Telecommunication technologies

Conclusion:
In conclusion, waveguide paths are essential structures for guiding electromagnetic waves at high frequencies. The elements of waveguide paths, including straight sections, bends, and transitions, are used to propagate the waves in a straight path, change the direction of the waves, and connect different types of waveguides or change the cross-sectional shape of the waveguide. The design and optimization of waveguide paths involve the knowledge of waveguide type, dimensions, and element configurations, and the understanding of the properties of the elements is essential for designing efficient and reliable waveguide paths. The attenuation and reflection coefficient of a waveguide path can be calculated using electromagnetic field theory and waveguide boundary conditions.
Here, we demonstrate that non-invasive ultrasonic waves can be used to confine and steer light deep (a few millimeters) into tissue without having to insert a physical light guide. The concept of acousto-optic confinement is shown schematically in Fig. 1a. Acoustic waves propagating in a tissue compress and rarefy the tissue and change its density locally. The medium is compressed at the intensity peak of the acoustic wave and this results in an increase in the local refractive index. Conversely, the medium is rarefied near the troughs and the refractive index is decreased. Optical waves can be confined within high refractive index regions if these are flanked by adjacent low index regions, thereby forming an optical waveguide (Fig. 1a); this is the basic principle behind optical waveguides such as optical fibers. Similar acousto-optic phenomena have been traditionally employed in acousto-optic tomography, optical modulators via acousto-optic crystals, tunable optical filters, tunable lenses and optical deflectors In this work, we show that the target medium (e.g., the tissue) itself can be modulated by ultrasonic standing waves to confine and guide light.

Ultrasound sculpts virtual optical waveguides. a Schematic illustration of acousto-optic waveguide formation in a tissue. Pressure-induced density gradients in the tissue result in a refractive index contrast profile that forms optical waveguides through which light can be confined. b Standing wave ultrasonic resonant mode of an infinite cylindrical transducer (radius = 19 mm, thickness = 3 mm) in water medium (FEM simulation result). The pressure intensity is shown with the Pascal units. c Refractive index profile calculated at a radial cross-section of the cylindrical waveguide. d–g The intensity profiles of a subset of confined optical modes calculated using finite difference mode analysis. In each case, the intensity is normalized to its maximum

