Radek Smid

Conversion of stability of femtosecond mode-locked laser to optical cavity length

In this contribution we propose a scheme for a generation of precise displacements through conversion of relative stability of components of a femtosecond laser into the length of a Fabry-Perot cavity. The spacing of mirrors of a Fabry-Perot interferometer represents a mechanical length standard referenced to stable optical frequency of a femtosecond mode-locked laser. With the help of a highly selective optical filter, it is possible to get only a few discrete spectral components. By tuning and locking the Fabry-Perot cavity to a selected single component it is possible to get a mechanical length standard with the uncertainty of the repetition frequency of the femtosecond laser. To verify the method, an auxiliary single-frequency laser is locked to the resonance mode of the cavity and simultaneously it is optically mixed with an independent optical frequency standard He-Ne-I2. The stability of the beat-frequency between these 2 lasers represents the stability of the Fabry-Perot cavity length. The stability recording evaluated through Allan variances for one hour of operation is presented. The pilot experimental setup is able to generate the length standard in the order of 0.01 nm for 20 min of integration time.

Study of the thermal stability of Zerodur glass ceramics suitable for a scanning probe microscope frame

The work presents measurements of the length stability of Zerodur glass ceramic with temperature change. Measurement of this thermal characteristic is necessary for determination of the optimal temperature at which the Zerodur glass ceramic has a coefficient of thermal expansion close to zero. The principle of the measurement is to monitor the length changes using an optical resonator with a cavity mirror spacer made from the Zerodur material to be studied. The resonator is placed inside a vacuum chamber with a temperature control. A tunable laser diode is locked to a certain optical mode of the resonator to monitor the optical frequency of this mode. A beat-note signal from optical mixing between the laser and a stabilized femtosecond frequency comb is detected and processed. The temperature dependence of the glass ceramics was determined and analyzed. The resolution of the length measurement of the experimental set-up is on the order of 0.1 nm.

Two-Stage System Based on a Software-Defined Radio for Stabilizing of Optical Frequency Combs in Long-Term Experiments

A passive optical resonator is a special sensor used for measurement of lengths on the nanometer and sub-nanometer scale. Astabilized optical frequency comb can provide an ultimate reference for measuring the wavelength of a tunable laser locked to the optical resonator. If we lock the repetition and offset frequencies of the comb to a high-grade radiofrequency (RF) oscillator its relative frequency stability is transferred from the RF to the optical frequency domain. Experiments in the field of precise length metrology of low-expansion materials are usually of long-term nature so it is required that the optical frequency comb stay in operation for an extended period of time. The optoelectronic closed-loop systems used for stabilization of combs are usually based on traditional analog electronic circuits processing signals from photodetectors. From an experimental point of view, these setups are very complicated and sensitive to ambient conditions, especially in the optical part, therefore maintaining long-time operation is not easy. The research presented in this paper deals with a novel approach based on digital signal processing and a software-defined radio. We describe digital signal processing algorithms intended for keeping the femtosecond optical comb in a long-time stable operation. This need arose during specialized experiments involving measurements of optical frequencies of tunable continuous-wave lasers. The resulting system is capable of keeping the comb in lock for an extensive period of time (8 days or more) with the relative stability better than 1.6 × 10−11.

Frequency Noise Suppression of a Single Mode Laser with an Unbalanced Fiber Interferometer for Subnanometer Interferometry

We present a method of noise suppression of laser diodes by an unbalanced Michelson fiber interferometer. The unstabilized laser source is represented by compact planar waveguide external cavity laser module, ORIONTM (Redfern Integrated Optics, Inc.), working at 1540.57 nm with a 1.5-kHz linewidth. We built up the unbalanced Michelson interferometer with a 2.09 km-long arm based on the standard telecommunication single-mode fiber (SMF-28) spool to suppress the frequency noise by the servo-loop control by 20 dB to 40 dB within the Fourier frequency range, remaining the tuning range of the laser frequency.

An Ultra-stable Generator of Absolute Length Based on Femtosecond Mode-lock Laser and Optical Resonator

In the work, we present a proposal of a system converting excellent frequency stability of components generated by the mode-locked laser into a set of discrete values of length represented by a spacing of mirrors of an optical resonator.

