DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

[0053] The present invention provides a method and a CARS system such as spectrometer or microscope carrying out this method based on inducing the entire CARS process by producing a single (unitary) ultrashort optical excitation pulse that supplies all three photons (the pump photon, Stokes photon and probe photon) required for the CARS process.

[0054] The principles and operation of the CARS spectrometry and microscopy according to the present invention may be better understood with reference to the drawings and the accompanying description, it being understood that these drawings and examples in the description are given for illustrative purposes only and are not meant to be limiting. The same reference numerals will be utilized for identifying those components which are common in the CARS spectrometer and microscope systems shown in the drawings throughout the present description of the invention.

[0055] It should be noted that the inducing of the entire CARS process by a single excitation pulse is feasible when the pulse duration is shorter than the vibrational period of the molecules of the medium under investigation. For example, a length of this excitation pulse can be in a femtosecond range. In this case, the CARS signal is produced by an intra-pulse four-wave mixing process. Each of the different components of the CARS signal is the resultant of the interference of all the quantum paths that contribute to the nonlinear polarization process.

[0056] It should also be noted that inducing the CARS process with a single excitation pulse is associated with several inherent difficulties. First of all, a technical difficulty arises from the partial spectral overlap between the spectral bands of the excitation pulse and the CARS signal, which can be orders of magnitude weaker than the pulse signal.

[0057] This difficulty, according to one embodiment of the invention, can be overcame by means of a partial blocking of the excitation pulse spectrum in the range of the expected CARS signal, and an appropriate spectral filtering of the measured CARS signal.

[0058] Moreover, if a medium is excited by a single transform limited pulse (i.e., a pulse in which all frequency components have the same phase), then the CARS process can encounter the following difficulties:

[0059] One of the difficulties arises from the fact that all vibrational levels having the energy within the bandwidth of the transform limited pulse are excited. As a result, the spectral resolution of the CARS signal is limited by the excitation pulse bandwidth.

[0060] Another known difficulty, which is common to all CARS techniques utilizing femtosecond pulses and is therefore relevant also to the single-pulse CARS spectrometer and method of the present invention, results from a strong nonresonant background signal. As the bandwidth of the excitation pulse is increased (in other words, as the shorter excitation pulse having higher peak intensity is used), the magnitude of the background signal increases much more rapidly than the resonant CARS signal. The nonresonant background signal thus can be detrimental to the ability to spectrally resolve resonant transitions.

[0061] The present invention provides for eliminating the above difficulties by applying a quantum coherent control technique to the transform limited optical pulse. According to the invention, the quantum coherent control is achieved by means of a predetermined shaping of the transform limited pulse to produce a unitary optical excitation pulse that enables identification of a CARS signal induced by this pulse from any other optical signals.

[0062] Referring to FIG. 2 A, there is schematically illustrated a CARS measurement system (spectrometer) 20 according to one embodiment of the present invention associated with a sample holder 29 containing a medium under investigation. The CARS spectrometer system 20 includes a single laser 21 adapted for producing optical transform-limited driving pulses 210 wherein each such pulse carries a pump photon, a Stokes photon and a probe photon which are necessary for exciting the medium and inducing the CARS process therein, a programmable pulse shaper 22 operable for shaping the input transform limited driving pulse to produce a unitary optical excitation pulse carrying the pump, Stokes and probe photons, a detector unit 26 for collecting a CARS signal coming from the medium and generating data indicative thereof, and a light directing optics for directing the input pulses to the medium and directing the CARS signal to the detector.

[0063] The laser 21 can be any laser capable to generate transform limited pulses in a femtosecond (fs) time range. For example, the transform limited pulses can be in a range of about 5 fs to 100 fs and, preferably, between 10 fs and 20 fs). For example, a Ti:Sapphire laser oscillator capable of generating 20 fs full-width at half maximum (FWHM) transform limited pulses at 80 MHz, centered at 815 nm (corresponding to a bandwidth of about 75 nm or an energy span of 1100 cm ⁻¹ ) can be employed for the purpose of the present invention. The programmable pulse shaper 22 is configured for shaping the input transform limited driving pulses by assigning a desired phase to each wavelength component of the transform limited optical pulse, preferably only in a predetermined wavelength range, i.e., outside that where the CARS signal is most likely to occur. The use of such a pulse shaper enables for coherently controlling the CARS process.

[0064] A sample of the input transform limited pulse 210 generated by the laser 21 is directed to the pulse shaper assembly 22 by a mirror 23 a , and a shaped pulse 220 produced by the shaper assembly 22 is directed to the holder 29 by a further mirror 23 b . Obviously, each of these single-mirror elements of the light directing optics may be replaced by one or more beam splitter and/or a set of mirrors, or any other known light deflecting means.

[0065] In the present example of FIG. 2 A, the programmable pulse shaper 22 is a 4-f shaper that includes an input dispersive assembly 221 , an output dispersive assembly 222 ; an input focusing element 223 , an output focusing element 224 ; and a programmable Spatial Light Modulator (SLM) 226 located at the Fourier plane defined by the focusing elements 223 and 224 . In the present example, also provided in the pulse shaper 22 is a blocking element 225 .

[0066] For example, the dispersive assemblies 221 , 222 can be thin ruled reflective gratings with 1200 lines/mm and the focusing elements 223 , 224 can be achromat lenses (e.g., with a focal length of 100 mm). Though the above embodiment uses ruled reflective gratings at the input and output of the pulse shaper to spatially disperse and recombine the various frequency components of the pulses, it should be pointed out that any other suitable dispersive elements can be used, e.g., transmission gratings, prisms, or combinations thereof. Furthermore, the function of the focusing elements 223 , 224 in defining the system Fourier plane (focal plane) at which the SLM 226 is located, can be fulfilled by any other element having positive focusing power, e.g., a concave mirror.

