PROBING TWO-DIMENSIONAL SEMICONDUCTOR AND BIOLOGICAL TISSUE BY NONLINEAR OPTICAL MICROSPECTROSCOPY

Two-dimensional materials, such as graphene and semiconductor transition metal dichalcogenides (TMDCs), exhibit remarkable optical properties which are of great potential for applications in modern electronics. The first part of this dissertation focuses on the dispersion of the second order resonant nonlinearity (χ (2) ) in the single layer TMDC. We begin with the study of the nonlinear optical properties of monolayer TMDC, WSe2. We experimentally obtain the χ (2) dispersion data from the single layer sample of WSe2 by using broadband ultrashort pulse laser sources. The broadband pulse is generated by specially designed photonic crystal fiber (PCF). This PCF fiber is pumped by TiS mode-locked laser to generate continuum pulse that spans from visible to near-infrared. This continuum broadband pulse is used as a fundamental beam to generate signal at the second harmonic frequency in 2D semiconductor material. We detect the signal generated in the sample by using monochrometer and charge-coupled device (CCD), which provide the spectrum of the second harmonic signal that carries the signature of the materials. To get the images of these materials, we employ an optical parametric oscillator (OPO) tuning at reasonable wavelengths. Then we shine the beam on the sample, and after the signal has been generated in the sample, it gets reflected and this beam is then collected by photomultiplier (PMT) before angle scanned using galvo-mirror scanner to provide 200x200 μm 2 imaging area. The   2  dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.410 -19 m 2 /V range. We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the   2  dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV. In the second half of this work, we study two other materials. First, we show resolution of fine spectral features within several Raman active vibrational modes in potassium titanyl phosphate (KTP) crystal. Measurements are performed using a femtosecond time-domain coherent anti-Stokes Raman scattering spectroscopy technique that is capable of delivering equivalent spectral resolution of 0.1 cm -1 . The Raman spectra retrieved from our measurements show several spectral components corresponding to vibrations of different symmetry with distinctly different damping rates. In particular, linewidths for unassigned optical phonon mode triplet centered at around 820 cm -1 are found to be 7.50.2 cm -1 , 9.10.3 cm -1 , and 11.20.3 cm -1 . Second, we demonstrate the quantitative spectroscopic characterization and imaging of biological tissue using coherent time-domain microscopy with femtosecond resolution. We identify tissue constituents and perform dephasing time (T2) measurements of characteristic Raman active vibrations. This was shown in subcutaneous mouse fat embedded within collagen rich areas of the dermis and the muscle connective tissue. The demonstrated equivalent spectral resolution (<0.3 cm -1 ) is an order of magnitude better compared to commonly used frequency-domain methods for characterization of biological media.

single layer sample of WSe2 by using broadband ultrashort pulse laser sources. The broadband pulse is generated by specially designed photonic crystal fiber (PCF). This PCF fiber is pumped by TiS mode-locked laser to generate continuum pulse that spans from visible to near-infrared. This continuum broadband pulse is used as a fundamental beam to generate signal at the second harmonic frequency in 2D semiconductor material. We detect the signal generated in the sample by using monochrometer and charge-coupled device (CCD), which provide the spectrum of the second harmonic signal that carries the signature of the materials. To get the images of these materials, we employ an optical parametric oscillator (OPO) tuning at reasonable wavelengths. Then we shine the beam on the sample, and after the signal has been generated in the sample, it gets reflected and this beam is then collected by photomultiplier (PMT) before angle scanned using galvo-mirror scanner to provide 200x200 µm 2 imaging area. The   2  dispersion obtained with better than 3 meV photon energy resolution showed peak value being within 6.3-8.410 -19 m 2 /V range.
We estimate the fundamental bandgap to be at 2.2 eV. Sub-structure in the   2  dispersion reveals a contribution to the nonlinearity due to exciton transitions with exciton binding energy estimated to be at 0.7 eV.
In the second half of this work, we study two other materials. First, we show resolution of fine spectral features within several Raman active vibrational modes in potassium titanyl phosphate (KTP) crystal. Measurements are performed using a femtosecond time-domain coherent anti-Stokes Raman scattering spectroscopy technique that is capable of delivering equivalent spectral resolution of 0.1 cm -1 . The Raman spectra retrieved from our measurements show several spectral components corresponding to vibrations of different symmetry with distinctly different damping rates. In particular, linewidths for unassigned optical phonon mode triplet centered at around 820 cm -1 are found to be 7.50.2 cm -1 , 9.10.3 cm -1 , and 11.20.3 cm -1 .
Second, we demonstrate the quantitative spectroscopic characterization and imaging of biological tissue using coherent time-domain microscopy with femtosecond resolution. We identify tissue constituents and perform dephasing time (   (1) and (2)  x Figure 2. Time-domain CARS signal obtained from the ~16 µm diameter fat area located at the center of the mouse tissue for the image shown in Fig. 1(b). Solid green line represents non-resonant CARS signal obtained in microscope glass slide that was detected in the same (i.e. backward) direction and under the same other conditions.
Dash dotted line represents the best fit to the data obtained by using formulae (2)- (4) and varying the corresponding line parameters (see text)…………………………. ..51  The Raman active vibrations near a) ≈1070 cm -1 and b) 1265 cm -1 were targeted and probed. The solid line represents the best fit to the data obtained using formulae (2) are also provided. We believe that our experimental results will aide in developing refined theoretical models for 2D materials.
The experimental idea is presented in Fig. 1 Si substrate. Figure 2(a) shows SHG image of the flake. We present SEM image of the flake in Fig. 2(b). The flake also characterized in a separate photoluminescence measurement. The latter reveals a narrow (~45 meV) peak at 746 nm (~1.662 eV) that is shown in Fig. 2(b) and corresponds to the first exciton line characteristic for single layer. We have checked the SHG signal dependency versus incident power of the fundamental beam to reveal the quadratic increase shown in Fig. 2(d). The SHG image shown in Fig. 2(a) displays high contrast and absence on any appreciable signal from interfaces other than the one created by the flake. Fairly large SHG signal variations (up to 30%) are observed even within the unripped parts of the flake (Fig 2(e)). We believe that this is due to local field variations affecting   2  at the flake/SiO 2 interface. The SHG spectrum is shown in Fig. 3(a) by the blue curve. We have also performed, for comparison purposes, point-by-point wavelength tuning SHG measurements with wavelength tunable Ti:sapphire oscillator (filled circles data in Fig   3(a)). The SHG signal fluctuations are significantly higher (σ=±54% ) for this case.
We believe that much higher SHG signal variations versus wavelength observed in the point-by-point measurements are couple of additional sources of the variation. Namely , changes in the fundamental field parameters like pulsewidth and spatial mode while the wavelength is tuned. The lowered precision for the SHG spectra were also observed in the referred point-by-point measurements [5] as authors pointed to the uncertainties in the pulsewidths while the wavelength was tuned as being the main reason.
The observed increase in the resonant nonlinearity  

