Fiber-based Optical Frequency Research Articles

Optical frequency dissemination via 103-km urban fiber link with remote passive phase stabilization

In this paper, we propose a technique for a fiber-based optical frequency dissemination system with remote passive phase noise cancellation. At the remote site, a 1×2 fiber pigtailed acousto-optic modulator (AOM) with two diffraction order outputs (0 and −1 order) is employed as the phase-compensated device, the undesired phase noise of fiber link introduced by environmental perturbations are passively canceled at remote sites. Different from other existing schemes, the proposed technique harnesses the benefits of remote radio frequency (RF) independence and low-temperature sensitivity in this noise-suppression configuration. Consequently, the system noise floor of the proposed optical frequency dissemination system achieves 9.44 × 10−21 without requiring a precise remote RF reference, and the phase-temperature coefficient is reduced to about 2 fs/K. A real-world experiment is conducted over a noisy round-trip 103 km urban fiber link. After being passively compensated, we demonstrate a fractional frequency instability of 1.57 × 10−14 at the integration time of 1 s and scales down to 3.96 × 10−20 at 10,000 s in terms of modified Allan deviation. The frequency uncertainty of the retrieved light after transferring through this noise-compensated fiber link relative to that of the input light achieves 1.80 × 10−18. This work demonstrates the system’s capability to disseminate the ultra-stable optical frequency standards and is a significant step towards realizing multi-node dissemination of the state-of-the-art optical clock signal with remote noise compensation via a tree-like topology fiber network.

Limitations due to residual interference in a fiber-based optical frequency reference at 1.55 µm

We present an experimental investigation of the stability limits specific to optical frequency standards using fiber optic architecture and semiconductor lasers. A compact setup composed of a semiconductor laser frequency-locked onto an acetylene transition detected in saturated absorption has been implemented using only fiber optic components. Fiber optic technology allows compact and reliable solutions for various applications. However, for high sensitivity and stability applications such as metrology, residual reflections induced by optical index inhomogeneities in connectors and fiber-coupled components leading to spurious interference significantly limit performance. We have examined the origin of the interference fringes superimposed on the detected signal and the limitations they cause to the frequency stability of the reference. The effects of temperature and beam power fluctuations are also examined. Our results show that the frequency stability is limited in the 10 − 13 range by the effect of interference fringes due to use of fiber components.

Multi-branch erbium fiber-based femtosecond optical frequency comb for measurement of cavity ring-down spectroscopy

<sec>In this paper, we demonstrate an optical frequency comb (OFC) based on an erbium-doped-fiber femtosecond laser, for the measurement of cavity ring-down spectroscopy (CRDS) with wavelengths of 1064, 1083, 1240, 1380, 1500, 1600, 1750 and 2100 nm. We adopt a multi-branch structure to produce high power at the specific wavelengths to meet the requirement for application in the spectral measurement. The OFC is developed by using a mode-locked fiber ring laser based on the nonlinear amplifying loop mirror mechanism. The laser is self-starting by introducing a nonreciprocal phase bias in the cavity and insensitive to the environmental perturbation. Using the chirped pulse amplification and highly nonlinear fibers, the broad spectra at the specific wavelengths are obtained. By optimizing the parameters of the pulses, the power of per mode at each target wavelength is greater than 300 nW.</sec><sec>The<i> </i><i>f</i><sub>rep</sub> is obtained by detecting the output of the femtosecond laser directly, while the<i> </i><i>f</i><sub>ceo</sub> is detected by <i>f</i>-2<i>f</i> interference. The signal-to-noise ratio of the<i> </i><i>f</i><sub>ceo</sub> is about 35 dB with a 300-kHz resolution bandwidth. By controlling the intra-cavity electro-optic modulator and piezoactuator , the <i>f</i><sub>rep</sub> is stabilized with high bandwidth and large range (about megahertz bandwidth and 3 kHz range). The <i>f</i><sub>ceo</sub> is stabilized by using feedback to the pump current of the femtosecond laser dynamically. The in-loop frequency instability degree of the <i>f</i><sub>ceo</sub>, evaluated by the Allan deviation, is approximately 4.95 × 10<sup>–18</sup>/<i>τ</i><sup>1/2</sup> at 1 s and integrates down to 10<sup>–20</sup> level after 2000 s, while that of the <i>f</i><sub>rep</sub> is well below 5.85 × 10<sup>–13</sup>/<i>τ</i>. The all polarization-maintaining erbium fiber-based femtosecond optical frequency comb with multi-application branches we demonstrate in this paper is efficient and reliable for many other applications including optical frequency metrology and optical atomic clocks.</sec>

All polarization-maintaining Er:fiber-based optical frequency comb for frequency comparison of optical clocks