[0067] The blocking element 225 is, for example, a plate arranged for blocking at the Fourier plane wavelengths shorter than a predetermined wavelength (e.g., 780 nm) in is the range of a CARS signal, as they can spectrally overlap an output CARS signal 211 . In the present example of FIG. 2 A, the blocking element 225 is arranged between the SLM 226 and the output focusing element 224 . However, as can be appreciated by a person skilled in the art, the blocking element 225 can be arranged either upstream or downstream of the SLM 226 . Furthermore, the function of blocking element 225 can be fulfilled by any sharp-edge long-pass filter, e.g., a dielectric filter.

[0068] The programmable SLM 226 may be a liquid crystal based SLM of the type described by A. M. Weiner in the article published in Rev. Sci. Inst., 2000, V. 71, P. 1929. This SLM includes an SLM pixel array having 128 pixels at its Fourier plane. The spectral resolution, determined by the spot size at the Fourier plane, can be better than 0.5 nm (equivalent to about 8 cm ⁻¹ ).

[0069] The operation of the 4-f pulse shaper 22 is as follows. The input dispersive element 221 operates to spatially separate the frequency components of the input transform limited pulse. The input focusing element 223 focuses each of these frequency components to its specific position at the focal plane, where the SLM 226 is located. The blocking element 225 blocks at the Fourier plane wavelengths shorter than the predetermined wavelength. The SLM 226 is operative as an updateable filter for spectral manipulation of the incoming pulses, and allows the independent control of the phase and amplitude of each of the light components passing through 128 pixels, thereby modifying the pulse shape and temporal profile according to the desired pulse properties. For example, the width of each pixel is 97 μm, the inter-pixel gap is 3 μm, while the spot size at the focal plane is about 80 μm. The output focusing element 224 and output dispersive element 222 then recombine each of the separate frequency components to produce a shaped pulse 220 .

[0070] Thus, the programmable pulse shaper 22 of FIG. 2A is operable by a suitable control unit 27 for separating between different frequency components of the input pulse, blocking the predetermined frequencies (higher frequencies, which can overlap the CARS signal); and assigning the desired phase to each frequency component of the remaining (non-blocked) portion of the input pulse by using any desired spectral phase function.

[0071] The CARS spectrometer system 20 may utilize an open loop control, in which the applied spectral phase function is derived theoretically for each experiment, or may utilize a closed feedback loop for determining the applied spectral phase function.

[0072] The shaped pulse 220 produced by the pulse shaper 22 carries a pump photon, a Stokes photon and a probe photon (which are necessary for exciting the medium and inducing the CARS process therein) and is therefore also referred to as “the unitary optical excitation pulse”.

[0073] The unitary optical excitation pulse 220 reflected from the mirror 23 b is focused by a focusing assembly 24 a onto the medium under investigation for exciting thereof and inducing a CARS process. In the present example, the focusing assembly 24 a includes an objective lens arrangement having an NA=0.2 numerical aperture.

[0074] The light directing optics further includes a lens assembly 24 b accommodated for collection of the output CARS signal of the medium. This lens assembly 24 b , preferably, has numerical aperture similar or larger than that of the lens 24 a . It should be noted that the focusing assembly 24 a can also serve as a collecting optics in a back-scattered mode.

[0075] Further provided in the CARS spectrometer system 20 is a filtering assembly 25 operable for filtering the CARS signal obtained from the medium. In the present example, the filtering assembly 25 includes a spectral filter 251 (e.g., a bandpass or short-pass filter), and preferably includes a computer-controlled monochromator 252 or a spectrograph (not shown). An example of the filter 251 includes, but is not limited to, a 40 nm FWHM bandpass filter centered at 750 nm, while an example of the computer-controlled monochromator 252 includes, but is not limited to, a computer-controlled monochromator with a spectral resolution of 0.5 nm (equivalent to about 8 cm ⁻¹ at 750 nm).

[0076] The filtered output of the filtering assembly 25 is collected by the detector unit 26 , which includes a detector 261 of the kind receiving a light signal and generating an electrical output indicative thereof, and may also include a lock-in amplifier 262 operable by the control unit (computer) 27 .

[0077] It should be appreciated that the construction and operation of the filter 251 , monochromator 252 , detector 261 and a lock-in amplifier 262 as well as the elements of the light directing optics, are known per se, and therefore need not be specifically described.

[0078] It should be noted that the measurable Raman energy range of the system 20 can, for example, be about 300 cm ⁻¹ -900 cm ⁻¹ , that is typical of carbon-halogen bond stretching. The lower limit of the measurable energy range is determined by the need to filter out the excitation pulse, while the upper limit is dictated by the excitation pulse bandwidth. Since the technique does not require an electronic resonance with the driving input field, it can be implemented with any broadband optic source 21 . The measurable Raman energy range of the system 20 can be extended to the fingerprint region (900 cm ⁻¹ -1500 cm ⁻¹ ) by using pulses of duration 10 fs-20 fs, available in the state-of-the-art commercially available lasers.

