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J. Abe et al.
been received much attention since more than a half-century ago. One of the most
important nonlinear optical phenomena is a two-photon absorption (2PA) process [7,
8]. The 2PA process can be divided into two categories: simultaneous and stepwise
processes. The simultaneous 2PA occurs when two photons are absorbed instantaneously via a virtual state. The simultaneous 2PA can produce the excited state with
lower energy photons than the energy level of the excited state, and the probability
for the excitation depends on the square of the light intensity. Therefore, the simultaneous 2PA has high spatial selectivity and can be induced deep inside of matters.
Because of these characteristics, the simultaneous 2PA has been applied to biological
imaging [9, 10] and three-dimensional (3D) micro-fabrications [11, 12]. However,
the simultaneous 2PA requires the absorption of another photon during the interaction of the first photon and the matter (~1–2 fs) because the virtual state is not a
stationary electronic state. Therefore, high-power light sources such as femtosecond
and nanosecond pulse lasers are required to induce the simultaneous 2PA.
Another 2PA process is called the stepwise 2PA, which is the absorption of another
photon by the photogenerated transient state. This process occurs via an actual
stationary electronic state such as an excited state or a short-lived species. Therefore,
the probability of the stepwise 2PA depends on the lifetime of the intermediate transient state. If the lifetime of the intermediate transient state is long enough, the power
threshold to induce the stepwise 2PA is greatly reduced and the stepwise 2PA could
be induced even by CW LEDs and sunlight. There are mainly three types of intermediate transient states for the stepwise 2PA reported so far: the singlet excited (S 1 )
state, the triplet excited (T 1 ) state, and the ground state of a photoproduct [13]. The
first and second cases are the stepwise 2PAs via the S 1 and T 1 states to produce the
higher excited singlet (S n ) and triplet (T n ) states, respectively. These two processes
utilize the electronically excited states as the intermediate state of the stepwise 2PA
process. The lifetimes of the S 1 states are usually nanosecond time scales, while those
of T 1 states (microseconds to tens of microseconds) are usually more than a thousand
times longer than those of the S 1 states in solution at room temperature due to the
spin selection rule. Since the long-lived excited states have more chances to absorb
another photon, the power threshold of the stepwise 2PA via the T 1 state is lower
than that of the S 1 state. However, the lifetime of the T 1 state is still short to induce
the stepwise 2PA with conventional CW light sources. Therefore, a pulse laser is
usually necessary to promote these stepwise 2PA processes. Alternative approaches
are necessary to reduce the power threshold to induce the stepwise 2PA with CW
LEDs and sunlight. In the third case, the stepwise 2PA occurs via not an electronically excited state but a ground state of photogenerated transient species produced
by a photochemical reaction. The lifetimes of the photogenerated transient species
are usually longer than tens of nanoseconds. In some cases, photogenerated transient
species can survive more than milliseconds and exist as photoproducts permanently.
If we utilize these long-lived transient species as an intermediate of the stepwise
2PA, the power threshold of the stepwise 2PA can be significantly reduced.
There has been a growing interest in the development of advanced photofunctional materials whose photoresponses involve multiple photons and molecules
J. Abe et al.
been received much attention since more than a half-century ago. One of the most
important nonlinear optical phenomena is a two-photon absorption (2PA) process [7,
8]. The 2PA process can be divided into two categories: simultaneous and stepwise
processes. The simultaneous 2PA occurs when two photons are absorbed instantaneously via a virtual state. The simultaneous 2PA can produce the excited state with
lower energy photons than the energy level of the excited state, and the probability
for the excitation depends on the square of the light intensity. Therefore, the simultaneous 2PA has high spatial selectivity and can be induced deep inside of matters.
Because of these characteristics, the simultaneous 2PA has been applied to biological
imaging [9, 10] and three-dimensional (3D) micro-fabrications [11, 12]. However,
the simultaneous 2PA requires the absorption of another photon during the interaction of the first photon and the matter (~1–2 fs) because the virtual state is not a
stationary electronic state. Therefore, high-power light sources such as femtosecond
and nanosecond pulse lasers are required to induce the simultaneous 2PA.
Another 2PA process is called the stepwise 2PA, which is the absorption of another
photon by the photogenerated transient state. This process occurs via an actual
stationary electronic state such as an excited state or a short-lived species. Therefore,
the probability of the stepwise 2PA depends on the lifetime of the intermediate transient state. If the lifetime of the intermediate transient state is long enough, the power
threshold to induce the stepwise 2PA is greatly reduced and the stepwise 2PA could
be induced even by CW LEDs and sunlight. There are mainly three types of intermediate transient states for the stepwise 2PA reported so far: the singlet excited (S 1 )
state, the triplet excited (T 1 ) state, and the ground state of a photoproduct [13]. The
first and second cases are the stepwise 2PAs via the S 1 and T 1 states to produce the
higher excited singlet (S n ) and triplet (T n ) states, respectively. These two processes
utilize the electronically excited states as the intermediate state of the stepwise 2PA
process. The lifetimes of the S 1 states are usually nanosecond time scales, while those
of T 1 states (microseconds to tens of microseconds) are usually more than a thousand
times longer than those of the S 1 states in solution at room temperature due to the
spin selection rule. Since the long-lived excited states have more chances to absorb
another photon, the power threshold of the stepwise 2PA via the T 1 state is lower
than that of the S 1 state. However, the lifetime of the T 1 state is still short to induce
the stepwise 2PA with conventional CW light sources. Therefore, a pulse laser is
usually necessary to promote these stepwise 2PA processes. Alternative approaches
are necessary to reduce the power threshold to induce the stepwise 2PA with CW
LEDs and sunlight. In the third case, the stepwise 2PA occurs via not an electronically excited state but a ground state of photogenerated transient species produced
by a photochemical reaction. The lifetimes of the photogenerated transient species
are usually longer than tens of nanoseconds. In some cases, photogenerated transient
species can survive more than milliseconds and exist as photoproducts permanently.
If we utilize these long-lived transient species as an intermediate of the stepwise
2PA, the power threshold of the stepwise 2PA can be significantly reduced.
There has been a growing interest in the development of advanced photofunctional materials whose photoresponses involve multiple photons and molecules