Abstract
The advent of chirped-pulse amplification in the 1980s and femtosecond
Ti:sapphire lasers in the 1990s enabled transformative advances in
intense laser–matter interaction physics. Whereas most of experiments
have been conducted in the limited near-infrared range of 0.8–1 μm,
theories predict that many physical phenomena such as high harmonic
generation in gases favor long laser wavelengths in terms of extending
the high-energy cutoff. Significant progress has been made in
developing few-cycle, carrier-envelope phase-stabilized,
high-peak-power lasers in the 1.6–2 μm range that has laid the
foundation for attosecond X ray sources in the water window. Even
longer wavelength lasers are becoming available that are suitable to
study light filamentation, high harmonic generation, and laser–plasma
interaction in the relativistic regime. Long-wavelength lasers are
suitable for sub-bandgap strong-field excitation of a wide range of
solid materials, including semiconductors. In the strong-field limit,
bulk crystals also produce high-order harmonics. In this review, we
first introduce several important wavelength scaling laws in
strong-field physics, then describe recent breakthroughs in short-
(1.4–3 μm), mid- (3–8 μm), and long-wave (8–15 μm) infrared laser
technology, and finally provide examples of strong-field applications
of these novel lasers. Some of the broadband ultrafast infrared lasers
will have profound effects on medicine, environmental protection, and
national defense, because their wavelengths cover the water absorption
band, the molecular fingerprint region, as well as the atmospheric
infrared transparent window.
© 2022 Optica Publishing Group
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Equations (64)
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(1)
$$I(r,t) = {I_0}{e^{ -
\frac{{{r^2}}}{{{w^2}}}}}{e^{ - 4\ln 2\frac{{{t^2}}}{{\tau
{{{}_p}^2}}}}},$$
(2)
$$w(z) = {w_0}\sqrt {1 +
{{\left( {\frac{z}{{{z_R}}}} \right)}^2}} .$$
(3)
$$I(\lambda ) = {I_0}{e^{ -
2\ln (2)\frac{{{{(\lambda - {\lambda _0})}^2}}}{{\Delta {\lambda
^2}}}}},$$
(4)
$${I_0} =
1.88\frac{{{\varepsilon _p}}}{{{\tau _p}\pi {w^2}}}.$$
(5)
$$E(t) = {E_0}{e^{ - 2\ln
2{{\left( {\frac{t}{{{\tau_p}}}} \right)}^2}}}\cos ({\omega _0}t +
{\varphi _{CE}}),$$
(6)
$${I_0} =
\frac{1}{2}{\varepsilon _0}c{E_0}^2,$$
(7)
$$\overrightarrow E
(\vec{r},t) ={-} \frac{{\partial \overrightarrow A
(\vec{r},t)}}{{\partial t}} - \nabla \phi
(\vec{r},t).$$
(8)
$$A(t) \approx{-}
{A_0}{e^{ - 2\ln 2{{\left( {\frac{t}{{{\tau_p}}}}
\right)}^2}}}\sin ({\omega _0}t + {\varphi _{CE}}),$$
(9)
$${a_0} =
\frac{{{q_e}{A_0}}}{{{m_e}c}} = \frac{{{q_e}{E_0}}}{{{m_e}c{\omega
_0}}},$$
(10)
$$p(t = \infty ) ={-}
{q_e}A({t_0}).$$
(11)
$${I_{rel}} =
\frac{1}{2}{\varepsilon _0}{c^3}{\left( {\frac{{{m_e}}}{{{q_e}}}}
\right)^2}{\omega _0}^2 = 2{\pi ^2}{\varepsilon _0}{c^5}{\left(
{\frac{{{m_e}}}{{{q_e}}}} \right)^2}\frac{1}{{{\lambda
_0}^2}},$$
(12)
