperature changes of the CFBG do not have observable effects on the magnitude of FSR, however coiling of the fiber deceases spectral interference fringe amplitude without sensible effect on FSR magnitude. The results of this work can be utilized in bending sensors.

Interferometric Near-Infrared Spectroscopy (iNIRS) for determination of optical and dynamical properties of turbid media.

We introduce and implement interferometric near-infrared spectroscopy (iNIRS), which simultaneously extracts optical and dynamical properties of turbid media through analysis of a spectral interference fringe pattern. The spectral interference fringe pattern is measured using a Mach-Zehnder interferometer with a frequency-swept narrow linewidth laser. Fourier analysis of the detected signal is used to determine time-of-flight (TOF)-resolved intensity, which is then analyzed over time to yield TOF-resolved intensity autocorrelations. This approach enables quantification of optical properties, which is not possible in conventional, continuous-wave near-infrared spectroscopy (NIRS). Furthermore, iNIRS quantifies scatterer motion based on TOF-resolved autocorrelations, which is a feature inaccessible by well-established diffuse correlation spectroscopy (DCS) techniques. We prove this by determining TOF-resolved intensity and temporal autocorrelations for light transmitted through diffusive fluid phantoms with optical thicknesses of up to 55 reduced mean free paths (approximately 120 scattering events). The TOF-resolved intensity is used to determine optical properties with time-resolved diffusion theory, while the TOF-resolved intensity autocorrelations are used to determine dynamics with diffusing wave spectroscopy. iNIRS advances the capabilities of diffuse optical methods and is suitable for in vivo tissue characterization. Moreover, iNIRS combines NIRS and DCS capabilities into a single modality.

Dynamics of soliton explosions in passively mode-locked fiber lasers

A soliton explosion is an instability whereby a dissipative soliton undergoes a sudden structural collapse but remarkably returns back to its original shape after a short transient. We recently reported the first experimental observation of this effect in a fiber laser [Optica2, 36 (2015)10.1364/OPTICA.2.000036]. Here, we expand on our initial work, presenting a more detailed experimental and numerical study of the characteristics and dynamics of soliton explosions in passively mode-locked fiber lasers. Specifically, we explore different cavity configurations and gain levels, observing and characterizing explosion events using spectral and temporal real-time single-shot techniques. Our results highlight that the explosion characteristics observed in experiments depend critically on the position in the cavity where the output coupler is located. Furthermore, we find that the probability with which explosions occur depends on the pump power. We also identify a new kind of “partial” explosion, where strong spectral interference fringes appear on the pulse spectra, but a full collapse is avoided. Finally, we perform numerical simulations based on a realistic iterative cavity map and obtain results that are in good qualitative agreement with experimental measurements. Careful analysis of the simulation results provides strong credence to the interpretation that soliton explosions can be linked to a multipulsing instability.

Control of spectral interference patterns in broad Rabi sidebands toward quasi-comb structures.

The pattern of spectral interference fringes in broad dynamic Rabi sidebands allows for a considerable degree of control by shaping the picosecond driving pulse. We demonstrate experimental evidence of such control and report an analytic and numerical investigation of possibilities to control the fringe pattern to produce a comb-like optical structure. The temporal phase and amplitude shaping of a picosecond driving pulse influence the spectrum envelope, fringe contrast, and fringe spacing variation in the sideband spectra. The sideband spectrum envelope depends on the sharpness of the driving pulse, that is, on the rate at which the temporal distance between the leading and trailing edges grows away from the pulse maximum. Increasing this parameter reduces the variation of the envelope amplitude across the sideband. The fringe contrast, defined by the maximum-to-minimum difference, depends strongly on the asymmetry of the driving pulse. The imbalance between the leading and trailing edges leads to a decrease of the contrast. The variation of interpeak distance within a sideband was controlled using the temporal shape of the driving pulse. In the particular case of a blue-shifted sideband emitted by excited oxygen atoms driven by a picosecond pulse of 800 nm carrier wavelength and ∼5×10¹⁰ W cm⁻² intensity, a Gaussian pulse shape results in an interpeak distance increasing almost five times over the interval from 1.60 to 1.66 eV, whereas a super-Gaussian shape leads to almost equidistant fringes producing a comb-like spectrum.