We demonstrate an optical frequency comb (OFC) based on a turnkey mode-locked laser with a figure-9-shape structure and polarization-maintaining fibers, for the comparison of frequency among optical clocks with wavelengths of 698 nm, 729 nm, 1068 nm, and 1156 nm. We adopt a multi-branch approach in order to produce high power OFC signals at these specific wavelengths, enabling the signal-to-noise ratio of the beatnotes between the OFC and the clock lasers to exceed 30 dB at a resolution bandwidth of 300 kHz. This approach makes the supercontinuum spectra much easier to be generated than a single branch OFC. However, more out-of-loop fibers degrade the long-term frequency instability due to thermal drift. To minimize the thermal drift effect, we set the fiber lengths of different branches to be similar, and we stabilize the temperature as well. The out-of-loop frequency instability of the OFC due to the incoherence of the multi-branch is about 5.5 × 10−19 for 4000 s, while the in-loop frequency instability of f ceo and that of f beat are 7.5 × 10−18 for 1 s and 8.5 × 10−18 for 1 s, respectively. The turnkey OFC meets the requirement for the comparison of frequency between the best optical clocks.

Er:fiber-based femtosecond frequency comb stabilized to an Yb+ single-ion optical frequency standard

An erbium fiber-based femtosecond optical frequency comb stabilized to an Yb+ single-ion optical frequency standard was created. For the first time, a combination of an extra-cavity acousto-optic frequency modulator with fiber outputs and an intracavity electro-optic phase modulator based on a KTP crystal were used to stabilize offset frequency and one of the optical components of the Er:fiber femtosecond comb. As a result a locking bandwidth of 30 kHz for the optical comb offset frequency has been obtained. It is shown that the relative instability introduced by the stabilization and measurement systems into the output radio frequencies (in addition to the instability of the reference optical signal) is no worse than 5 × 10−14 for averaging times of 1 s and 2 × 10−16 for averaging times of 400 s.

Validating frequency transfer via interferometric fiber links for optical clock comparisons

We investigate the validation of fiber-based optical frequency transfer for frequency comparison applications. We specifically consider the frequency transfer validation for remote optical clock comparisons and want to ensure interferometric fiber link uncertainty contributions below the combined uncertainty of the clocks under test. The validation is based on signals obtained via looping back from the remote end to the sender site and comparing the input with the output of the loop. These loop-back data need to be averaged over intervals for reaching the validation goal, as the short-term instability of long-distance interferometric fiber links is typically higher than that of optical clocks. We introduce a two-step validation approach and address the finding of a compromise between opposing aspects of averaging: reaching low uncertainties versus achieving a high data coverage of the validated data set via a high temporal resolution of the fault identification. We discuss the impact of different averaging types and of the tolerance of filtering criteria on the achievable estimated uncertainty and on the coverage of the validated data set. Data from four multiple-week-long measurement campaigns on the fiber link between Physikalisch-Technische Bundesansanstalt and University of Strasbourg are used for this assessment.

Polarization Scramblers to Solve Practical Limitations of Frequency Transfer

Polarization variations in optical fibers are complex and would severely affect the performances of polarization-sensitive signal distribution systems. Owing to advances in experimental techniques and theoretical tools, we observe the effect of polarization variations in the optical fibers and we demonstrate that polarization mode dispersion (PMD) dominates the free-running fiber noise. Ultrahigh correlation, over 99%, is found between the phase fluctuation induced by polarization variation and the temperature fluctuation impacted on the optical fibers. By means of a polarization scrambling technique, the polarization variations in the optical fiber are averaged and the phase perturbations are minimized. It provides a promising solution for suppressing the random disturbances of polarization in the fiber-based optical frequency transfer system and quantum key distribution (QKD) system.

Fiber-based optical frequency comb at 3.3 µm for broadband spectroscopy of hydrocarbons [Invited

A 125 MHz fiber-based frequency comb source in the mid-infrared wavelength region is presented. The source is based on difference frequency generation from a polarization-maintaining Er-doped fiber pump laser and covers a spectrum between 2900 cm−1 and 3400 cm−1 with a simultaneous bandwidth of 170 cm−1 and an average output power up to 70 mW. The source is equipped with actuators and active feedback loops, ensuring long-term stability of the repetition rate, output power, and spectral envelope. An absorption spectrum of ethane and methane was measured using a Fourier transform spectrometer to verify the applicability of the mid-infrared comb to multispecies detection. The robustness and good long- and short-term stability of the source make it suitable for optical frequency comb spectroscopy of hydrocarbons.