2D
 matches well with split-off band transitions (i.e. B-exciton) if one considers bandstructure parameters for 5 single layer of WSe 2 at K-point such as bandgap ( g E ) and split-off energy ( SO  ) [5,6]. A similar effect has been observed in MoS 2 involving a different energy valley that is at  point [3].
We have obtained  

2D
 spectra two approaches. The first one exploits the relationship between the fundamental and SH powers. In the other one we used comparative approach when a material with known second order nonlinearity is used.
We have chosen thin KTP crystal. The crystal is well characterized from many aspects. The second order effective nonlinearity ( eff d ) is between 1.72-2.01 pm/V [7] for the incoming beam polarization and crystal orientation that we used. By normalizing our WSe 2 SH data to the one obtained from the crystal ( ), we obtain a ratio ( = 2 2 2 ⁄ ) that provides dispersion of the absolute value of 2 (2) and is free from measurement artifacts (e.g.,  2 T , etc.). The result is displayed in Fig. 3(b) by blue curve for a comparison. Some difference can be seen at lower photon energies. We note that SHG and fundamental signal have been detected by different spectral devices in the first method. The second method is free from artifact.
Bloembergen et al [8] were first to consider SHG from thin layers and interfaces.
SHG power has been derived by Merano [9] by considering real experimental situation of a sheet of 2D material on the top of the layered substrate. Following the approach developed in [9,10] and making use of the results by Boyd et al. [11] SHG pulse peak power from 2D material ( D P 2 2 ) and bulk crystal ( P 2 B ) can be expressed as shown in Supplement [12]. Based on that, the absolute value of  

2D
 expressed in terms the crystal's effective nonlinearity eff d , refractive index ( b n ), numerical aperture of the objective lens (  ) and the measured ratio (  ) is: It is important to note that the two-layered substrate can lead to the enhancement or attenuation of the SHG intensity due to interference effects that depends on the thickness of the SiO 2 layer. This is taken into account in the factor containing complex field reflectivity (  n ) changes by only few percent within the photon energy range that we have.
The median peak value of 2 (2) for WSe 2 monolayer at the SH photon energy of 2.76 eV can be estimated at 7.310 -19 pm 2 /V. We provide 15% range owing to several factors such as the range for eff d itself and taking into account signal variations across the flake that were discussed earlier. The value is on the same order of magnitude with the one quoted for the measured MoS 2 sheet nonlinearity in [13] and factor of 2.7 smaller than the one provided by Merano [9] for MoS 2 . If we straightforwardly use solutions provided in [8] and assume that the sample still has bulk refractive index [14] and nonlinearity   In the formula above,   n f  is a factor containing refractive indices of bulk WSe 2 and is coming from solutions for the SH field [17], -factor accounts for the interference effects. Additional details are provided in Supplement [12]. This approach may cause controversy and disagreement. We, however, we would like to provide an estimate just for sake of comparing the material's nonlinearity with the one of other bulk noncentrosymmetric semiconductors. The estimated  