$${I_{rel}}\;[\textrm{W/c}{\textrm{m}^2}] = 1.37 \times
{10^{18}}/{\lambda _0}^2\;[\mathrm{\mu m}].$$
(13)
$${w_{PPT}}({E_0},{\lambda _0}) \propto {e^{ -
\frac{{2{{(2{I_p})}^{3/2}}}}{{3{E_0}}}g(\gamma )}},$$
(14)
$$g(\gamma )=
\frac{3}{{2\gamma }}\left[ {\left( {1 + \frac{1}{{2{\gamma^2}}}}
\right){{\sinh }^{ - 1}}\gamma - \frac{{\sqrt {1 + {\gamma^2}}
}}{{2\gamma }}} \right],$$
(15)
$$\gamma = \frac{{2\pi
c}}{{{\lambda _0}{E_0}}}\sqrt {2I{}_p} .$$
(16)
$$\begin{aligned}
&{\hbar {\omega _X}({t,{t_0}} )= {I_p} +
\frac{1}{{2{m_e}}}p{{(t,{t_0})}^2} = {I_p} +
\frac{{{q_e}^2}}{{2{m_e}}}{{[A(t) - A({t_0})]}^2}}\\ &= {I_p}
+ \frac{{{q_e}^2{E_0}^2}}{{2{m_e}{\omega _0}^2}}{{[\sin ({\omega
_0}t) - \sin ({\omega _0}{t_0})]}^2}. \end{aligned}$$
(17)
$$\hbar \omega _c^{atom}
= {I_p} + 3.17\frac{{{q_e}{E_0}^2}}{{4{m_e}{\omega _0}^2}} = {I_p}
+ 3.17{U_p}.$$
(18)
$${U_p}[\textrm{eV}] =
9.33 \times {10^{14}}{I_0}[\textrm{W/c}{\textrm{m}^2}]{\lambda
_0}{[\mathrm{\mu m}]^2}.$$
(19)
$$\hbar \omega _c^{solid}
\simeq {\Delta _{gap}} + n\hbar {\omega _B},$$
(20)
$$k(t) = k({t_0}) +
\frac{{{q_e}}}{\hbar }\int_{{t_0}}^t {E(t^{\prime})dt^{\prime}}
.$$
(21)
$$P_{cr}^{Kerr}({\lambda
_0}) \approx 3.77\frac{{{\lambda _0}^2}}{{8\pi {n_0}({{\lambda_0}}
){n_2}({\lambda _0})}}, $$
(22)
$$LIDT({\tau _p},{\lambda
_0}) = \sqrt {\frac{{{\tau _p}}}{{{\tau _{spec}}}}} LID{T_{spec}},
$$
(23)
$${G_0}{(\lambda )^{s.e.}} =
{e^{{\sigma _{em}}(\lambda )\Delta NL}},$$
(24)
$${\tau _p} = \frac{{2\ln
2}}{{\pi c}}\frac{{\lambda {{{}_0}^2}}}{{\Delta \lambda {}_{FWHM}}} =
\frac{{2\ln 2}}{\pi }{T_0}\frac{{{\lambda _0}}}{{\Delta \lambda
{}_{FWHM}}}. $$
(25)
$$\Delta {\lambda _{FWHM}} =
\Delta {\lambda _a}\sqrt {\frac{3}{{10{{\log }_{10}}G({{\lambda_0}} )-
3}}} , $$
(26)
$${f_{k,j}}(T) =
\frac{{{g_j}}}{{{Z_k}(T)}}{e^{ - \frac{{{E_{k,j}} -
E{}_{k,1}}}{{{k_B}T}}}}, $$
(27)
$${Z_k}(T) =
\sum\limits_j {{g_j}} {e^{ - \frac{{{E_{k,j}} -
E{}_{k,1}}}{{{k_B}T}}}}. $$
(28)
$${g_0}(T,r,z) =
\{{{\sigma_{em}}(T)\beta (r,z) - {\sigma_{ab}}(T)[1 - \beta
(r,z)]} \}{N_{tot}}, $$
(29)
$${G_{small}}(T,r =
0) = {e^{\int_0^L {{g_0}(T,r = 0,z)dz} }}. $$
(30)
$${\beta _{th}}(T) =
\frac{{{\sigma _{ab}}(T)}}{{{\sigma _{em}}(T) + {\sigma
_{ab}}(T)}}, $$
(31)
$${\alpha
_0}({\lambda _p}) = \{{{\sigma_{ab}}({\lambda_p})[1 - \beta ]
- {\sigma_{em}}({\lambda_p})\beta } \}{N_{tot}}. $$
(32)
$${\sigma
_{em}}({\lambda ,T} )= \sum\limits_{i,j}
{\frac{{{g_j}}}{{{Z_u}(T)}}} {e^{ - \frac{{{E_j} -
{E_1}}}{{{k_B}T}}}}{\sigma _{ji}}(\lambda ){g_i},
$$
(33)
$${\sigma
_{em}}({{\lambda_s},T} )= {\sigma _{ab}}({{\lambda_s},T} ){e^{
- \frac{{hc}}{{{k_B}T}}\left( {\frac{1}{{{\lambda_s}}} -
\frac{1}{{{\lambda_u}(T)}}} \right)}}, $$
(34)
$${\lambda _u}(T) =
\frac{{hc}}{{{k_B}T}}\frac{1}{{\ln
\frac{{{Z_g}(T)}}{{{Z_u}(T)}}}}. $$
(35)
$${F_{s,sat}} =
\frac{{hc}}{{[{\sigma _{em}}({\lambda _s}) + {\sigma
_{ab}}({\lambda _s})]{\lambda _s}}}, $$
(36)
$$F{}_{out} =
{F_{s,sat}} \cdot \ln [{1 +
{e^{{g_0}}}({{e^{{F_{in}}/{F_{s,sat}}}} - 1} )} ].
