Continuous wave optical two-way time transfer

Embodiments herein describe a continuous wave two-way optical time two-way transfer system. The embodiments herein lock a local frequency comb to a clock (e.g., optical/microwave atomic clock, Fabry-Perot optical reference cavity, etc.) in a local platform. The platform then generates two CW optical signals with different frequencies and locks those optical signals to the local frequency comb. The local platform then transmits its two CW optical signals to a remote platform and receives CW optical signals (having approximately the same frequencies as the two CW optical signals generated by the local platform) from the remote platform. Based on comparing its local CW optical signals with the received CW optical signals, the local platform can determine a timing deviation between its clock and a clock in the second platform.

BACKGROUND

Two-way optical time transfer often involves two sites or two vehicles exchanging optical pulses in free space with predefined repetition rates. Determining when the pulses arrive at each site enables the sites to extract timing deviation (if any) between the respective clocks and perform clock synchronization. In a simplistic example, each site can include a photodetector for detecting when the optical pulses transmitted by the other site arrives. However, jitter in the electronics does not allow the sites to determine the pulse arrival time with an accuracy greater than a picosecond. That is, the electronics distort the converted optical pulse which makes it difficult to accurately determine (e.g., with an accuracy greater than a picosecond) when the center of the pulses arrive. In many clock synchronization systems, greater accuracy is desired (e.g., femtosecond accuracy) between the clocks at the sites.

One strategy for the synchronization and syntonization of atomic clocks over optical free-space utilizes two frequency combs at each link site. The first frequency comb is stabilized to the local reference oscillator (e.g., atomic clock, Fabry-Perot optical reference cavity, etc.), and a second frequency comb is exchanged between sites over the link. In one implementation, the repetition rate of the exchanged comb is purposely offset from the reference oscillator stabilized comb. While this strategy has proven successful, it possesses several drawbacks. Notably, the use of a second comb at each site that is launched over the free-space link increases the complexity, power consumption, and expense of the system. Furthermore, the derived timing information and the SNR of its retrieval is limited by the duty cycle of the pulse-based system. This approach also requires careful dispersion management between the local frequency comb and the received frequency comb in order to avoid undesirable pulse broadening, which decreases the measurement sensitivity.

An alternative approach utilizes a continuous wave (CW) laser to transfer optical timing information between two sites over a free-space link. In this implementation, the master site splits the light to be transferred. One portion of it remains at the master site while the other portion is frequency shifted and sent across the free-space link to the remote site. At the remote site, a portion of the received light is sent back to the master site, where it is compared to the original local light sample. However, this method is prone to cycle slips and Doppler cancellation only works after the light has traversed the link twice (out to the remote site and back to the local site). Since the one-way link loss is squared, the power requirement for this approach is significantly higher.

SUMMARY

One embodiment described herein is a system that includes an optical subsystem configured to lock a frequency comb to a clock in a first platform and lock two continuous wave (CW) optical signals in the first platform to the frequency comb, wherein the two CW optical signals have different frequencies. The system also includes an electrical subsystem configured to determine a timing deviation between the clock in the first platform and a clock in a second platform based on exchanging, in free space, the two CW optical signals generated in the first platform with two CW optical signals generated in the second platform.

Another embodiment described herein is a method that includes locking a frequency comb to a clock in a first platform, locking two continuous wave (CW) optical signals in the first platform to the frequency comb where the two CW optical signals have different frequencies, and determining a timing deviation between the clock in the first platform and a clock in a second platform based on exchanging, in free space, the two CW optical signals generated in the first platform with two CW optical signals generated in the second platform.

Another embodiment described herein is a system that includes a first platform configured to transmit, in free space, two continuous wave (CW) optical signals having different frequencies to a second platform and the second platform is configured to transmit, in free space, two CW optical signals having different frequencies to the first platform. Moreover, the first and second platforms are configured to synchronize high-precision clocks based on exchanging the CW optical signals.