2D
 value is in the 932-1233 pm/V range for peak SH photon energy while the off-peak value is about 440 pm/V.The values are comparable with the ones for well known non-centrosymmetric semiconductors (GaAs, CdTe, ZnSe [15]) that are used in parametric devices and frequency converters in the infrared [16]. Comprehensive theoretical treatment and modeling of the second order nonlinearity is based on rigorous approaches outlined in [17,18]. Here we will use an approach based on parabolic bands approximation, accounting for Coulomb effects via exciton continuum states above bandgap in order to estimate dispersion of the absolute value of   2  due to interband transitions first.
The expression for   2  along the electric field and induced dipole moment in xdirection can be represented by [18]: 1    [6]. We have also considered momentum matrix elements and dephasing rates are k-, and therefore energy, independent. The summation over k-states can be replaced by integral over energy that couples the resonant denominator in formula (4) and joint density of states factor for the first conduction and top valence bands for continuum Figure 4 shows the results of our calculations when  was set to 35 meV. It is important to note that the nonlinearity is sensitive to a change of g E . This is shown by comparing two simulations when g E is changed from 2.22 eV (green curve) to 2.15 eV (dash-dotted curve). It is apparent that when the bandgap is set at ~ 2.2 eV a better match with the experimental data around the peak area is obtained. We believe that band nonparabolicity becomes critical to explain the experimental data at higher photon energies. On the lower energy side one finds that the rise in simulated   2  is noticeably sharper when compared to our experimental data. The discrete exciton contributions can be represented mainly by resonant factors that are similar to the term in formula (4)  is assumed. Figure 4(b) shows total nonlinearity due to the interband transitions and multiple exciton lines (n=1-5) below 9 the first conduction band states. The best fit is obtained for the exciton binding energy of 0.71 eV while the bandgap ( g E ) parameter was set at 2.22 eV. The obtained value for the bandgap matches well with the ones reported in [5,6]. Exciton binding energy obtained from our data is also in close agreement with the value of 0.60.2 eV reported by Wang et al. [5].
In conclusion, we have demonstrated precise measurements of the second order nonlinearity in atomically thin layer of semiconducting material within broad range of photon energies. Using ultra-broadband continuum pulses, we were able to detect fine features in the   2  dispersion with high spectral resolution (<3 meV). The nonlinearity onset is primarily due to monolayer WSe 2 states that couple valence bands, excitonic levels and the continuum states above the first conduction band.
Using our data, we estimate peak nonlinearity range for a sheet of WSe 2 at 6.      Precise information on fine structure and decay of Raman active modes is essential from both fundamental and device applications point of views. Time-domain studies provide direct information on decay and dephasing processes for vibrational modes and, for solid-state media, provide most valuable information as concerned parametric phonon interaction due to deformation potential anharmonicity. In frequency domain, dispersion of the corresponding nonlinear optical susceptibility is an essential charcateristic in order to get an insight into physics of intra-and interatomic groups interactions. In this paper we focus on an important nonlinear optical gain material that is used both as intracavity and external gain material in multi-wavelength laser devices. The attention has recently grown due to possible applications of efficient frequency converters in generating phase-locked frequency combs for attosecond waveform generation. Potassium titanyl orthophosphate KTiOPO 4 (KTP) is a widely known optical material that is particularly attractive for nonlinear optical applications. Because of its high nonlinear optical coefficient and its optical and mechanical stability, the crystal is used in laser sources as an optical frequency converter. Its large electro-optic coefficient, low dielectric constant and ion exchange properties also make it suitable for electro-optic [1] and waveguided laser devices [2]. The crystal was previously shown to be an efficient source for multiwavelength pulse generation via stimulated Raman scattering (SRS) [3,4] or as a combination of SRS and efficient second order frequency conversion [5]. Renewed interest came with recent SRS experiments on high-frequency crystal vibrations that promised a pathway towards a solid-state sub-optical-cycle waveform source [6][7][8]. In other words, materials with high second and third order nonlinearity associated with several Raman active vibrations at high frequency range are of interest from the standpoint of generating a frequency comb that would ultimately support attosecond waveforms [9]. Knowledge of key properties of lattice vibrations is thus important in the light of the applications of this material as a nonlinear gain (of both second and third order) medium.
KTP's vibrational spectra are quite complex. The spectra consist of about 100 Raman active peaks as a result of the crystal's multiatomic unit cell. The complexity makes it difficult to perform comprehensive and unambiguous phonon line assignment, to precisely measure bandwidth and separation of individual Raman active peaks, as well as to estimate Raman cross-section for each individual phonon line. Even though the material has been known for more than three decades, detailed spectroscopic studies on its Raman active vibrations are relatively scarce [10][11][12]. The performed studies helped to elucidate contributions to Raman and infrared spectra from major atomic units within the primitive cell, as represented by TiO 6 octahedra and PO 4 tethrahedra. Also, important details concerning line assignments and their major characteristics were provided by the studies. However, the information ultimately proved to be contradictory and detailed spectral features of some peaks were not provided by these experiments. In particular, the first comprehensive Raman study of KTP [10] [11]. A study that followed later stated that the Raman line detected at ~830 cm -1 is an intergroup (Ti-O-P) vibration, but provided no details on the detected linewidths and separations for the different peaks [12].
At room temperature, the Raman spectroscopy of KTP has also been investigated from 10 to 1400 cm -1 [13][14] and also studied as a function of high pressure revealing the existence of two additional phase transitions near the critical pressures of 5.5 and 10 GPa [15]. Temperature dependent Raman scattering were studied [16][17] and found that no phonon mode coalesces to central peak near T c and reported it as a sign of damped soft mode [16]. A study on polarized Raman spectra showed strongest phonon 20 line located at 234 cm -1 [18]. It is worth mentioning that no experimental or theoretical study can be found which addresses phonon dispersion properties or mechanisms for phonon line decay. As was mentioned above, there is a motivation for a more detailed characterization of phonon vibrations in the material in the light of a search for an efficient solid-state media for a sub-optical-waveform source. Indeed, the crystal possesses several high-scattering cross-section phonon modes within energy range of 200-1000 cm -1 . The modes are conveniently spaced apart so that generation of a frequency comb, via SRS with intrinsically phase-locked spectral components, would provide multi-octave bandwidth to support sub-femtosecond pulses.
In this work, we present data on the decay of some of the KTP crystal phonon modes within 640-850 cm -1 . We reveal the fine structure of the vibrations by retrieving the vibrational system's response function and Raman spectra. Our data provide details on the crystal's complex vibrational spectra supported by important quantitative results. The data obtained for an unassigned vibrational mode at 820 cm -1 supports the conclusion that the modes decay noticeably slower when compared to high-frequency modes originating from vibrations of the main TiO 6 or PO 4 atomic groups. We attempt to explain our linewidth results within the framework of parametric phonon interaction due to the deformation potential anharmonicity.  [19,20]. The experimental set up is schematically shown in Figure 1. The two pulses that are needed to coherently drive lattice vibrations within a sample's macroscopic volume are provided by synchronously pumped optical parametric oscillators (OPOs) running at 76 MHz. The OPOs utilize high parametric gain periodically poled lithium tantalate (PPSLT) crystals. The OPOs were simultaneously pumped by a split output of a high-power mode-locked Ti:sapphire oscillator tuned to 765 nm. Detailed OPO characteristics and performance were reported in our recent publications [21,22]. The OPOs with pulsed outputs at 970-1020 nm and 1050-1100 nm, served to coherently drive lattice vibrations with energies within 600-990 cm -1 .
