Numerous fiber-optic, waveguide, refractometric, and biochemical sensors, as well as photonic sensing structures, work on this principle. Designing them, however, requires much more than checking whether light propagates through the structure. Analysis of modes, effective refractive index, dispersion, birefringence, losses, coupling, and the distribution of the electromagnetic field may be necessary.
More advanced designs add microstructures, thin metal layers, dispersive materials, periodic structures, and interaction of the field with the medium under test. Sensor design is therefore a good example of a problem in which the simulation method should follow from the physics of the device.
In the Optiwave ecosystem you can use, among others, OptiMode, OptiBPM, OptiFDTD, OptiFiber, and OptiGrating, while Lambda Research tools, primarily TracePro, come into play when the sensor must also be analyzed as part of a larger optical or opto-mechanical system.
Waveguide as a sensor: what does the measurement rely on?
The simplest waveguide consists of a light-guiding region and surrounding materials with suitably chosen optical properties. The electromagnetic field of a propagating mode, however, is not entirely confined to the core: part of the field can extend into the surroundings of the structure as an evanescent field. If the properties of the material in this region change, the behavior of the mode can change as well.
For example, a change in the refractive index of the medium can affect:
- the effective refractive index,
- the propagation constant,
- the mode profile,
- the level of field confinement,
- coupling between structures,
- resonance conditions,
- propagation losses.
It is precisely the dependence of a measurable optical parameter on a physical or chemical quantity that underlies the operation of many photonic sensors.
Modal analysis: the first step in sensor design
Before analyzing the whole sensor, it is worth answering a basic question: what modes can the designed structure guide? For each mode you can analyze, among other things, its field profile and effective refractive index.
In Optiwave, this task is handled by OptiMode, an environment intended for designing and modal analysis of waveguide structures. The manufacturer points to the ability to identify the supported modes and determine their characteristics, including the mode profile and the effective refractive index (n_eff).
For a sensor this is particularly important, because the designer is interested not only in the value of n_eff, but also in how it changes as the measured parameter changes. We can therefore run a series of simulations sensor parameter → modal analysis → n_eff and observe Δparameter → Δn_eff. Such a model is the starting point for determining the sensitivity of the designed structure.
Why is the field distribution so important?
Two waveguides can guide light at the same wavelength, yet their usefulness as sensors can be completely different. Among other things, this is determined by the distribution of the electromagnetic field. If most of the mode energy sits deep in the core, a change in the surroundings may have little effect on propagation. If, on the other hand, a significant part of the field interacts with the analyzed medium, the sensor response can be stronger.
Designing a waveguide sensor is therefore often a compromise between good light guiding and sufficiently strong interaction of the field with the surroundings. Increasing the interaction with the medium can improve sensitivity, but it can also affect losses, confinement, or the structure's susceptibility to other disturbances. That is exactly why analyzing the mode profile is one of the basic stages of a project.
Parametric sweep: how do you calculate sensitivity?
A single simulation tells us how the sensor behaves at one operating point. Sensor design, however, requires checking the response for many values of the measured parameter. Suppose the sensor is meant to detect a change in the refractive index of the medium: you can run a series of calculations n₁ → n_eff,1, n₂ → n_eff,2, n₃ → n_eff,3, and so on, and use them to analyze how the optical characteristic changes with the medium under test.
A similar sweep can be run for:
- temperature,
- geometric dimensions,
- wavelength,
- refractive index,
- layer thickness,
- element position,
- material parameters.
OptiFiber has automatic parameter scanning functions, and Optiwave lists fiber sensor design as one of its key applications.
PCF sensors: when geometry becomes part of the measurement
A particularly interesting class of devices is Photonic Crystal Fibers (PCF), that is, microstructured optical fibers. Unlike a classical fiber, the cladding geometry can contain an arrangement of air holes or other structures, which gives the designer considerable freedom in shaping the modal properties.
Optiwave points out that PCFs can be used in chemical, biomedical, and environmental applications, and that chemical, biological, or inorganic materials can be introduced into selected holes. A change in the properties of the material inside the microstructure can then affect the propagating modes, which makes it possible to build sensors that respond to changes in the surroundings.
Temperature sensor based on PCF
Optiwave publishes the example Photonic Crystal Fiber Temperature Sensor using OptiMode. In structures of this type, the PCF geometry makes it possible to shape properties such as modal dispersion, birefringence, confinement, or the number of supported modes. The properties of the sensor result from the dependence of the structure's electromagnetic parameters on temperature and on the materials used in its construction.
