Nonlinear optics usually describes elastic and inelastic light scattering phenomena from interactions between light and materials. Many materials exhibit intrinsic nonlinear optical properties. These nonlinear optical materials are widely used in photon generation, manipulation, transmission, detection, and imaging^1-7. Some endogenous structures in biological samples also have capabilities to produce intrinsic nonlinear optical signals. Besides, materials which show strong nonlinear optical effects can serve as exogenous label of biological samples. Thus, nonlinear optics has been extensively explored for developing new research tools for biology, and are, in most cases, combined with microscopy, which further extends their applications in bio-imaging. Many nonlinear optical processes, such as multiphoton fluorescence, harmonic generation, four-wave mixing, stimulated Raman resonance and pump-probes have been implemented for the imaging of various biological samples. Nonlinear optical microscopy can provide label-free imaging, three-dimensional optical sectioning, and deep observation in tissues and can also reduce the photo damage to biological samples. In addition, nonlinear optics can provide chemical specific and high-speed imaging strategies, which enable the biomedical dynamic process studies. Firstly, we introduce the basic principles of the nonlinear optical processes. Next, we overview the conventional nonlinear optical materials and structures. Then we highlight several nonlinear optical processes which are extensively investigated for recent advances in bio-imaging applications. Lastly, we give our outlook in this field.

Nonlinear optics is a branch of optics in which the interaction between intense light and matter is studied. The optical properties of a material system can be modified in response to the high-intensity coherent light, i.e. laser beam. This leads to the nonlinear optical processes, such as harmonic generation, four-wave mixing, multiphoton fluorescence, self-focusing, solitons and saturable absorption. The field of nonlinear optics started as the experiment of the second-harmonic generation by Franken et al. in 1961⁸. This is the first nonlinear optical effect ever observed in an experiment, which occurred shortly after the laser was invented in 1960⁹. After that, numerous nonlinear optical effects have been observed. All these nonlinear effects may consist of two aspects, firstly the medium produces nonlinear responses under the action of strong light, and then in reaction, modulation of incident light field by medium.

When the electric field is applied to the material, the induced polarization P(t) can be expressed as a power series in terms of the electric field strength E(t):

where ${\varepsilon _0}$ is the permittivity of free space; ${\chi ^{(1)}}$ is the linear susceptibility which describe the linear optics process; ${\chi ^{(2)}}$and${\chi ^{(3)}}$are the second and third order nonlinear optical susceptibilities, respectively. When the incident light is strong enough, or the nonlinear optical susceptibilities are large, the nonlinear terms become non-ignorable. The output light frequency could be different from the input light frequency. The typical examples of second-order nonlinear optical effects include second-harmonic generation, sum-frequency generation, difference-frequency generation, and optical parametric amplification and oscillation. The third-order nonlinear optical effects include third-harmonic generation, four-wave mixing, and optical Kerr effect. The high-order nonlinear optical effects include higher order harmonic generation and higher order multiphoton fluorescence. These effects, especially the second- and third- order nonlinear optical effects, are widely applied in photon generation, frequency manipulation, and imaging.

The second-order nonlinear optical processes come from the second-order contribution to nonlinear polarizatio${\boldsymbol{P}^{(2)}}(t) = {\varepsilon _0}{\chi ^{(2)}}\boldsymbol{E}{(t)^2}$. In the case of the second-harmonic generation, incident beam with frequency ω converts to the radiation with frequency 2ω. The second-harmonic generation is due to the interaction and exchange of photons with different frequencies. Two photons of frequency ω are absorbed by the medium, and produce a photon of frequency 2ω simultaneously. For sum or difference frequency generation, the incident optical field containing two frequency components interacts within a second order nonlinear optical material. The various frequencies of the polarization could be produced, including 2ω₁, 2ω₂, ω₁+ω₂, and ω₁-ω₂. The latter two describe the process of sum-frequency generation and difference-frequency generation, respectively. Since the nonlinear polarization can only produce output signal efficiently when the condition of phase matching is satisfied, which can only occur for one frequency component. Thus, there is only one new major frequency that will be present in the radiation. In optical parametric amplification and oscillation, a weak input beam is amplified with the help of a strong high frequency pump beam through difference-frequency generation process. When an optical resonator is used to hold the nonlinear material, the radiation at lower frequencies can be largely amplified.