Another small part of the Ti:sapphire oscillator was delayed and served as a probe pulse. All of the three pulses were intrinsically synchronized, made to overlap in space, and focused by a high numerical aperture (NA~1.25) objective lens. In the detection arm, we used a high numerical aperture (NA~0.9) condenser followed by a diffraction grating and a set of bandpass filters. This permitted efficient detection of the signal of interest on the background of other signals generated within the focal volume. A photomultiplier tube (PMT) with high gain and quantum efficiency (Hamamatsu model #R10699) was used to detect anti-Stokes signal photons at selected wavelengths. The PMT current output was digitized by a high-speed data acquisition card. Using this experimental arrangement, we can routinely detect CARS signals versus probe pulse delay times within five decades. The corresponding total power on the sample from the three beams does not exceed 15-20 mW. Other details and characteristics of the set up are described in our most recent work [20]. Figure 2 (a) demonstrates sensitivity and the attainable time resolution using the experimental arrangement. In addition, using theoretical algorithms and owing to the experiment's great sensitivity, we can retrieve the vibrational system's response function and Raman spectra for several vibrational modes. The flux-grown KTP crystal used in the experiment was cut at =40 and =90. Polarizations of all the three beams were made parallel and aligned in XY-plane of the crystal. Thus, technically, all the four symmetry tensor components [10,11] are involved in Raman mode excitation and scattering processes during CARS.
Lattice dynamics in condensed matter is modeled as time-dependent behavior regarding the expectation value of molecular/atomic displacement amplitude under a driving force. This driving force consists of a pair of pulsed fields with an optical frequency difference matching the energy of vibration quanta [23][24][25]. Quantitatively, the scattering signal at anti-Stokes frequency (S as (t d )) can be expressed as the following: (1).
In the above equation, ( ) and (t) are normalized time-dependent envelopes for atomic displacement amplitude and probe pulse, respectively. This also implies that (2).
In the equation above, g(t) represents the response function of the corresponding vibrational system to -pulsed driving fields. Both equations are of Fredholm type-I and can be solved using the Fourier transform method [26]. This is ensured by the correlation integral theorem and the fact that spectra and/or envelopes of  1 , 2 , pr pulses are known and can be measured. In the case when ( ) is a real function, the response function g(t) and its Fourier transform can be ultimately obtained. The condition holds true for many types of vibrational systems that do not involve diffusional phase shifting events. As a consequence, precise spectra and fine features in the vicinity of Raman active vibrations can be effectively resolved. Figure 2 ( the excitation and probe pulses can not be considered as -functions (t p~3 T 1 ) and an approach reported earlier by our group, described in Ref. [27], yields in somewhat 24 distorted spectral data. Thus, equations above need to be solved in order to retrieve Raman spectra along with the dispersion of the real part of the associated resonant third order nonlinearity (χ (3) (ω)). The Fourier transform (S as ()) of the measured time-dependent CARS signal is a first step in solving the equations. The corresponding result is shown in Figure 2  damping rates for in-plane and along long axis vibrations within the TiO 6 octahedron [10]. A third component is also pronounced in the spectra with a position shifted to lower energies by 65 cm -1 . This mode has a different symmetry and represents ν 2 (E g ) anti-phase stretching vibration within TiO 6 octahedra. The peak can be better resolved under condition when one of the OPOs is detuned to provide more efficient coherent excitation for the ν 2 (E g ) mode. As a result, the time-dependent CARS signal exhibits a more pronounced quantum beats pattern. Using this arrangement, the spectral bandwidth of the ν 2 (E g ) mode was determined to be 21.30.7 cm -1 . The obtained parameters for the main  1 (A 1g ) doublet and for the  2 (E g ) modes are in good general agreement with the referenced reports [10,11]. We must note, however, that consistent bandwidth and Raman shift data for the doublet components could not be found throughout Raman spectroscopy characterization studies of KTP crystal published in the past [10][11][12][13][14][15][16][17][18][28][29][30][31]. The result of fitting imaginary part of the resonant third order nonlinearity (i.e. Raman spectrum) using Lorentz-shaped multi-peak curves is also shown in Fig. 2 14.0-16.4 cm -1 respectively reported by spontaneous Raman spectroscopy study [11].
The spread for both parameters is dependent on particular experimental conditions (e.g. crystal axes orientations with respect to laser polarization) when different scattering tensor elements have been accessed within the measurements. And finally we report a component amplitude ratio of 46:5:31. The value is not available for comparison from spontaneous Raman spectroscopy studies Phonon line bandwidths are approximately two times narrower (i.e. the corresponding phonon decay rate is two times lower) when compared to the high frequency modes ( 1 (A 1g ) and  2 (E g )) that are stronger in Raman scattering. We explain this by the fact that the latter modes have a variety of efficient overtone or combinational phonon decay channels within either of the TiO 6 or PO 4 groups, resulting in lower energy vibrations. Therefore, we think, that based on the fact that the investigated ~820 cm -1 mode has a significantly lower damping rate, the mode is not a vibration originating from either of the two main atomic groups and it is rather within Ti-O-P intergroup vibrations. The complex structure (i.e. presence of the triplet line) can be explained by shifted frequencies for vibrations of different symmetry within the group. Lower phonon damping rates (i.e. higher effective dephasing time T 2 *=T 1 ) makes up to a certain degree for the difference in the steady state SRS gain between the relatively weak mode at 820 cm -1 and the strong  1 (A 1g ) and  2 (E g ) vibrations. By using proper crystal orientation, it is possible to produce in SRS experiments (Stokes and anti-Stokes scattering) a nearly equal intensity and equidistant comb of frequencies that includes ~820 cm -1 mode. The comb can be used for ultrafast waveform synthesis.
34 coherent Raman microscopy studies were primarily applied to highlight tissue and cells constituent by producing high-contrast images at targeted Raman active vibration [5,6]. Spontaneous Raman version has been applied with greater focus towards detection of spectral features within cells and tissue [7]. However, the reported results have been limited to obtaining characteristic multi-line spectra and detecting relative changes in the intensities and spectral shifts with a goal to correlate those with biomolecular alterations occurring on sub-cellular level [8]. The true spectroscopic strength, that would ultimately include resolution of molecular vibration damping rates  (or linewidths, =1/) and line shapes, has not been enabled and demonstrated. It is worth noting that the damping rate is directly affected by inter-and intra-molecular  within a decade translates to better than few percent precision in T 2 () measurements [10]. In other words, t-d CARS can result in the Green's function (G(t)) for the molecular system as a response to the ultrashort (E 1 (t),E 2 (t))-pulse excitation. An ability to measure (G(t)) on extended time scale and within high dynamic range provides much more fine information about the corresponding Raman lineshape [10]. Lower limit for the equivalent spectral resolution is determined by one's ability to trace t-d CARS signal for as long time delays as possible.

