Supplementary
Giant refractive-index modulation by two-photon reduction
of fluorescent graphene oxides for multimode optical
recording
Xiangping Li*, Qiming Zhang, Xi Chen, & Min Gu*,
Centre for Micro-Photonics, Faculty of Engineering and Industrial Sciences, Swinburne University of
Technology, Hawthorn VIC 3122, Australia
*Corresponding author: mgu@swin.edu.au & xiangpingli@swin.edu.au
1
Figure S1. The laser-induced temperature rise as a function of the number of pulses.
The temperature rise caused by the absorption of successive fs pulses and the subsequent heat
dissipation can be approximately calculated by using the heat conduction equation 1. In the
calculation, the energy per fs pulse is assumed to be 100 % absorbed by GOs within the focal region
and then dissipated the heat into the surrounding thin film. The position and time dependent
temperature change within the focal region in the GO thin film is given by 1
∇𝑇(𝑟, 𝑡) = ∑𝑚
𝑛=1
𝐸(𝑟0 )
1
3
𝑘
8𝑘(
)2 (𝜋𝑛𝑡)2
𝜌𝑐𝑝
exp⁡(
(𝑟−𝑟0 )2
𝑘
𝑛𝑡
𝜌𝑐𝑝
4
)
(1)
where 𝐸(𝑟0 ) is the pulse energy distribution given by the objective, 𝜌, 𝑐𝑝 and 𝑘 is the density (2000
𝑘𝑔 ∙ 𝑚−3), the heat capacity (1.7 𝐽 ∙ 𝑐𝑚−3 ∙ 𝐾 −1 ) 2 and the thermal conductivity of GOs (4 𝑊 ∙ 𝑚−1 ∙
𝐾 −1 ) 3, respectively, 𝑡 is the time interval between two successive pulses (12 ns for the 82 MHz
repetition rate), 𝑛 is the number of pulses, 𝑟0 is the relative distance. The parameters of GOs varies
among samples with a different strength of oxidization. Reasonable agreement between the
experiment and the calculation was obtained when the parameters of GOs were chosen close to
those of amorphous carbon 2. Figure S1 shows that the accumulative heat raises the temperature to
2
~ 320o C at the end of 1 million pulses with a power of 15 mW, corresponding to an exposure time of
10 ms in the experiment.
Figure S2. (a) AFM images of a grating of reduced GOs patterned at the power of 15 mW and its
cross section view (b).
3
Figure S3. The overall phase modulation (blue circles) and the laser-induced height change (black
squares) as a function of the fs laser power.
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References
1
2
3
Ullah, M. A. et al. Low energy-density recording with a high-repetition-rate laser beam in
gold-nanorod-embedded discs. Opt. Express 20, 24516-24523 (2012).
Zhou, Y. et al. Microstructuring of graphene oxide nanosheets using direct laser writing. Adv.
Mater. 22, 67-71 (2010).
Shamsa, M. et al. Thermal conductivity of diamond-like carbon films. Appl. Phys. Lett. 89
(2006).
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