DETAILED DESCRIPTION

Embodiments herein describe a continuous wave (CW) two-way optical time transfer (TT) system that relies on fewer frequency combs than previous two-way optical TT techniques and does not require high power lasers like previous CW techniques. The embodiments herein lock a local frequency comb to a local reference oscillator (e.g., optical atomic clock, microwave atomic clock, Fabry-Perot optical reference cavity, etc.) in a local platform. The platform then generates two CW optical signals with different frequencies and locks those optical signals to the local frequency comb. The local platform then transmits its two CW optical signals to a remote platform and receives CW optical signals (having approximately the same frequencies as the two CW optical signals generated by the local platform) from the remote platform. Based on comparing its local CW optical signals with the received CW optical signals, the local platform can determine a timing deviation between its local reference oscillator (e.g., a local clock) and a remote reference oscillator (or clock) in the second platform.

FIG.1illustrates a CW optical TT system100, according to one embodiment. The CW TT system100includes Platform A and Platform B which may be disposed at different locations on the earth's surface that are within line of sight (LOS) of each other, either directly or through the use of one or more mirrors. In another embodiment, one of the platforms is disposed at a stationary location (or site) on the earth's surface while the other platform is disposed on a moving vehicle—e.g., a ground vehicle or a flying vehicle such as a plane, drone, or satellite. In yet another embodiment, both of the platforms may be disposed on moving platforms such as a car and a plane, two planes, two satellites, one plane and one satellite, etc.

In this example, Platforms A and B have the same components—i.e., an atomic clock105, clock laser110, frequency comb115, two CW lasers120,125, an optical subsystem130, an electrical subsystem135, and free-space terminal optics140. While an atomic clock105is shown, any kind of high precision clock can be used. The atomic reference105is used the stabilize the frequency of the clock laser110, which generates an optical signal that is transmitted to the optical subsystem130. The frequency comb115also generates an optical signal that is transmitted to the optical subsystem130. The frequency comb115generates a train of light pulses with a repetition rate that is in the easy-to-measure radio-frequency range, unlike the optical frequency of the clock laser110.

As discussed in more detail below, the optical subsystem130locks (or stabilizes) the optical signal generated by the frequency comb115(which may be self-referenced) to the optical signal generated by the clock laser110. This process transfers the fractional instability of the atomic clock105to the optical signal generated by the self-referenced frequency comb115. Thus, any jitter in the clock105is transferred to the optical signal generated by the frequency comb115. However, instead of using a self-referenced comb115, the frequency comb115can be locked to two lasers. For example, the second harmonic of a seed laser could be used to generate a second laser which can be locked to the frequency comb115.

The CW lasers120,125transmit two optical signals to the optical subsystem130. In one embodiment, the two optical signals are not pulsed. That is, unlike TT schemes that transmit pulsed optical signals, the two optical signals are CW waves that are not pulsed (e.g., are unmodulated). However, these optical signals are CW waves at different frequencies. For example, the optical signals may have frequencies that differ by more than 50 GHz, and in one embodiment, differ by 100 GHz or more. The frequency difference or offset between the lasers120,125may vary based on the application. As discussed below, the smaller the frequency difference, the easier it is for the platforms to track the cycles (or fringes), but it is also more difficult to discriminate timing jitter between the clock105A in Platform A and the clock105B in Platform B. Thus, the frequency difference or offset can depend on the particular implementation.

In one embodiment, the CW lasers120,125have wavelengths that are around 1550 or 1560 nanometers since these lasers are common in many telecommunication systems.

The optical subsystem130locks (or stabilizes) both of the CW lasers120,125to the optical signal generated by the frequency comb115. Thus, the fractional instability of the atomic clock105is transferred to the optical signals generated by the CW lasers120,125. That is, any jitter in the clock105is transferred to the optical signal generated by the frequency comb115, which in turn transfers that jitter to the optical signals generated by the CW lasers120,125.