40
The goal of this work is the first direct dephasing time (T 2 ) measurement of specific molecular vibrations within biological tissue. Another novelty is that we demonstrate detection of time-domain replica within biological tissue, traced within more than one decade, for important and previously unresolved Raman signature line within fat cells. The ability to measure the corresponding dephasing times with high precision resulted in equivalent spectral resolution of better than 0.3 cm -1 . This constitutes another important point since the achieved resolution is an order of magnitude better than the one that can be ultimately achieved by frequency-domain approaches applied to tissue or cell characterization. These highlight the strong potential of the time-domain approach with regard to biochemical and biomedical applications that seek reliable molecular level indicators for early disease diagnosis, etc. The only demonstration of the time-domain CARS microscopy showed lower sensitivity and was limited to artificial structures like polysterene beads probed at much stronger Raman resonance [11].
The ultrashort pulses (E 1 ,E 2 ) are provided by independently tunable (960-1120 nm) optical parametric oscillators (OPO) running at 76 MHz [12]. A small part of femtosecond Ti:sapphire laser output, that simultaneously pumped the OPOs, served as a third color pulse (E pr ) that can be delayed. The three pulses are intrinsically synchronized in time.
For the case of biological tissue, generated SHG and CARS signals are detected in backward direction. SHG and CARS signals were filtered by the appropriate bandpass filter (BP) and diffraction grating (GR) with 1200 grooves/mm.
The cooled PMT detector has a gain of up to 10 7 , high cathode sensitivity, and a dark 41 current below 1 nA. The detected signal was digitized by data acquisition card. The card also provided synchronized analog signals to drive x-y galvo-scanners in order to generate raster scans for imaging. SHG and time-delayed CARS images can be generated with a spatial resolution of 300 nm using high-numerical aperture (NA=1 .2) objective.
The tissue samples used in this investigation were dissected from above the longisimus dorsi muscle of C57BL/6 mice under after euthanasia with outer and inner surfaces of the adipose tissue identified. Slices of up to 100 µm in thickness were fixed for 1 hr in 4% PFA at 3°C. The coverslips were treated with gelatin-chromium potassium sulfate solution for optimal tissue contact. Fig.1 (a) shows a SHG image obtained with scanned fundamental beam, at optical frequency ω 2 , delivered by one of the OPOs tuned to ~1095 nm. The image shows a high SHG signal within the collagen type-II rich areas within the dermis and connective muscle tissue for which the second order optical nonlinearity is strong due to the lack of inversion center in the molecular structure of this type of protein.
There are fairly large areas in between the collagen areas where the SHG signal is absent. The collagen bundles could sustain 30-40 mW average power levels at this wavelength in the scanning mode of 2 frames/sec without the collagen fibrils being visibly altered or damaged. With the focused beam fixed on one spot within the collagen rich area a detectable damage could occur within the timeframe of few minutes. Figure 1(b) shows CARS image of the same area at zero time delay. The OPO wavelengths were tuned to 978 nm and 1095 nm respectively so that the targeted Raman active mode is at a frequency shift of ω 1 -ω 2 ≈ 1072 cm -1 . Some collagen bundles seen in Fig. 1(a) can be still fairly well identified on the CARS image.
However, the contrast is significantly lower with respect to surrounding areas. The image shows very strong signals coming from the areas where SHG signal was absent.
These parts are filled with dense mouse fat as this was further confirmed by timedomain CARS measurements. Unlike the collagen, the structure of the fat molecules is centro-symmetric and therefore the areas with the fat are not seen on the SHG image.
The CARS image clearly resolves a blood vessel with red blood cells ( (~20x20 µm 2 ) to match large piece of fat located at around the center of the image shown in Fig 1(b). Signal fluctuations are fairly high and the signal-to-noise ratio is about factor of 5 despite the fact that the data were effectively averaged across more 43 than 4000 pixel area. The data quality degraded further if the scanning was not performed and this has been the case for fairly moderate (i.e. <25 mW in combined power for the three beams) average power levels focused into the fat area. Some observations indicate that the tissue samples have been altered due to accumulated excess heat and high peak powers that lead to molecular ionization. The detailed study on this issue has not been performed. The obtained CARS transient clearly shows at least two spectral components that result in the coherent beat signal. The decay time is fairly long (~2 ps) and there is an indication of different decay times for the components. This can be noticed in decreased modulation depth for the beat signal at longer time delays. The obtained transients have been further analyzed by generating theoretical curves to fit the experimental data. We have applied a model that is based on time dynamics of the macroscopic coherent amplitude (Q) [13]. Time-domain CARS signal can then be calculated by using the following formulae: In the equations above,  1 , 2 , pr (t) stand for unit area driving and probe pulses,  0detected anti-Stokes signal at zero delay, G(t) -response (Green's) function of the corresponding vibrational system to -pulsed driving fields. Applying certain solution algorithms for the above Fredholm type-I equations the G(t) can be retrieved for arbitrarily shaped pulses [8]. We can also seek solution for G(t) function for our case of i) Gaussian pulses and ii) when molecular collisions dominate the dephasing process. As was discussed in the introduction, the latter condition represents the case 44 of homogenously broadened line. Therefore, where h(t) is Heaviside step function, A j -Raman line component amplitude, T 2j -the component's dephasing time,  j -the component's shift from reference frequency (e.g. from ( 1 - 2 )). By varying the above parameters we can find the best fit to our experimental data. For the vibrational modes in the vicinity of ( 1 - 2 )≈1072 cm -1 the best fit corresponded to the presence of two vibration lines with a frequency difference of ∆ 12 = ∆ 1 − ∆ 2 =28.7 cm -1 , dephasing times of 2.6 and 1.7 ps and the amplitude ratio of A 1 /A 2 =19:5 respectively. The dephasing times (T 2j ) obtained from our measurements suggest, if we apply formula (1), that the two homogenously broadened vibrations have linewidths of ∆ 1 = 4.1 cm -1 and ∆ 2 =6.3 cm -1 . Some comparison can be made with spontaneous Raman data available for fats [14,15]. We did not find any data on the relevant case that is obtained with a coherent frequency-domain technique.
Spontaneous Raman spectroscopy of adipose tissue in mice has shown two not well resolved C-C bending vibrations within ~1060-1120 cm -1 range sitting on a broad shoulder [15]. The line separation within the doublet at around 1080 cm -1 is not reported and could not be inferred from the data. The two, strongly overlapping and merging lines, show the combined width of about 25 cm -1 which is about the separation ∆ 12 that we found using our data. Thus, our results represent first measurement of the linewidths and the spectral difference for the C-C vibrations in fat and clearly demonstrate the power of the time-domain method. Another feature that follows from our data is that the individual components with the doublet have different linewidth.