[0079] Referring to FIG. 2B, a schematic view of a CARS spectrometer system 200 according to another embodiment of the present invention is schematically illustrated. The CARS spectrometer system 200 , distinguishes from the CARS system 20 shown in FIG. 2A in that its shaper assembly additionally to the phase modulator or as an alternative thereto comprises a polarization control assembly including a frequency-selective filter, such as grating 221 , and a 90 degree polarization rotator accommodated in the optical path of the frequency components emerging from the filter and operable for applying a 90 degree polarization rotation to the predetermined frequency range of the input transform limited laser pulse, and comprises a crossed polarizer unit P _y accommodated in the optical path of a signal propagating from the medium to the detector for extraction of the cross-polarized CARS signal.

[0080] In the present example of FIG. 2 B, the polarization rotator is constituted by an SLM arrangement 226 , but it should be understood that any other suitable means can be used (e.g., a half-wavelength assembly). Additionally, in the example of FIG. 2 B, the polarization control assembly also includes a polarizer P _x accommodated in the optical path of the transform limited laser pulse propagating towards the shaper assembly. It should however be understood that the provision of this input polarizer P _x is optional, and can be eliminated by using a laser source producing linearly polarized light. In the example of FIG. 2 B, the SLM unit can be operable for performing both the phase shaping and polarization rotation of the frequency components of the transform limited pulse. Generally, the phase assembly may comprise only a polarization rotator of any known suitable type. The SLM assembly suitable to be used in the system of the present invention may, for example, be of the type described by T. Brixner et al. in the articles published in Opt. Lett., 2001, V. 26, P. 557 and Appl. Phys., 2002, V. B74, P. S133. Such a programmable liquid crystal SLM 226 includes two SLM liquid crystal pixel arrays (dual cell SLM) whose preferential axes are at right angles to each other and are rotated by ±45° relative to the polarization of the input laser pulse (denoted as the x direction). Any difference in the applied retardance between the two arrays results in modification of the input pulse polarization. In this technique, the SLM can act as both a controlled spectral phase mask and as a controlled waveplate.

[0081] Thus, in this specific example, the programmable pulse shaper, in operates for both assigning the desired phase to each frequency component of the driving laser pulse, and a polarization control of the pulse. In particular, the polarization control can be used to break the ultrashort input pulse 210 into a broadband pump and a narrow-band probe with orthogonal polarizations.

[0082] The nonlinear polarization producing the CARS signal driven by an electric field of the excitation pulse whose spectrum is E(ω) can be approximated for nonresonant transitions, by using time dependent perturbation theory, as (for more details see, for example, Oron et al., Phys. Rev. Lett., 2002, V. 88, P. 63004): 1 $\begin{array}{cc}{P}_{\mathrm{nr}}^{\left(3\right)}\propto {\int }_0^{\infty }\Omega E\left(\omega -\Omega \right)A\left(\Omega \right),\mathrm{where}A\left(\Omega \right)={\int }_0^{\infty }{\omega }^{\prime }E^{*}\left({\omega }^{\prime }-\Omega \right)E\left({\omega }^{\prime }\right)& \left(1\right)\end{array}$

[0083] is the probability amplitude to populate a vibrational level with energy Ω (henceforth, the population amplitude), while E(ω−Ω) represents the probe field.

[0084] Similarly, the nonlinear polarization for a singly resonant Raman transition through an intermediate level |i at an energy of Ω _R and a bandwidth Γcan be approximated by 2 $\begin{array}{cc}{P}_r^{\left(3\right)}\propto {\int }_0^{\infty }\Omega \frac{E\left(\omega -\Omega \right)}{\left({\Omega }_R-\Omega \right)+i\Gamma }A\left(\Omega \right).& \left(2\right)\end{array}$

[0085] The CARS process can be controlled by controlling the population amplitude A(Ω). The control of A(Ω) is accomplished by controlling the spectral phase of the single broadband excitation pulse. Such a phase-only pulse shaping of the pulse merely means multiplication of the electric field E(ω) (that includes pump, Stockes and probe photons) by a phase function exp(iΦ(ω)).

[0086] The population of a vibrational level at energy Ω _R is proportional to

| A (Ω)| ² =|∫dωE (ω) E *(ω−Ω _R )| ² , (3)

[0087] where E=|E(ω)|exp(iΦ(ω)) is the complex spectral amplitudes of the applied field. Each level is thus excited by all frequency pairs separated by Ω _R . The interference between the multiple paths leading to the population of the level Ω _R is determined by the relative phase of each contribution Φ(ω)−Φ(ω−Ω _R ). Thus, constructive interference is achieved when Φ(ω)=Φ(ω−Ω _R ) for all frequency components of the excitation pulse. Therefore, if the excitation pulse is a transform-limited pulse (all frequency components having the same phase), then the constructive interference holds for all values of Ω _R , thus spectral resolution is lost.

[0088] According to one example of the phase control, that has been first described by the inventors in an article entitled “ Single - pulse coherently - controlled nonlinear Raman spectroscopy and microscopy ” published in Nature, V. 418, PP. 512-514 (August 2002), the spectral phase of the excitation pulse is modulated periodically with a period Ω ₀ . In such a case, the constructive interference can be induced for all energy levels only for Ω _R =NΩ _R (where N is an integer). FIGS. 3 A- 3 C illustrate an effect of a modulated spectral phase function on the temporal shape of the pulse and on the population amplitude, according to this specific example of the phase control.

[0089] FIG. 3A shows an example of an input pulse spectral intensity 31 , a spectral phase 32 of the transform limited pulse, and a modulated spectral phase 33 of the shaped pulse (unitary excitation pulse). Also shown is a typical spectral region where the CARS signal can be measured. Thus, in order to avoid the spectral overlap between the input pulse and a CARS signal, the power spectrum of the input pulse is blocked at 730 nm. (Note that the spectral intensity of the CARS signal is identified by a reference numeral 34 ).