It is a good example showing that sensor design is not just a matter of drawing the fiber geometry: you have to model the materials, the microstructure, and the electromagnetic field appropriately.
Biochemical sensors: the field as a measuring probe
Biochemical sensors are an even more demanding example. Optiwave presents the example Photonic Crystal Fiber Bio-chemical Sensor using OptiMode, in which the analyzed structures can include both the PCF geometry and thin metallic layers supporting strongly confined plasmonic modes.
In such a case, the model has to handle elements of very different geometric scales at once: on one hand the size of the whole PCF structure, on the other much thinner layers and a locally rapidly varying field. This is a good example of a situation in which the quality of the modal solver and the way the geometry is discretized have a direct impact on the reliability of the result.
OptiMode: not just one type of solver
For advanced structures, it is important not to reduce OptiMode to a single kind of numerical method. OptiMode is a platform for modal analysis of waveguide structures and can work with the propagation tools OptiFDTD and OptiBPM: a calculated mode can be used as the excitation in a further component simulation.
This makes it possible to build a logical workflow:
- Sensor geometry.
- Modal analysis.
- Mode selection.
- Introducing the mode into the propagation model.
- Analysis of the whole component.
This is especially important when analysis of the cross-section alone does not yet answer all the design questions.
OptiBPM: propagation in the sensor
The next level is propagation analysis. OptiBPM is an environment intended for designing complex optical waveguides using the Beam Propagation Method. Among its applications, Optiwave lists guiding, coupling, switching, splitting, as well as multiplexing and demultiplexing of light. On the product page, the manufacturer also publishes application examples related to optical sensors.
BPM can be useful when the design question concerns how the field changes during propagation in a structure, rather than only what modes exist in a given cross-section. For example, you can analyze coupling between waveguides, branches, changes of geometry along the propagation direction, transitions between structures, field evolution, and the dependence of propagation on device parameters.
When is BPM not enough?
The Beam Propagation Method is a very useful tool, but it is not a solution to every electromagnetic problem. In more complex structures, strong reflections, resonances, propagation in many directions, periodic structures, diffraction, strongly inhomogeneous fields, and local electromagnetic interactions can matter. A full-wave method may then be more appropriate.
OptiFDTD: full-wave sensor modeling
OptiFDTD uses the Finite-Difference Time-Domain method and enables analysis of the electromagnetic field through numerical solution of Maxwell's equations. It can be used for advanced passive and nonlinear photonic components and for analysis of propagation, scattering, reflection, diffraction, and polarization.
Optiwave is also developing integration of OptiFDTD with the OptiMode modal solvers, so that a modal solution can be used in an FDTD simulation. Such a model is particularly useful when we want to see not only the final value of a parameter, but also where the field is located, how it interacts with the structure, and where local electromagnetic effects arise.
Resonant photonic sensors
Not every sensor has to measure a change in power directly. A very useful mechanism is a change in the resonance condition. If the frequency or wavelength of a resonance depends on the effective refractive index, a change in the properties of the surroundings can shift the resonance.
The measurement scheme can therefore look as follows: change of medium → change of optical properties → change of n_eff → shift of the spectral characteristic → measurement signal. From the design point of view, this means analyzing not just one operating point, but the entire spectrum or an appropriate wavelength range.
Fiber-optic sensors: the role of OptiFiber
If the project concerns a classical or specialty optical fiber, OptiFiber becomes useful. The program is intended for analyzing fiber properties and includes solutions for analyzing LP and vector modes, propagation in multimode fibers, dispersion, birefringence, and PMD. Among the program's key applications, the manufacturer directly lists Fiber Sensor design, as well as analysis of parameters, sensitivity, and tolerances. This is especially important when the sensor makes use of changes in the parameters of the fiber itself.
Stress, birefringence, and PMD
A change in the environment does not have to affect only the refractive index of the surrounding medium. In fiber-optic sensors, stress, deformation, structural asymmetry, thermal changes, and birefringence can also matter. OptiFiber makes it possible to analyze birefringence and PMD resulting from internal or external perturbations. In a suitably designed sensor, a change in the polarization state or in the difference between the parameters of two polarization modes can form part of the measurement mechanism.