Combining fiber Brillouin amplification with a repeater laser station for fiber-based optical frequency dissemination over 1400 km

We investigate optical frequency dissemination over a 1400 km long fiber link in looped configuration over a pair of underground fibers between Braunschweig and Strasbourg. This fiber link is the first to combine fiber Brillouin amplifiers with a repeater laser station. Phase-coherent operation over more than five days is demonstrated. We analyze the repeatability of the performance over four campaigns and present results of 65 d in total. The weighted mean of the fractional frequency offset of the transferred optical frequency over the complete data set is (−1.1 ± 0.4)×10–20. By analyzing the stabilization signals of the two individual fibers, the correlation of the phase noise on the two fibers is shown to be >98%.

Frequency measurement on the 5s5p P23−5s4d D33 transition of Sr88 atoms using the photon-momentum-transfer technique

We report a frequency measurement on the $5s5p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{-}5s4d\phantom{\rule{0.16em}{0ex}}^{3}D_{3}$ transition of $^{88}\mathrm{Sr}$ atoms at $2.9\phantom{\rule{0.16em}{0ex}}\ensuremath{\mu}\mathrm{m}$. The excitation spectra are obtained by measuring the photon momenta transferred to ultracold atoms. The transition frequency is determined to be 102 550 196 205(9) kHz using an erbium fiber-based optical frequency comb. We numerically investigate possible frequency corrections by taking an acceleration of atoms and attenuation of the excitation light into account. This measurement technique is particularly useful for transitions where laser-induced fluorescence is difficult to observe but the spatial imaging of atoms is possible.

Refractive index sensing with temperature compensation by a multimode-interference fiber-based optical frequency comb sensing cavity.

We proposed a refractive index (RI) sensing method with temperature compensation by using an optical frequency comb (OFC) sensing cavity including a multimode-interference (MMI) fiber, namely, the MMI-OFC sensing cavity. The MMI-OFC sensing cavity enables simultaneous measurement of material-dependent RI and sample temperature by decoding from the comb spacing frequency shift and the wavelength shift of the OFC. We realized the simultaneous and continuous measurement of RI-related concentration of a liquid sample and its temperature with precisions of 1.6 × 10-4 RIU and 0.08 °C. The proposed method would be a useful means for the various applications based on RI sensing.

Control of Kerr-microresonator optical frequency comb by a dual-parallel Mach-Zehnder interferometer

A technique to integrate key functions of a Kerr-microresonator optical frequency comb into one device, i.e., a dual-parallel Mach-Zehnder interferometer (DP-MZI), is proposed. In the technique, a DP-MZI enables the control of carrier envelope offset frequency (fceo), as well as repetition frequency (frep), in addition to generating a stable dissipative Kerr soliton. In experiments, influences on fceo and frep by pump frequency and power modulation via a DP-MZI are investigated, followed by a demonstration of long-term full stabilization of a microresonator soliton comb to a fiber-based optical frequency comb. As another example demonstration, timing jitter of a microresonator soliton comb is significantly suppressed by referencing to a fiber through a two-wavelength delayed self-heterodyne interferometer (TWDI).

Quantitative depolarization measurements for fiber-based polarization-sensitive optical frequency domain imaging of the retinal pigment epithelium.

A full quantitative evaluation of the depolarization of light may serve to assess concentrations of depolarizing particles in the retinal pigment epithelium and to investigate their role in retinal diseases in the human eye. Optical coherence tomography and optical frequency domain imaging use spatial incoherent averaging to compute depolarization. Depolarization depends on accurate measurements of the polarization states at the receiver but also on the polarization state incident upon and within the tissue. Neglecting this dependence can result in artifacts and renders depolarization measurements vulnerable to birefringence in the system and in the sample. In this work, we discuss the challenges associated with using a single input polarization state and traditional depolarization metrics such as the degree-of-polarization and depolarization power. We demonstrate quantitative depolarization measurements based on Jones vector synthesis and polar decomposition using fiber-based polarization-sensitive optical frequency domain imaging of the retinal pigment epithelium in a human eye.

Improving the accuracy of a dual-comb interferometer by suppressing the relative linewidth

We present a compact system of synchronization for two fiber-based optical frequency comb lasers. We use a free-running continuous wave laser as an intermediary to obtain the relative noise of two combs and employ an intra-cavity electro-optic modulator (EOM) to achieve active phase feedback for fast synchronization. The EOM bandwidth is 150 kHz and the relative linewidth is suppressed markedly from 300 kHz to sub-hertz values. The relative effective timing jitter of the two pulse trains is also decreased from 680 fs to 25 fs. The proposed method shows promise for developing a high-performance, low-cost, fiber-based dual-comb interferometer for ranging or spectroscopy.

Mode-filtering technique based on all-fiber-based external cavity for fiber-based optical frequency comb.