[0090] FIG. 3B shows in time domain a temporal intensity of transform limited pulse 35 corresponding to the uniform phase ( 32 in FIG. 3A ), and a modulated phase shaped pulse 36 corresponding to the modulated phase ( 33 in FIG. 3A ). As can be understood from FIG. 3B, a periodic spectral phase is equivalent to splitting the pulse in time domain to several equally spaced pulses, each delayed by τ ₀ =2π/Ω ₀ . This pulse train is capable of resonantly exciting only vibrations with a period T=τ ₀ /N.

[0091] FIG. 3C shows a calculated population amplitude A(Ω) for the transform limited pulse 37 and for the pulse having the modulated phase 38 . As can be seen in FIG. 3 C, for the case of the transform limited pulse, the population amplitude decays monotonically versus the vibration energy. On the other hand, for the case of a modulated phase function, an oscillation appears where the peak of each oscillation reaches the transform limited result.

[0092] The resonant and nonresonant processes described above have different spectral responses, which result from the different weights that multiply the population amplitude in Eq. (2) and Eq. (3), as determined by the resonance levels.

[0093] According to Eq. (2), the resonant CARS process can be expressed as 3 $\begin{array}{cc}{P}_r^{\left(3\right)}\approx C\left[\mathrm{\pi }E\left(\omega -{\Omega }_R\right)A\left({\Omega }_R\right)+\zeta {\int }_0^{\infty }\Omega \frac{\Omega -{\Omega }_R}{{\left(\Omega -{\Omega }_R\right)}^2-{\Gamma }_R^2}E\left(\omega -\Omega \right)A\left(\Omega \right)\right]& \left(4\right)\end{array}$

[0094] where ζ is the principal value of Cauchy. The first term in Eq. (4) corresponds to the “on-resonant” contribution, while the second term corresponds to integration over the contribution of the “off-resonant” spectral components. The resonant signal thus has a narrow response around Ω=Ω _R .

[0095] The weight function of the integrand of the second term inverts its sign around the resonance, therefore the total contribution of the integral depends on the symmetry of E(ω−Ω)A(Ω) around Ω=Ω _R . In the transform limited case, both A(Ω) and E(ω−Ω) are nearly symmetric for all values of ω. Therefore, the off-resonant term is negligible. The polarization spectrum can be approximated in this case by

P _r ⁽³⁾ ≈iπCE (ω−ω _R ) A (Ω _R ) (5)

[0096] which is a replica of the pulse spectrum shifted by ω _R . Spectral phase manipulation will change the symmetry of E(ω−Ω)A(Ω) for different values Ω, and will therefore induce variations of the polarization spectrum.

[0097] However, when the modulation frequency significantly exceeds 2π/Δω (here, Δω is the pulse spectral bandwidth), the total signal intensity averages out and is proportional to |A(Ω _R )| ² .

[0098] By the same token, the measured nonresonant intensity averages out to become proportional to 4 ${\int \frac{\Omega }{\Omega }A\left(\Omega \right)}^2.$

[0099] The total measured signal is the interference of he signals generated by the two different processes. In the common case where the nonresonant background is considerably larger than the resonant signal, the resonant signal is measured by a “heterodyne detection” with it, to yield

| P ⁽³⁾ (ω)| ² =|P _r ⁽³⁾ ( 107 )+ P _nr ⁽³⁾ (ω)| ² ≈|P _r ⁽³⁾ (ω)| ² +2 ReP _r ⁽³⁾ (ω) P _nr ⁽³⁾ (ω) ^* . (6)

[0100] By exploiting the different spectral response of the resonant and nonresonant components, it is possible to significantly reduce the nonresonant background while maintaining the resonant signal. Following the above derivation, it can be clear to a person versed in the art that properly choosing the periodicity of the phase function, the population and thus the resonant CARS signal is reconstructed to nearly the value achieved by a transform limited pulse.

[0101] Thus, it was shown above that the coherent control of the CARS process via manipulation of the vibrational level population amplitude A(Ω) can be accomplished by applying periodic spectral phase function (e.g., sinusoidal function) producing periodical modulation of the spectral phase of the excitation pulse.

[0102] Referring to FIGS. 4 A- 4 C, measurements of the Raman spectrum are exemplified. The Raman spectrum has been obtained by monitoring the total CARS signal, while varying the phase function periodicity. According to this examples, a simple periodic spectral phase function Φ(ω)==1.25cos (Cω) (wherein C is a constant) has been applied to the input transform limited pulse for its shaping. Presented in FIGS. 4 A- 4 C are the intensities of the CARS signal versus the number of periods of the sinusoidal phase across the spatial light modulator (SLM). The insets show the Raman spectrum, derived by Fourier transformation of the corresponding measured intensity signals.

[0103] More specifically, FIG. 4A illustrates single-pulse CARS spectroscopy of methanol molecules in the liquid phase. As can be seen for methanol, which has no Raman resonance levels at the measured frequency range, only a monotonic decrease of the nonresonant signal is observed as the number of oscillation periods is increased.

[0104] FIG. 4B illustrates single-pulse CARS spectroscopy of CH ₂ Br ₂ molecules in he liquid phase. As can be seen, for CH ₂ Br ₂ , which has a single resonance at Ω _R =577 cm ⁻¹ , the Raman signal oscillates periodically, whenever the modulation period is an integer fraction of Ω _R . The Fourier transform operation retrieves the single Raman resonant level with a resolution that is inversely proportional to the number of modulation periods.