The terminal optics140transmit the two CW optical signals to the other platform via a free space optical link160. In this case,FIG.1is from the perspective of Platform A where its local CW signals145are transmitted to the free-space terminal optics140B of Platform B while the remote CW signals150generated by Platform B are received at the terminal optics140A of Platform A. That is, the two platforms exchange their two CW optical signals. In general, the CW optical signals have similar frequencies in that a first one of the local CW optical signals145generated by Platform A has a same frequency (or a known frequency offset) as a first one of the remote CW signals150generated by Platform B and a second one of the local CW optical signals145generated by Platform A has a same frequency (or a known frequency offset) as a second one of the remote CW signals150generated by Platform B.

The local and remote CW signals145,150are compared to each other in the optical subsystem130. In one embodiment, two beatnotes are produced in the optical subsystem130between the two pairs of CW lasers. The electrical subsystem135can then determine a differential phase jitter between these two beatnote pairs which reveals the relative group delay jitter between the two frequency combs115in the two platforms. This is discussed in more detail inFIGS.2-4. Using the differential phase jitter, the platforms can determine a timing deviation between the atomic clock105A and the atomic clock105B. Determining the timing deviation is discussed in more detail inFIGS.5and6.

FIG.2is a flowchart of a method200for determining a timing deviation from performing CW optical TT, according to one embodiment. The technique illustrated inFIG.2may be performed simultaneously at both Platform A and Platform B inFIG.1.

At block205, a first platform locks a frequency comb to a clock optical signal. Referring toFIG.1, the optical subsystem130A receives optical signals from the clock laser110A and the frequency comb115A. The subsystem130A locks (or stabilizes) the optical signal of the frequency comb115to the optical signal generated by the clock laser110, thereby transferring the fractional instability of the atomic clock105to the optical signal generated by the frequency comb115A. In some embodiments, the comb115A is self-referenced, or alternatively, the frequency comb115A can be locked to two lasers.

At block210, the first platform locks two local CW optical signals to the optical signal generated by the frequency comb. For example, the optical subsystem130A receives optical signals from the CW lasers120A and125A which are then locked to the optical signal of the frequency comb115A so now the fractional instability of the atomic clock105is transferred to the optical signals generated by the CW lasers120A and125A. Notably, the frequencies of the optical signals generated by the CW lasers120A and125A are different.

At block215, the first platform determines a timing deviation between its clock and a clock in the second platform by exchanging, in free space, the two CW optical signals generated in the first platform with the two CW optical signals generated in the second platform. This is illustrated inFIG.1where the local CW signals145generated by Platform A are transmitted to Platform B and the remote CW signals150generated by Platform B are received at Platform A. The details for determining the timing deviation are discussed in the figures that follow.

Once the timing deviation is determined, one or both of the atomic clocks in the platforms can be adjusted so they have the same time, which can include performing both frequency synching (syntonization) and phase adjustment (synchronization). For example, measurements made at each platform can be transmitted to the other using conventional means (e.g., radio frequency transmission) to stabilize the link.

FIG.3is a flowchart of a method300for performing CW optical TT, according to one embodiment. The technique illustrated inFIG.3may be performed simultaneously at both Platform A and Platform B inFIG.1. Further, each block in the method300is discussed in tandem withFIG.4A, which illustrates a photonic integrated circuit and electrical components for performing a CW optical TT.

At block305, a first platform locks a frequency comb to a clock optical signal. Referring toFIG.4A, it illustrates a photonic integrated circuit (PIC)400that receives an optical signal from the frequency comb115A and an optical signal from the clock laser110A. The clock laser110A can have a frequency foptAand has been stabilized to an atomic reference (e.g., an atomic clock).

