SOFTWARE & COMPUTING: Rapid characterization and reference tools for active photonic materials

MARY POTASEK, EVGUENI PARILOV, and KARL BEESON

Many advances in optics and optoelectronics are made possible by novel algorithms used to calculate electromagnetic interactions and light propagation in materials. Some of these algorithms, including the beam-propagation method, the finite-difference method, and the split-step method, form the basis for a series of well-known software packages used in optoelectronics and telecommunications.¹

Simphotek has developed a new algorithm—the active photonics building block (APBB) method—to make calculations of photophysical interactions in materials a fast and straightforward process.^2,3 The APBB method uses uniquely defined mathematical expressions (a variation of computational building blocks) to link icons on the user interface defining active photonic interactions to the main simulation engine. We use the word "active" to designate nonlinear optical materials and nonlinear optical interactions with materials.

By writing the governing partial differential equations in terms of matrices and vectors, nearly unlimited changes and additions can be made to the photophysical interactions in real time. Each icon is linked to a specific matrix describing one fundamental type of interaction—for example, single- or multiphoton absorption, spontaneous or stimulated emission, energy transfer, upconversion, and chemical reactions such as singlet oxygen formation, to name a few.

Material energy-level diagrams can be quickly revised or added because their fragments are uniquely formulated in terms of building blocks, which provide links between input icons and the simulation engine. The algorithm, combined with well-known electromagnetic algorithms (some of which are listed above), can be used for applications in fiber lasers, rare-earth amplifiers, solar cells, silicon photonics, solid-state lighting, displays, bioimaging, confocal microscopy, microlithography, and others.

The newest version of the SimphoSOFT software (v.3) enables users to eliminate writing tedious mathematical equations, stop writing and debugging software, and reduce modeling time and cost by more than an order of magnitude. Users can explore material performance under various conditions of cause-effect relationships and model complex multilayer materials (for example, a diffusion-bonded multisegment gain medium).

Active-material vs. active-device modeling

How does modeling active materials with the APBB method compare to the well-known commercial and in-house methods for modeling active devices? With the growing emphasis on active photonics, it is critical to develop novel algorithms for software modeling.⁴ To date, the majority of commercial software modeling has emphasized active-device aspects, such as lasers, optical amplifiers, solar cells, displays, lighting, lithography, silicon photonics, and so on using established electromagnetic-modeling algorithms such as those mentioned above. While inclusion of active materials is present, it is usually done in a painstaking, time-consuming differential-equation mode, requiring lengthy adjustments (when possible at all) each time the device model changes.

Because devices ultimately depend on materials, a better way to model the photophysics of active materials is needed to improve these devices. In addition to devices, active photonics materials are of growing importance in biomedical diagnostics, bioimaging, and microscopy.

The APBB method is a rapid and cost-efficient method of simulation; this method actually compliments rather than competes with legacy software, both commercial and in-house. For example, legacy software for modeling lasers, telecommunications, and so on can benefit from optimizing optical materials, concentrations, input laser power, material sample length, material type, and so on as we put more emphasis on the material itself and allow defining more advanced types of photophysical interactions not available with conventional models based on simplifications. The software can optimize material and laser parameters that serve as input to legacy programs; in addition, experimental data plots or calculation plots from commercial codes such as MatLab, Mathematica, and others can be inserted into SimphoSOFT for fitting or further analysis.

Case study 1: Amplification in rare-earth materials

SimphoSOFT is well-suited to look at complex interactions such as amplification, cross-relaxation, upconversion, and stimulated emission in rare-earth materials whose ions may occupy many excited-state energy levels and undergo several competing optical transitions. In this study, we investigate thulium-ion-doped materials that can be used to produce devices to amplify light at wavelengths near 1900 nm using 790 nm pump light.

Figure 1a shows a partial SimphoSOFT screenshot of the experimental setup with the pump and the seed (delayed in time from the pump) laser beams combining and traversing the rare-earth-amplifier material. Figure 1b shows a partial screenshot of the complex energy-level diagram used for modeling amplification. Figures 1c and 1d show the intensity of the pump and seed pulses, respectively, calculated along the propagation-material length, and red (yellow) areas correspond to increased (decreased) intensity. Figure 1d confirms that the pump transfers significant energy to the seed. Figures 1e and 1f show the 3D plots of the pump and seed pulses, respectively, at the midpoint through the material.