The third-order nonlinear optical processes come from the third-order contribution to nonlinear polarization${\boldsymbol{P}^{(3)}}(t) = {\varepsilon _0}{\chi ^{(3)}}\boldsymbol{E}{(t)^3}$. As a typical third-order nonlinear optical process, the third-harmonic generation describes a process that a radiation with frequency 3ωis created by an incident field with frequency ω. In this process, three incident photons with frequency ω are destroyed and simultaneously one photon with frequency 3ω is created. In the four-wave mixing process, three input light of frequencies ω₁, ω₂, and ω₃, interact with material and produce a signal at frequency ω₄. The four-wave mixing output can be enhanced due to the vibrational or electronic properties of the materials. The coherent anti-Stokes Raman scattering, stimulated Raman scattering and optical Kerr effect are typical examples of vibrationally enhanced four-wave mixing. When the incident light field satisfies the material's electron transition resonance condition, the electronically enhanced four-wave mixing signal can be observed.

It should be noted that the nonlinear optical susceptibility is a tensor, and it depends on the structures of materials. Actually, the independent component number of the tensor can be reduced due to intrinsic symmetry of the material. Thus, the nonlinear optical effects provide sensitive tools for detecting the orientation of materials. The second-order and other even-order nonlinear optical effects can only occur in the noncentrosymmetric materials. While the third-order nonlinear optical effects can occur in the materials regardless of being centrosymmetric or not^1-2.

According to the induced polarization formula, the materials for nonlinear optics should have large susceptibilities. Besides this basic requirement, the nonlinear optical materials also need to meet other conditions. For example, the materials should be chemically stable that could resist laser power; they should be transmissive and have fast response to the input laser pulse; for the second order or other even order nonlinear optical materials, there is an extra requirement of noncentrosymmetry.

As discussed previously, only the materials without center of inversion symmetry can have a second-order nonlinear effect. Besides, the materials need to satisfy the standard phase matching to have a high efficiency of nonlinear process. The birefringent crystals that allow compensation for dispersion is an important category of second-order nonlinear optical materials, such as AgGaSe₂, BaB₂O₄, LiIO₃, LiNbO₃, KH₂PO₄ and so on¹⁰. Since the birefringence phase matching suffers from the limited tuning wavelength range, small nonlinear coefficient, increased phase matching temperature, and difficult coupling angle, the approach of quasi-phase matching, which can periodically reverse the nonlinear interaction to compensate for phase mismatching, is preferred. The periodic poling to the materials is the commonly used method to realize it¹¹. These periodically poled materials are one of the types of nonlinear optical materials, such as periodically poled KTiOPO₄¹², RbTiOAsO₄¹³, LiTaO₃^14-15, BaTiO₃¹⁶, and KNbO₃¹⁷. In addition, the electric asymmetric organic molecules which have large molecular hyperpolarizability can present second-order nonlinear optical effects. To build long-range ordered structures for realizing applicable scale of nonlinear optical effect, film structure is preferred.

Some materials with nano or micro structures can present strong second-order nonlinear optical effects. The inorganic materials including ZnO¹⁶, KNbO₃¹⁹, GaN²⁰, GaP²¹ and GaAs^22-23 nanowires and atomically layered two-dimensional MoS₂²⁴ and GaSe²⁵ can realize second harmonic generation. The organic materials including tripeptides nanostructures²⁶, dipeptides microtubes²⁷, electrospun α-helical poly(α-Amino Acid) nanofibers²⁸, and self-assembled 3–methyl–4-methoxy–4–nitrostilbene hexagonal micro-prisms²⁹ also have shown strong second-harmonic generation.

