Advancing Detector Shielding with Thermo-Optic Defocusing in

PMMA Integrated on Silicon Nitride

Soon Thor Lim

1 a

, Thomas Ang

1 b

, Zifeng Yuan

, Thanh Xuan Hoang

1 c

, Dewen Zhang

2 d

Ching Eng Png

1 e

, Aaron Danner

2 f

and Gandhi Alagappan

1 g

Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore

Dept. of Electrical and Computer Engineering National University of Singapore, Singapore

Keywords: Thermo-Optic Defocusing, Polymethyl-Methacrylate (PMMA), Optical Power Limiter (OPL).

Abstract: This study develops an on-chip optical power limiter (OPL) based on the thermo-optic defocusing effect in

PolyMethyl-Methacrylate (PMMA) to protect an avalanche photodiode (APD) from high optical power

damage. The OPL is designed to operate within a reduced power range of 0.1 mW to 10 mW by adjusting

waveguide dimensions, taper widths, and free-space region (FSR) lengths. Detailed calculations, modelling,

and simulations are presented, demonstrating the efficacy of the OPL in limiting optical power reaching the

APD, preventing damage and ensuring stable performance in high-power applications.

1 INTRODUCTION

Silicon photonics plays a pivotal role in data

communications, quantum key distribution (QKD),

and sensing applications. As these systems evolve,

protecting photonic circuits from high-intensity

optical signals becomes crucial, particularly for

safeguarding sensitive components like avalanche

photodiodes (APDs). Optical Power Limiters (OPLs)

(Lee, 1993) are essential for preventing damage from

excessive power and ensuring stable operation. While

technologies such as silicon waveguides with strong

two-photon absorption (Osgood, 2009) and photonic

crystals (Zheng, 2015) face limitations in integration

and fabrication, polymer-based OPLs, like those

using PMMA (Gandhi, 2024), offer advantages in

thermal management and power handling. This paper

presents a PMMA-based OPL design using the

thermo-optic defocusing effect to protect APDs,

ensuring reliable performance and extending device

https://orcid.org/0000-0003-2350-823X

https://orcid.org/0000-0002-1914-988X

https://orcid.org/0000-0002-6815-487X

https://orcid.org/0009-0005-5426-5869

https://orcid.org/0000-0002-7797-1863

https://orcid.org/0000-0002-9090-9626

https://orcid.org/0000-0002-4730-2503

lifespan in variable environments. Avalanche

photodiodes (APDs) are widely used in high-speed

optical communication systems due to their high

sensitivity. However, they are prone to damage when

exposed to optical powers beyond a few milliwatts.

Therefore, an optical power limiter (OPL) is essential

to protect APDs from high intensity light. In this

paper, we design an OPL that operates in the power

range of 0.1 mW to 10 mW. The OPL employs a

thermo-optic defocusing mechanism in PMMA, a

material with a negative thermo-optic coefficient.

This mechanism induces beam divergence with

increasing input power, which limits the amount of

light reaching the APD. Building on the principles

from our high-power OPL designs, we reduce the

maximum limiting power range from 10 mW - 102

mW to 0.1 mW - 10 mW.

Lim, S. T., Ang, T., Yuan, Z., Hoang, T. X., Zhang, D., Png, C. E., Danner, A. and Alagappan, G.

Advancing Detector Shielding with Thermo-Optic Defocusing in PMMA Integrated on Silicon Nitride.

DOI: 10.5220/0013148400003902

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 13th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2025), pages 92-94

ISBN: 978-989-758-736-8; ISSN: 2184-4364

2 OPL DESIGN

The OPL design incorporates a pair of tapered

waveguide antennas separated by a free-space region

(FSR) filled with PMMA, modelled as a dielectric

material with refractive indices of 1.4716 and 4.04 ×

10-6 and a thermal optic coefficient of -1.3 × 10-4 K-

1 as shown in figure 1. Using COMSOL Multiphysics

for 3D thermal-optic simulations for the free-space

region (FSR) and nonlinear regression model for

output threshold power. Our devices exhibited

insertion losses between 2.5 and 10 dB and maximum

powers in the range of 10 to 102 mW, demonstrating

effective on-chip optical power limiters based on

thermal defocusing effects (Gandhi, 2024).

Figure 1: Schematic of the on-chip optical power limiter.