[0105] FIG. 4C illustrates single-pulse CARS spectroscopy of (CH ₂ Cl) ₂ molecules in the liquid phase. As can be seen, for the material with two resonant levels, such as (CH ₂ Cl) ₂ , two resonant peaks (at 652 cm ⁻¹ and 750 cm ⁻¹ ) are observed in the Raman spectrum.

[0106] The spectral resolution of the Fourier transform operation is better than the pulse bandwidth by a factor of 40 (i.e., about 30 cm ⁻¹ ). It is limited by the maximal number of phase modulation periods on the spatial light modulator (SLM), technically determined by the number of pixels on the SLM.

[0107] Thus, spectral resolution can be optimized by employing a simple sinusoidal phase function. Breaking the single pulse into a longer train, than used in the above example, containing a larger number of pulses can further reduce the nonresonant background, which depends directly on the pulse peak intensity. This is achieved by adding higher harmonics orders to the applied phase functions. This phase function can be expressed as a summation of the different harmonics orders as 5 $\Phi \left(\omega \right)=\sum _nA_n\cos \left(C_n\omega \right),$

[0108] where A _n are the different harmonic order coefficients.

[0109] Referring to FIGS. 5 A- 5 B, a demonstration of the nonresonant background suppression by using periodic spectral functions with additional harmonics is illustrated for methanol (nonresonant component only) and CH ₃ I (a single resonance at 523 cm ⁻¹ ), respectively. The CARS signal of relative intensity is shown versus the number of phase oscillation periods across the spatial light modulator for both a sinusoidal phase function Φ(ω)=1.25cos(Cω) (curve 51 ) and a phase function Φ(ω)=1.4cos(Cω)−1.4cos(2Cω) which contains an additional harmonic component (curve 52 ). The CARS signal is plotted relative to that obtained by a transform-limited pulse (0 phase function oscillations). It should be noted that to achieve adequate suppression of the nonresonant background at least several oscillation periods of the phase function across the pulse spectrum are necessary.

[0110] FIG. 5A shows how the use of a phase function containing only one additional harmonic allows for attenuating the nonresonant background by nearly two orders of magnitude.

[0111] FIG. 5B shows that the use of a phase function containing two components attenuates significantly the nonresonant background, while the resonant component is almost completely restored. The achieved contrast between the resonant signal and the nonresonant background is thus greatly improved.

[0112] According to another example of the phase control, the spectral phase of the excitation pulse can be controlled by applying to the excitation pulse a narrow-band phase gate near its short wavelength (high-energy) end. In other words, a narrow-band feature is applied to the pulse for inducing sharp changes in the phase of the factor E(ω−Ω) in Eqs. (1) and (2). Preferably, but not necessarily, the phase of the phase gate spectral function can be shifted by π at ω−Ω. Such spectral phase function hereinafter will be referred to as a π phase gate. For example, a bandwidth of the π phase gate can be in the range of about 0.5 nm to 3 nm (i.e., 5-30 cm ⁻¹ ). Preferably, the π phase gate is spectrally located in the vicinity of a short wavelength end of the excitation pulse.

[0113] In this scheme, a narrow spectral band in the excitation pulse is phase shifted, serving as an effective probe, and the Raman spectrum is extracted from the interference pattern of the resonant signal with the nonresonant background.

[0114] Referring to FIGS. 6 A- 6 C, there is illustrated an effect of a π phase gate on the temporal shape of the pulse and on the population amplitude, according to this specific example of the phase control.

[0115] FIG. 6A shows an example of the excitation pulse spectral intensity 61 , a spectral phase 62 of the transform limited (unshaped) pulse, and a π phase-gate 63 of the shaped pulse. In this example, the π phase-gate 63 has the bandwidth of about 1.5 nm centered at 790 nm. Also shown is a typical spectral region where the CARS signal can be measured. Thus, in order to avoid the spectral overlap between the input pulse and a CARS signal the power spectrum of the input pulse is blocked at about 780 mn. Note that the spectral intensity of the CARS signal is identified by a reference numeral 64 .

[0116] FIG. 6B shows in time domain a temporal intensity (temporal envelope) of a transform limited pulse 65 and a temporal intensity of a π phase-gate shaped pulse 66 . As can be seen, the narrow π phase gate hardly effect the form of the pulse, merely reducing the peak intensity by about 15%.

[0117] FIG. 6C shows a calculated population amplitude A(Ω) for the transform limited pulse 67 and for the pulse having the modulated phase 68 . As can be seen in FIG. 6 C, for the case of the transform limited pulse, the population amplitude decays monotonically versus the vibration energy. The changes due to the phase gate slightly modify the population amplitude A(Ω). This modification depends on the width of the phase gate. Thus, the population amplitude A(Ω) is hardly modified for a narrow gate, since the energy content in a narrow spectral band part is negligible compared with the entire pulse energy.

[0118] The resonant signal from a level Ω _R at any given frequency ω is centered at ω−Ω _R due to a rather narrow band probe. In contrast, the nonresonant background signal is a coherent sum contributed by a large portion of the pulse bandwidth. Thus, phase changes over a narrow spectral band, while dramatically affecting the phase of the resonant signal, hardly modify the phase of the nonresonant signal. The relative phase between the nonresonant background signal and the resonant signal should therefore vary rapidly, inducing either constructive or destructive interference at the phase gate edges. Measuring the total CARS spectrum, the interference pattern between the resonant signal and the nonresonant background can be interpreted to reveal the vibrational energy level diagram.