Third-order materials have the third-order nonlinear optical responses, leading to the processes such as two photon absorption and third-harmonic generation. The insulating crystals typically have third-order nonlinear optical susceptibilities around 10^-14–10^-13 esu. Semiconductors often have larger third-order susceptibilities of 10^-13–10^-10 esu which is wavelength dependent. The susceptibility depends on the incident photon energy and the bandgap of the semiconductor. When the photon energy is smaller than the energy of bandgap, there is little difference between the semiconductors and the insulating crystals. When the photon energy is close to the bandgap energy, the excitation resonance is the main nonlinear optical mechanism in the semiconductors. When the photon energy is larger than the bandgap energy, the nonlinear response results from the electron excitation from valence band to conduction band, and leads to the change of optical properties of the materials³⁰. Organic materials are another important category of third-order nonlinear optical materials, and large optical nonlinearities have been reported in them. For example, polydiacetylene and derivatives can have third-order nonlinear optical susceptibilities around 10^-10 esu. Organic molecules with metal ions like phthalocyanine and porphyrin^31-33 also have promising third-order optical nonlinearities. Moreover, very strong nonlinear optical effects are often reported in the composite materials. For example, when embedding semiconductor or metal nanoparticles in glass with only a small volume concentration, the nonlinear susceptibility can be increased six orders larger than that of the glass³⁴.

Some nano or micro structures also have been built for realizing third-order nonlinear optical properties. For example, anisotropic two-photon excited fluorescence has been observed in ZnO nano/microwires³⁵; two-photon pumped lasing has been achieved using CdS microwires³⁶ and ZnO nanowires³⁷ and nanoparticle³⁸. Organic materials like 2-(N, N-diethylanilin-4-yl)-4, 6-bis (3, 5-dimethylpyrazol-1-yl)-1, 3, 5-triazine nanowires can serve as two-photon absorbers and waveguides³⁹. In the hybrid material fabricated through embedding cationic dye 4-[p-(dimethylamino)styryl]-1-methylpyridinium to anionic metal-organic framework, two-photon pumped lasing was observed⁴⁰.

The nonlinear optical properties of materials play an important role in many optical applications, including bio-imaging, material structure analysis, optical signal processing, optical manipulation, photon generation, photon detection, and many others (Fig. 1). For bio-imaging specifically, various structures in biomedical samples show intrinsic nonlinear optical signals, and the signals can also be enhanced by extra nonlinear optical materials. Thus, the nonlinear optical imaging for biomedical applications has been extensively studied. Herein, our review focuses on the nonlinear optical bio-imaging and their recent advances.

To our knowledge, the nonlinear optical imaging techniques, including two-photon excited fluorescence, second-harmonic generation, third-harmonic generation, coherent anti-Stokes Raman scattering, stimulated Raman scattering and pump-probe imaging (Fig. 2), are promising in studying the biological samples, because of their high optical spatial and temporal resolution, no requirement for extra label, non-contact/non-destructive operation, and chemical specificity. Figure 3 shows the energy diagrams of these nonlinear optical processes.

In the two-photon excited fluorescence (TPEF) process, which is the most common in multiphoton fluorescence process, the molecule is excited by the absorption of two photons simultaneously. This technique can prolong the incident light wavelength to infrared range, compared to the excitation by one photon in the range of ultraviolet or visible light. The infrared light can improve the penetration depth in the tissue and reduce potential photodamag^41-42. Therefore, it is thought as one of the most popular noninvasive imaging tools which allows for imaging hundreds of microns deep in tissues (Fig. 4)⁴³.

The TPEF microscopy was first reported by Denk et al. in 1990. They demonstrated intrinsic three-dimensional spatial resolution with laser scanning⁴⁴. The TPEF microscopy can image some of the endogenous fluorophores such as nicotinamide adenine dinucleotide (NADH)^45-47, flavin adenine dinucleotide (FAD)⁴⁸ and elastin⁴⁹. These endogenous fluorophores whose absorption bands are in ultraviolet range can be excited by using infrared illumination⁵⁰. Such intrinsic contrasts enable the investigation of native cell and tissue structures without introducing artificial label compounds. Yu et al. reported on two photon excited fluorescence polarization and lifetime imaging of intrinsic NADH in breast cancer and normal cells for quantitatively analyzing the concentration and ratio between two different conformations (free or enzyme bound) of NADH. They revealed the sensitivity in detecting intracellular NADH concentration and conformation to cell physiology at the single-cell level⁵¹. Kasischke et al. reported TPEF imaging of intrinsic NADH and their geometric association with the cortical microcirculation, revealing the well-defined boundaries of the tissue oxygen diffusion in mouse cortex⁵². Balu et al. monitored changes in two photon-excited NADH fluorescence in human epidermal cells during blood-supplied oxygen deprivation in vivo, noninvasively revealing the depth dependent sensitivity of keratinocytes to vascular oxygen supply and their metabolism in human skin⁵³.