Bragg gratings and FBG sensors
Fiber Bragg Gratings (FBG) are also an important class of fiber-optic sensors. A Bragg grating is a periodic modulation of the optical properties of the fiber; under the right conditions, a specific part of the spectrum is reflected. If temperature or stress changes the parameters of the structure, the characteristic response wavelength of the grating can change as well.
In the Optiwave ecosystem, the design of periodic structures and gratings can be carried out in OptiGrating, while the properties of the fiber itself can be analyzed in OptiFiber. This is another example of a multi-level approach: fiber → periodic structure → spectral response → measured quantity.
Sensitivity is not everything
When designing a sensor, it is easy to focus solely on maximizing sensitivity, but this does not always lead to the best device. You must also take into account:
- measuring range,
- linearity,
- losses,
- temperature dependence,
- influence of manufacturing tolerances,
- selectivity,
- ability to couple light,
- parameter stability,
- feasibility of fabricating the structure.
A design with a very large theoretical signal change may be of little use if its response depends just as strongly on random variations in geometric dimensions. After the sensitivity analysis, another stage should therefore follow: analysis of tolerances and disturbing parameters.
Nominal sensor versus a sensor that can be manufactured
Suppose the model shows a very good response for a waveguide width W. The real manufacturing process, however, gives W ± ΔW. Similar deviations can apply to the height of the structure, the diameter of PCF holes, layer thickness, the refractive index of the material, or the position of the active layer.
It is therefore worth running two kinds of sweeps:
- The first: change of the measured quantity → change of the sensor response.
- The second: change of technological parameters → change of the sensor response.
Only comparing them shows whether the designed measurement signal is clearly distinguishable against the variations resulting from manufacturing tolerances.
From the sensor model to a complete device
At the electromagnetic level we can obtain a very good model of the structure. A real sensor, however, also requires:
source → coupling → sensing structure → output system → detector.
This is exactly where the scope of a single model ends and a system-level problem begins. For larger optics, sources, detectors, and mechanical elements, Lambda Research tools can be useful.
TracePro: the sensor as part of a real optical system
TracePro uses Monte Carlo ray tracing and lets you build three-dimensional models that include geometry, sources, materials, surfaces, and detectors. Sources can be defined as a Grid Source, Surface Source, or Ray File, and surface properties can include, among others, reflection, transmission, absorption, scattering, polarization, and grating parameters.
In a sensor project, TracePro can be useful, for example, when you need to analyze the delivery of light to the sensing element, the real source, the lens system, apertures, the detector, the housing, unwanted reflections, and losses resulting from the device geometry. TracePro provides, among other things, irradiance maps and reports on flux and other quantities resulting from ray tracing.
It should not, however, replace an electromagnetic solver for a waveguide microstructure. Lambda Research clearly states that TracePro is a geometric ray tracing program and does not model full electromagnetic effects or full Gaussian beam propagation. This is an important distinction.
One sensor: several levels of modeling
An advanced project may require several models.
Level 1: mode (OptiMode)
What modes exist? What is the field profile? How does n_eff change?
Level 2: propagation (OptiBPM)
How does the field propagate through the structure? How does coupling proceed?
Level 3: full electromagnetics (OptiFDTD)
What happens in a complex microstructure? What do the reflections, diffraction, and local field distribution look like?
Level 4: fiber (OptiFiber)
How do modes, dispersion, birefringence, and propagation behave in the fiber?
Level 5: optical system (TracePro)
How do the source, optics, mechanics, and detector affect the operation of the complete device?
The most important rule is therefore this: do not try to solve all levels of the problem with a single solver.
Example workflow for designing a waveguide sensor
1. Define the measured quantity
It can be temperature, stress, refractive index, the presence of a specific medium, or a change in the composition of the surroundings.
2. Choose the optical transduction mechanism
Determine how the physical change will be converted into an optical change. It can be, for example, Δn_eff, a change of the spectrum, a change of coupling, a change of polarization, or a change of losses.
3. Build the material and geometric model
At this stage we define the waveguide, the microstructure, the layers, and the medium under analysis.
4. Calculate the modes
In OptiMode you can determine the field profiles and the effective refractive index for the modes of interest.
5. Run a sweep of the measured parameter
A change in temperature, refractive index, or another parameter lets you determine the sensor response.
6. Check propagation
If the device requires analysis of propagation or coupling, the model can be extended in OptiBPM.
