Michelson Gires-Tournois Interferometer Research Articles

Optical analogue of the Thomas effect in special relativity using Michelson-Gires-Tournois interferometer: Comprehensive error analysis and recovery of the direction of the Thomas rotation angle

Previously, we reported a simple, low-cost, thin–film–based optical analogue of the Thomas Effect in Special Relativity (SR) using an ideal Michelson-Gires-Tournois interferometer (MGTI). This opens the door for other SR related phenomena to be studied analogously. Toward this goal, there are two important tasks. First, it is imperative to conduct a comprehensive evaluation of the technical limitations of this platform under two non-ideal (oftentimes unavoidable) operating conditions, namely: (i) an imperfect Gires-Tournois resonator (GTR), and (ii) the presence of interferometric error due to mismatch in the path-length arm difference of the MGTI. Second, it is also important to develop a technique to recover the direction information of the Thomas angle which is lost during the intensity measurement. Here, we report that (i) the GTR's imperfect back mirror must be fabricated with a minimum reflectance r0 value of greater than 0.9534 to limit the maximum phase deviation error by only less than 1%, (ii) the extracted Thomas angle is more sensitive to changes in interferometric error δl than the GTR imperfection. However, perfect extraction of the Thomas angle can be achieved for special range of the interferometric error δl, and (iii) the mimicked Thomas angle is distorted when the front reflectance coefficient r1 is greater than 0.7. Lastly, we introduce a method to recover the directional information of the Thomas angle by using a counter-intuitive additional positive/negative interferometric error. This method introduces no new optical components, and has high tolerance to fluctuation of the interferometric error.

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.

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.

General IIR optical notch filter based on Michelson Gires–Tournois interferometer

A general IIR optical notch filter design is presented from a digital filter design perspective for Michelson Gires–Tournois Interferometer structure. Optical notch filter with arbitrary notch frequency, notch point number, and 3 dB rejection bandwidth can be designed easily. According to the spectral requirement of desired notch filter, in frequency domain we firstly calculate the transfer function of desired allpass filter. Then the numbers of reflectors in Gires–Tournois etalon can be determined. We calculate the transfer function of this multi-cavity Gires–Tournois etalon by using Z-transform. By making the transfer function of allpass filter in frequency domain equal to that of the multi-cavity Gires–Tournois etalon, the notch filter can be directly realized. Different design examples are given in detail in the paper. The change of output spectrum is also investigated for the reflectance of the reflectors and the distance between the reflectors deviating from the ideal value. The results show that the notch filter has the tunability of notch frequency and 3 dB rejection bandwidth. The chromatic dispersion characteristic of the notch filter is analyzed finally. It shows that the notch filter has excellent chromatic dispersion characteristic.

Universal Michelson Gires-Tournois interferometer optical interleaver based on digital signal processing

Optical interleavers based on Michelson Gires-Tournois interferometer (MGTI) with arbitrary cascaded reflectors for symmetrical or asymmetrical periodic frequency response with arbitrary duty cycles are defined as universal MGTI optical interleaver (UMGTIOI). It can significantly enhance flexibility and applicability of optical networks. A novel and simple method based on digital signal processing is proposed for the design of UMGTIOI. Different kinds of design examples are given to confirm effectiveness of the method.

任意占空比不等带宽迈克耳孙Gires-Tournois干涉型光交错复用器的设计方法

任意占空比不等带宽迈克耳孙Gires-Tournois干涉型光交错复用器的设计方法

A novel super-high extinction ratio comb-filter based on cascaded Mach-Zehnder Gires-Tournois interferometers with dispersion compensation

In this paper, we propose a novel Mach-Zehnder Gires- Tournois interferometer (MZGTI) and a scheme to realize super high extinction ratio flat-top comb filter based on cascaded MZGTIs. Two sets of novel multi-cavity transmissive Gires-Tournois etalon (MCT-GTE) composed of cascaded Mach-Zehnder interferometer loops are added to the two arms of Mach-Zehnder interferometer (MZI) respectively, which forms a new MZI, i.e., MZGTI. MZGTI has the same characteristics as Michelson-Gires-Tournois interferometer (MGTI), which is suitable for dense wavelength division multiplexing systems. The super-high extinction ratio comb filter (SHERCF) we proposed has good passband flatness and wide bandwidth (passband or stopband bandwidth) when the extinction ratio is fairly high, which is quite superior to MGTI or MZGTI. For the severe chromatic dispersion problems, we propose a set of multi-cavity ring resonator (MC-RR) as a tunable dispersion compensator (TDC) for MZGTI, which is a set of cascaded ring resonators. Moreover, we demonstrate that a set of cascaded MC-RRs is an efficient dispersion compensator for SHERCF with the optimized results.

Multifunction optical filter with a Michelson–Gires–Tournois interferometer for wavelength-division-multiplexed network system applications

We propose using a novel multifunction optical filter with a Michelson-Gires-Tournois interferometer (MGTI) for future smart wavelength-division-multiplexed network system applications. The MGTI filter is a typical Michelson interferometer in which one of its reflecting mirrors is replaced with a Gires-Tournois resonator. One unique feature of this device is that it can function as a channel-passing (CP), a channel-dropping (CD), or a wide-bandpass (BP) filter, depending on the interferometer arm-length difference. Other interesting features are that (1) the linewidths of both the CP and the CD filter are twice as narrow as that of a typical Fabry-Perot filter with similar parameters, (2) theoretical visibility is always unity regardless of the mirror reflectance value, and (3) the BP filter has an excellent boxlike response function. Numerical results showing these characteristics are presented.