(Color online) Fractional frequency instabilities of various high-stability microwave and optical frequency references. References are given in the text.
(cover image) Ultrastable frequency/timing references are distributed through a kilometer-scale optical fiber network to facilities for several precision applications, including: atomic clock comparison and synchronization, also enabling mapping of the Earth’s geoid; a long-baseline array of phase-coherent radio telescopes; and an accelerator-based advanced light source for generating x-ray pulses. Image courtesy of Jeff Fal, JILA.
(Color online) (a) Phase noise spectrum for of optical power from a femtosecond laser split equally onto identical photodetectors, and subsequently mixed to measure the excess phase noise in detection of the 10 GHz harmonics of the laser’s repetition rate. For , amplifier flicker noise behaves as . The sharp features between 100 Hz and 1 kHz are due to amplitude-to-phase noise conversion. Above 10 kHz the shot/thermal noise floor is reached. (b) The shot noise and thermal noise limits are plotted as functions of the incident optical power. Note that shot noise and thermal noise introduce a white phase noise spectral density with magnitude independent of the carrier frequency; thus, their relative contributions to frequency instability and timing jitter decrease with an increasing carrier frequency.
(Color online) Principle of operation for a typical actively compensated fiber network for distributing frequency and timing references. A partial retroreflector or transceiver at the remote end returns the signal through a round trip of both the fiber network and the actuator. Accurate comparison between the phase of the round-trip signal and the original reference allows the double-pass actuator to compensate for the fiber link’s phase perturbations for time scales longer than . The actuator can act on the group delay for modulated-cw transfer or frequency comb (pulse-timing) transfer, or it can act on the optical phase for direct optical carrier transfer.
(Color online) Various experimental schemes for transfer of frequency references. (a) Actively-stabilized transfer of a microwave reference by modulating a diode laser. (b) Direct transfer of the optical carrier by stabilizing the optical phase of the fiber link. (c) Transfer of simultaneous microwave and optical frequency references by transferring an optical frequency comb. Either optical or microwave information from the round trip can be used to stabilize the group delay and/or optical phase delay of the fiber link.
(Color online) Measured instability of amplitude-modulated light transmitted through a short fiber (squares) and through a round trip of the BRAN fiber (open triangles). The rf modulation signal carried by the fiber-transmitted light is heterodyne detected against the original signal source, which has been frequency shifted by 10 kHz via a single-sideband generation rf interferometer. Also shown for comparison is the stability of NIST’s Cs-referenced hydrogen maser (solid line).
(Color online) (a) Phase of the 7-km round-trip BRAN fiber for a transferred rf frequency of 950 MHz, showing long-term fractional frequency offsets of . (b) Time derivative of the phase data, with a rolling box average of 100 s applied, showing the fractional frequency offset induced by the passive fiber transfer setup.
(Color online) (a) Simplified energy level diagram for neutral Sr atoms, showing the two cooling transitions at 461 and 689 nm, and the clock transition at 698 nm. (b) Frequency-counting record for , showing the achieved 2.8 Hz statistical uncertainty (maser-transfer-limited) in the red-striped box and the 19 Hz systematic uncertainty as the outer blue lines.
(Color online) Fourier spectral analysis of the heterodyne beat linewidth between the original laser beam (before the AOM) and the returned light after a round trip through the fiber link. Without phase compensation, the beat linewidth is broadened by the fiber to . The inset shows the beat signal with a much narrower 1 kHz span and a 0.048 Hz resolution bandwidth when the fiber noise cancellation is activated. This is to be contrasted with the white noise floor showing in the same spectral window when phase noise is not canceled. Notice the noise level is lowered by due to the emergence of the recovered carrier signal when cancellation is activated. (Adapted from Ref. 86.)
(Color online) Counted heterodyne beat signal between the original laser and the returned light after a round trip. The top left panel corresponds to the case when the fiber noise is uncompensated, and the bottom left panel shows the compensated case, both with a 1 s gate time. Allan deviations determined from the time records are shown at right. (Adapted from Ref. 86.)
(Color online) Optical measurement between the transmitted and the standards is shown as filled circles. The local measurement between two standards is shown as open squares, and the measurement between the transmitted standard and the NIST maser reference is shown as triangles. (Adapted from Ref. 86.)
(Color online) The carrier-envelope offset frequency is found by taking the difference of the frequencies of a comb mode at and the second harmonic of a mode at .
(Color online) The frequency instability for transfer of the comb repetition frequency is measured by counting the 10 kHz mixing product between the shifted reference signal from the mode-locked fiber laser and the transmitted signal. SSB gen., single-sideband generator; VOA, variable optical attenuator. (Adapted from Ref. 141.)
(Color online) (a) The Allan deviation for microwave-frequency transfer over the BRAN fiber using various bandwidths for the transmitted fiber laser pulses and several different average optical powers incident on the receiving photodetector. The lowest instability is achieved with the narrowest bandwidth, which provides a sufficient SNR for the received microwave signal with the smallest optical power. The measurement noise floor, obtained with a short piece of fiber, is the same for all operating conditions. (b) The pulse spectra for the three mode-locking conditions used in (a). bw, bandwidth. (Adapted from Ref. 141.)
(Color online) To cancel the phase noise introduced during transfer of the comb repetition frequency, the phase noise is first measured by mixing the 81st harmonic of the repetition frequency obtained from the transmitted pulses and a reference portion of the fiber laser output. The resulting error signal is then applied to an adjustable delay line after appropriate filtering and amplification. The transmission fiber is either the dispersion-compensated BRAN fiber, or the DSF. A FFT provides spectral analysis of the in-loop timing jitter. The out-of-loop frequency instability is determined from the eighth harmonic of the repetition frequency obtained from the lower pair of photodetectors as in Fig. 13. VOA, variable optical attenuator. (Adapted from Ref. 142.)
(Color online) The Allan deviation for microwave-frequency transfer through the DSF and dispersion-compensated BRAN fiber indicates that the active noise cancellation reduces the transfer instability for transfer through the DSF to the measurement noise floor, and nearly to the noise floor for transfer through the dispersion-compensated BRAN fiber. The noise floor is determined using a short piece of fiber. (Adapted from Ref. 142.)
(Color online) (a) The rms timing jitter spectral density (left axis) for transfer over the dispersion-compensated BRAN fiber and the equivalent single-sideband (SSB) phase noise of the transmitted 81st harmonic of the comb repetition frequency (right axis) with active noise cancellation. (b) The integrated rms jitter over a bandwidth from 1 Hz to vs for transfer over the BRAN fiber. The measurement noise floor is obtained by replacing the transmission fiber with a short piece of fiber. (Adapted from Ref. 142.)
(Color online) High-level diagram showing the setup for remote synchronization of two femtosecond fiber lasers. The repetition rate of the reference laser is transmitted through 4.5 km of dispersion-shifted fiber with active stabilization of the group delay. The remote laser is synchronized to the pulse trains exiting the fiber link using rf techniques, and an out-of-loop optical cross correlation is used to characterize the net performance of the system. (Adapted from Ref. 143.)
(Color online) Optical cross-correlation measurement of the timing jitter for (a) local synchronization, and (b) slave synchronization through a fiber link. Both traces are shown with a 50 MHz low-pass filter that allows us to observe the timing jitter up to the Nyquist frequency. (Adapted from Ref. 143.)
(Color online) All-optical generation of an error signal for synchronization of two combs. When the combs are close in repetition rate, we can express one (the slave) as having a slight amount of frequency noise on its repetition rate as compared to the master comb. By spectral leveraging, this noise can be greatly amplified during the detection process to produce an improved error signal.
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