7. Apply FDTD where full electromagnetics is needed
Complex microstructures, resonances, or strong local interactions may require a more accurate electromagnetic model.
8. Perform a tolerance analysis
Varying the technological parameters lets you check whether the sensor will keep the expected characteristic after fabrication.
9. Add the real optical path
If the sensor works with a source, lenses, apertures, and a detector, you can move on to a model of the whole device, for example in TracePro.
10. Compare the simulation with measurement
The final stage should be comparing the model's characteristic with a real prototype and, if needed, updating the model parameters.
Which tool should you choose?
| Task | Tool |
|---|---|
| Waveguide mode analysis | OptiMode |
| Field profile and effective refractive index | OptiMode |
| Propagation in a waveguide | OptiBPM |
| Coupling of waveguide structures | OptiBPM |
| Full-wave analysis of a microstructure | OptiFDTD |
| Complex electromagnetic effects | OptiFDTD |
| PCF sensor design | OptiMode / a suitable propagation solver |
| Fiber analysis | OptiFiber |
| Dispersion, birefringence, PMD | OptiFiber |
| FBG sensor / grating structures | OptiGrating |
| Source, optics, and detector in a larger device | TracePro |
| Opto-mechanical analysis and unwanted light paths | TracePro |
The most common mistakes in sensor modeling
Analyzing only one operating point
A sensor should be analyzed as a function of the measured quantity, not just for a single value of the parameter.
Maximizing sensitivity without tolerance analysis
High sensitivity to the medium under test is not enough if the structure is just as sensitive to random manufacturing deviations.
Incorrect computational mesh
In structures containing thin layers or strong field gradients, the local resolution of the model can be crucial.
Ignoring material dispersion
In spectral analyses, material properties can depend on wavelength. The model should reflect the operating range of the device.
Using BPM for every waveguide problem
BPM is an efficient propagation method, but for problems with strong reflections, complex resonances, or propagation in many directions, a full-wave method may be more appropriate.
Using FDTD when it is not needed
The most detailed method is not automatically the best choice. If the question mainly concerns mode parameters, a suitable modal solver can deliver the required information much more efficiently.
Neglecting the input system and the detector
An excellent sensing structure does not guarantee a good device if light is not delivered properly or the output signal is not efficiently detected.
From simulation to sensor
The greatest value of simulation appears when the designer treats it not as a single picture of the field, but as a tool for making design decisions. A well-prepared model should help answer the questions: which geometry parameter increases sensitivity, which mode should be used, how strong the influence of the medium under test is, how the spectral response changes, which tolerances are critical, whether the measurement effect is larger than the variations resulting from the manufacturing process, and how to couple light in and out efficiently.
Only the answers to these questions lead from an interesting photonic structure to a sensor that can actually be built and used.
Summary
Advanced modeling of waveguides and optical sensors requires combining modal, propagation, electromagnetic, and, in many cases, system-level analysis. There is no single solver suited to every stage.
In the Optiwave environment, OptiMode lets you analyze modes and their parameters, OptiBPM is used to model propagation in waveguide structures, OptiFDTD enables full-wave electromagnetic analysis, and OptiFiber is aimed at the properties and design of optical fibers, including sensing applications. Official Optiwave materials also show specific examples of PCF sensors for temperature measurement and for biochemical applications.
TracePro from Lambda Research, in turn, can complement such a workflow at the level of the whole device, especially when you need to account for the real source, optical elements, detector, mechanics, scattering, or unwanted light paths.
The most important stage, however, remains a correct definition of the sensor's operating mechanism. Only then can you choose the appropriate numerical method and decide which part of the problem requires modal analysis, which propagation analysis, which full-wave analysis, and which modeling of the entire optical system.
Manufacturer resources
Environment for designing and modal analysis of waveguide structures: Optiwave: OptiMode
Example of a temperature sensor based on PCF: Optiwave: Photonic Crystal Fiber Temperature Sensor using OptiMode
Example of a biochemical sensor based on PCF: Optiwave: Photonic Crystal Fiber Bio-chemical Sensor using OptiMode
Environment for designing waveguides with the beam propagation method: Optiwave: OptiBPM Optical Waveguide Design
Overview of OptiFiber capabilities, including fiber sensor design: Optiwave: OptiFiber Overview
Information about TracePro and Monte Carlo ray tracing modeling: Lambda Research: TracePro