Angular Airy function: a model of Fabry-Perot etalons illuminated by arbitrary beams

Scaling down the dimensions of a Fabry-Perot polymer film acoustic sensor for photoacoustic endoscopy

Significance

A Fabry-Perot (FP) polymer film sensor can be used to detect acoustic waves in a photoacoustic endoscope (PAE) if the dimensions can be adequately scaled down in size. Current FP sensors have limitations in size, sensitivity, and array configurability.

Aim

We aim to characterize and demonstrate the imaging performance of a miniature FP sensor to evaluate the effects of reduced size and finite dimensions.

Approach

A transfer matrix model was developed to characterize the frequency response of a multilayer miniature FP sensor. An analytical model was derived to describe the effects of a substrate with finite thickness. Finite-element analysis was performed to characterize the temporal response of a sensor with finite dimensions. Miniature 2 × 2    mm 2 FP sensors were designed and fabricated using gold films as reflective mirrors on either side of a parylene C film deposited on a glass wafer. A single-wavelength laser was used to interrogate the sensor using illumination delivered by fiber subprobes. Imaging phantoms were used to verify FP sensor performance, and in vivo images of blood vessels were collected from a live mouse.

Results

The finite thickness substrate of the FP sensor resulted in echoes in the time domain signal that could be removed by back filtering. The substrate acted as a filter in the frequency domain. The finite lateral sensor dimensions produced side waves that could be eliminated by surface averaging using an interrogation beam with adequate diameter. The fabricated FP sensor produced a noise-equivalent pressure = 0.76 kPa, bandwidth of 16.6 MHz, a spectral full-width at-half-maximum = 0.2886 nm, and quality factor Q = 2694 . Photoacoustic images were collected from phantoms and blood vessels in a live mouse.

Conclusions

A miniature wafer-based FP sensor design has been demonstrated with scaled down form factor for future use in PAE.

Increasing the Q-factor of Fabry-Perot etalons using focused Bessel beam illumination

Sensing and filtering applications often require Fabry-Perot (FP) etalons with an Interferometer Transfer Function (ITF) having high visibility, narrow Full Width at Half Maximum (FWHM), and high sensitivity. For the ITF to have these characteristics, the illumination beam must be matched to the modes of the FP cavity. This is challenging when a small illumination element size is needed, as typical focused beams are not matched to the FP cavity modes. Bessel beams are a potential alternative as their structure resembles the FP cavity modes while possessing a focused core. To study the feasibility of using Bessel beam illumination, in this Letter, ITFs of an FP etalon were measured using Bessel and Gaussian illumination beams. A Bessel beam with core size of 28 µm provided an ITF with visibility 3.0 times higher, a FWHM 0.3 times narrower, and a sensitivity 2.2 times higher than a Gaussian beam with waist 32 µm. The results show that Bessel beam illumination can provide ITFs similar to that of collimated beam illumination while also having with a focused core.

ABCD transfer matrix model of Gaussian beam propagation in plano-concave optical microresonators

Plano-concave optical microresonators (PCMRs) are optical microcavities formed of one planar and one concave mirror separated by a spacer. PCMRs illuminated by Gaussian laser beams are used as sensors and filters in fields including quantum electrodynamics, temperature sensing, and photoacoustic imaging. To predict characteristics such as the sensitivity of PCMRs, a model of Gaussian beam propagation through PCMRs based on the ABCD matrix method was developed. To validate the model, interferometer transfer functions (ITFs) calculated for a range of PCMRs and beams were compared to experimental measurements. A good agreement was observed, suggesting the model is valid. It could therefore constitute a useful tool for designing and evaluating PCMR systems in various fields. The computer code implementing the model has been made available online.

Numerical model of light propagation through Fabry-Perot etalons composed of interfaces with non-planar surface topography

We present a model that calculates optical fields reflected and transmitted by a Fabry-Perot (FP) etalon composed of interfaces with non-planar surface topography. The model uses the Rayleigh-Rice theory, which predicts the fields reflected and transmitted by a single interface, to account for the non-planar surface topography of each interface. The Rayleigh-Rice theory is evaluated iteratively to account for all round trips that light can take within the FP etalon. The model predictions can then be used to compute Interferometer transfer function (ITF)s, by performing wavelength or angle resolved simulations enabling predictions of the bandwidth, peak transmissivity, and sensitivity of FP etalons. The model was validated against the Pseudospectral time-domain (PSTD) method, which resulted in good agreement. Since the model accuracy is expected to reduce as the Root mean square (RMS) of the topographic map increases, the error in the model's predictions was studied as a function of topographic map RMS. Finally, application of the model was exemplified by predicting the impact of roughness on ITFs and computing the changes in FP etalon transmissivity as cavity thickness is modulated by an ultrasonic wave.

ABCD transfer matrix model of Gaussian beam propagation in Fabry-Perot etalons

A numerical model of Gaussian beam propagation in planar Fabry-Perot (FP) etalons is presented. The model is based on the ABCD transfer matrix method. This method is easy to use and interpret, and readily connects models of lenses, mirrors, fibres and other optics to aid simulating complex multi-component etalon systems. To validate the etalon model, its predictions were verified using a previously validated model based on Fourier optics. To demonstrate its utility, three different etalon systems were simulated. The results suggest the model is valid and versatile and could aid in designing and understanding a range of systems containing planar FP etalons. The method could be extended to model higher order beams, other FP type devices such as plano-concave resonators, and more complex etalon systems such as those involving tilted components.

Transfer function asymmetry in Fabry-Perot-based optical pressure sensors

Optical resonators are some of the most promising optical devices for manufacturing high-performance pressure sensors for photoacoustic imaging. Among these, Fabry-Perot (FP)-based pressure sensors have been successfully used for a multitude of applications. However, critical performance aspects of FP-based pressure sensors have not been studied extensively, including the effects that system parameters such as beam diameter and cavity misalignment have on transfer function shape. Here, we discuss the possible origins of the transfer function asymmetry, ways to correctly estimate the FP pressure sensitivity under practical experimental conditions, as well as show the importance of proper assessments for real-world applications.

Pressure sensing with high-finesse monolithic buckled-dome microcavities

We describe the use of on-chip buckled-dome Fabry-Perot microcavities as pressure sensing elements. These cavities, fabricated by a controlled thin-film buckling process, are inherently sealed and support stable optical modes (finesse >10³), which are well-suited to coupling by single-mode fibers. Changes in external pressure deflect the buckled upper mirror, leading to changes in resonance wavelengths. Experimental shifts are shown to be in good agreement with theoretical predictions. Sensitivities as large as ∼1nm/kPa, attributable to the low thickness (<2µm) of the buckled mirror, and resolution ∼10Pa are demonstrated. We discuss potential advantages over traditional low-finesse, quasi-planar Fabry-Perot pressure sensors.