Control of adiabatic light transfer in coupled waveguides with longitudinally varying detuning

We study adiabatic light transfer in systems of two coupled waveguides with spatially varying detuning of the propagation constants, providing an analogy to the quantum phenomena of rapid adiabatic passage (RAP) and two-state stimulated Raman adiabatic passage (two-state STIRAP). Experimental demonstration using a photoinduction technique confirms the robust and broadband character of the structures that act as broadband directional couplers and broadband beam splitters, respectively.

Figure 1

(a) Schematics of the waveguide structure providing an optical analogy to the RAP process and (b) corresponding longitudinal evolution of the coupling constant $C\left(z\right)$ and of the detuning $\mathrm{\Delta }\beta \left(z\right)$. (c) Schematics of the waveguide structure providing an optical analogy to the two-state STIRAP process and (d) corresponding evolution of $C\left(z\right)$ and $\mathrm{\Delta }\beta \left(z\right)$ (case A). Note that in panels (a) and (c) the longitudinal and transverse dimensions are not in scale.

Figure 2

Schematics of the technique to create the reconfigurable waveguide structures. A control beam at the wavelength $\lambda =532$ nm carries the structure of the waveguides. The latter is shaped by a spatial light modulator (SLM) and imaged to the surface of the SBN crystal, to which an electric field is applied along its polar axis. The probe beam (alternatively at $\lambda =633$ nm or $\lambda =850$ nm) propagates through the resulting waveguide structures to test their functionalities.

Figure 3

Theoretical expectation and experimental verification of the RAP-like light transfer for the parameter given in the text. (a) Numerically calculated spatial evolution of the intensity in $WG1$ (blue dashed curve) and $WG2$ (solid red curve) for $\lambda =633$ nm. (b) Same for $\lambda =850$ nm. (c) Measured intensity output distribution with $WG1$ but in the absence of $WG2$ (reference, blue dashed line) and with the presence of both waveguides (solid red line). (d) Same for $\lambda =850$ nm and the same structure.

Figure 4

Counterexample to the RAP process in absence of the detuning $\left[\mathrm{\Delta }\beta \right(z)=0]$. (a) Expected evolution of the intensity in $WG1$ (blue dashed curve) and $WG2$ (solid red curve) according to Eq. (1) for $\lambda =633$ nm. (b) Same for $\lambda =850$ nm. (c) Measured intensity output distribution with $WG1$ but in the absence of $WG2$ (reference, blue dashed line) and with the presence of both waveguides (solid red line). (d) Same for $\lambda =850$ nm and the same structure.

Figure 5

(a) Landscape of the expected output intensity of $WG2$ for the RAP process as calculated using coupled-mode theory under variation of the parameters $C_{\max }$ and $\mathrm{\Delta }{\beta }_{\max }$. The red area corresponds to the region where the adiabatic condition is fulfilled the best and the light transfer is complete. The blue circle and the green square correspond to the experimental conditions of Fig. 3 for probing at 633 and 850 nm, respectively. (b) Corresponding landscape for the two-state STIRAP process (case A) showing the relative intensity transferred from $WG1$ to $WG2$. The green area gives the region where the adiabatic condition is best fulfilled and the waveguide structure gives essentially a 50:50 beam splitter. The blue circle and the green square correspond to the experimental conditions of Fig. 7 for probing at 633 and 850 nm, respectively.

Figure 6

Theoretical expectations for a two-state STIRAP-like waveguide structure modeled for propagation of light at the 633-nm wavelength. Panels (a), (c), and (e) correspond to case $A$, and panels (b), (d), and (f) correspond to case $B$. Panels (a) and (b) show the evolution of the mixing angle $\theta \left(z\right)$ with the propagation distance $z$. Panels (c) and (d) show the intensity evolution in $WG1$ (dashed blue line) and $WG2$ (solid red line) obtained from coupled-mode theory. Panels (e) and (f) show the corresponding evolution of the light distribution obtained with the alternative beam propagation method. For both cases the system leads to an equal splitting of the input intensity among the two waveguides.

Figure 7

Experimental output intensity distribution for the case of two-state STIRAP as probed for cases $A$ and $B$ at two different wavelengths. Panels (a) and (b) show probing at $\lambda =633$ nm. Panels (c) and (d) show probing at $\lambda =850$ nm. Panels (a) and (c) correspond to case $A$, while panels (b) and (d) correspond to case $B$ (see text).