Two procedures have been devised for tuning a photonic filter that comprises multiple whispering-gallery-mode (WGM) disk resonators. As used here, “tuning” signifies locking the filter to a specific laser frequency and configuring the filter to obtain a desired high-order transfer function.

Figure 1. Five WGM Resonators are arranged to form a filter chain. Through adjustment of gaps and voltages, guided by monitoring of optical power levels, desired transfer function (Pout/Pin versus frequency detuning) can be obtained. The underlying principles of design and operation are also applicable to a chain of more or fewer than five WGM resonators.

The main problem in tuning such a filter is how to select the correct relative loading of the resonators to realize a prescribed filter function. The first of the two procedures solves this problem.

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Figure 2. These Curves Represent Optimal Coupling of the first two resonators in an intermediate step toward realizing a fifth-order Butterworth filter. On the abscissa, δω denotes the frequency detuning and γc denotes the full frequency width of the resonance spectral peak at half maximum in the fully loaded condition.

As temperature gradients develop during operation, the spectra of individual resonators tend to drift, primarily because of the thermorefractive effect. Thus, there arises the additional problem of how to adjust the tuning during operation to maintain the desired transfer function. The second of the two procedures solves this problem.

To implement the procedures, it is necessary to incorporate the resonators into an apparatus like that of Figure 1. In this apparatus, the spectrum of each resonator can be adjusted individually, via the electro-optical effect, by adjusting a bias voltage applied to that resonator. In addition, the positions of the coupling prisms and resonators can be adjusted to increase or reduce the gaps between them, thereby reducing or increasing, respectively, the optical coupling between them. The optical power (Pi) in resonator i is monitored by use of a tracking photodiode. Another tracking diode monitors the power reflected from the input terminal (Pr), and still others monitor the input power (Pin) and output power (Po). The readings of these photodiodes are used to guide the tuning adjustments described below.

The steps of the first procedure are the following:

  1. Uncouple all the resonators and prisms by increasing all the gaps.
  2. Overload resonator 1 with the input coupling prism, then measure the input power (Pin), reflected power (Pr), and the power in resonator 1 (P1) as functions of frequency detuning from resonance, and use the measurement data to determine the resonance quality factor (Q).
  3. Couple resonator 2 to resonator 1, then measure Pin, Pr, P1, and P2 as functions of frequency detuning from resonance. Adjust the gap between resonators 1 and 2 until Pr/Pin, P1/Pin, and P2/Pin as functions of frequency detuning match a set of theoretical template functions (see Figure 2) calculated to contribute to the desired high-order transfer function.
  4. Couple resonator 3 to resonator 2, then measure Pin, Pr, P1, P2, and P3 as functions of frequency detuning from resonance. Adjust the gap between resonators 2 and 3 until Pr/Pin, P1/Pin, and P2/Pin as functions of frequency detuning match a different set of theoretical template functions calculated to contribute to the desired high-order transfer function.
  5. Repeat step 4, each time adding the next resonator (and then adding the output coupling prism after the last resonator has been added) and adjusting the gaps to obtain the desired responses.

The steps of the second procedure are the following:

  1. Measure and tabulate the dependence of each resonance frequency of each resonator on the bias voltage applied to that resonator.
  2. Introduce, into the filter operation, “dark” periods, during which the laser and the resonators are scanned over some finite frequency band.
  3. During a dark period, apply a specified voltage to resonator 1 to shift its resonance frequency by some amount. Measure the shift, then compensate it by applying another voltage to shift the resonance to the middle of the scan of the laser frequency.
  4. Repeat step 3 for resonator 2 and subsequent resonators except the last one.
  5. Adjust the voltage on the last resonator to scan its frequency until the filter exhibits maximum transmission, at which point the desired high-order transfer function has been restored.

This work was done by Andrey Matsko, Anatoliy Savchenkov, Dmitry Strekalov, and Lute Maleki of Caltech for NASA’s Jet Propulsion Laboratory.

The software used in this innovation is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 395-2322. Refer to NPO-43872.