To improve the resolution and penetration depth, the exogenous labeling of the biological structure of interest is usually needed in most cases. Synthetic dyes and fluorescent proteins are the most widely used labeling agents. Recently, Mansour et al. reported the in vivo two photon imaging of blood vessels and functional neuronal networks through the introduction of Texas Red dextran, genetic encoding green fluorescent protein, and calcium fluorescent protein indicator in human brain organoids, which are transplanted into the adult mouse brain⁵⁴. New synthetic fluorescent probes with improved optical properties such as large two photon absorption cross section and high quantum yield, which could lower the excitation power and reduce the photodamage and photobleaching, are being continuously developed^55-59. In addition, some nanoparticles with good two photon fluorescence properties, such as gold nanoparticles^60-61, gold-silver hybrid nanoparticles^61-63, upconverting nanoparticles⁶⁴, surface modified carbon dots^65-66, and polymer nanoparticles^67-68, have been developed for in vivo TPEF imaging.

The three-photon excitation can further prolong the incident light wavelength over the two-photon excitation. Xu's group demonstrated three-photon fluorescence imaging of subcortical structures in mouse brain at the spectral window of 1700 nm⁶⁹. They also reported three-photon imaging for recording neurons activity in mouse brain⁷⁰. Recently, they realized three-photon imaging of vasculature through mouse skull, and also calcium imaging in cortical layers in awake mice over weeks⁷¹. On the other hand, some researchers focused on the tissue heating problem of three-photon excitation which higher optical pulse power is needed. Recently, Rowlands et al. developed a wide field three-photon excitation scheme for imaging biological samples without causing photodamage⁷². Besides, Guesmi et al. reported an optimized multiband pulses source for three-photon excitation and realized fast deep tissue imaging with low tissue heating⁷³. Moreover, they think the development of proper sources which can provide efficient three-photon excitation of biological samples is critical for three-photon bio-imaging application.

In the second-harmonic generation (SHG) process, which is a second-order nonlinear optical process, two incident photons interact with the materials and convert to one emission photon with double of the excited photon energy. It can only occur in the noncentrosymmetric structures. Since some of the biological components can assemble into noncentrosymmetric structures, the second harmonic generation has been applied to image the biological structures such as collagen, microtubules and muscle myosin^74-75. It is a sensitive label-free probe method, and the signal can be well separated from the auto-fluorescence of biological samples (Fig. 5).

SHG is firstly reported in 1961⁸ shortly after the invention of laser. Then the microscopic demonstration of the SHG appeared in 1970s^76-77. In 1986, SHG imaging of the collagen fibers orientation in rat tail was shown by Freund et al.⁷⁸ As it continues to develop, with SHG imaging with intrinsic contrast generated from collagen, microtubules and muscle myosin, people do not need to introduce extra labelling agents. Type–I collagen is the most abundant structural protein in human body⁷⁹, thus the SHG signal can be effectively obtained from the cornea, the skin, bones or tendons^80-85. These capabilities make SHG a powerful tool for biological researches and disease diagnosis. For example, SHG was reported to delineate breast cancers in different stages^86-88; show the increase of collagen fiber formation in ovary cancers^89-90; identify the tumor boundary in skin cancers^91-94; detect fibrosis in liver and kidney^95-96; diagnose connective tissue disorders such as Osteogenesis imperfect⁹⁷, Sjogren's syndrome⁹⁸ and skin damages⁹⁹; and show collagen plaques intermingling with elastin in atherosclerosis^100-101. Chen et al. provided the detailed strategy to obtain and quantitatively analyze the structural information on the arrangement of collagen in tissues⁸³. Additionally, Prasad and Qu's teams applied SHG to produce light excitation of photosensitizer for photodynamic therapy¹⁰².