The frequency comb is split by the splitter S1(e.g., a Y-junction or Y-splitter). A portion of this comb light is combined with the clock light at splitter S2, where it exits the PIC400and is detected with photodetector (PD)410E. In one embodiment, the comb115A is then stabilized using the optical beatnote generated by the PD410E in a feedback path415A as well as a f-2f self-referencing scheme to generate a self-referenced comb115A (not shown, but may also be included on the PIC as shown inFIG.8). In this manner, the PIC400transfers the stability of the optical frequency reference (e.g., the atomic clock) to the frequency comb115A.

In another embodiment, the PIC400transfers the stability of the optical frequency reference (e.g., the atomic clock) to the frequency comb115A without self-referencing the frequency comb115A. In that example, two clock lasers are separately combined in the PIC400with the frequency comb115A where the two combined optical signals are detected by separate PDs. In one embodiment, the two clock lasers can be generated when adjusting the wavelength of a seed laser, where a second harmonic can be used as a second clock laser.

In another embodiment, if a microwave clock (e.g., a microwave atomic clock) is used as the local reference oscillator rather than an optical clock, instead of locking the frequency comb115A to a clock laser, the frequency comb115A can be locked to the microwave clock electronically. In that case, the PD410E can be used to detect the frequency comb115A repetition rate (without combining the frequency comb115A with any other optical signals). The repetition rate of the frequency comb115A can then be identified using the output of the PD410E and locked to the microwave clock. The other degree of freedom for the frequency comb115A is then locked with self-referencing.

At block310, the first platform locks two local CW optical signals to the optical signal generated by the frequency comb. Two CW lasers120A and125A are introduced onto the PIC400, and each is split with splitters S3and S4. The remaining comb light is split at splitter S5, where it is combined with the light from splitters S3and S4(i.e., the lasers120A and125A) by splitters S6and S7, respectively. The combined outputs from splitters S6and S7are detected by PD410C and PD410B, respectively. The beatnotes from the PD410C and PD410B are used to phase lock the lasers120A and125A to the frequency comb115A, respectively, via feedback paths415B and415C. This process transfers the stability of the atomic clock to the lasers120A and125A.

The electric field of the light exiting splitter S3can be expressed as: √{square root over (P1A)}. cos[2π(f1A+Δ1A) t], where P1Ais the power of laser120A at Platform A, f1Ais the frequency of the comb tooth to which the laser120A is phase-locked at Platform A, and g is the offset frequency between the laser120A and the comb tooth f1Aat Platform A. An analogous expression exists for the laser125A.

The laser120A stabilized light exiting the upper port of the splitter S3is then split again at coupler S8and a similar process occurs for laser125A at the coupler S9. One part of the outputs at couplers S8and S9exits the PIC400, where they are combined at an external wavelength division multiplexer (WDM)405, which can be a fiber optic component. The combined output of this WDM405is then transmitted, in free space, on the link160to the other platform (e.g., Platform B). In one embodiment, the WDM405is separate from the PIC400, but in other embodiments, the WDM405could be on the PIC400and be implemented using, for example, an arrayed waveguide grating (AWG).

Platform B can have an identical optical configuration with two lasers of nominally the same free-running frequency as those at Platform A. The stabilization process described above also occurs at Platform B. Thus, the two Platform B CW lasers possess the same frequency instability as the atomic reference or clock at Platform B, foptB.

At block315, the first platform receives a third CW optical signal and fourth CW optical signal from a remote platform. For example, the optical link160is bi-directional so that light from Platform B crosses the link, is received by the two-way terminal at Platform A, and enters the WDM405. The two lasers transmitted by Platform B are separated by the WDM405and are coupled onto the PIC400.

