This letter is intended as a comment on a recently published paper: “Surface plasmon interferometer in silicon-on-insulator: novel concept for an integrated biosensor” [1]. The referenced paper presents a theoretical waveguide analysis of a new and interesting approach to SPR sensing based on interference between two modes at an abrupt discontinuity in a very short waveguide (about 6μm). A similar approach based on two guided TM modes was also published recently by us [2, 3], showing high sensitivity values in a longer waveguide structure (about 350μm). In such a device, at the first transition (input to sensing section), the incoming mode is decomposed into all guided and radiation modes of the sensing section. As pointed out by Ctyroky, et al. [4], the radiation modes may be neglected for longer devices since they spread and attenuate while propagating through the sensing section. However, as shown here, for the case of almost total cancellation of the guided mode’s superposition and for short propagation distances, the residual part contribution of the radiation modes cannot be neglected.

We recalculated the transfer function of the device by two methods: first by neglecting the contribution of radiation modes (as done in Ref. [1]), and subsequently radiation modes were taken into account.

A custom approach to calculate radiation modes is by enclosing the waveguide structure between two ‘magnetic walls’ [4]. Such walls were used to discretize the radiation modes and were placed in our simulation 40μm above and below the guiding layer so that reflections from the walls could be neglected. Transfer matrix approach [5] was used to account for both guided and radiation modes in each section. Mode expansion and propagation method [5] was then applied to calculate the transition matrix for each interface using both guided and radiation modes. Multiple reflections were neglected as backwards reflected power from the second interface was relatively low and attenuation is high.

Calculated results show that about half of the power of the input section guided mode is transferred to the two SP modes in the sensing section and the rest is transferred mostly to forward propagating radiation modes. While these modes propagate through the sensing section they spread and their power density attenuate, but part of the power does reach the output section guided mode. Calculation for a sample optimized working point (5.7μm sensing section length) show that the contribution of power to the output guided mode originates from the first SP mode (about -18dB relative to the input power), the second SP mode(about -17dB) and from radiation modes (about -23dB). As the working point is optimized so that the guided modes interfere destructively, the contribution of the radiation modes becomes higher than the power of the interfering guided modes. Power transferred by the waveguide for the optimized case as a function of the refractive index of the superstrate is shown in Fig. 1 for two cases, namely with and without the contribution of radiation modes. This graph shows very high sensitivity values when the contribution from radiation modes was neglected (above 10,000dB/RIU) and relatively low sensitivity values when that contribution was added (below 1000 dB/RIU). Note also that in Fig. 1, the power transfer calculated here while neglecting radiation modes is slightly different than the one reported in Ref. [1] (Fig. 6 there) likely because we used the transition matrix approach (with all modes) which is different than the method based on overlap integrals used in Ref. [1]. The reduction in contrast seen in Fig. 1 can be qualitatively explained as a recapture of radiated power at the second transition of the sensing section.

 

Fig. 1. Calculated power transfer for the waveguide with and without the contribution of radiation modes (All modes / Guided Modes, respectively).

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As a final remark, one may conclude that a way of retaining high interference contrast and sensitivity in this device is to lengthen it up to a value where the contribution of radiation modes can be practically neglected.