Since many nanostructures also have intense SHG signals^{18, 19, 103-105}, including ZnO nanowires¹⁸, GaN nanowires²⁰, KNbO₃ nanowires¹⁹, noble metallic nanoparticles^106-108, Fe(IO₃)₃, KTiOPO₄, BiTiO₃ nanocrystals^{103, 104, 109–110}, some of them have been used as probes for specific biomolecules¹⁰⁹. SHG signals can be used to track the nanoparticles in cells and tissues^109-111. Magouroux et al. used KNbO₃ nanoparticles to label the membrane of embryonic stem cells and monitored the evolution of embryonic stem cells (ESCs) by capturing ESC-derived cardiomyocytes beating within a three-dimensional cluster¹¹². Recently, de Boer et al. demonstrated that second harmonic near infrared absorption of gold nanoparticles can optically evoke neuronal activity in mouse cortical neurons in acute slices and in vivo. And they also used this approach to stimulate individual epitheliomuscular cells and evoke body contractions in Hydra vulgaris¹¹³.

In the third harmonic generation (THG) process, which is a third-order nonlinear optical process, three incident photons generate one photon with triple of the excited photon energy. The THG can occur in the materials regardless of their centrosymmetry, which is different from the SHG. Since its signal from homogenous material can vanish because of the Gouy phase shift of the incident field across the focus^{2, 114}, it is sensitive to the interfaces and inhomogeneities. It has been applied to the imaging of biological samples without labels. Besides, the THG can prolong the excitation wavelength to near infrared (NIR) II range (1100–1350 nm). The light within this range can penetrate deeper in tissues than the NIR I (600–800 nm) light¹¹⁵. This feature makes THG a promising choice for deep tissue imaging.

THG at the interface was firstly demonstrated using a focused intense femtosecond pulsed laser by Tsang in 1995¹¹⁶. Then the THG microscopy was reported by Barad et al. in 1997¹¹⁷. After that, THG microscopy was applied in biology. The live neurons in cell culture and yeast cells were imaged by Yelin et al. in 1999¹¹⁸. So far, the THG microscopy has been applied to the imaging of many biological samples, such as lipid bodies¹¹⁹, zebrafish embryos^120-122, zebra fish nervous system¹²⁰, vocal folds¹²³, retina¹²⁴, oral mucosa^125-126, rat tympanic membrane¹²⁷, bone^128-129, fat tissue¹³⁰, skin tissue^{94, 131-136}, epithelial tissues^{131, 136-137}, and brain structures^{69-71, 138-141}. Recently, Kazarine et al. developed a technique of THG image scanning cytometry and applied it to malaria detection. The technique is based on their previous work that revealed hemozoin, which is a metabolic byproduct of the malaria parasite and present a significant third harmonic generation signal. They used this endogenous contrast to label-free image scanning cytometry of patient blood smears for the automated malaria detection¹⁴². ​Huizen et al. applied the THG combined SHG microscopy to imaging of fresh unprocessed healthy human tissue. They compared the images with the gold standard hematoxylin and eosin histological images and identify the key structural components in the tissue¹⁴³.

On the other hand, for long term cell tracking, non-bleachable THG contrast from nanoparticles is usually required. Since the THG signal from nanoparticles can be enhanced by surface plasmon resonances¹⁴⁴, which commonly occur in gold^145-146 and silver^147-148 nanoparticles, it is feasible to image these nanoparticles through the THG microscopy and also make use of them as potential biomarkers. Besides, semiconductor nanomaterials, such as Si, ZnO and CdSe nanostructures, have also been found presenting the THG signals^149-151. For example, Jung et al. reported imaging of Si nanowires with high resolution in vivo¹⁴⁹. Recently, Dubreil et al. observed BiFeO₃ nanoparticles labeled stem cells 1.3 mm deep in tissue by a 1300 nm femtosecond laser¹⁵². Lee et al. developed a new type of mesostructured α-FeOOH nanorods, which exhibit an enhanced THG signal under excited wavelength of 1230 nm because of the sub‐wavelength heterogeneity of refractive index. They also applied these nanorods as non-bleaching biocompatible third harmonic generation contrast agents for long-term observation in vivo (Fig. 6)¹⁵³.