[0119] The effect of the phase control by using an excitation phase with a narrow-band phase gate is demonstrated in the numerical simulation results shown in FIGS. 7 A- 7 D.

[0120] FIG. 7A shows a calculated CARS electric field as a function of frequency (spectrum) of both the resonant contribution 71 and the nonresonant contribution 72 along with the relative phase 73 between them for a transform limited pulse illuminating of iodomethane (resonant at 523 cm ⁻¹ ). FIG. 7B shows the calculated resulting CARS spectrum 74 for the illuminating of iodomethane with a transform limited pulse.

[0121] As can be seen, the nonresonant background spectrum 72 monotonically decreases towards higher energies (short wavelengths), while the resonant signal 71 resembles the excitation pulse spectrum, shifted by the Raman level energy. The relative phase 73 between the two is nearly constant at about π/2, rising to about π below 749 nm.

[0122] FIG. 7C shows a calculated CARS spectrum of both the resonant contribution 75 and the nonresonant contribution 76 along with the relative phase 77 between them for the illuminating of iodomethane by a π phase gate shaped pulse. FIG. 7D shows the calculated resulting CARS spectrum 78 for the transform limited pulse illuminating of iodomethane. Three effects can be seen in FIG. 7C . First, there is some reduction of the nonresonant background component. Second, the relative phase between the resonant component and the nonresonant background component varies between 0 (constructive interference) at the high-energy (short wavelength) side of the gate, and π (destructive interference) at the low energy (long wavelength) side. Third, two new peaks 79 appear in the resonant spectrum 75 , at both ends of the phase gate. The peaks 79 are due to a transient enhancement effect demonstrated by Oron et al. previously in conventional multi-beam CARS and described in Phys. Rev. Lett., 2002, V. 88, P. 63004.

[0123] As can be seen in FIG. 7 D, the net result is a sharp peak 710 , followed by a deep dip 720 in the total CARS signal 78 . It should be noted that this peak-dip feature determines the energy of the vibrational level with an accuracy of the phase gate width. For example, the phase gate can be defined by three pixels on the SLM, corresponding, to about 25 cm ⁻¹ , that is about 40 times better than the excitation pulse width.

[0124] Referring to FIGS. 8A and 8B , there are illustrated measured normalized CARS spectra for the case of a transform limited pulse (curves 81 a and 81 b ) and the case of a phase gate shaped pulse (curves 82 a and 82 b ), respectively, for methanol (having nonresonant component only) and for iodomethane (having a resonant at 523 cm ⁻¹ ). The peak-dip feature due to the resonant contribution at 523 cm ⁻¹ can be seen in the iodomethane spectrum ( FIG. 8B ), while the normalized methanol spectrum ( FIG. 8A ) remains nearly unchanged.

[0125] The Raman level structure can be easily extracted from the measured spectrum by considering, for example, the normalized spectral intensity variation of the CARS signal 6 $\begin{array}{cc}f\left(\Omega \right)=-\frac{I\left({\omega }_g+\Omega -\Delta /2\right)-I\left({\omega }_g+\Omega +\Delta /2\right)}{{\int }_{{\omega }_g+\Omega -\Delta /2}^{{\omega }_g+\Omega +\Delta /2}I\left(\omega \right)\omega }& \left(7\right)\end{array}$

[0126] where ω _g is the central frequency of the phase gate and Δ is the gate width. It should be understood that the normalization is required to compensate for the decrease in the nonresonant background towards higher energies.

[0127] Referring to FIGS. 9 A- 9 D, plots of the normalized spectral intensity ƒ(Ω) derived from the measured CARS spectra (curves 91 , 92 , 93 and 94 ) are given in for several materials, along with simulation predictions (curves 95 , 96 , 97 and 98 ) obtained by computer simulations.

[0128] As can be seen in FIG. 9 A, nearly flat line is observed for methanol, having no Raman level in this range. The 459 cm ⁻¹ level of carbon tetrachloride is easily observed in FIG. 9B . For mesitylene ( FIG. 9C ), having two Raman levels at 515 cm ⁻¹ and 575 cm ⁻¹ two well-separated peaks can be seen. At the high-energy end, the 652 cm ⁻¹ level of carbon disulfide is shown in FIG. 9D . It should be noted that the spectral resolution observed in these figures is of the order of about 30 cm ⁻¹ , (i.e., almost a factor of 40 better than the excitation pulse bandwidth). The resolution is determined by both the width of the phase gate (25 cm ⁻¹ ) and the monochromator resolution (about 8 cm ⁻¹ ). The minimal phase gate width is determined by both the pixellization of the SLM and by the spot size of the incident beam on it. In all the examples presented above the phase gate consisted of three pixels on the SLM.

[0129] It should be understood that for detection of a given Raman level, it is possible to control the relative intensity ratio between the resonant and the nonresonant components by varying the spectral location of the phase gate. This is due to the fact that the nonresonant background decreases towards higher energies. Additionally, a further control is possible by varying the phase gate width. Thus, a wider probe width can improve the resonant to nonresonant intensity ratio (while resulting in lower spectral resolution). In this case, even weak Raman levels can be observed by using this scheme.

[0130] The benefits of broadband excitation can be fully exploited when attempting to detect materials with several vibrational bands in the measured energy range. In this case, a spectral phase mask having multiple phase gates at appropriate locations can be used to generate a large coherent spectral feature in the CARS spectrum, due to the constructive interference of the resonant contributions from the various levels.

[0131] According to another embodiment of the invention, the CARS process is controlled by controlling the polarization of the excitation pulse. It should be appreciated that the polarization control can be carried out in addition to the shaping, i.e., correcting of the dispersion of the input pulse and assigning of the desired phase to each frequency component of the driving pulse.