$$
(37)
$${F_{p,sat}} =
\frac{{hc}}{{[{\sigma _{em}}({\lambda _p}) + {\sigma
_{ab}}({\lambda _p})]{\lambda _p}}}. $$
(38)
$$\Delta {\nu
_{FWHM}}(\textrm{GHz}) = 5.71{P_{C{O_2}}} + 4.19{P_{{N_2}}} +
3.66{P_{He}}, $$
(39)
$${\tau
_R}[{\textrm{ns}} ]= {({9.75{P_{C{O_2}}} + 9.0{P_{{N_2}}} +
4.5{P_{He}}} )^{ - 1}}. $$
(40)
$${\omega _i} = {\omega _p} -
{\omega _s}, $$
(41)
$${\vec{E}_{i,s,p}}(z,t) =
{\vec{A}_{i,s,p}}(z){e^{i({\omega _{i,s,p}}t - {k_{i,s,p}}z)}},
$$
(42)
$${\vec{\tilde{P}}_i}({\omega
_i}) = {\varepsilon _0}{\chi ^{(2)}}({\omega _i}; - {\omega
_s},{\omega _p}):{\vec{\tilde{E}}_s}{({\omega _s})^\ast
}{\vec{\tilde{E}}_p}({\omega _p}). $$
(43)
$$\Delta \vec{k} =
{\vec{k}_p} - {\vec{k}_s} - {\vec{k}_i} = 0, $$
(44)
$$\frac{{d{A_i}}}{{dz}} ={-}
i\frac{{2{d_{eff}}\omega _i^2}}{{{k_i}{c^2}}}{A_s}^\ast {A_p}{e^{ -
i\Delta kz}}, $$
(45)
$$\frac{{d{A_s}}}{{dz}} ={-}
i\frac{{2{d_{eff}}\omega _s^2}}{{{k_i}{c^2}}}{A_i}^\ast {A_p}{e^{ -
i\Delta kz}}, $$
(46)
$$\frac{{d{A_p}}}{{dz}} ={-}
i\frac{{2{d_{eff}}\omega _p^2}}{{{k_p}{c^2}}}{A_i}{A_s}{e^{i\Delta
kz}}, $$
(47)
$$G_0^{OPA}({{\omega_s}}
)\cong \frac{1}{4}{e^{2\sqrt {{\Gamma ^2} - {{\left( {\frac{{\Delta
k}}{2}} \right)}^2}} L}}, $$
(48)
$${\Gamma ^2} =
\frac{{2{\omega _i}{\omega _s}}}{{{\varepsilon
_0}{c^3}}}\frac{{{d_{eff}}^2}}{{{n_i}{n_s}{n_p}}}{I_p}. $$
(49)
$$\scalebox{0.92}{$\displaystyle\Delta k({{\omega_s}} )\approx \Delta
k({{\omega_{s0}}} )+ \left. {\left( {\frac{{\partial {k_i}}}{{\partial
{\omega_i}}} - \frac{{\partial {k_s}}}{{\partial {\omega_s}}}}
\right)} \right|{}_{{\omega _{s0}}}({{\omega_s} - {\omega_{s0}}} )+
\frac{1}{2}{\left. {\left( {\frac{{{\partial^2}{k_s}}}{{\partial
{\omega_s}^2}} + \frac{{{\partial^2}{k_i}}}{{\partial {\omega_i}^2}}}
\right)} \right|_{{\omega _{s0}}}}{({{\omega_s} - {\omega_{s0}}} )^2}
+ \ldots$}$$
(50)
$$\left.