The coherent anti-Stokes Raman scattering (CARS) process is a vibrational resonance enhanced four-wave mixing process, which is a third-order nonlinear optical process. In this process, two beams, one is pump beam with frequency ω_p and the other is Stokes beam with frequency ω_s, interact with the material and generate a signal at anti-Stokes frequency 2ω_p-ω_s. The signal can be enhanced when ω_p-ω_s is close to the frequency of a vibrational energy state of a chemical bond in the sample. It can provide chemical contrast without exogenous labels, and has already been used in the label-free chemically specific imaging for characterization of biological samples (Fig. 7).

The CARS process was first reported by Terhune and Maker in 1965¹⁵⁴. And then the CARS spectroscopy was developed and used for chemical analysis¹⁵⁵. In 1982, the CARS microscopy in two-dimension was reported by Duncan et al. In 1999, the three-dimensional CARS microscopy was developed for imaging live cells by Zumbusch et al.¹⁵⁶ After that, the high-speed laser-scanning CARS microscopy¹⁵⁷, Epi-detected CARS microscopy¹⁵⁸, and multiplex CARS microscopy^159-160 have been developed for biomedical applications. The CARS is a sensitive tool for probing strong CH-related vibrations in lipids. The signal allows for monitoring lipid metabolism in living cells and model organisms^161-166 and lipid droplets transport, lipolysis and growth^167-169. In addition, since the lipid structures are widely distributed in tissues, CARS imaging has been applied to many organism and tissue observation, such as observing skin^170-171, adipose tissue, kidney tissue, retina¹⁷², lung tissue¹⁷³, smooth muscle in colon¹⁷⁴ and blood vessels¹⁷⁵, nerve bundle^176-179, and brain tissue^180-181. Besides, the typically weak fingerprint region of Raman signals could be probed through intrapulse three colour excitation and non-resonant background amplification. This technique enables the identification of nuclei, collagen, protein, as well as lipid droplets in two- or three-dimensional tissues, expanding the prospect of CARS in biological imaging and potential clinic use¹⁸². Furthermore, CARS has also been used to identify healthy and diseased tissue in skin cancer¹⁷¹, colon cancer^183-184, and brain cancer¹⁸⁵.

Recently, Karuna et al. reported label-free three-dimensional quantitative imaging of chemical composition of the human osteosarcoma cell division by using the hyperspectral CARS microscopy¹⁸⁶. Niedieker et al. applied CARS imaging to characterize the myopathological features in muscles from patients with different myopathies, and to identify the distinct specific disease features¹⁸⁷. Hirose et al. developed a CARS rigid endoscope using two individual optical fibers to image rat sciatic nerves and also rabbit prostatic fascia without sample slicing, which revealed the potential application of the CARS endoscope to robot-assisted surgery¹⁸⁸.

The CARS microscopy also serves as a tool to map the drug molecules dynamics without any fluorescent labels. For example, Kang et al. visualized the distribution and release of paclitaxel in a polymer matrix¹⁸⁹; Hartshorn et al. mapped the chemical components in indomethacin tablets¹⁹⁰; Fussell et al. studied the distribution of micronized salmeterol xinafoate and budesonide on the surface of lactose carrier¹⁹¹. Additionally, CARS is sensitive to polymer-based nanoparticles because of their abundant C-H bonds. The CARS has been used to observe the intracellular trafficking of the nanoparticle drug carriers and monitor the drug release process^192-195.

The stimulated Raman scattering (SRS) process is another vibrational resonance enhanced four-wave mixing process. In this process, when the frequency difference of two incident beams, pump beam and stokes beam, matches the vibrational resonance, a small part of the input energy transfers from one beam to the other. The intensity of one beam is modulated in response to the variation, and this modulation can be transferred to the other beam. In such process, the intensity of Stokes beam has a gain and pump beam has a loss. The SRS signal can be measured by sensitive photodetection, such as lock-in amplifier^196-201 or tuned amplifier²⁰². The main advantage of SRS over CARS is the absence of non-resonance background. Some examples of stimulated Raman scattering imaging of biological samples are shown in Fig. 8.

