Optical isolation is a property to transmit optical signals in one direction and block them in the opposite direction. This property is especially important for integrated optical devices in order to avoid interference effects due to reflections at the waveguide transitions. Among integrated optics platforms, silicon photonics plays a major role due to the developed lithography processes and the possibility to combine it with electronics. The conventional way to isolate optical signals is to use magneto-optical materials that can induce non-reciprocal polarization rotation under an applied constant magnetic field. Silicon has weak magneto-optic activity and combination with other materials is required to achieve optical isolation in a small footprint1. Also, the magneto-optic isolation requires external magnetic fields with magnets or currents. Alternatively, other schemes of optical isolation have been developed, employing optical nonlinearity or spatiotemporal modulation of the optical parameter. The nonlinearity fails to isolate optical signals simultaneously propagating in the forward and backward directions2. On the other hand, optical isolation via spatiotemporal modulation is a promising alternative to magneto-optics3. Now, writing in Nature Photonics, Kittlaus and colleagues describe travelling-wave modulation realized by an optical excitation of an acoustic wave in a suspended silicon waveguide4.

A time-dependent switch is the simplest non-reciprocal device for pulses if it is known when forward and backward pulses are coming and when the arrival times are sufficiently different. The problem begins when both signals are coming simultaneously. It has been shown that travelling-wave modulation might still transmit forward-propagating signals and block backward-propagating signals5. The travelling-wave modulation of permittivity ε can be described as:

$${\mathrm{\Delta }}\varepsilon \left( {x,y,z,t} \right) = {\mathrm{\Delta }}\varepsilon \left( {x,y} \right) \exp \left( {\Omega t - qz} \right)$$

where z is the propagation direction along the waveguide, x and y are orthogonal directions, t is time, Ω is the frequency of the modulation and q is the wavenumber. If the permittivity perturbation in the waveguide cross-section Δε(x,y) can lift the orthogonality between two optical modes E1(x,y) and E2(x,y), then energy can be exchanged between these modes. To exchange energy efficiently along the waveguide the phase-matching condition should be fulfilled for frequency ω2 = ω1 + Ω and wavenumber k2 = k1 + q. Thus, the frequency and wavenumber of the travelling-wave modulation should be adjusted to bridge the corresponding points on the dispersion curves of optical modes 1 and 2 (Fig. 1). In this case, mode 1 at point ω1,k1 in the dispersion curve can be coupled to mode 2 at ω2,k2, or vice versa. At the same time, the same travelling-wave modulation cannot couple mode 1 excited in the opposite direction ω1,−k1 to mode 2 (ref. 5). It can be seen as well that the phase-matching condition in the forward direction can be fulfilled in a broadband frequency range if two modes have similar group velocity, or, in other words, if the two dispersion curves are parallel to each other.

Fig. 1: Dispersion diagram for forward and backward propagation.
figure 1

The inter-mode transition is provided by the travelling-wave permittivity modulation. The wavenumber q and the frequency Ω of the travelling wave define the transition vector (green arrows). This vector can bridge the even (1) and odd (2) modes from the ω1,k1 point to the ω2,k2 point, correspondingly (right). The same modulation cannot couple back-propagating modes as can be seen for mode ω1,−k1 (left). Axes are angular frequency, ω and wavenumber, k.

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The required permittivity modulation can be excited electro-optically. Silicon is not electro-optically active, but modulation can be induced by free-carrier injection. In this case, a microwave travelling wave, which modulates the free-carrier concentration, can couple two modes of the same waveguide. But the doping of silicon and the complex waveguide and electrode designs lead to insertion losses on the order of 70 dB (ref. 6). Recently, a lot of attention has been paid to acousto-optical modulation, where an acoustic wave is guided in the same waveguide as the optical signals. This modulation changes the permittivity via the photoelastic effect, representing a special case of the inter-modal Brillouin scattering3,7,8. Silicon photoelastic coefficients that connect strain with permittivity modulation are relatively small and show opposite signs for different tensor elements. Only through thorough consideration of the radiation pressure and electrostriction effects in silicon waveguides9 as well as geometry optimization has efficient stimulated Brillouin scattering in suspended silicon waveguides finally been demonstrated8. This progress thus led to the realization of non-reciprocal modulation in silicon waveguides as reported by Kittlaus and colleagues.

The researchers designed a suspended acoustic waveguide (Fig. 2a) that contains two optical waveguides. One of the optical waveguides is excited with even and odd optical modes to generate an acoustic wave (Fig. 2b). The acoustic wave then couples the modes of the adjacent optical waveguide in the forward direction only. The researchers conducted an experiment slightly differently to that presented in Fig. 1. They showed that the even optical mode is modulated in the forward direction and that the odd optical mode is not modulated in the backward direction (Fig. 2c). The optical power of 104 mW excites an acoustic wave with a power of 0.1 nW propagating in a suspended silicon strip with 2.39 cm length. This acoustic wave is shown to modulate an optical signal propagating in the adjacent optical waveguide with 1% efficiency. This modulation is non-reciprocal, and the optical signal sent back experiences 38 dB smaller modulation. The bandwidth of 125 GHz is demonstrated that is limited only by the residual group velocity mismatch between odd and even optical modes. This is orders of magnitude larger than what was possible with resonant concepts10. The bandwidth can be even further increased by dispersion engineering of the optical modes.

Fig. 2: The view and the operation scheme of the suspended silicon waveguide.
figure 2

a, Artistic view of a suspended silicon strip with two optical waveguides. b, One of the waveguides is excited with even and odd optical modes to generate an acoustic wave in the silicon strip, represented by the green arrows. c, The acoustic wave can modulate the even mode propagating in the forward direction, but cannot modulate the odd mode propagating in the backward direction. Figure reproduced from ref. 4, Springer Nature Ltd.

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The concept presented by Kittlaus and colleagues is remarkable in two ways. First, the non-reciprocal modulation is achieved in a pure silicon waveguide using an acoustic wave. Previously, other materials were considered with larger photoelastic coefficients such as chalcogenide or silica glasses. Second, the acoustic wave is generated optically using the optomechanical coupling in the adjacent waveguide as a drive. This allows decoupling the driving optical power and the modulated signal. Thus, other nonlinear effects such as Kerr nonlinearity and free-carrier dispersion do not influence the signal.

Research on optomechanical coupling for non-reciprocal modulation is progressing rapidly. Just in the beginning of this year, a concept for non-reciprocal modulation was presented using a piezoelectrically driven acoustic wave in AlN (ref. 10). Now, optical driving has been used to launch an acoustic wave in silicon. The non-reciprocal modulation can be extended into an optical isolator if the power of the acoustic mode is enhanced to 20 nW. This two orders of magnitude increase is possible only with a one order of magnitude increase of the driving optical power. Alternatively, the suspended silicon waveguide can be excited electromechanically. This would allow orders of magnitude larger powers of the acoustic mode and thus a shorter device for optical isolation. Such an excitation mechanism is still to be developed.