2.1 Theory

The core mechanism behind this OPL is the thermo-

optic effect in PMMA, where the refractive index

decreases with increasing temperature due to the

negative thermal-optic coefficient. The change in the

refractive index Δ𝑛 of PMMA is given by Δ𝑛=𝑛

+βΔ𝑇, where 𝑛 = 1.4716 (refractive index at room

temperature), β=−1.3×10 K (thermal-optic

coefficient), Δ𝑇 is the temperature rise. For powers

between 0.1 mW and 10 mW, we estimate the

temperature rise as Δ𝑇= α𝑃, 𝑤𝑖𝑡ℎ α=0.5 K/mW.

Hence Δ𝑇 (0.1 mW) =0.05 K, Δ𝑛= −6.5×10, Δ𝑇

(1 mW) =0.5 K, Δ𝑛=−6.5×10, Δ𝑇 (10 mW) =5 K,

Δ𝑛=−6.5×10. For low powers, the output power 𝑃out

closely follows the input power. However, as power

increases, the output power saturates due to the

decreased CE. Figure 2 depicts the relationship

between input power and output power.

Figure 2: Output Power vs. Input Power.

This leads to increased beam divergence as the

input power increases. The divergence angle 𝜃(𝑃) of

the beam in the free-space region (FSR) is a function

of input power P.

Figure 3: Collection Efficiency vs. Input Power.

At low powers, the divergence angle follows a

Gaussian beam, while at higher powers, it becomes a

nonlinear function: 𝜃(𝑃) = 𝜃 ∘ +𝑘𝑃 where 𝜃 is the

divergence angle of the equivalent Gaussian beam in

the low-power regime, k is a constant depending on

the material and waveguide geometry, P is the input

optical power. Therefore, for input power =

0.1 mW, 1 mW, and 10 mW, the divergence

angles are 2.04, 2.4

and 6

respectively. As beam

divergence increases with power, the collection

efficiency (CE) at the output waveguide decreases as

shown in figure 3. 𝐶𝐸(𝑃) = 𝐶𝐸 ⋅ 𝑒 where 𝐶𝐸 is the

initial collection efficiency at low powers, k is the

same constant as in the divergence equation. The CE

for powers of 0.1 mW, 1 mW, and 10 mW are 0.89,

0.82 and 0.37 respectively, give 𝐶𝐸 =0.9 and k=0.1.

In the linear regime (low power), insertion loss (IL)

is given by the ratio of output power 𝑃out to input

power 𝑃in. 𝐼𝐿 = 10𝑙𝑜𝑔(𝑃𝑖𝑛/𝑃𝑜𝑢𝑡). In the nonlinear

regime, insertion loss increases rapidly with input

power. The OPL demonstrates insertion losses

Advancing Detector Shielding with Thermo-Optic Defocusing in PMMA Integrated on Silicon Nitride

ranging from 2.5 to 6.0 dB across the tested input

power levels. The low insertion loss is crucial for

keeping signal integrity in optical systems.

2.2 Geometrical Adjustments and

Defocusing Effect

To obtain the optimal structure for the Optical Power

Limiter (OPL) design, we performed a detailed

numerical analysis of how varying input power

affects output power under different geometrical

configurations. By adjusting the waveguide width,

taper length, and Free-Space Region (FSR) length, we

observed their combined effects on the defocusing

behaviour caused by the thermo-optic effect in Poly-

Methyl-Methacrylate (PMMA). The analysis showed

that the optimal structure for maximum power

limiting involves a small waveguide width of 3 μm, a

short taper length of 200 μm, and a compact FSR

length of 1 mm.

3 CONCLUSIONS

This configuration maximises beam divergence at

lower input powers by confining the optical mode

more tightly, which accelerates the thermo-optic

defocusing effect. A smaller waveguide width

increases mode confinement, enhancing the

defocusing and saturating output power faster at high

input levels. The short taper length ensures a quicker

transition to a diverging beam profile, while the short

FSR confines the beam’s interaction distance,

promoting more significant refractive index changes

in the material. Together, these parameters ensure that

the output power remains low (below 1 mW) across a

wide input range (up to 50 mW), providing effective

protection for sensitive devices like avalanche

photodiodes (APDs). This design offers technical

significance by preventing potential damage to APDs

in high-power applications, ensuring safe operation

while improving the OPL's efficiency.

ACKNOWLEDGEMENTS

This research is supported by the National Research

Foundation, Singapore, and by the Agency for

Science, Technology and Research, Singapore under

the Quantum Engineering Programme (NRF2021-

QEP2-02-P12).

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PHOTOPTICS 2025 - 13th International Conference on Photonics, Optics and Laser Technology