[0132] In particular, the polarization control can be used to break the ultrashort input pulse into a broadband pump and a narrow-band probe with orthogonal polarizations.

[0133] The nonlinear polarization producing the CARS signal driven by an electric field whose spectrum is E(ω) can be approximated for nonresonant transitions: 7 $\begin{array}{cc}{P}_{\mathrm{nr}\left(j\right)}^{\left(3\right)}\propto {\chi }_{\mathrm{jklm}}^{\mathrm{nr}}{\int }_0^{\infty }\Omega E_k\left(\omega -\Omega \right)A_{\mathrm{lm}}\left(\Omega \right),\mathrm{where}A_{\mathrm{lm}}\left(\Omega \right)={\int }_0^{\infty }{\omega }^{\prime }E_l^{*}\left({\omega }^{\prime }-\Omega \right)E_m\left({\omega }^{\prime }\right)& \left(8\right)\end{array}$

[0134] is the population amplitude and χ _jklm ^nr is the third order susceptibility tensor.

[0135] In turn, for a singly resonant Raman transition through an intermediate level |i at an energy of Ω _R and a bandwidth Γ one can obtain: 8 $\begin{array}{cc}{P}_{r\left(j\right)}^{\left(3\right)}\propto {\chi }_{\mathrm{jklm}}^{\mathrm{nr}}{\int }_0^{\infty }\Omega \frac{E_k\left(\omega -\Omega \right)}{\left({\Omega }_R-\Omega \right)+i\Gamma }A_{\mathrm{lm}}\left(\Omega \right).& \left(9\right)\end{array}$

[0136] The two main differences between the resonant and nonresonant components are as follows. First, the resonant component has a narrow spectral response, centered at Ω=Ω _R , whereas the spectral response of the nonresonant component is broad. Second, the response of the resonant component inverts sign at about Ω=Ω _R while the nonresonant response has a constant phase. It will be shown hereinbelow how these differences are used to reduce the nonresonant component while enhancing the resonant component.

[0137] One approach to single-pulse polarization controlled CARS would be to rotate by π/2 the polarization of the excitation pulse in a narrow band at its high energy end, from an x-plane to a y-plane, and to monitor the CARS signal in the y-plane. As a result, the monitored signal will effectively dependent only on A _xx (as the polarization field), and on E _y (as the probe). This is true for both the resonant and nonresonant terms.

[0138] As was mentioned above for the case of the coherent control by means of a phase gate, the ratio of the resonant signal to the nonresonant signal of the background as well as the spectral resolution can be improved when the probe pulse becomes longer. According to this embodiment of the invention, the duration of the probe pulse is determined by the spectral width of the polarization shifted band.

[0139] Referring to FIGS. 10 A- 10 D, examples of the CARS spectra from iodomethane obtained with polarization-only shaping are plotted for various polarized probe spectral bandwidths. The total bandwidth of the polarized probe decreases as follows: 4.5 nm (for the example shown in FIG. 10 A); 2.3 nm (for the example shown in FIG. 10 B); 1.2 nm (for the example shown in FIG. 10C ) and 0.6 nm (for the example shown in FIG. 10D ). As the probe bandwidth is decreased from 4.5 nm (corresponding to 400 fs) to 0.6 nm (corresponding to 3 ps, the resonant component, due to its narrow spectral response, becomes narrower but maintains its strength. In contrast, the nonresonant background component, having a broad spectral response, becomes weaker but maintains its spectral shape. Since the two are coherent, they generate an interference pattern, interfering constructively at the low-energy end of the probe pulse, and destructively at its high-energy end. This interference pattern obscures the interpretation and calls for further reduction of the nonresonant background.

[0140] Further reduction of the nonresonant background is achieved by using both the polarization control and the phase control. It will be shown below that the combination of both the phase and the polarization controls can lead to nearly complete suppression of the nonresonant component, yielding background-free single-pulse multiplex CARS spectra with a high spectral resolution.

[0141] FIG. 11 exemplifies the spectral intensity of a phase and polarization shaped excitation pulse. According to this example, a π phase-shifted gate 110 is introduced at a y polarization -shifted band 111 , serving as a probe. The probe is thus split into two, spectrally distinct longer probe pulses with opposite phase. Due to the broad nonresonant spectral response, the nonresonant background from these two probe pulses interferes destructively. Since the A _xx (Ω) component of the amplitude is a very smooth function, these two probe pulses are almost equal in magnitude. As a result, the nonresonant background component of the CARS signal can be reduced by orders of magnitude.

[0142] This reduction can be alternatively viewed in time domain. FIG. 12 shows a schematic drawing of the electric field envelope versus time in both the x polarization (curve 121 ) and the y polarization (curve 122 ) for both phase and polarization shaped pulse. For convenience, the x polarization field has been reduced by about two orders of magnitude. As can be appreciated, the π phase gate modifies the temporal shape of the y polarized probe so that the electric field envelope crosses zero at the peak of the x polarized driving field.

[0143] Due to the instantaneous nonresonant response, the nonresonant background is almost completely suppressed. The resonant signal response is different. It should be noted that the π phase gate compensates for the sign inversion of the denominator in Eq. 9, leading to an increased resonant signal over a narrow spectral band shifted by the Raman level energy from the π phase gate location.

