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Abstract
We shape the spectrum of an octave spanning supercontinuum from an erbium fiber laser. The group delay dispersion is controlled through the temperature profile of a chirped fiber Bragg grating. We demonstrate control of spectral broadening, switching in spectral windows, and optimizing power at six wavelengths corresponding to Yb, Ca, and Sr clock transitions, an f-2f pair, and a C-band reference for frequency transfer applications. We verify locking of the shaped f-2f beat note, and the coherence of the shaped supercontinuum by interference with an unshaped supercontinuum branch with relative frequency deviation of 10−17 at 1 s averaging time.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Supercontinuum generation lets a laser provide light at wavelengths far from its spectral gain region, making it a key process for many applications from linear spectroscopy [1] to nonlinear microscopy [2]. It is particularly important for time and frequency metrology, where it expands the spectrum of optical frequency combs [3] to overlap with different clock types [4], as well as providing an octave spanning spectrum for the f-2f interferometry needed to measure and stabilize the carrier envelope offset frequency of the frequency comb [5].
When generating supercontinuum from a given pulse in nonlinear fiber, the main controls available are the laser power and fiber lengths. Optimizing one wavelength this way is straightforward, but satisfactory output for two or more wavelengths may not even be possible. This assumes a clean, short pulse, but supercontinuum and self-phase modulation is highly dependent on pulse shape. Changing the pulse shape entering the nonlinear fiber alters the entire supercontinuum process. Previous work has shown programmable supercontinuum optimization from Ti:sapphire lasers with spatial light modulators at one [6,7] or two [8,9] wavelengths with mostly sub-octave bandwidths.
Here, we work in an uncommon but more practical fiber system, using a chirped fiber Bragg grating (FBG) as a phase shaper [10,11] to achieve detailed spectral shaping. First we briefly show examples of coarse resolution spectral tuning, with phase-controlled spectral broadening as might be used in a tunable source, and as a light switch in three spectral regions as might be used for observing different components in microscopy [12]. We then show fine resolution shaping and verify coherence, optimizing the spectrum at six wavelengths including an octave spanning pair for frequency transfer applications. The high nonlinearity needed to span an octave increases sensitivity, but also results in a greater variety of possible spectra.
Optical clock frequency comparisons often use an erbium fiber frequency comb with multiple fiber amplifier and supercontinuum branches, such as an octave spanning f-2f branch, and a branch for each type of clock being compared. Branches are specialized for specific tasks because of the limited flexibility in tuning the supercontinuum spectrum without a pulse shaper. Having different fiber branches adds significant frequency noise, for example as path length changes with fiber temperature. With enough environmental control, a multibranch system can reach stability sufficient for most clock comparisons with Allan deviations of $5 \times 10^{-17}$ [4] and lower when referencing to another wavelength [13,14]. A single-branch erbium system can reach $3 \times 10^{-18}$ at 1 s, but with relatively low comb tooth power that limits the signal to noise, particularly after frequency doubling to operate directly at the clock’s fundamental wavelength [15].
With our shaped supercontinuum, we generate high power output and measure a high degree of coherence between all the target wavelengths. The optical frequency drift between wavelengths of a shaped and unshaped supercontinuum had Allan deviations of about $10^{-17}$ at 1 s averaging, making them suitable for high precision frequency transfer. The shaped supercontinuum has the high power advantage of a multibranch system with lower stabilization requirements and amplifier costs, as well as the common path stability of a single branch system, without low power detection issues.
Our work shows that supercontinuum shaping can be very flexible and generate complex shapes for efficient spectral manipulation. As a new way to control light, this could drive many new applications ranging from femtosecond optics to biological and chemical sensing and imaging [12,16,17].
2. Experiment
The supercontinuum source, illustrated in Fig. 1 starts with a 100 MHz frequency comb oscillator (1560 nm femtosecond erbium fiber laser, polarization maintaining, nonlinear amplifying loop mirror [18]) [19] which seeds a core-pumped amplifier. The amplified beam is temporally compressed by adjusting fiber lengths for spectral broadening in small core fiber. The supercontinuum then exits to free space from a reflective collimator with about 170 mW average power.
Fig. 1. Illustration of shaped supercontinuum fiber laser (lower branch); unshaped reference supercontinuum with frequency shift (upper branch); and interference and narrow band spectral filtering in free space for coherence tests. Relative fiber length is stabilized by comparing beating at 1558 nm with the driving frequency. Blue lines: optical fiber, red lines: free space beam, black lines: electrical wires.
