## 1 Introduction  
Optical digital data storage, for example CD or DVD, is extensively used in the recordings of music, movies, and others. In order to increase their storage capacity, two approaches have been developed. One is the multi-layer system, with a maximum four layers at this moment. The other is the reduction of bit size by using a shorter wavelength laser, _i.e._, Blue-Ray disc. However, the amount of information data is notably increasing now, and in the future, and, thereby, further enlargement of the capacity is necessary. According to this request, optical memory using two-photon absorption (2 PA) [1,2] has been focused on as the quadratic dependence of 2 PA, through the use of a tightly focused laser beam, as mentioned below, allows for 3D spatial selective mapping and high-density recording. 2 PA is a nonlinear optical process in which two photons are simultaneously absorbed to promote a molecule to the excited state by combination of their energy, as shown in Figure 1. 2 PA can occur even at wavelengths where one-photon absorption (1 PA) does not take place. When a one-color optical source is used, the energy of the two photons is the same, and almost half of that in the 1 PA process. Due to quadratic dependence of 2 PA on the incident light intensity, the maximum absorption occurs at the focal point of laser, allowing high spatial selectivity. These features can find a variety of optical applications, such as photodynamic therapy (PDT) [3,4], 3D optical data storage [1,2], and optical limiting [5]. 2 PA was first predicted by [PERSON] in 1931 [6] and was demonstrated experimentally by [PERSON] and [PERSON], using a Ruby laser [7]. The efficiency of 2 PA is quantified by the 2 PA cross-section \(\sigma^{(2)}\) measured in GM. Although the study on 2 PA materials had been inactive until the 1990s, new classes of organic molecules, exhibiting large 2 PA cross section values (\(\sigma^{(2)}\)), have been reported and the strategies employing donor/acceptor sets with a \(\pi\)-conjugation system in a symmetric (D-\(\pi\)-D or A-\(\pi\)-A) [8] or asymmetric (D-\(\pi\)-A) arrangement [9] have been proposed. A wide variety of molecules with large \(\sigma^{(2)}\) have been developed, using both organic and inorganic materials. The most efficient of such materials are composed of donor (D) or acceptor (A) molecules linked by a conjugated \(\pi\)-bridge [8, 9, 10, 11, 12, 13, 14]. Donor and acceptor parts enhance polarization of molecule, which was also found to be a factor in enhancing 2 PA. Electron-donating and accepting groups can cause a redistribution of the \(\pi\)-electronic density that leads to increase of electron delocalization in the first excited state S\({}_{1}\) (by absorption of the first photon) and results in increase in the S\({}_{1}\) to S\({}_{2}\) transition dipole moment, which is a major factor in increasing \(\sigma^{(2)}\)[8]. There have been conflicting reports on the role of symmetry/asymmetry of the molecule in 2 PA enhancement [8,9]. However, the significant role of the \(\pi\)-bridge has been emphasized in both reports. The \(\pi\)-bridges also provide delocalization and conjugation, which is extremely effective in increasing \(\sigma^{(2)}\). Several well-known \(\pi\)-bridges that have been reported are _trans_-stilbene [8,10,11], fluorene [9], dithienothiophene [12,13], and butadiyne [13,14] linkers (Scheme 1). Elongation and dendrimerization [15,16] of the molecules also results in the enhancement of 2 PA (Scheme 2). Figure 1: Energy diagram for one-photon and two-photon absorption (left side) and schematic drawing of 3D optical memory using two-photon absorption. **Scheme 1. ** Two-photon absorbing molecules. Porphyrins, which have an 18\(\pi\)-electron system, are also attractive candidates for 2 PA materials. [PERSON] [17,18], and [PERSON] [19] reported monomeric porphyrin derivatives with relatively large \(\sigma^{(2)}\) values (Scheme 3).