The SRS process was first reported in 1962²⁰⁴. After that, the SRS spectroscopy with continuous-wave laser was developed in 1977²⁰⁵. In 2007, the SRS imaging was demonstrated on polystyrene beads with femtosecond laser²⁰⁶. In 2008, Xie's group demonstrated highly sensitive imaging of biological samples with picosecond laser, and opened the new era of SRS microscopy for biomedical imaging¹⁹⁶. SRS provides a new tool for lipid study without non-resonant background. It has been applied to the study of fat storage in C. elegans²⁰⁷, transport of lipid droplets in early fruit fly embryos²⁰⁸, fat droplets, cholesterol-rich lysosomes, and lipid oxidation in C. elegans²⁰⁹, and myelin sheaths in Xenopus laevis tadpoles²¹⁰. SRS microscopy also allowed for co-mapping of lipids, protein, and DNA, through their distinct features in the C-H stretching vibration region. This enabled the multicolored stain-free histopathology of cells and organs tissues, such as skin and brain tissues, and is comparable with the conventional hematoxylin and eosin based histopathology^211-214. Some biochemicals, such as cholesterol, glyceryl trioleate and bovine serum albumin, can also be detected through their fingerprint Raman spectra. Cholesterol storage in intact atherosclerotic arterial tissues²¹⁵ and Esterified cholesterol accumulation in prostate cancer and metastases²¹⁴ were imaged by SRS microscopy. High-level unsaturated lipids were detected in ovarian cancer stem cells by SRS microscopy²¹⁶. Furthermore, SRS microscopy was applied to identify squamous cell carcinoma in human skin tissue²¹⁷, and detect brain tumor in mice in vivo²¹⁸. The Raman spectroscopy has been used for brain tumor detection during surgery on a patient²¹⁹. Recently, Ji et al. applied SRS microscopy to image amyloid plaques in brain tissue from the mouse model of Alzheimer's disease. They distinguished misfolded protein in Alzheimer's diseased brain tissues through SRS spectral blue shift of the amide I band. This method provided a new tool to study Alzheimer's disease and other protein misfolding associated neurodegenerative diseases²²⁰. Yan et al. applied hyperspectral SRS microscopy to image the lipid metabolites in normal and cancerous liver tissues from patients, and found aberrant accumulation of saturated fat in human liver cancer. Their finding revealed that saturated fat played an important role in liver cancer development and could serve as a potential biomarker for liver cancer ²²¹.

Besides, isotope substitution has been developed for Raman contrast, since the C-D bond Raman spectra can be separated from the endogenous Raman features. For example, deuterated fatty acids were imaged to study the conversion of palmitic acid into lipid droplets in live cells and the fat storage in C. elegans¹⁹⁹; deuterated amino acids were used to image the protein synthesis in cells²²²; deuterated glucose was used to visualize de novo lipogenesis in pancreatic cancer cells²²³. ¹³C-labeled phenylalanine also served as Raman contrast and was used to monitor proteome degradation process in cells²²⁴. Recently, Li et al. applied multiple vibrational tags, including alkyne-tagged fatty acid, deuterium-labeled saturated fatty acid and unsaturated fatty acid, to image the lipid synthesis and lipolysis in C. elegans²²⁵.

SRS microscopy has also been applied to monitor the drug molecules using chemical Raman fingerprint. For example, Slipchenko et al. mapped the active pharmaceutical ingredient and excipients in amlodipine besylate tablets²²⁶; Fu et al. imaged the tyrosine kinase inhibitors distribution in living cells²²⁷; Chiu et al. measured the deuterated water, propylene glycol and dimethyl sulphoxide molecular diffusion in the human nail²²⁸.

The pump-probe transient absorption technique can be used to detect the molecules that have no fluorescence because of non-radiative decay from the excited state, and it is based on the third-order nonlinear optics. In this process, a transient absorption is induced by the pump beam and changes the excited state of the material first. Then such change is detected by a probe beam, and the dynamics of the excited state can be deduced through varying the delay time between probe and pump beam pulses. This technique has been used for imaging non-fluorescent chromophores, such as cytochromes and hemoglobin^229-231.