Evaluation of Fabry-Perot cavity length by the stabilized optical frequency comb and acetylene absorption

The ultra low expansion cavities play a crucial role in laser stabilization, and they are essential in ion clocks. We present a method to monitor the temperature distance changes in the Fabry-Perot cavity with a spacer from an ultra low expansion material with sub-nanometer resolution. The FPC was placed into a temperature-stabilized stainless steel chamber.

Precise monitoring of ultra low expansion Fabry-Perot cavity length by the use of a stabilized optical frequency comb

The use of an ultra low expansion cavity plays a crucial role in laser stabilization, and it is essential in atomic or ion clocks. In this work we present a method of mirror distance monitoring in an evacuated Fabry-Perot cavity (FPC) made from an ultra low expansion material (Zerodur expansion class 0). The FPC was placed into a temperature-stabilized stainless steel chamber and the FPC temperature was set to remain close to the point where the expansion coefficient of the cavity material is the lowest. The precise distance of the FPC mirrors in vacuum was indirectly proportional to the optical frequency of a laser. One of the frequency comb component chosen by FBG grating was locked to the FPC of 400 MHz free spectral range. The 100 MHz repetition frequency of the femtosecond laser comb was monitored with counter referenced to a crystal oscillator with short term stability < 10−12 and long term stability locked to a GPS.

Monitor of mirror distance of Fabry-Perot cavity by the use of stabilized femtosecond laser comb

The use of an ultra low expansion cavity plays a crucial role in laser stabilization, and in atomic or ion clocks. We propose an easy method of precise monitoring of optical path distance in Fabry-Perot interferometer. The spacing of mirrors of the Fabry-Perot interferometer in ambient air represents the optical path distance referenced to stable optical frequency of the femtosecond mode-locked laser. With the help of highly selective optical filter it is possible to get only a few of separate spectral components of laser comb. Optical path distance is transfered to optical frequency of the comb component and through the repetition frequency of the laser to the radio-frequency domain. Repetition frequency of the laser can be monitored with the uncertainty referenced to the any local oscillator or through the GPS to the atomic clock standard. By using this mehod we are able to measure and lock the Fabry-Perot cavity to a selected single component of optical frequency comb an to measure the optical path distance directly in rf domain.

Repetition rate multiplication of a femtosecond frequency comb

This paper presents the progress in the development of two Fabry-Pérot filter cavities for repetition rate multiplication of two femtosecond frequency combs. The optical design of both setups consists of mode matching optics and a resonant cavity for the repetition rate multiplication. In one case, the cavity consists of two dielectric mirrors with near-zero group velocity dispersion and in the other of two silver coated mirrors. We demonstrate multiplication of a 1 GHz repetition rate to 10 GHz for a Ti:Sa femtosecond frequency comb with central wavelength around 820 nm and of 250 MHz repetition rate to 1 GHz for a Er-doped fiber femtosecond frequency comb with central wavelength around 1560 nm.

Automatic unit for measuring refractive index of air based on Ciddor equation and its verification using direct interferometric measurement method

In scanning probe microscopy laser interferometers are usually used for measuring the position of the probe tip with a metrological traceability. As the most of the AFM setups are designed to work under standard atmospheric conditions the changes of the refractive index of air have an influence to measured values of the length with 1.0exp(-4) relatively. In order to achieve better accuracies the refractive index of air has to be monitored continuously and its instantaneous value has to be used for compensating the lengths measured by all of the interferometric axes. In the presented work we developed a new concept of an electronic unit which is able to monitor the refractive index of air on basis of measurement of ambient atmospheric conditions: temperature, humidity, pressure of the air and the CO2 concentration. The data processing is based on Ciddor equation for calculating the refractive index of air. The important advantage of the unit is a very low power consumption of the electronics so the unit causes only negligible temperature effects to the measured environment. The accuracy of the indirect measuring method employed by the unit was verified. We tested the accuracy in comparison with a direct method of measuring refractive index of air based on an evacuatable cell placed at the measuring arm of a laser interferometer. An experimental setup used for verification is presented together with a set of measurements describing the performance. The resulting accuracy of the electronic unit falls to the 4.1 exp(-7) relatively.