Figure 1h shows the electron-population densities of the ground state at the sample input surface (blue line) and at the midpoint of the amplifier material (orange line) during the time that the pump pulse is passing through the sample. At the sample input surface, the population of the ground state is nearly depleted by the pump beam, which can affect the amplification efficiency—once the ground state is depleted of ions, the state will no longer absorb the pump light.⁵ In contrast, at the midpoint of the sample, the ground state is about 25% depleted during the pump pulse.

Case study 2: Multiphoton-absorbing materials

For multiphoton-absorbing materials, the software can, for example, model nonlinear transmission for optical-limiting applications, model Z-scans or do Z-scan fitting to determine two-photon absorption cross-sections and model energy-level populations to determine if saturation of absorption is occurring. In Fig. 2a, Z-scan is simulated for a two-photon absorbing material. The APBB method allows defining energy-level diagrams with three and more energy levels, an improvement over simulations based on two-level approximation models that become inaccurate when applied to higher input energies.

FIGURE 2. A calculated Z-scan transmission curve is shown (a) along with an experimental data fit (b) with an analytical formula (blue dashed-dotted line) and SimphoSOFT simulation (red dashed line) [6].

SimphoSOFT numerical simulations can result in more accurate modeling of multiphoton absorber saturation than is possible with analytical models. Many researchers use analytical equations for multiphoton-absorber sample transmission that include a saturation intensity parameter to describe the population of the first excited state of the molecule.⁶ The calculated transmission of the sample depends on this parameter. Using such analytical equations can lead to incorrect interpretations of experimental results that indicate material-absorber saturation when, in fact, saturation is not present. Figure 2b shows a comparison of analytical and numerical simulation results for an example material. The analytical model shows saturation. The more accurate SimphoSOFT numerical model shows no saturation for the same laser pulse intensities.

Material database

SimphoSOFT requires the user to input many material parameters, as well as energy-level diagrams. To address this need, comprehensive searchable databases have been created. The first one, called MPA Info+, for multiphoton-absorbing (MPA) molecules, provides users with access to the published results for more than 1000 multiphoton absorbing materials and more than 20,000 parameter values. Each material is accompanied by the values of optical parameters, chemical structure, an energy-level diagram, and examples of applications referenced to the source for further exploration.

This database aids in structure-function relationships by correlating chemical structures and material parameters. It avoids tedious and costly literature searches to identify optimal materials with the best photophysical parameters. Unknown material parameters can be estimated from the thousands of measured parameters of similar materials. Data and energy-level diagrams ported from the database to SimphoSOFT v.3 enables users to answer probing questions before doing costly experiments; for example: what are the safe intensity levels, is there material degradation through depletion, is the pulse shape distorted during propagation, is the output signal strong enough, is the limiting level sufficient, and is the conventional analytical Z-scan fit accurate? Figure 3 shows examples of active materials found in the database that can be excited in the 700–900 nm wavelength range with multiphoton cross-sections between 2000 and 5000 GM (Göppert-Mayer; 1 GM = 10^-50 cm⁴ s photon^-1).

FIGURE 3. A partial screenshot shows the MPA Info+ database.

The case studies above resulted in more than an order-of-magnitude reduction in modeling time and cost as compared to the traditional method of writing and editing simulation software and obtaining material parameters from experiments or publications.

ACKNOWLEDGEMENT

SimphoSOFT is a registered trade name of Simphotek.

REFERENCES
1. www.nusod.org/inst/software.html.
2. E. Parilov and M. Potasek, J. Opt. Soc. Am. B, 23, 1894 (2006).
3. E. Parilov and M. Potasek , U.S. Patent No. 7,949,480 B2 (2011).
4. www.nap.edu/catalog.php?record_id=13491.
5. www.simphotek.com/application-notes.
6. G. He et al., J.Appl. Phys., 101, 083108-1 (2007).

Mary Potasek is president, Evgueni Parilov is executive vice president of R&D, and Karl Beeson is executive VP of engineering at Simphotek, 211 Warren St., Newark, NJ, 07103; e-mails: [email protected], [email protected], and [email protected]; www.simphotek.com.