To add spectral shaping, a pair of chirped fiber Bragg gratings reflectively stretch and compress the seed pulse, illustrated in the lower branch of Fig. 1. The gratings have the same specified group delay dispersion (10 ps/nm from 1540 to 1580 nm) but are inserted in opposite directions, nominally resulting in no net grating dispersion. The seed pulse is phase shaped by mounting the 5 cm long compressor grating on an array of 32 computer controlled heaters as in [11]. One heater can increase the group delay by up to about 1 ps through the temperature dependence of the refractive index by changing the wavelength that reflects at that position. The gratings are securely fixed to avoid changing the dispersion if the fibers are jostled. The FBGs are mounted on a thermoelectric cold plate which usually maintains the in-loop temperature to within a few mK with a standard temperature controller normally used for laser diodes. The cold plate is housed in and transmits heat to a temperature controlled metal enclosure. A temperature range of up to 1 K may be tolerable depending on the application, but it is not much more effort to reach the 10 mK level.
Regarding drift, we have seen the main spectral features of a given heater setting, such as having the clock lines within local peaks, stay reproducible for about 2 months until the apparatus was changed. The stability is very dependent on the setting though, as some spectra are much more nonlinear and sensitive to any changes than others. For example, using a narrow spectral peak at a target wavelength would tend to be more sensitive than a broad peak, as it is part of a complex interference structure, and if the peak moves a little in wavelength, the amplitude at the target wavelength can change dramatically. At shorter timescales, with the system shaped for 6 frequency transfer wavelengths, we measured a standard deviation in intensity at 1050 nm (1 nm bandwidth) of the shaped spectrum of 1.9% over 50 minutes, acquired at 1 kHz rate.
The unshaped supercontinuum arm shown in the upper branch of Fig. 1 does not have Bragg gratings, but does have an acousto-optic frequency shifter, which adds 70 MHz to the optical frequency so that pulses from the two branches will have a beat frequency of 70 MHz when combined on a photodiode. It outputs up to 50 mW of broadened light depending on pumping for wavelength optimization. The two beams are combined on a neutral density filter. The relative delay of the two arms is controlled by a piezoelectric fiber stretcher, and thermoelectric cooling of a coiled fiber. The fiber lengths of the two branches are not matched in length, so the interfering pulses originate from different pulses in the train. This adds a small amount of noise from variations of the free-running, temperature-stabilized oscillator that would otherwise cancel.
The shaped supercontinuum can also be separately directed into a free space f-2f interferometer operating near 1055 and 2110 nm, with frequency doubling in periodically poled lithium niobate. For an actual frequency transfer device, the f-2f frequency doubling can be performed in line with the supercontinuum output along a single path, with a filter and grating for separating the wavelengths of interest.
The nonlinear fiber in the shaped arm has a 9 cm and 5 cm piece of small core fiber with zero dispersion near 1.5 $\mathrm{\mu}$m, with an additional 2 cm section of small-core, strongly normally dispersive fiber in between. This particular arrangement seemed to help reduce sensitivity by reducing nonlinear fiber length while still generating an octave span, but we have not performed a systematic study on fiber length or type. The unshaped arm uses a single long piece of the low dispersion nonlinear fiber.
3. Shaped spectra
To find heater array settings to generate a desired spectrum, we recorded spectra with a broadband spectrometer as the heater settings were randomly varied overnight. Being a relatively slow thermal process, 30 s was allotted for settling at each new setting. The resulting database of setting/spectrum pairs was used as a lookup table, and sorted by a fitness function designed to assign high values to spectra with the desired properties. The best settings were manually tested and tweaked as needed. If the resulting spectrum was insufficient, more random data could be taken.
3.1 Variable broadening
We start with a familiar example of spectral broadening. We lower the average power to 57 mW so that spectral broadening is not saturated, and acquire a random shaping database. We then sort the database by spectral broadness (using fitness of $\sum S(\lambda ) \cdot | \lambda - 1560 \textrm { nm} |$ for spectral intensity $S$, ignoring wavelengths from 1360 to 1760 nm), and plot some examples across the range of the database in Fig. 2. The spectral progression looks similar to power tuning, with the notable difference that the peak heights and average power do not greatly change, making it closer to a purely wavelength tuned source with phase shaping. The comb line power is estimated by scaling the spectrum by the average power from a thermal power meter. Independent spectrometer sensitivity calibration was not performed. Note that comb line density per nm is higher at shorter wavelengths.