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We next targeted higher-frequency and stronger line at ~1265-1275 cm -1 , assigned as a =C-H bending vibration, to get a better comparison with available spontaneous Raman studies since the line is better resolved in them. Fig. 3 shows the transient signal when Raman active vibrations at around ~1270 cm -1 frequency shift were excited and probed within the fat tissue. By fitting the data, using the model described above, we found that there are two closely spaced vibration modes at 1272 cm -1 with the frequency difference of ∆ = . cm -1 , dephasing times of 550 fs (∆ = . cm -1 ) and 670 fs (∆ = . cm -1 ) , and the amplitude ratio of 33:13.
The study reported in [15] identifies this C-H bending doublet positioned at 1264 cm -1 and 1301 cm -1 resulting in a frequency spacing of 35-40 cm -1 with linewidths that could not be obtained from the data. The doublet line frequency differences show some agreement with the one detected in our experiments. As concerned the linewidths, our work is again the first to address and report that. Overall, none of the Raman studies that we found on fatty acids, proteins, DNA [16] provided explicit line bandwidths. This is presumably due to the limited (~3-7 cm -1 ) spectral resolutions and low scattering signals. Thus, we find our data to be the first to reveal the more precise information on line separations and the only one available for the corresponding linewidths.
We have compared our results in mouse fat with identical time-domain CARS measurements that we performed in olive oil. Oils and lipids in fats have similar molecular composition and thus should have similar Raman active vibrational spectra.
Raman active lines corresponding to C-C stretching vibration at ~1070 cm -1 and scissoring (C-H) modes at 1267 cm -1 [17] were targeted. The corresponding results are shown in Fig. 4 (a) and (b). Since the data quality had been substantially better we were able to determine the parameters (see figure caption) more precisely. We point out again that a comprehensive comparison with data obtained by frequency-domain methods could not be performed since linewidths data were not available for the two modes in oil either. In general, from our experiments, fairly good agreement is found between fat and oil data as concerned linewidth and spectral separation parameters.
However, the small differences, above spectral resolution, still noticeable. More detailed studies are needed, especially for different types of oils and fatty acids, in order to come up with a credible explanation for the detected differences. If we turn to the data for mouse fat again, one can see that there is a factor of 3-4 difference in linewidths for the targeted C-C and =C-H bending vibrations. We attribute this to the differences in character and lengths of the bonds and we think that those play a larger role in determining the dephasing times (damping rates, linewdith) for the vibrations compared to the heterogenous molecular environment.
In conclusion, we reported on implementation of spectroscopic imaging and characterization approach based on time-resolved version of CARS. We can identify tissue constituents and measure dephasing times for the associated vibrational modes.
We show that the time-domain nonlinear microscopy of tissue delivers much more precise information on molecular fingerprints of the tissue constituents. Relating this type of information to diagnostics of diseases will be the task of major importance for future efforts.  Time-domain CARS signal obtained from the ~16 µm diameter fat area located at the center of the mouse tissue for the image shown in Fig. 1(b). Solid green line represents non-resonant CARS signal obtained in microscope glass slide that was detected in the same (i.e. backward) direction and under the same other conditions. Dash dotted line represents the best fit to the data obtained by using formulae (2)