Ultrasonic standing waves sculpt optical modes in the medium

Piezoelectric transducers convert electrical energy to mechanical vibrations that generate acoustic waves in a medium. Such acoustic waves are widely used for clinical imaging at ultrasonic frequencies and can propagate into the tissue with minimal scattering and absorption (propagation loss in tissue is ~0.3–0.6 dB cm⁻¹ MHz⁻¹). We employ an ultrasound transducer array to produce standing waves within a cylindrical cavity at discrete resonance frequencies, for which the location of peaks and troughs are fixed in space. The cavity walls are made from piezoelectric ceramics that vibrate to generate ultrasound resonance modes, which possess well-defined spatial patterns. The pressure amplitude profile of a cylindrical ultrasonic cavity at the resonance frequency of 1.0235 MHz is shown in Fig. 1b for a 13 V drive voltage; note the pressure maximum at the center (see Methods). As expected, the refractive index profile is a function of the ultrasonic standing wave pressure (the radial cross-section is shown in Fig. 1c); a maximum refractive index contrast of 1.8 × 10⁻³ is achieved. Given this refractive index contrast, the standing waves support multiple confined optical guided modes, some of which are shown in Fig. 1d–g, calculated using a finite difference mode analysis method (http://www.lumerical.com/tcad-products/mode/). This ultrasonically sculpted optical waveguide is multimode and the modes are similar to those of a graded index (GRIN) fiber. GRIN fibers are made by doping the fiber core material to change the refractive index along the radial direction with a maximum in the center. The most common radial refractive index profile in a GRIN fiber is a parabolic profile, with a typical maximum refractive index contrast of Δn = 2 × 10⁻² that results in a numerical aperture of NA = 0.24 . However, a major difference between a traditional GRIN fiber and our ultrasonically sculpted waveguides is that the GRIN fibers are made of minimally scattering materials, whereas the ultrasonically sculpted waveguides are realized in tissue, which is a scattering medium. Therefore, the ultrasonically-defined optical waveguides within the tissue support leaky modes. As a consequence, the confined and guided modes are partially coupled to radiation modes, contributing to a larger propagation loss compared to a traditional GRIN fiber. Nevertheless, our experimental results demonstrate confinement and waveguiding through the sculpted waveguides.
Another difference between the in-tissue ultrasonically sculpted optical waveguides and traditional GRIN fibers is the smaller numerical aperture (NA = 0.0694 due to the smaller refractive contrast Δn = 0.001808. Despite this smaller refractive index contrast, the formed optical waveguide supports confined guided modes. The fundamental guided mode (Fig. 1d) is very well confined in the central high-pressure region of the ultrasonic wave and has an effective index of n_eff = 1.3342. The full width at half maximum (FWHM) of the fundamental mode is 67.6 μm, which is much smaller than the FWHM of the central lobe of the refractive index profile (i.e., 876.7 μm).
The high-pressure regions of the ultrasonic standing wave shown in Fig. 1b oscillate in time; every half-cycle, the peak positive pressure becomes peak negative pressure. When attempting to exploit the pressure peaks in the cavity, the input light needs to be pulsed and synchronized with the positive peak pressure of the ultrasonic wave. This keeps light guided in the central ultrasonically sculpted optical waveguide. The temporal dynamics of light (~2 femtosecond) are much faster than that of ultrasound (~1 μs); by pulsing the input light at the same frequency of ultrasound waves but with a duty cycle of 10%, photons are guided through the central waveguide for ~100 ns every 1 μs.
To quantify the extent and depth of optical confinement in the cylindrical cavity (19 mm radius, 30 mm height), an expanded and modulated laser beam at λ = 650 nm was collimated into a DI water tank containing the cylindrical ultrasonic cavity (Fig. 2a). The transducers were driven by pulsed electrical signals generated by a commercial waveform generator (Keysight 33522B, Keysight Technologies, USA) and amplified by a linear RF power amplifier (ENI A300, Electronics & Innovation Ltd., USA). A custom designed water-immersion microscope was used to image the 2D cross-section of the optical beam profile from the top in the transmission path (see Methods and Supplementary Fig. 1).

Light is confined by pressure patterns. a Schematic of the characterization setup. Experimental 2D cross-section image of the optical beam profile b with ultrasound and laser light not synchronized, c with ultrasound and laser light synchronized and phase locked at +90° to form only the central waveguide and d with the phase shift at −90° to form only the ring waveguide. The intensity of each 2D cross-section is normalized to its maximum value. The scale bar is 1 mm
Figure 2b shows a transverse optical beam profile at the resonance frequency of 1.028 MHz when the laser and ultrasound are not synchronized. Both the center waveguide and the first and the second ring waveguides corresponding to the high-pressure rings surrounding the central pressure peak are shown. The peaks and troughs of the standing pressure waves oscillate with time. The first ring in the pressure profile is completely out of phase with respect to the central pressure peak (Fig. 1b). When the center is at the highest positive pressure, the first ring is at the highest negative pressure and cannot confine light. To verify this, we pulsed the laser in synchrony with the ultrasound. When the laser modulation was phase locked with the ultrasound at a +90° phase shift, only the central waveguide guided the light beam (Fig. 2c). Conversely, when the laser modulation was phase locked at −90°, only the first ring waveguide was present (Fig. 2d).