Fig. 2. Shaped spectra sorted by spectral breadth, vertically offset by 100 nW. Unlike power tuning, the average power and power at spectral peaks remains about the same.
3.2 Switched ranges
We next increase the task complexity, returning to 174 mW average power where spectral broadening has saturated. We define three spectral windows centered at 1125, 1300, and 1425 nm, each 50 nm wide, and seek to turn the light in these regions on and off independently. Such switching might be of interest for controlling excitation of certain processes or markers like nanoparticles, quantum dots, or dyes in a microscope [2,12,17]. Figure 3 shows example spectra for four permutations of on and off states. This example does illustrate one limitation of phase shaping, in that there is a limit to how much spectrum can be turned off while maintaining the same average power. The fitness function in this case was the sum of the integrated power in each window multiplied by $+1$ for an on state and $-1$ for an off state. Additional terms for contrast, or specific powers for the on state could be added if needed. These spectra were from a one-day database without optimization of the database setting.
Fig. 3. Switching light on and off in three spectral regions with supercontinuum shaping. Four permutations are shown, vertically offset by 700 nW. The shaded blocks show the 50 nm spectral windows with green coding an on state, and red an off state.
4. Specific wavelengths for metrology
We now turn to replacing multibranch supercontinuum systems with a single shaped branch. We found a setting for a spectrum with high power at wavelengths for Yb, Ca, and Sr optical clocks, an f-2f octave spanning pair, and a 1558 nm C-band reference. The shaped spectrum used in the frequency stability measurements below is shown as the blue curve in Fig. 4. We were able to produce strong peaks at all the target wavelengths, which combined with the relatively high 173 mW average power, provides about 100 nW comb teeth at all target wavelengths. This is more than enough power for direct beating, as well as frequency doubling for f-2f interferometry or reaching the fundamental clock frequencies. For a single comb line, this corresponds to a low relative intensity shot noise floor of −115 dBc/Hz. The unshaped spectrum is shown in the filled background, with effectively random comb tooth powers of 29, 122, 24, 17, 336, and 586 nW from short to long target wavelength for a factor of 7 improvement at the originally weakest clock line.
Fig. 4. Blue curve shows the shaped supercontinuum spectrum optimized for the optical clock wavelengths: 1156.8 nm (Yb), 1314.9 nm (Ca), and 1396.9 nm (Sr); f-2f wavelength pair at 1050 and 2100 nm; and 1558 nm for C-band referencing. Comb tooth powers are about 100 nW in all lines, enabling clean beat note detection and frequency doubling. The filled background spectrum is with the heater array turned off.
The shaped spectrum was found from a database of about 1 day of random searching, and then manual adjustment. Spectra with about 200 nW in all lines can be made without much difficulty with a little more searching. The fitness function for the search was $\sum _{n=1}^{6} A_n P_n$, where $P_n$ is the power in a narrow wavelength window, and the weight coefficients $A_n$ are positive numbers, with higher values chosen for the generally weaker clock wavelengths. The 1558 nm peak was weighted to zero as there was always significant light in that region. For more flexibility, we also let the f and 2f wavelengths float to match the peak between 1000 and 1100 nm for each spectrum.
4.1 Coherence
To test the coherence of the shaped supercontinuum generation for metrology, we performed f-2f locking; measured interference with the reference supercontinuum; and measured the relative frequency drift between the two supercontinuum arms.
Figure 5 shows some examples of radio frequency beat notes at 100 kHz resolution bandwidth. The f-2f beat note involves only the shaped supercontinuum arm, while the other beat notes are between the shaped and unshaped arms as in Fig. 1, with about 1 nm bandwidth. The beat notes have signal to noise ratios of about 40 dB or more, which is a good level for frequency comb measurements and locking, and comparable to standard supercontinuum sources. Note that interference between pulses involves multiple comb modes, rather than a single comb mode when interfering with a continuous wave beam from an optical clock.
Fig. 5. Measured radio frequency beating from shaped supercontinuum in f-2f interferometry, and against an unshaped, frequency shifted supercontinuum from the same oscillator. Resolution bandwidth is 100 kHz. All beats have a good signal to noise ratio, suitable for tight locking and frequency comparisons.
