Photonic Crystal Fiber
Temperature Sensor
Applications

Overview•

Chemical and environmental sensors•

Bio-medical sensors•

Particle trapping•

Nonlinear optics•

High-power beam delivery•

Extreme dispersion values•

Endlessly single-mode fibers•

Sub-wavelength optics•

Bent waveguides

Photonic crystal fibers (PCF) have been extensively investigated forchemical, bio-medical, and environmental sensing applications. PCF
provides a unique platform for realizing the desired modal dispersion,
birefringence, confinement, and multiplicity characteristics. This canbe attributed to the freedom in designing the microstructure geometry.
Of significant importance for sensing applications, various chemical,
biological, and inorganic materials can be introduced by selective
infiltration of the holes or using deposition techniques. PCF sensors
often involve structural and electromagnetic field features that span
multiple orders of magnitude in variation, e.g. sub-wavelength metal
films supporting tightly confined surface plasmon modes in a PCF
with mode areas, air-holes and cladding dimensions of 10s and 100sof wavelength, respectively. These properties require a mode solverthat can both efficiently and accurately approximate the geometry andthe electromagnetic fields over the entire simulation domain.

OptiMode Software Features

Simulation Description•The surface plasmon assisted PCF temperature sensor proposed in[1] is simulated in OptiMode software. The temperature variation in
the sensor affects the phase matching between the core and the lossy
plasmonic modes resulting in loss incurred by the fundamental mode.
A triangular lattice with a pitch of 2μm for a silica PCF is depicted inFig. 1. The central and 1st layer of the air-holes have diameters of1μm and 1.2μm, respectively. The 2nd layer of holes (diameter=1.6μ)
are filled with a temperature sensitive liquid (nLiq=1.35 at 25°C) andselectively coated with a 40nm thick gold layer.

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Includes a vector finite element method (VFEM),
which is fast and accurate relative to other mode
solving algorithms.
Triangular mesh can be adapted to accurately
approximate the fine features of the geometry,refractive index profile, and electromagnetic fields.
Built-in VBScript capabilities accelerate the designand optimization of complex waveguide profiles.
Exploiting the symmetric boundary conditions
reduces the simulation domain, and modes of certain
symmetry can be readily targeted.
Full vector formulation for lossy, dispersive, andanisotropic materials.
Uniaxial perfectly matched layer (UPML) enables
identification of leaky modes.
Accurate and spurious-solution proof higher orderhybrid vector/nodal elements capabilities.
Specific modes can be targeted through a userspecified modal index estimate.
Accurate analysis of arbitrary bent waveguides usingtransformation optics.

LiquidAu

Air

Figure 1: Schematic of the PCF (inset) and the actual simulation window with theFEM mesh superimposed.

Imposing the symmetric magnetic/electric boundary
conditions along the X/Y axis in OptiMode reduces thesimulation domain by a factor of 4. As shown in Fig. 1, thetriangular mesh is configured to precisely represent boththe sub-wavelength Au coatings and the hole boundaries.
This mesh enables efficient modeling of both the surface
plasmonic modes and the core modes with high accuracy.
VFEM solver in OptiMode is used to calculate the complex
effective modal indices of both the core-guided and theplasmonic modes of the PCF at 25°C. The loss spectra of
the fundamental mode, obtained from the imaginary partof the modal index, is shown in Fig. 2 (a). The Peaks in
the loss spectra, marked on the figure and reported inTable 1, correspond to the phase-matched wavelengths
where the dispersion relations of the core-mode and aplasmonic mode intersect, as shown in Fig. 2 (b).

Strong wavelength dependant coupling between the core and theplasmonic modes is also evident in the electric field profiles depicted
in Fig 3. Comparing the field profiles of an off-resonant wavelength,e.g. 700nm shown in Fig. 3 (b) with shorter and longer loss-peakwavelength depicted in Fig 3 (c) and Fig. 3 (d) respectively, a higher
coupling is noticeable between the core mode and a plasmonic mode
bonded to the Au (silica)-liquid interface. The corresponding modal
indices calculated in OptiMode (presented in Table 2) are wellmatched with the reported values in Ref. [1]. Assuming a temperaturedependant Sellmeier (Drude) model for the silica (gold), thermal
sensitivity of -4x10-4(°C-1) for the liquid filling and thermal expansionof the gold coating as in Ref. [1], the temperature response of thePCF sensor was simulated in OptiMode and shown in Fig. 4.

(a)

(b)

(c)

(d)

(a)

Peak I
Peak III

Peak II

Figure 3: Electric-field amplitude profiles (|Ex|) at specified wavelengths: (a) Auliquid interface bound plasmonic mode at 560nm and (b-d) X-polarized fundamentalcore mode at 700nm, Peak I and Peak III (see table 1 and Fig. 2), respectively.

(b)

Table 2: Modal indices of the fundamental core and Au-liquid interface bonded
surface plasmon mode (SPLiq) at selescted wavelenghts calculated in OptiMode andcompared with Ref. [1].
Modeλ (nm)OptiMode
Peng et al. [1]
SPLiq
CoreCoreCore

560
608
700
903

1.4673+7.746e-3i
1.4377+1.066e-4i
1.4297+1.6280e-5i
1.4126+1.355e-4

1.467+7.739e-3i
1.438+1.063e-4i
1.430+1.627e-5i
1.413+1.361e-4i

Figure 2: Modal analysis of the PCF at 25°C in OptiMode: (a) Loss
spectra of the core-mode calculated from the imaginary part of themodal indices. (b) dispersion relation of the core the plasmonic modes.
Table 1: OptiMode calculated Peak-loss wavelengths at 25°C, asindicated in Fig. 2 and compared with Ref. [1].
λ (nm)

OptiMode

Peng et al. [1]Peak I
608
608
Peak II
784
780*
Peak III
905
903*estimated from Fig. 2 (b) in [1].

Figure 4: Loss spectra of the core mode of the PCF sensor (shortest wavelength peakloss) at selected temperatures calculated in OptiMode.

References[1] Y. Peng, J. Hou, Z. Huang, and Q. Lu, "Temperature sensor based on surface
plasmon resonance within selectively coated photonic crystal fiber," Appl. Opt.
51, 6361-6367 (201 2).