APPENDIX Detailed experimental procedure and alignment:
In this section, we will discuss the light sources at first, which is the pivotal part of the experiment, and then we will briefly describe the concept and set up of our two experimental techniques, Coherent Anti stokes Raman scattering (CARS) microspectroscopy and SHG microspectroscopy.

The sources of light:
Mode-locked Ti. Sapphire laser: The main laser source we have used is the mode-locked ultrafast laser that uses Titanium: sapphire as the gain medium (Mira-HP, Coherent), tunable from 700 to 1000 nm. This laser is also pumped by another laser, green laser, with power 17W.The repetition rate (or frequency) of this laser is 76 MHz. The output power (~ 3-3.7 mW) of this mode-locked laser is then passed through the two cavity prism to compensate the pulse. A small portion of this pulse is out coupled through the sideport of the Glan-Taylor prism. The large portion of the beam, however, spilt into two equal parts, and used to synchronously pump the two OPOs. On the other hand, the small portion of the beam is used as probe pulse for CARS experiment.

OPO-1.
The nonlinear gain media, allowing quasi-phase matching condition, for OPO1 is the stoichiometric lithium tantalate (PPSLT) nonlinear crystal, generating parametric oscillation at the near IR-pump wavelengths in both for continuous wave (cw) and short pulse mode.
The crystal is 1 mm width, 0.5 mm thick, and 15 mm long-z cut that was pooled within 13 mm distance along the height. The grating period is varied from 17.50 to 24.80 micron with 0.6 micron differences between consecutive periods. The pump power is 1.15 mW, delivered by TiS mode-locked laser. The pump beam is focused onto the crystal by a 76 mm focal length lens. The OPO cavity is consist of two concave mirrors and three plane parallel substrate mirrors. A pair of Brewster cut angle prisms was used to compensate the dispersion. The optimal distance between the two prisms (apex to apex) was found to 280 mm in order to get the short pulses within the tuning range from 960 to 1050 nm. The pulse characteristics are shown in figure 1.

OPO-2
OPO2 is based on a periodically pooled lithium niobate (PPLN) nonlinear crystal. This OPO serves the wavelengths ranging from 1050 to 1100 nm.
Detailed OPOs characteristics and performance were reported in [1,2]

Super continuum generation:
Supercontinuum generation was first observed in 1970 by Alfano and Shapiro [3].
Supercontinuum generation is the production of ultra-broadband spectrum pumped by a high power laser source-femtosecond pumped pulse, in our case. A photonic crystal that has 1.2 µm core diameter and zero group dispersion at 750 nm was used to produce broadband (450-1150nm) continuum. A characteristic spectrum is shown in Figure 2.

CARS microspectroscopy
CARS as spectroscopic technique was first reported in 1965 [4], showing that two coherent light beams of frequency w1 and w2 can be used to drive a Raman vibrational mode at frequency ω R = ω 1 -ω 2 . When the two beams are overlapped in space and time, it was observed ω+ ω R signal, which is the CARS signal.

Experimental set up
The experimental set up is schematically shown in Figure 3. wavelengths. The PMT current output is digitized by a high-speed data acquisition card (DAQ, NI-6361). Using this experimental arrangement, we can routinely detect CARS signals versus probe pulse delay times within five decades.

SHG microspectroscopy
As illustrated in fig 6, SHG is the nonlinear process where the energy of a short optical pulse of frequency ω propagating through a nonlinear medium is converted to a wave of 2ω, at twice the original frequency. SHG is also known as frequency doubling, which is special case of sum frequency generation (SFG).

Experimental set up
We employ high-repetition rate femtosecond Ti: The SHG signal is also sent to photomultiplier tube (PMT) to enable sample imaging.
The SHG signal beam is effectively de-scanned for the signal detection geometry shown here which helps to focus into the monochromator and use narrow slit in order to achieve higher spectral resolutions. Data acquisition have been performed using data acquisition card, in the case of sample imaging, and the monochromator's USB interface, in the case of spectral measurements, with both controlled by LabView interface software.

Making 0 (zero) time delay for CARS experiment
One most important condition for generation of a CARS signal is the spatial and temporal overlap of the three color beams. To ensure the spatial overlap two irises were placed after the dichroic mirror, and then the beams were guided in such way that the beams pass through the center of iris. On the other hand, in order to set up the correct timing between the beams, the optical path lengths of all beams were first measured by the measuring tape. In order to take into account the retardation as the beams pass through any optic, an additional lengths equivalent to the thickness of any 59 optic along each beam path were added to the length that was measured by the measuring tape. After measuring the optical path lengths, translational stages for the delay lines were adjusted to make the path lengths equal.
To find the zero-delay point , a nonlinear optical crystal , Beta-Barium Borate (BBO), was used to observe the sum frequency generation (SFG) signal generated when the two beams are focused at the crystal that are spatially and temporally overlapped. During the observation, all light in the lab room was off.

Supercontinuum generation setup
The broad band continuum pulses needed for the SHG set-up are based on the generation of the supercontinuum from a photonic crystal fiber (PCF).
Using the beam splitter and the steering mirror, the Tis:S beam is aligned at the optical

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The stage (466A XYZ fixture, Newport Corp.) is installed in order to focus into the fiber by a 40x microscopic objective lens, maintaining the focusing length of the objective and fiber as well. In order to make sure the right focusing, we reflect the beam from the facet back to nearest starring mirror.
At the very first, however, the focusing objective lens was removed and a white paper was placed about five inches away and the beam position was marked. The focusing objective lens was then replaced and the XYZ stage was adjusted to center the beam to the target. The transmitted beam was observed using an IR viewer on the white paper.
The vertical and horizontal axes of the stage were alternately fine-tuned until the central spot was minimized and completely diminished and evenly diffused light was observed. The X-axis of the stage along the optical axis of the fiber was adjusted to focus the beam into the fiber core. The steering mirrors were also adjusted to get the maximum output power.
Once the continuum pulse was observed, the input power was increased to 100 mW.
Then output power was optimized by fine tuning of the stage and steering mirror as well. The collimating objective lens (20X, Newport Corp.) was then installed. The lens was then adjusted to collimate and adjust the spot size of the output beam.
It is important to note that the properties of the generated continuum pulse are defined by the amount of the coupled power rather than the coupling frequency. The coupled power is the measured power after the collimating objective and power before the        In order to derive expression for the second harmonic intensity we start off with the Maxwell's equation. We neglected the free charges and free currents in the equations: Where ⃗ ⃗ is displacement field vector, ⃗ is the electric field, ⃗ is the magnetic field, and c is the speed of light. The following relationship between D, E, and P is given by the following equation- Where P is the incident field induced polarization. Now solving the two curl equations (2), and (4), and using equation (5), we obtain the following: We can also represent the total polarization (P) as the combination of linear and nonlinear parts (P= P+P NL ). Using the above two relationships, we can get the following wave equation: Using the relationship D=εΕ, we again obtain length L. For the case of undepleted fundamental E 1 is constant over z. Then the final result for the second harmonic field is the following: The intensity of the second harmonic wave is given by the magnitude of the timeaveraged Poynting vector, Using the solution (11) for the field in equation (12) we can obtain Now expressing the incident field in terms of the intensity, we have the second harmonic intensity as

SHG in bulk media under tight focusing condition
Note that the solution (14) is for the power density. I 2 and I 1 are expressed in power densities. Power density is proportional to the square of the electric field, or alternatively the power divided by the beam size. Now the question is if we try to do the experiment, instead of having power density, how much power we have in the second harmonic power in Watts, or energy in Joule.
So the power density does not provide the real solution. If we focus the beam, and we want to know the power in the output power in Watt, we take into account the focusing factors.