We locked the f-2f beat note using an electro-optic modulator in the oscillator to control the carrier envelope offset frequency. The locked beat note is shown in Fig. 6 in orange. The conversion of the beat to approximate in-loop integrated phase noise is shown in blue and is 187 mrad from 3.5 MHz to 0.2 Hz, showing that a tight f-2f lock is possible with a shaped supercontinuum spectrum.
Fig. 6. Locked f-2f beat note from shaped supercontinuum (orange, lower) and conversion to integrated phase noise (blue, upper). The low phase noise shows tight locking.
4.2 Frequency stability
To better quantify the frequency stability, we used a phase meter to simultaneously measure the evolution of the beat frequency near the fundamental at 1558 nm, and at one of the five other target wavelengths. While free-running, the frequencies vary by about 1 Hz from the nominal 70 MHz acousto-optical shifting frequency due to relative thermal fiber length changes between the two branches, unrelated to the supercontinuum generation. To reduce the effect of relative thermal drift, a piezoelectric fiber stretcher and a thermoelectric fiber loop cooler, shown in Fig. 1, act as fast and slow actuators to stabilize the phase of the 1558 nm beat to the 70 MHz shifting frequency [20]. This feedback reduces the frequency drift to tens of mHz.
If the supercontinuum is fully coherent, the phase relation between two wavelengths will be constant, resulting in a fixed phase relation between the 70 MHz beat note of the target wavelength and the stabilized fundamental beat note. If the supercontinuum is altered, such as by a drifting pump diode or a changing grating temperature, the relative spectral phase between wavelengths changes, which becomes a temporary frequency offset from 70 MHz as the beat notes change relative phase. Recording the drifting of the beat notes provides a measure of coherence and frequency stability.
The Allan deviations of the corrected frequency offsets scaled to their optical frequencies are shown in Fig. 7. The phase meter measures phase at a 1 kHz rate, and we record the phase at the end of each 0.5 s interval ($\Pi$ mode, solid lines). The dashed curves record the average of the phases measured during the last 0.5 s for rejecting white phase noise ($\Lambda$-like mode). While we do stabilize the 1558 nm beat note, we still subtract the 1558 nm offset from the target wavelength offset after scaling by wavelength in fused silica, eg., $(1558/n_{1558}) / (1314.9/n_{1314.9})$ [13,14]. The longer and thinner 1157 nm curve is from a later dataset with slightly better fiber length locking, taken over about two days to verify long term stability of the noisiest clock wavelength furthest from the fundamental.
Fig. 7. Allan deviations of the optical frequency of the shaped clock wavelengths relative to an unshaped supercontinuum, providing an upper limit on the frequency noise of the shaped supercontinuum. Dashed lines use averaged phase values over 0.5 s to remove white noise. Deviations at 1 s are at the $10^{-17}$ level, which is already comparable to the best optical clocks.
The Allan deviation at 1 s is below $6 \times 10^{-17}$ for all three clock wavelengths, similar to or better than even corrected multibranch systems [4,20,21], and comparable to the best optical clocks [22]. Given the minimal environmental controls and visibly increased frequency offset when the laboratory air conditioning is running, the shaped supercontinuum stability is likely better than this measurement indicates.
5. Heater settings
To find a good setting for the heater pixels, our examples used random database searching with a fitness function. Many useful variations are possible. Once a promising candidate setting has been found, we can use pixel-by-pixel optimization, or randomly adjust single pixels, while periodically returning to the original candidate. Being a slow thermal process, data can also be acquired while the temperature changes, greatly increasing the acquisition rate, but requiring estimation of the heater setting based on elapsed time since the heater change. Smaller steps can reduce the uncertainty of the estimation, while increasing acquisition time. Given the high nonlinearity and sensitivity, the available phase space is enormous so finding a global optimum is unlikely, but finding useful spectra is quite possible. Practically, once a system is built, a large database would be collected once, and candidate settings can then be found from the database almost instantly. More predictive methods using neural networks [23] or genetic algorithms [7] may be possible and would be very useful for finding desired spectra.
6. Conclusions
Supercontinuum generation is a foundational optical process. We have shown that phase shaping with chirped fiber Bragg gratings can coherently generate complex tailored spectra in octave-spanning bandwidths. We have verified that the shaped supercontinuum has coherence and frequency stability comparable to optical clocks, potentially making it a compact, flexible, low noise, and low cost replacement for multibranch supercontinuum systems for bridging frequency standards. The ability to efficiently change a broadband spectrum is a new capability that is difficult to achieve otherwise and should lead to many new applications.
Disclosures
All authors: IMRA America, Inc. (F,E).
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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