Two-photon photopolymerization

Two-photon polymerization (2PP) is a localized nonlinear polymerization process which is used to fabricate polymeric micro/nanostructures by focusing a near-infrared (NIR) laser beam into photoresists. In this fabrication method, the resin is polymerized by simultaneous absorption of two photons with almost double wavelength than that used in 1PP. [72, 91] Two-photon absorption (TPA) was experimentally discovered in 1961 by Kaiser and Garrettthough it was theoretically predicted as early as 1931 [92].

For years, it was only used for spectroscopical purposes until its usage for polymerization induction was reported in 1965 by Pao and Rentzepis [93]. The method was further developed as a tool for lithographic microfabrication by Kawata’s group in 1997 [94]. In 1990s, the commercialization of femtosecond lasers in addition to recognition of high-efficiency PIs significantly accelerated the micro/nanofabrication in solid and liquid media through 2PP. Properties such as ultrashort pulse duration (less than 5 fs), high beam quality, coherence, substantial nonlinearity, power and frequency stability, high transient power, and strong localization of femtosecond lasers, have enabled controllable processing of variety of materials by these lasers. [72, 91] Since then, this direct laser writing (DLW) technique has been widely applied to fabricate various photonic, micro-optical, and microchemical components [72].

The principle of TPA is based on the nonlinear response of two-photon transition rate to the optical intensity [88]. PIs in the ground state (S₀) are excited to an excited state (S1) by simultaneously absorbing two photons, followed by nonradiative relaxations and radical formation. If the energies of two photons are exactly of the same amount, this process is called degenerate TPA otherwise it is a non-degenerate one. In the case of degenerate TPA, equations (16) and (17) can be re-written as:

𝑃𝐼^2ℎ𝜈→ 𝑃𝐼^{2 ∗}→ 𝑅. (21) 𝑃𝑆^2ℎ𝜈→ 𝑃𝑆^{2 ∗}⋯→ 𝑃𝐼^{𝑃𝐼 ∗} → 𝑅. , (22) where 𝜈₂~ 𝜈₁⁄2 is the photon frequency in two-photon excitation process. To make the case clear, it can be assumed that when the first photon is absorbed by the molecule, a virtual intermediate state is created. The lifetime of the virtual state is as short as several femtoseconds. If the second photon irradiates the molecule before decaying of the virtual state, TPA happens successfully. This mechanism is called simultaneous TPA. In addition to simultaneous TPA, there is another mechanism of absorption which is called stepwise absorption. The requirement for stepwise absorption is the existence of a real intermediate energy state. First, a population of electrons from the ground state (S0) is excited to an actual intermediate state (S1) through absorption of the first photon. Then,

the excited population will be further pumped to the final level (S₂) by absorbing another photon with usually the same energy of the first one. This process can be considered as two sequential single-photon absorptions. [72] A schematic drawing to show the difference between stepwise and simultaneous TPA mechanism is presented in Figure 9.

Figure 9: Schematic of (a) simultaneous TPA with a virtual intermediate energy level and (b) stepwise TPA with an actual intermediate energy level.

In a nonlinear optical process such as TPA, the imaginary part of the nonlinear susceptibility is responsible for the energy transfer from the light beam to the medium.

The energy change through light-matter interaction per unit time, per unit volume is 𝑑𝑊

𝑑𝑡 = 〈𝐸⃗ . 𝑃⃗ 〉 , (23)

where 𝐸⃗ is the electric field vector, 𝑃⃗ is the material polarization vector, and brackets define the average over time. The relation between electric field and polarization is

𝑃 = 𝜒⁽¹⁾𝐸 + 𝜒⁽²⁾𝐸²+ 𝜒⁽³⁾𝐸³+ ⋯, (24) where 𝜒⁽¹⁾, 𝜒⁽²⁾, and 𝜒⁽³⁾ refer to linear, second-order and third-order susceptibilities, respectively. Susceptibilities with even orders like 𝜒⁽²⁾ do not contribute to resonance processes while imaginary part of 𝜒⁽³⁾ plays a major role in nonlinear TPA. In the case of degenerate absorption of photons, the energy transfer rate is

𝑑𝑊

𝑑𝑡 = 8𝜋²𝜔

𝑐²𝑛² 𝐼²Im[𝜒⁽³⁾] , (25)

in which, 𝜔 is the angular frequency, 𝑛 is the refractive index of the medium, and 𝐼 is the light intensity. The equation shows the quadratic dependence of the TPA rate on the

S₁

S₀

Virtual state hν₂

hν₂

S₂

S₀ S1

hν₂

hν₂

Actual state

(a) (b)

light intensity that results in improvement of 3D spatial resolution with better accuracy than that in conventional single-photon processes. [72]

Most of the resins that are polymerized by UV or visible light exposure in 1PP can undergo the same reactions when absorbing two photons in 2PP procedure. The only requirement in the case of 2PP is that the light intensity has to be sufficiently high.

Utilizing pulsed laser technology, it is possible to enhance the energy of a single pulse to more than four orders of magnitude making the polymerization threshold of any kind

of resin accessible. For instance, the energy of an individual pulse in a Ti: Sapphire laser amplifier is 1mJ, which is sufficient to polymerize any

UV-polymerizable resin. However, features such as usability, TPA efficiency, tolerance to variation of exposure dose, and laser-induced breakdown are still material dependence factors. [72]

A determinant factor in TPA efficiency, is the absorption cross-section 𝛿 which describes the capability of the sample material to absorb photons, and is defined by

𝛿 =8𝜋²ℎ𝜈²

𝑐²𝑛²𝑁 𝐼²Im[𝜒⁽³⁾] , (26)

where 𝑁 is the number density of absorbing molecules [72]. Another important parameter, which effects on TPA efficiency, is the fraction of excitations resulting in polymer initiation Φ0. In order to obtain efficient absorption and initiation, 𝛿 and Φ0

need to be high enough. This condition can be met by choosing high-efficiency PIs and radical based polymerization mechanisms. Radical based processes amplify the photo-induced procedure by adding lots of monomers to the polymer chain in every single initiation event. [95]

Process of 2PP occurs in a minuscule 3D volume at the focal point, less than the cubic wavelength (𝜆³). That leads to a unique advantage of 2PP that is high 3D resolution in polymer resins (Figure 8.b). Another benefit is that the excitation process is a heat insulating process where the photon energy deposition is so fast that there is not enough time for electrons to consume it for phonon emissions. This feature is valuable in photochemical and photophysical reactions where non-localized thermal effects are undesirable. In addition, polymers usually exhibit negligible linear absorption in red-NIR regime. It allows the laser beam to penetrate deeply into the sample and directly induce the polymerization inside the material without disturbing outside of the focal volume. All of these features make 2PP a beneficial tool for various applications. [72] However, since TPA has extremely small transition probability, using a short-pulsed laser source such as Ti: Sapphire is essential, and these sources are usually expensive compared to conventional CW sources which are used in 1PP.

Therefore, microfabrication through 1PP, using CW lasers with a spatial resolution comparable to that of 2PP can be more cost-effective for many purposes. [88]