At block320, the PIC combines the first CW optical signal and the third CW optical signal to generate a first combined optical signal. The PIC also combines the second CW optical signal with the fourth CW optical signal to generate a second combined optical signal. InFIG.4A, the received CW optical signals enter the couplers S8and S9, where they mix with the local CW lasers120A and125B of Platform A. The combined fields of the optical signals at splitters S10and S11may then be written as:
ES10=√{square root over (P1,LOA)}·cos[2π(f1A+Δ1A)t]+√{square root over (Tlink·P1,linkB)}·cos[2π(f1B+Δ1B)·(t−n1L/c)]
ES11=√{square root over (P2,LOA)}·cos[2π(f2A+Δ2A)t]+√{square root over (Tlink·P2,linkB)}·cos[2π(f2B+Δ2B)·(t−n2L/c)]

where Tlinkis the link loss and n1,2are the indices of refraction of the link for lasers120A and125A. It should be noted that differential phase noise between the two ports of the WDM405and the PIC400can be captured by defining unique indices of refraction n1,2for each laser.

At block325, the first platform converts the first and second combined optical signals into respective electrical signals. InFIG.4A, the combined light fields are detected at PD410A and PD410D. The photocurrent at PD410A is expressed as:
i4A=R·{P1,LOA+Tlink·P1,linkB+2√{square root over (Tlink,P1,LOAP1,linkB)}·cos[2π(f1A−f1B)t+2π(Δ1A−Δ1B)t+2π(f1B+Δ1B)·n1L/c]}

where R is the photodiode responsivity, and the signal has been appropriately low-pass filtered. The first two terms of this expression for the detected photocurrent appear at DC, but the third term appears at AC. The first term of the AC sinusoid is what the Platforms A and B detect in order to identify the timing deviation. It is nominally a very small temporal variation that describes the relative frequency instability of the atomic clock at Platform A with respect to the one at Platform B. The second term is user controllable and is determined by the offset lock frequencies at the two platforms. The third term can vary rapidly since the link distance L and/or index of refraction may be unstable during the acquisition. A similar expression describes the photocurrent at PD410D:
i5A=R·{P2,LOA+Tlink·P2,linkB+2√{square root over (Tlink,P2,LOAP2,linkB)}·cos[2π(f2A−f2B)t+2π(Δ2A−Δ2B)t+2π(f2B+Δ2B)·n2L/c]}

Referring to the structure inFIG.4A, in one embodiment, the PIC400and the optical components therein (e.g., the splitters) form the optical subsystem130inFIG.1. However, instead of implementing the optical subsystem130as a PIC, in other embodiments, the optical subsystem130may be discrete splitters that are coupled by optical fibers. In yet another embodiment, the optical subsystem130may include optical components that are coupled using free-space communication paths. Thus, the PIC400is just one example of a suitable optical subsystem130.

The PDs410A-E, the feedback paths415A-C, and a processing module420may form part of the electrical subsystem135. In addition, the electrical subsystem135may include other optical components (e.g., hardware or software) for processing the signals output by PDs410A and410D, which is discussed inFIGS.5and6. The electrical subsystem135can include an application specific IC (ASIC), FPGA, computer system, and the like for implementing the processing module420.

In one embodiment, the WDM405is part of the free-space terminal optics140. In addition, the optics140may include other optical components such as a telescope or focusing element to direct the CW optical signals towards the remote platform.

FIG.4Billustrates PIC450and electrical components for performing a continuous wave two-way optical time transfer, according to one embodiment. Like the PIC400inFIG.4A, the PIC450includes the lasers120A and125A, the comb115A, and the clock laser110A. However, unlike the PIC400, the system includes a WDM455that combines the lasers120A and125A into a combined optical signal and then transmits that optical signal onto the PIC450. This combined optical signal is split at S3where a portion of this signal is combined, at S4, with a portion of the comb115A. This correlates to S7and S6in the PIC400inFIG.4A. However, instead of using separate waveguides to combine the laser signals with the comb115, the PIC450uses one waveguide. A WDM465can then be used to separate out the signals according to frequency into two signals. One signal is detected by the PD470C and used in feedback415C to adjust the laser120A while the other signal is detected by PD470D and used in feedback path415B to adjust the laser125A. In one embodiment, the beatnotes from the PD470C and PD470D are used to phase lock the lasers120A and125A to the frequency comb115A, respectively, via feedback paths415B and415C. This process transfers the stability of the atomic clock to the lasers120A and125A as discussed above.