{\frac{{{\partial^2}{k_s}}}{{\partial {\omega_s}^2}}}
\right|{}_{{\omega _{s0}}} = \left.
{\frac{{{\partial^2}{k_i}}}{{\partial {\omega_i}^2}}}
\right|{}_{{\omega _{s0}}} = 0. $$
(51)
$${\varphi _{CE,i}} ={-}
\frac{\pi }{2} + {\varphi _{CE,p}} - {\varphi _{CE,s}}. $$
(52)
$$I({\omega _X})
\propto {\omega _X}^4{|{FT[D(t)]} |^2}. $$
(53)
$$\vec{D}(t) =
\left\langle {a{\psi_a} + b{\psi_b}}
\right|\vec{r}(t)|{a{\psi_a} + b{\psi_b}} \rangle \approx
\left\langle {a{\psi_a}} \right|\vec{r}(t)|{b{\psi_b}} \rangle
. $$
(54)
$$\vec{D}(t) =
i{\int_0^\infty {d\tau \left( {\frac{\pi }{{ \in{+} i\tau
/2}}} \right)} ^{3/2}}b(t){\vec{d}^\ast }(t){e^{iS(t,\tau
)}}a(t - \tau )\vec{E}(t - \tau )\vec{d}(t - \tau ),
$$
(55)
$$I({\omega _X})
\propto 1/\lambda {{}_0^5}. $$
(56)
$${|{d({\omega_x})}
|^2} \propto 1/{\omega _x}^{7/2}. $$
(57)
$${n_p}(\omega {}_0)
\approx 1 - \frac{{q{{{}_e}^2}}}{{2{\varepsilon
_0}{m_e}}}\frac{{{N_e}}}{{{\omega _0}^2}}. $$
(58)
$${n_a}({{\omega_0}}
)\approx 1 + \frac{{{q_e}^2}}{{2{\varepsilon
_0}{m_e}}}\frac{{{N_a}}}{{{\omega _r}^2 - {\omega _0}^2}},
$$
(59)
$${n_{IR}}({{\omega_0}} )\approx 1 +
\frac{{{q_e}^2}}{{2{\varepsilon _0}{m_e}}}\left(
{\frac{{{N_a}}}{{{\omega_r}^2 - {\omega_0}^2}} -
\frac{{{N_e}}}{{{\omega_0}^2}}} \right) = 1 +
\frac{{{q_e}^2N}}{{2{\varepsilon _0}{m_e}}}\left( {\frac{{1 -
{b^2}}}{{{\omega_r}^2 - {\omega_0}^2}} -
\frac{{{b^2}}}{{{\omega_0}^2}}} \right). $$
(60)
$${b^2} = {\left(
{\frac{{{\omega_0}}}{{{\omega_r}}}} \right)^2} = \frac{{4{\pi
^2}{c^2}}}{{{\omega _r}^2{\lambda _0}^2}}, $$
(61)
$$\hbar \omega
_c^{atom} = {I_p} + \frac{{0.5I_p^{3.5}{\lambda
_0}^2}}{{{{\left[ {\ln \left( {\frac{{0.86{I_p}{3^{2{n^\ast }
- 1}}{G_{lm}}C_{{n^\ast }{l^\ast }}^2}}{{ - \ln [{1 -
{b^2}({{\lambda_0}} )} ]}}{\tau_p}} \right)} \right]}^2}}}.
$$
(62)
$${\lambda _p} = 2\pi
c/{\omega _p}, $$
(63)
$$P_{cr}^{rel} =
17{\left( {\frac{{{\lambda_p}}}{{{\lambda_0}}}}
\right)^2}[{\textrm{GW}} ], $$
(64)
$${n_p} = \sqrt {1 -
\frac{{{\omega _p}^2}}{{{\omega ^2}}}} . $$