Supplementary material for “Mach-Zehnder refractometric sensor using long-range
surface plasmon waveguides”
Asad Khan,1 Oleksiy Krupin,2 Ewa Lisicka-Skrzek,1 and Pierre Berini1,3,*
1
School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, K1N
6N5, Canada
2
Department of Biological and Chemical Engineering, University of Ottawa, Ottawa, Canada
3
Department of Physics, University of Ottawa, Ottawa, Canada
*Corresponding author
APPENDIX
Appendix A.1: Preparation of refractive index solutions used to generate the transfer
characteristic of MZIs
PBS (phosphate buffered saline) solution was prepared from the package by dissolving 1
package of PBS (Sigma-Aldrich, P5368) in 1 L of deionized water producing a buffer of the
following constitution: 0.01 M phosphate buffer saline, 0.138 M NaCl and 0.0027 M KCl
(according to the manufacturer). Distilled water was deionized using Millipore filtering
membranes (Millipore, Milli-Q water system at 16 MΏ·cm).
Solutions for Fig. 4(a): Stock mixtures were prepared by adding glycerol (Sigma-Aldrich,
49767) to the PBS solution producing a refractive index of n = 1.3334 (13.39 % w/w glycerol)
and n = 1.3374 (17.96 % w/w glycerol). The refractive indices of the prepared stock solutions
were measured at λ0 = 1312 nm using a prism-coupler based instrument (Model 2010, Metricon,
Prism 200-P1) to an accuracy of about ±1×10-4. Sixteen sensing solutions having a refractive
index ranging from about 1.33365 to 1.33655 in increments of about 2×10 -4 RIU (except for the
first one having an increment of ~1×10-4 RIU) were prepared by serial dilutions of the stock
solutions. The absolute starting refractive index is unknown to greater accuracy due to
instrument limitations.
Solutions for Fig. 4(b): Ten solutions were prepared in a similar manner as described
above but covering a refractive index range from about 1.3290 to ~1.3304 with an increment of
1.6×10-4 RIU from two stock solutions with n = 1.329 (8.69 % w/w glycerol) and n = 1.331
(10.79 % w/w glycerol) The precise index increment was determined by comparing the
theoretical MZI response to the measured one.
Appendix A.2: Derivation of Eq. (3) of the main text
Referring to Fig. 2(b) of the main text, we treat the Y-junctions of the MZI as non-radiative
equal-split/equal-combine structures. Adopting the same symbols as in Fig. 2 and as defined in
the main text, we write the root mean squared electric field phasor representing the LRSPP at the
output of the MZI as:
Eout = Ein e-CL0 √TC [(1/√2)( 1/√2)√TF√TF e-FLF e-jF + (1/√2)( 1/√2) e-CLF e-jR] (A.1)
where: F is the insertion phase through the fluidic channel and R is the insertion phase through
the reference arm of the same length (LF). Eq. (A.1) simplifies straightforwardly to:
Eout = (1/2) Ein e-CL0 √TC [TF e-FLF e-jF + e-CLF e-jR]
(A.2)
Using the above along with its complex conjugate we write the power at the output of the MZI:
Pout = EoutEout* = (1/4)Pin TC e-2CL0 [TF2e-2FLF + TFe-FLFe-CLFe-jFejR +
TFe-FLFe-CLFejFe -jR + e-2CLF]
(A.3)
where Pin = EinEin*. Defining D = F - R and  = F - C, Eq. (A.3) can be simplified to:
Pout = (1/2) Pin TC e-2C(L0+LF)[(TF2 e-2∆LF + 1)/2]{1 + [2TF e-∆LF / (TF2 e-2∆LF +1)] cos(D)} (A.4)
The power penalty (W) is identified as the first term in square brackets and the visibility (V) as
the second term in square brackets, which when substituted into Eq. (A.4) yields Eq. (3) of the
main text. We also note that D = F - R = (2LF/0)(neff,F - neff,C).