The upper output of the splitter S3is then split again at coupler S5. One part of the output at coupler S5exits the PIC450and is then transmitted, in free space, on the link160to the other platform (e.g., Platform B). The combined signal received from Platform B on the link160is received at the coupler S5and combined with the combined signals of the lasers120A and125A at coupler S6. The output of the coupler S6is separated according to frequency into two signals by a WDM460, which are detected by the PDs470A and470B. The resulting electrical signals are transmitted to the processing module420as discussed above.

The PIC450also includes a splitter S1and coupler S2for combining the comb115A and the clock laser110A which is essentially the same as the PIC400. This output is detected by the PD470E and used in the feedback path415A.

FIG.5is a block diagram of a processing module for synchronizing clocks between two platforms, according to one embodiment.FIG.5is one example of the processing module420inFIG.4A.FIG.5illustrates a pair of IQ demodulators510A and510B receiving the electrical signals generated by the PD410A and410D as discussed above. A frequency synthesizer505provides known offset frequencies Δ1A−Δ1Band Δ2A−Δ2Bwhere each signal is demodulated by the IQ demodulators510at the known offset frequencies Δ1A−Δ1Band Δ2A−Δ2B, respectively. Phase extraction modules515A and515B extract the phase of the demodulated signals:
ψ1A=2π(f1A−f1B)t+2π(f1B+Δ1B)·n1L/c,

with a corresponding equation for ψ2A.

These two phases are then subtracted from each other to yield:
Φ1A−ψ2A=ψA=2π(f1A−f2A)t−2π(f1B−f2B)t+ϕlinkB

where the optical phase of the link ϕlinkBexperienced by the two CW lasers originating at Platform B is given as ϕlinkB=2π(n1f1B−n2f2B+n1Δ1B−n2Δ2B)L/c. The extracted phase of each signal can rapidly vary in time due to turbulence in the optical path and may wrap between 0 to 2π. As a result, the signal can be sampled fast enough to capture the phase wraps in the difference signal so that they can be unwrapped, for example, in a digital signal processor. Since the two CW laser frequencies are similar, the rapid phase fluctuations are highly correlated and only lead to momentary glitches in the phase difference near the phase wrap points, which can be rejected using an appropriate thresholding condition by a glitch removal module520.

The optical frequency f1Ais re-written as if f1A=f1A+δf1A, wheref1Ais the steady-state value of the comb tooth f1A, and δf1Arepresents the slow temporal jitter of this tooth that originates from atomic clock instabilities. Similar representations exist for the three other considered comb frequencies: f2A, f1B, and f2B. This then allows writing the de-modulated phase ψAas:
ψA=2π(δf1A−δf2A)t−2π(δf1B−δf2B)t+ϕlinkB

where it is assumed that the average frequency spacing between the stabilized CW lasers at the two sites are equal:f1A−f2A=f1B−f2B. The differential phase jitter between the frequencies f1Aand f2Bis proportional to the group delay jitter of the frequency comb to which the two lasers are locked with a proportionality constant given by the frequency spacing between the two lasers. Stated differently, this measurement scheme reveals the time evolution of the linear spectral phase between the two CW laser frequencies, and linear spectral phase is directly responsible for group delay of the frequency comb pulse train. This permits a phase extraction module515to recast the differential spectral phase 2π(δf1A−δf2A)t as:

2π(δf1A−δf2A)t=2π(f1A−(f2A)·τA=2π·Δf12A·τAwhere τAis the group delay jitter of the frequency comb at Platform A. The de-modulated phase ψAis finally written as:
ψA=2πΔΔf12(τA−τB)+ϕlinkB

where the requirement of equal CW laser spacings between the two sites allows writing Δf12A=Δf12B=Δf12.