We developed a mode-filtering technique based on the all-fiber-based external cavity for a fiber-based optical frequency comb for high repetition rate (frep) frequency comb, and the carrier envelope offset frequency (fceo) can be detected and stabilized and is robust to environmental fluctuations. To achieve multiplication of the frep with a high multiplication factor using the fiber ring cavity, a long fiber was developed to mitigate the physical limitation inhibiting the shortening of the cavity length. In this study, the length of the fiber cavity was set to 6.7 m (free spectral range = 44.7 MHz) as the fiber-based comb length was 6.1 m. We were able to demonstrate a multiplication factor of 11, i.e., frep increased from 48.7 MHz to 536.0 MHz with a side mode suppression ratio of about 25 dB using the double-pass configuration.

Optical frequency synthesizer for precision spectroscopy of Rydberg states of Rb atoms

We have developed an optical frequency synthesizer for the precision spectroscopy of highly excited Rydberg states of Rb atoms. This synthesizer can generate a widely tunable 480 nm laser light with an optical power of 150 mW and an absolute frequency uncertainty of less than 100 kHz using a high-repetition-rate (325 MHz) Er fiber-based optical frequency comb and a tunable frequency-doubled diode laser at 960 nm. We demonstrate the precision two-photon spectroscopy of the Rydberg states of 87Rb atoms by observing the electromagnetically induced transparency in a vapor cell, and measure the absolute transition frequencies of 87Rb to nD (n = 53–92) and nS (n = 60–90) Rydberg states with an uncertainty of less than 250 kHz. It is the first direct frequency measurements of these transitions using an optical frequency comb.

Fiber-based femtosecond optical frequency comb stabilized to iodine frequency standard

A fiber-based femtosecond optical frequency comb spanning wavelengths from 1 to 2 μm was stabilized precisely to an iodine frequency standard by means of heterodyne optical phase-locked loops. It enables transfer of frequency stability across electromagnetic spectrum and implementation of compact optical clocks with ∼10-15 long-term instability.

Polarization dependence of the direct two photon transitions of 87Rb atoms by erbium: Fiber laser frequency comb

The femtosecond fiber-based optical frequency combs have been proved to be powerful tools for investigating the energy levels of atoms and molecules. In this paper, an Er-doped fiber femtosecond optical frequency comb has been implemented for studying the polarization dependence of 5S–5D two-photon transitions in thermal gas of atomic rubidium 87 using an entirely symmetrical optical configuration. By changing the polarization states of the counter-propagating light beams, the polarization dependence of direct two photon transition spectrum is demonstrated, and a dramatic variation (up to 5.5 times) of the two-photon transitions strength has been observed. The theory for the polarization dependence of two photon transition based on the second-order perturbation was established, which is in good agreement with the experimental results. The measurement results indicate that the polarization state manipulation with the existing frequency comb is used for femtosecond optical frequency comb based two photon transition spectroscopic purposes, which will improve the precision measurement of the absolute transition frequency and related applications.

Dual-frequency comb generation with differing GHz repetition rates by parallel Fabry–Perot cavity filtering of a single broadband frequency comb source

We present a dual-comb-generator based on a coupled Fabry–Perot filtering cavity doublet and a single seed laser source. By filtering a commercial erbium-doped fiber-based optical frequency comb with CEO-stabilisation and 250 MHz repetition rate, two broadband coherent combs of different repetition rates in the GHz range are generated. The filtering doublet consists of two Fabry–Perot cavities with a tunable spacing and Pound–Drever–Hall stabilisation scheme. As a prerequisite for the development of such a filtering unit, we present a method to determine the actual free spectral range and transmission bandwidth of a Fabry–Perot cavity in situ. The transmitted beat signal of two diode lasers is measured as a function of their tunable frequency difference. Finally, the filtering performance and resulting beat signals of the heterodyned combs are discussed as well as the optimisation measures of the whole system.

Precision Frequency Measurement of 87Rb 5S1/2 (F = 2)→5D5/2 (F″ = 4) Two-Photon Transition through a Fiber-Based Optical Frequency Comb**Supported by the National Natural Science Foundation of China under Grant Nos 61405002, 91336103, 10934010, 61535001 and 61078026.

The absolute frequency of 87Rb 5S1/2 (F = 2)→5D5/2 (F″ = 4) two-photon transition at 778nm is measured in an accuracy of 44 kHz. A home-made erbium-doped fiber laser frequency comb with frequency stability of 5.0 × 10−13@1 s is employed for the light source. By using a periodically poled lithium niobate, the femtosecond pulse operating in 1556nm is frequency-doubled to 778nm to obtain the direct two-photon transition spectroscopy of thermal rubidium vapor. Through sweeping the carrier envelope offset frequency (fceo), the 5S1/2 (F = 2)→5D5/2 (F″ = 4) two-photon transition line is clearly resolved and its absolute frequency is determined via the peak-finding of the fitting curve. After the frequency correction, the measured result agrees well with the previous experiment on this transition. The entire system configuration is compact and robust, providing a potential candidate of optical frequency standard for telecommunication applications.