The transient absorption microscopy was firstly applied in biology for measuring dye fluorescence lifetime in cells by Dong et al. in 1990s²³². Then in 2007, the transient absorption imaging with high frequency modulation was reported by Fu et al. and used for imaging melanin and oxy-/ deoxyhemoglobin^233-234. Min et al. demonstrated the three-dimensional imaging of non-fluorescent chromoproteins, chromogenic reporter in gene expression, transdermal drug distributions, and microvasculature which is based on hemoglobin²³⁵. Besides, the transient absorption microscopy can differentiate eumelanin and pheomelanin, which are two types of melanins, due to their different transient absorptive response²³⁶. The transient absorption imaging has been used to monitor melanoma progression²³⁷ and assess metastatic potential of melanomas²³⁸. Recently, Chen et al. studied the dynamics of heme storage and distribution in C. elegans by using high-resolution transient absorption microscopy²³⁹ (Fig. 9). Dong et al. applied transient absorption imaging to differentiate glycated hemoglobin from hemoglobin due to their different excited state dynamics. They studied heme modification and quantified the glycated hemoglobin fraction at single red blood cell level. They found that the distribution of glycated hemoglobin fraction was different in diabetic whole blood from that in healthy whole blood. They also developed a mathematical model to derive the blood glucose concentration and monitored the long-term bloodstream glucose concentration²⁴⁰.

Moreover, transient absorption imaging can also be realized through exogenous contrast agents such as nanoparticles. The non-fluorescent contrasts have been generated from several nanostructures in biological samples, including semiconducting and metallic carbon nanotubes²⁴¹, nanodiamonds²⁴², gold nanorods²⁴³ and graphene/graphene oxide²⁴⁴.

Nonlinear optics can provide label-free, chemical specific and high-speed imaging strategies, which facilitate the studies of the biomedical dynamic process both in vitro and in vivo. It plays an important role in the bio-imaging for decades. Each nonlinear optical imaging strategy has distinct viability to certain structures or molecules. This is the advantage of nonlinear optical imaging. On the other hand, each nonlinear optical imaging strategy may rely on specific chemicals or certain optical probes, not able to simultaneously observe different structures and interaction in bio-samples. To visualize the complex biological system, the combination of these nonlinear optical imaging techniques is desired. This promotes the development of multimodal nonlinear optical imaging platforms. The two/three-photon excited fluorescence microscopy and second-/third-harmonic generation microscopy are one-beam systems. The coherent anti-Stokes Raman scattering, stimulated Raman scattering and pump-probe transient absorption microscopy are two-beam systems. The two-beam system coherent anti-Stokes Raman scattering microscopy can serve as a base platform for building other nonlinear optical modules. Such integration enables the simultaneous visualization of different structures or molecules and even their interaction in the complex biological samples. In our opinion, the current development bottleneck of nonlinear optical bio-imaging is in the aspects of imaging depth, spatial resolution, detection sensitivity and acquisiton speed. Although many exciting developments have been made, to achieve the goal of clinic translation, new technical breakthroughs are still needed. The further improvement on imaging depth, spatial resolution, detection sensitivity and acquisition speed is expected. For deeper imaging, new active focusing technique, or the optical fiber delivery, even endoscopy may be the direction of development. For higher spatial resolution, the combination with the super resolution imaging techniques could be a direction. For increasing the detection sensitivity, especially to achieve the single molecule detection, combining the coherent Raman scattering microscopy with force measurement of chemical bond vibration may be a solution. For higher acquisition speed, frequency multiplexed schemes²⁴⁵ could be used to monitor fast process. As more breakthrough emerges, the nonlinear optical imaging is believed to have great promise to become a powerful tool for both fundamental biomedical studies, and clinic application such as diagnostic and therapeutic evaluation.

This work was supported in part by the National Natural Science Foundation of China (61722508/ 61525503/ 61620106016/ 61835009/ 61935012/ 61961136005), (Key) Project of Department of Education of Guangdong Province (2016KCXTD007), and Shenzhen Basic Research Project (JCYJ20180305124902165).

The authors declare no competing financial interests.