An analogous detection scheme is implemented at Platform B, which recovers the de-modulated phase ψBas:
ψB=2πΔf12(τB−τA)+ϕlinkA

Each platform then proceeds in one of two possible manners to report/receive phase over a communication channel. One approach (referred to as an open loop approach) is to log the retrieved phase ψA,3at each platform. Due to turbulence of the free-space link, the phase ϕlinkA,Bcan rapidly vary between 0 and 2π. If the free-space link is reciprocal, the optical phases associated with the link path length are equivalent, i.e., ϕlinkA=ϕlinkB. Hence, the rapid fluctuations in the de-modulated phases ψA,Bare highly correlated. Notably, this condition is only strictly true if:
n(flAaser1A)flaser 1A−n(flaser 2A)flaser 2A=n(flaser 1B)flaser 1B−n(flaser 2B)flaser 2B,

where n(f) is the index of refraction at frequency f, and flaser 1,2A,Bare the frequencies of the CW lasers1and2at platform A and B, respectively. This condition can be satisfied with the appropriate choice of Δ1,2A,B(the CW laser offset from the comb teeth) for a given index of refraction profile for the optical path between the platforms.

After recording these phase measurements at each platform, the information is exchanged with the other site via an optical or microwave communication channel where the difference between the local and remote phases can be extracted. This allows deducing the relative jitter of the comb at one site with respect to the other as:
τA−τB=(ψA−ψB)4πΔf12.

The derivation of this information may be used to steer the repetition rate of one frequency comb with respect to the other. There are at least two ways to do this: feedback on the comb repetition rate, or feedback on the clock laser to synchronize both the optical and microwave outputs of the clock.

A second approach (referred to as a closed loop approach) is for each platform to implement a servo that stabilizes its locally retrieved phase ψA,Bto a fixed value. One possibility is to continually tune the phase or frequency of the CW laser offset locks. The quantitative relationship between this control signal and the phase ψA,Bdepends upon the manner in which the servo is implemented. The control signal at each platform is then directly proportional to the locally measured phases ψA,B. Thus, the relative timing deviations and link length are directly mapped onto the control effort. The control signal at each platform is exchanged with the other site via an optical or microwave communication channel where the difference between the local and remote phases can be extracted. This approach effectively linearizes the phase fluctuations with the servo and removes the phase wraps. At the end of this process, the combs on the two Platforms are synchronized similar to the first approach by feeding back on comb repetition rate or clock laser frequency.

One advantage of the techniques above is that they are not sensitive to the fringe number of the recovered heterodyne beat at each platform. The optical path length induced by turbulence may vary by distances much larger than the synthetic wavelength λ12=c/Δf12with no loss of information provided that both platforms are able to retrieve and log the phases ψA,Bfaster than the characteristic timescale of their fluctuations.

Additionally, the techniques above are not sensitive to the absolute fringe number, which means that changing the fringe number following a period of signal dropout has no effect on the information retrieval so long as the two atomic clocks do not drift away from each other by more than one fringe period during any blackout. For example, a typical fringe period is several picoseconds which would be an abnormally large drift for an atomic clock during a blackout period of even several seconds.FIG.6is a block diagram of a processing module for synchronizing clocks between two platforms, according to an alternate embodiment.FIG.6is one example of the processing module420inFIG.4A. In situations where the phase fluctuations due to turbulence make it challenging to extract the phase of each photodetector signal directly, each signal can be mixed down to two intermediate frequencies with mixers610A and610B and a pair of frequencies fLO1and fLO2generated by a frequency synthesizer605at slightly different frequencies. The intermediate frequencies are mixed by a third mixer610C to generate a tone at the difference frequency, which can be demodulated by an IQ demodulator615at the difference frequency of the two original synthesizers to extract the phase difference between the original two signals. The rest of the signal processing can be the same as discussed above inFIG.5. As a specific example, two distributed feedback (DFB) lasers designed for the dense wavelength-division multiplexing (DWDM) ITU grid could be used for the TT system, referenced to a 1560 nm Erbium fiber frequency comb used as the optical frequency divider at each site. A good compromise between precision and dynamic range is to choose lasers on two adjacent ITU channels, such that their frequency separation is ˜100 GHz. With this frequency separation, 0-2π phase range on ψA−ψB, corresponds to a timing deviation range of 10 ps. A modest signal-noise-ratio (SNR) of 2500:1 at 1 second of integration time is sufficient to measure the relative time offset of the two sites with a precision of 1 fs.

