Optimization of optical frequency combs in SNAP bottle microresonators

The generation of optical frequency combs with low repetition rates in microresonators is a challenging problem. SNAP microresonators are promising candidates to solve it. We show how the generation of frequency combs via parametric modulation of SNAP microresonators can be optimized.
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Optical frequency combs are being used to explore everything from the tiniest atoms to the vast expanse of space. From testing fundamental physics to searching for exoplanets, detecting trace gases, and more, optical frequency combs are revolutionizing the way we explore the world around us, opening up new avenues for scientific discovery and innovation. But what exactly are they and how do they work? They are a spectrum of evenly spaced frequencies, like the teeth of a comb. Think of them as rulers made of light but unlike traditional rulers that measure distance in millimeters or inches, optical frequency combs measure time. Specifically, they measure the oscillations of light directly, which is pretty mind-blowing when you think about it!

Optical frequency combs can be generated using three primary techniques: through mode-locked lasers, electro-optic modulation of a continuous wave laser, and ring-like resonators or whispering-gallery microresonators. At this point, let me spend a bit more time in explaining what whispering-gallery microresonators are, since they are the core element of my research. They are tiny structures that are used to trap light waves and make them bounce around a circular path, creating a special type of wave pattern known as whispering gallery modes. They are named after the phenomenon of "whispering galleries," which are circular rooms where sound waves can travel around the room and be heard clearly from far away, like in St Paul’s Cathedral in London. The frequencies or wavelengths of these modes are determined by the number of light oscillations that fit inside the circumference of the microresonator and the difference in frequency between two consecutive modes is called the free spectral range (FSR) of the microresonator. Whispering gallery modes microresonators are usually made of materials like glass or silicon and have a very small size, typically a few micrometres in diameter. The light trapped in the microresonator can circulate around the structure for a long time. This creates a very high intensity of light within the microresonator that can be used for frequency comb generation by means of nonlinear effects of light.

There are other ways to generate optical frequency combs in microresonators besides using nonlinear effects of light. Imagine that we somehow change the parameters of the microresonator in an oscillating and controlled way. This “parametric modulation” modulates the light trapped inside the microresonator in a way that causes it to generate many new frequencies of light, all evenly spaced apart... and like this, we generate an optical frequency comb!

The frequency repetition rate of optical frequency combs (the separation between the comb's teeth) is a crucial characteristic for their applications. Mode-locked lasers and microresonators can achieve high repetition rates of several GHz or even THz. On the other hand, electro-optic modulation of laser beams is limited to repetition rates in the MHz range. When it comes to miniaturization, microresonator-based optical frequency combs are the only technology that can be integrated onto a chip. However, achieving low repletion rates with microresonators is quite challenging. Indeed, the repetition rate frequency of microresonator-based frequency combs is usually equal to the microresonator FSR which, for the commonly used ring, toroidal, and spherical microresonators, is inversely proportional to their size. In order to obtain an optical frequency comb of, let’s say, 50 MHz, a spherical microresonator would need to have a radius of 65 cm! This is not ideal for miniaturization, is it?

Is there a technology that can generate optical frequency combs with low repetition rates for applications like high-resolution spectroscopy or precision metrology? The answer is yes, and it's called Surface Nanoscale Axial Photonics, or SNAP for short. SNAP is a platform invented by Prof Misha Sumetsky that allows the fabrication of whispering-gallery microresonators at the surface of regular optical fibres. The most exciting feature of SNAP microresonators is that they can have a small FSR while remaining miniature. This makes them a promising candidate for a frequency comb device with low repetition rate that can be miniaturised!

In our research, we proposed the generation of optical frequency combs by the parametric modulation of SNAP microresonators. The light can be coupled into the microresonator by an optical waveguide to excite one of the whispering gallery modes (see Figure 1). The distinctive and interesting aspect of SNAP microresonators is that contrary to other microresonators shapes, the elongated SNAP microresonators allows us to change the spatial distributions of the modulations and optimise the optical frequency comb spectrum. This allows us to minimise the power necessary to generate the frequency comb and make the system more efficient.

Figure 1: Generation of optical frequency combs by the parametric modulation of a SNAP microresonator.
We have studied two regimes of parametric modulation. The first one is called adiabatic modulation, where the microresonator's geometry or refractive index varies slowly and smoothly, thereby modulating the frequency of the excited whispering gallery mode. The light stays at the same mode, while a set of sidebands separated by the frequency of the modulation are formed. Figure 2 shows how the frequency comb becomes wider when the modulation is uniform along the microresonator's size, which is the optimal one to enhance the formation of frequency combs.

Figure 2: Optical frequency combs generated by the adiabatic modulation of a SNAP microresonator. Two cases are shown: the modulation is localized at the centre of the microresonator and the modulation is uniform along microresonator.

The second method is the resonant modulation, when the frequency of the modulation is a multiple of the FSR of the microresonator. Figure 3 shows the optical frequency combs obtained for different spatial distributions of the parametric modulation along the SNAP microresonator. In this case, neither a localized distribution nor a uniform one can generate a wide optical frequency comb. The optimal distribution, as shown in Figure 3b, was a bit unexpected!

Figure 3: Optimisation of the generation of optical frequency combs by resonant modulation of a SNAP microresonator. Different spatial distributions of the parametric modulations are shown.

The next step in my research is to demonstrate this concept experimentally. There are a few different ways to modulate a SNAP microresonator parametrically and I describe them briefly in the paper.

I hope that I have sparked your curiosity in the realm of optical frequency combs and that my research has ignited your interest to learn more about SNAP microresonators and all the technological possibilities they offer!

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