Confining light in scattering media using ultrasound

To characterize ultrasonically sculpted optical waveguides in scattering media, we first characterized homogeneous scattering tissue phantoms made of different concentrations of Intralipid 20% emulsion in an agar gel host matrix (see Methods)29. The level of scattering in tissue phantom samples discussed in this paper can be quantitatively characterized using the scattering coefficient, μ_s and the optical thickness (OT). It is common to define a reduced scattering coefficient as μ′s=μs×(1−g)), where μ_s is the scattering coefficient and g is the anisotropy factor that characterizes the directionality of the scattered photons. In most biological samples, g = 0.9 (ref. 30). The scattering mean free path, defined as ℓs=1/μsℓs=1s is the average path length between two successive scattering events. The transport mean free path (TMFP), defined as ℓ∗=1/μ′sℓ∗=1/ ′ is the average distance beyond which the direction of photons can be assumed to be effectively random. The optical thickness, OT, is defined as the geometrical thickness of the tissue phantom divided by the scattering mean free path, i.e., ℓsℓs.
The ultrasonically sculpted optical waveguide was first imaged in a homogeneous agar sample (2% agar) in the form of a cylindrical phantom (13.55 mm radius and 8 mm height). 2D cross-sectional images of the optical beam profile were captured in transmission mode for different input drive voltages (Fig. 3a–d): laser beam is coupled in from the bottom (z = −8 mm) and the output is imaged on the top side of the tissue phantom (slightly below the top surface at z = -0.1 mm), just 100 µm below the surface to avoid inconsistencies of the facet. As the drive voltage increases and the pressure wave intensity increases, the waveguide becomes narrower. By increasing the pressure, the refractive index contrast becomes larger, which results in increased confinement of the waveguide modes. To demonstrate the application of this method for confining and guiding light within a scattering medium, we prepared a rod-shape tissue phantom (13.55 mm radius and 8 mm height) composed of 2% agar mixed with 0.2% Intralipid as the scattering agent. This tissue phantom has a reduced scattering coefficient of μ′s=2.35cm−1�s′=2.35cm−1, measured using the oblique incidence reflectometry (OIR) technique31. This 8 mm tissue phantom has an optical thickness of 18.8 scattering mean free paths (i.e., OT = 18.8 ℓs). Since the optical thickness of the medium at the wavelength of illumination is much larger than the scattering mean free path length (i.e., ℓs), light is confined in a regime where at least a few successive scattering events happen. 2D cross-sectional images of the optical beam profile are shown in Fig. 3e–h at different input drive voltages. When a narrow beam of laser impinges upon this tissue phantom, the whole phantom is illuminated due to the high level of scattering (Fig. 3i).
Fig. 3

Light is confined within tissue phantoms. Optical beam profile imaged experimentally 100 μm below the top surface of the tissue phantom in agar and in a scattering tissue phantom. a–d 2D cross-sections of the optical beam profile and radial cross-section plots in 2% agar when ultrasound is: a off, b driven at 6 V, c 8 V, and d 10 V. In each case, the intensity has been normalized to the maximum intensity of (d). e–h 2D cross-sections of the optical beam profile and radial cross-section plots in a scattering tissue phantom composed of 2% agar mixed with 0.2% Intralipid when ultrasound is: e off, f driven at 6 V, g 8 V, and h 10 V. In each case, the intensity has been normalized to the maximum intensity of (h). Side view of agar and the scattering tissue phantoms shown in i when illuminated by a narrow (2 mm) collimated beam of laser. Extinction ratios measured according to the definition of Extinction Ratio 1 (ER1) (blue) and Extinction Ratio 2 (ER2) (orange) in: j 2% agar and in k the scattering tissue phantom. The scale bar is 1 mm
To quantify the enhancement achieved using ultrasound to form an optical waveguide to guide ballistic photons within the scattering tissue, we define two figures of merit, Extinction Ratio 1 (ER1) and Extinction Ratio 2 (ER2). ER1 is the extinction ratio defined as the maximum intensity of light in the waveguide core divided by the intensity of light at the location of the first ring (point A in Fig. 3d). As discussed earlier, when the pressure in the central spot is at the positive peak value, the pressure at the first ring is at the negative peak value. As a result, the medium is compressed in the center region and rarefied in the surrounding region. The refractive index of the medium is slightly increased in the center region and slightly decreased in the surrounding region, thus photons are confined in the center region due to the induced refractive index contrast. This pronounced contrast is quantified by ER1. On the other hand, ER2 is the extinction ratio defined as the maximum intensity of the waveguide mode divided by the background intensity at the same location when ultrasound is off. These two figures of merit are compared for different input voltages in agar sample (Fig. 3j) and the scattering tissue phantom sample (Fig. 3k). As expected, optical confinement is lessened with more scattering. Taken together, these results demonstrate that ultrasonically sculpted optical waveguides can confine and guide light through an optically thick scattering tissue phantom (~8 mm, OT ~18.8 ℓs) with an extinction ratio of ER1 ≈ 3.7. The extinction ratio increases and the spot size decreases as we increase the input voltage.
When ultrasonic waves are launched into the tissue, they create a pressure standing wave that modulates its local refractive index. The tissue is compressed in the central high-pressure region, so its density increases and the local refractive index increases. On the other hand, the negative pressure regions, flanking the central region, are rarefied and as a result both the density and the local refractive index will be decreased (Fig. 4a).