Taking the sum of the phase measurements (ψA+ψB) instead of the difference allows the platforms to measure the path length between the two sites with sub-nm precision and could be used for ranging applications. As mentioned above, while ambiguity range of the system does not pose a big challenge for syntonization, for synchronization or ranging applications, an unambiguous knowledge of timing offset or the link path may be desired. One way to extend the dynamic range of the system is to include sidebands on one of the CW lasers with a modulation system, an example of which is shown inFIG.7. The modulation frequency of the phase modulation defines another synthetic wavelength (λmod=c/fmod) and a timing deviation range (1/fmod) that may be utilized to resolve the typically millimeter (ps) range ambiguity of the synthetic wavelength (timing deviation) defined by the two CW lasers.

FIG.7illustrates using a modulation system705when performing a CW optical TT, according to one embodiment. Examples of the modulation system705can include an optical single sideband modulator or a combination of an electro-optic modulator (EOM) with an amplitude modulator.FIG.7illustrates disposing the modulation system705between the CW laser120A and a PIC710. The PIC710can be the PIC400inFIG.4A, or the PIC800, the PIC900, or the PIC1000discussed inFIGS.8-10.

For applications where synchronization is required or laser ranging, unambiguous knowledge of the timing offset or the link path is required. This means the ambiguity range of the system should be extended until a more conventional ranging/synchronization system can resolve the offset (with less precision). Adding the modulation system705to one of the lasers to create a sideband at a much smaller frequency offset than the frequency offset between the two CW optical signals creates a coarser but larger dynamic range measurement. For example, 100 MHz modulation frequency extends the ambiguity range to 3 meters or 10 ns. This ambiguity can easily be resolved with a conventional optical or RF link. Similar to the method described above, the signal from the photodiode that detects the modulated laser light is demodulated at the modulation frequency. A comparison of the extracted phases at the baseband and modulation frequency reveals the link distance. The modulation frequency of the modulation system705may be dynamically tuned to provide an adjustable ambiguity range.

FIGS.8-10illustrate photonic integrated circuits, according to one embodiment.FIG.8illustrates a PIC that includes an additional splitter S12and a loop mirror805on the clock laser110A input for Doppler cancellation of the clock light. The loop mirror805retro-reflects a portion of the clock light back to the clock laser110A and can be compared to the outgoing light to cancel out phase shifts due to changes in the optical path between the clock laser110A and the PIC800.

FIG.9illustrates a PIC900that includes supercontinuum generation region905for self-referencing of the optical frequency comb115A. In this example, the comb light is split in two with an additional splitter S12at the input and some portion of the light is used to generate an octave spanning supercontinuum to generate the f-2f self-referencing signal which can be used as a feedback signal along with the feedback path415A shown inFIG.4A.

The advantage of this implementation is that all degrees of freedom of the comb115A and the CW TT system are stabilized using a single PIC900, which eliminates all out-of-loop paths for improved temperature stability. In this implementation, the PIC900would be made of a nonlinear material such as silicon nitride, lithium niobate, or tantalum pentoxide.

FIG.10illustrates a PIC1000that includes supercontinuum generation region1005for cases where the clock laser is not within the original bandwidth of the comb spectrum. Supercontinuum generation region1005can be employed to extend the bandwidth of the comb115A to the clock laser frequency to enable the optical beatnote on the PIC1000. This includes the use of the optical splitters S12, S13, and S14in order to combine the frequency comb115A with the clock laser110A.