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The second harmonic power in Watt for this system is given by the following expression: Where, is the effective length of focus and is defined by Now we obtain Where we have introduced the expression: Where, is the numerical aperture of the objective, 0 is the spot size of the beam, and λ is the fundamental wavelength.
Note that equation (17) is derived considering the fact there are no interface. In other words, the crystal is immersed in the medium in such a way that the refractive indices match.
However, in our case, the beam is incident from air to crystal. In order to that feature into account, we consider the following transmission factors: Where, 1 is the refractive index of the fundamental beam in the crystal, and 2 is the refractive index of the second harmonic in the crystal.
Using the factors of equation (18), the equation (17) Neglecting the dispersion in the crystal, i.e., the refractive index at fundamental is close to that of at the second harmonic; the equation (19) This equation is very important for our study because it will be used to obtain the absolute value of the second order nonlinear susceptibility.

SHG in two-dimensional crystal
Since we have very thin material, we need to consider the SHG in thin layer. The nonlinear two-dimensional crystal is placed between the linear bulk media. The crystal is treated as a zero-thickness interface, and the second harmonic signal generate from the boundary.
After writing the right boundary conditions and solving, we obtain the second harmonic filed for s and p polarized light as The second harmonic is written as The second harmonic power is defined by 2 2 = ∫ 2 ( , ) 74 The total reflected second harmonic power in terms of the input fundamental power can be written as Where, ξ is defined as = |(1 + ) 2 (1 + 2 )| 2 Where, is reflection coefficient at fundamental and 2 is the reflection coefficient at second harmonic.
The equation (25) will also be used for absolute calibration of second order nonlinearity.
To estimate the second order nonlinearity, we normalize the two-dimensional second harmonic data to the one obtained from the reference crystal.
We obtain a ratio from equations (20) and (25) which will essentially provide the dispersion of the absolute value of second order nonlinear susceptibility: Now we can write the expression for the absolute value of second order nonlinearity in terms of the known reference crystal's nonlinearity, refractive index, numerical aperture of the objective lens, and the measure ratio: This equation was used to calibrate the second order nonlinear susceptibility in manuscript-2.

CARS theory
At the beginning, it is important to note that CARS signal is generated due to the third order nonlinear susceptibility while the SHG is due to the second order nonlinear susceptibility which is discussed above.
CARS is used to investigate Raman active resonances and modes. In this process, in general, one deal with three different incident waves at frequencies 1 , 2 , 3 . During the CARS process, a new wave at 4 = 3 + ( 2 − 1 ) is generated. This new generated wave is called anti-Stokes wave at optical frequency = 4 . However, when the opposite happens, i.e., when 4 = 3 − ( 2 − 1 ) , then one deals with Coherent Stokes Raman Scattering (CSRS) . CSRS is almost like CARS except for the fact that Stokes wave is detected which is at a lower optical frequency = 4 .
CARS can be described as two photon excitation process followed by a two-photon de-excitation process. Combined together the two constitute a resonantly enhanced four-wave mixing process. In an experiment, a degenerate CARS process is realized at least two laser beams with strong intensity. The first beam at the optical frequency 2 is often called pump and the second with frequency is 1 called Stokes beam. Both beams are focused onto the sample simultaneously. We not that 2 > 1 . The incident beam excite the corresponding Raman active transition. The same beam at will also serve, for this particular case, as a third or probe beam with frequency 3 = 2 . The beam is scattered off the excited vibrations to form a wave with frequency 4 = 2 − 1 + 1 = 2 1 − 2 which is anti-Stokes that is = 2 − 1 shifted from 2 . The new wave is resonantly enhanced since frequency difference 2 − 2 is matched to as was just mentioned. 76 = 2 ( ) − 2 ( ) 4 ( − ) = 2 ( ) + 3 ( ) − 1 ( ) Thus the anti-Stokes wave in the CARS process will follow at frequency If the 2 frequency is tunable a dispersion of the corresponding (3) can be measured by detecting anti-Stokes wave's intensity.
The third-order nonlinear polarization is used as a driving force in Maxwell's equations for the anti-Stokes field. In general, a set of coupled wave equations involving pump, Stokes, and anti-Stokes waves should be solved in order to obtain the coherent anti-Stokes field amplitude and the corresponding intensity.
The polarization drives the anti-Stokes field that builds up along the beam's interaction path and can be calculated using the following wave equation that is derived from the Maxwell's equations: Where is the electric field amplitude at anti-Stokes frequency of 2 − 1 + 3 .
As was mentioned above, the four waves , 1 , 2 , 3 (embedded into nonlinear polarization term (3) ), should interact in an efficient way so that their phase match along the path. In this case, the interaction yields in strong CARS signal. In order to demonstrate this we will consider a case of degenerate CARS ( i.e., = 2 − 1 + 2 = 2 2 − 1 ) with the three waves propagating along the same z-direction, i.e., a collinear interaction. A solution to the equation () will be sought in the following format: Also, we will assume that the CARS process efficiency is rather low so that (a) we can apply slowly varying (along z) amplitude approximation approach, and (b) assume that fields 1 ( ) and 2 ( ) are not attenuated or depleted in the interaction process (i.e., 1 ( ) = 1 − ( 1 − 1 ) , 2 ( ) = 2 − ( 2 − 2 ) ).
Taking into account equation (29) and the two conditions, equation (28) transforms into a simpler, first order differential equation: The solution for the anti-Stokes field is straightforward for the interaction length L. For the amplitude ( ) at the medium's output we obtain the following: Here we used the relationship for intensities and fields 1 2 = 1 2 1 0