The dynamics of Kerr frequency combs strongly depend on the dispersion of the microresonator. Bright dissipative Kerr solitons for example can only form with sufficient anomalous group velocity dispersion. Therefore the measurement of the dispersion is an important characterization step and by now there are a few different techniques in use in different groups with different advantages and disadvantages. Here I briefly summarize the techniques that are known to me and give some references.
The dispersion is typically taken from a transmission trace of a laser that scans over the resonances of a resonator in transmission. The dispersion is then derived from the measurement of the frequency spacing of the resonance dips. One requirement of all the techniques is that the range of the laser scan has to be large enough to make the effects of the group velocity dispersion (GVD) (or higher order dispersion, if this is what is supposed to be measured) visible. Therefore a large scan range of the laser is always an advantage for a precise measurement. Ideally the scan range is similar to the expected or desired bandwidth of the generated Kerr frequency combs and typically external cavity diode lasers (ECDLs) are used.
Frequency comb-assisted diode laser spectroscopy
In this approach the laser is swept over its full range and over many resonances within a few seconds to tens of seconds. The resulting transmission trace is recorded on an oscilloscope. To precisely calibrate the trace in relative frequency, the laser is split into two parts. One part is used to record the transmission trace of the microresonator and to record the resonance dips. The second parts is combined with a commercial frequency comb which ideally is fully self-referenced stabilized. The beat of the scanning laser with the frequency comb is recorded on a photodiode. The signal of the photodiode is filtered in the RF domain with a narrow bandpass filter and recorded on additional channels of the oscilloscope as a reference trace simultaneously with the transmission of the microresonator. Using the known RF filter frequency and the fixed repetition rate of the frequency comb it is possible to obtain a very precise relative calibration of the laser scan when processing the data.
Advantages:
- Very precise, MHz-precision can be obtained
- Very stable reference, exact characterization of the reference is no problem
- Using two (or more) filters, the calibration trace can be checked for consistency
- Bandwidth is only limited by the scanning laser and the bandwidth of the frequency comb. The latter can be extended by nonlinear broadening.
- Fast scans possible
- Resulting calibrated trace can be used for other puposes as well (Q measurements, …)
Disadvantages:
- Requires a frequency comb
- Limited in bandwidth by the bandwidth of the frequency comb
- Only relative referencing within the trace
- Requires a scanning laser that has no mode hops over the entire range
- Can result in large amounts of data. Typical resulting traces have several tens of millions of points.
References:
Chen, Master’s thesis: Dispersion Measurement for On-Chip Microresonators
(Fiber-loop) cavity calibrated diode laser spectroscopy
Of course one does not require a frequency comb in order to reference a scanning diode laser. Relative referencing can be achieved by for example using a reference resonator or a fiber-loop cavity with a FSR of tens of MHz. Because these resonators have a certain linewidth and some dispersion themselves, the calibration might not be as precise as with a frequency comb. Absolute referencing and a calibration over longer frequency ranges which helps to compensate the dispersion of the resonators can be achieved by gas cells. The setup is similar to the one with a frequency comb for calibration. The scanning laser is split into at least two parts, one for the microresonator transmission and one for the calibration.
Advantages:
- Simple and cheap to implement if used with a fiber-loop cavity
- Broadband, in principle limited only by the resonator/fiber used
- Spacing of the reference signal can be varied easily by changing the FSR of the reference resonator
- Resulting calibrated trace can be used for other puposes as well (Q measurements, …)
Disadvantages:
- The fiber dispersion has to be compensated or taken into account by additional measurements.
- Stability of reference is not guaranteed and can be difficult to assess
- Only relative referencing of the trace
- Requires a scanning laser that has no mode hops over the entire range
- Can result in large amounts of data. Typical resulting traces have several tens of millions of points.
References:
Huang, et al., PRL 114, 53901 (2015): Mode-Locked Ultrashort Pulse Generation from On-Chip Normal Dispersion Microresonators and its SI
RF-sideband laser spectroscopy
A different technique uses RF sidebands that are modulated onto the scanning laser as a reference. If these sidebands are close to the FSR of the microresonator that is measured, the transmission trace of the laser when scanned over a resonance shows three dips. One of the primary laser scanning across the “center” resonance and two of the sidebands scanning across the resonances to the left and right of the laser. Varying the RF modulation frequency allows to determine the precise position of the resonances to the left and to the right and from the changes of this spacing the dispersion is computed. This principle can also be extended by generating a full EOM comb around the scanning laser and using a filter to single out individual resonances.
Advantages:
- Simple setup, does not require a large mode hop-free tuning range of the laser
- Can be used at different wavelengths due to the simple setup
- Exact, direct referencing via RF tone
- Can be very precise and controlled, therefore measurement of the dispersion with only few resonances possible.
Disadvantages:
- Limited to microresonators with lower FSR (few tens of GHz) unless more sophisticated schemes with EOM combs are used to cover larger FSR
- Works only one resonance after the other or with only a few resonances in one trace
References:
Del’Haye, et al., PRL 112, 043905 (2014): Self-Injection Locking and Phase-Locked States in Microresonator-Based Optical Frequency Combs and its SI
Yang, et al., Nat. Phot. 10, 316 (2016): Broadband dispersion-engineered microresonator on a chip
Wavelength meter calibrated scans
Given a wavelength meter that is precise enough, it is possible to scan the laser from one resonance to the next and read the exact absolute position of each of the resonances of a wavelength meter. Combining the data of the resonances it is possible to determine the dispersion
Advantages:
- Absolute calibration included
- Simple to implement given a precise wavelength meter is available
- Small data sets with only relevant points
- Laser can be optimized for individual resonances (for example the laser polarization)
Disadvantages:
- Only one resonance after the other
- Taking a full resonance spectrum with multiple mode families takes probably a lot of time
- No calibrated transmission trace as a result
Commercially available high-resolution optical spectrum analyzer
Apex Technologies offers a optical spectrum analyzer (OSA) which is based on a heterodyne design. With the right options the internal scanning laser of the instrument can be coupled out and looped through the microresonator and back into the instrument which results in a setup very similar to the ones described above. The specified resolution of the resulting trace of down to 5 MHz is good enough for most microresonators and in addition the instrument also has an internal absolute calibration. However, the traces’ number of points might not be sufficient to get a good resolution over the full laser sweep.
Advantages:
- Out-of-the-box solution
- Absolute calibration
- High resolution
Disadvantages:
- Difficult to modify, limited flexibility
- Limited scan range, only in the telecom band
References:
Apex Technolgies optical spectrum analyzer data sheet
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