[0144] Referring to FIGS. 13 A- 13 C, examples of the CARS spectra from iodomethane obtained with both polarization and π phase gate shaping are plotted for various probe spectral bandwidths. According to this examples, the total probe bandwidth varies from 4.5 nm (for the example shown in FIG. 13A ) to 2.4 nm (for the example shown in FIG. 13B ), and then further to 1.2 nm (for the example shown in FIG. 13C ). When the measured spectra obtained by using the polarization and phase shaped probe pulses (shown in FIGS. 13 A- 13 C) are compared to the measured spectra obtained by using polarization-only shaped transform limited pulses (shown in FIGS. 10 A- 10 D), a dramatic decrease in the nonresonant background can be seen. It should be noted that the small nonresonant background that is still observed using the phase-shaped probe is in fact a small fraction (about 0.05%) of the χ _xxx component which “leaks” through the polarizer due to small birefringence of the microscope objective and collection optics. However, since this background component is independent on the applied phase and polarization, it can be easily subtracted.

[0145] Referring to FIGS. 14 A- 14 C, examples of Raman spectra of several simple molecules obtained with phase and polarization shaped pulses are illustrated. The total probe bandwidth has been about 1.2 nm, including a π phase gate at the bandwidth's center. The “raw” measured CARS spectra are shown in the left part of the figures. It should be noted that the small nonresonant background that is still observed is in fact a small fraction (about 0.05%) of the χ _xxx component which “leaks” through the polarizer due to small birefringence of the microscope objective and collection optics. Since this background component is independent on the applied phase and polarization, it can be easily subtracted. The extracted Raman spectra, from which the background due to birefringence was subtracted, are plotted on the right part of the figures.

[0146] FIG. 14A shows a peak 141 corresponding to the 523 cm ⁻¹ Raman level of iodomethane. The full-width at half maximum of this peak is about 15 cm ⁻¹ .

[0147] The measured Raman spectrum of 1,2-dichloroethane is shown in FIG. 14B . The levels at 652 cm ⁻¹ and 750 cm ⁻¹ , separated by 98 cm ⁻¹ are seen as two very well separated peaks 142 and 143 . This spectrum also has a peak 144 corresponding to the level at 298 cm ⁻¹ located at the lower limit of the detectable region.

[0148] The Raman spectrum of p-xylene, having a peak 145 corresponding to the level at 830 cm ⁻¹ is shown in FIG. 14C . This example demonstrates the ability of the technique of the present invention to observe the high-energy end of the detectable region. It should be noted that the measured energy range can be extended to higher frequencies (1000-15000 cm ⁻¹ ) by using shorter pulses.

[0149] Single-pulse CARS is particularly suitable for nonlinear microscopy. FIG. 15 exemplifies a single-pulse CARS microscope 150 according to the invention. Generally, the CARS microscope 150 includes all the elements of the single-pulse spectrometer ( 20 in FIG. 2A or 200 in FIG. 2B ) needed for inducing a CARS process in the molecules of a target material and for detecting the CARS signal scattered by the material. More specifically, the CARS microscope 150 includes means for inducing the CARS process by producing a beam constituted of unitary optical excitation pulses and directing it through the target material placed on the sample holder 29 . According to the technique of the present invention, each pulse is a unitary pulse that carries a pump photon, a Stokes photon and a probe photon. The CARS microscope thus includes a laser 21 adapted for generating at least one transform limited optical pulse and a programmable pulse shaper 22 (constituting a control means for coherently controlling the CARS process) operable for shaping the transform limited optical excitation pulse obtained from the laser 21 , a detector unit 26 , and a light directing optics. The shaping is carried out by correcting the pulse dispersion as well as assigning the desired phase (and, optionally, polarization) to the pulse, as described above.

[0150] The light directing optics of the CARS microscope 150 includes a focusing assembly (e.g., a microscope objective) 24 a arranged for creation a focal spot 152 formed by the beam on the target material; a lens assembly 24 b arranged for collecting the output CARS signal from the target material; and a filtering assembly 25 operable for filtering the collected output CARS signal propagating towards the detector unit 26 . All these components are similar to those described above in connection with the CARS spectrometer system ( 20 in FIG. 2A or 200 in FIG. 2B ).

[0151] The CARS microscope 150 utilizes scanning of at least a portion of the target material with the focal spot 152 , which can be implemented by supporting the sample holder on a stage 151 driven for movement, and/or by mounting at least some of optical elements for movement with respect to the sample holder to thereby appropriately deflect the incident beam. The microscope objective 24 a may for example be that commercially available from ZEISS. The stage driver may include a piezoelectric transducer, e.g., P-282 XYZ Nano positioners commercially available from Physik Instruments (PI) GmbH.

[0152] An example of single-pulse spectrally resolved microscopy is demonstrated herein below. A selected target material was a glass capillary plate with 10-μm holes filled with CH ₂ Br ₂ (having a resonant at 577 cm ⁻¹ ). The sample was raster-scanned around the focused laser beam using computer-controlled piezoelectric drivers.

[0153] An image shown in FIG. 16A was taken with a pulse shape maximizing the relative intensity of the resonant contribution, whereas the image shown in FIG. 16B was taken with a pulse shape minimizing this intensity.

[0154] The predominantly resonant signal from the filled holes shown in FIG. 16A is larger by a factor of 4 than that in FIG. 16 B, while the signals obtained from the glass is almost similar.

[0155] FIG. 16C shows an image that is a difference between the images in FIG. 16 A and FIG. 16 B, depicting the signal from the 577 cm ⁻¹ vibrational level of CH ₂ Br ₂ . This image appears inverted relative to that obtained by using a transform-limited pulse (shown in FIG. 16D ), where the glass, having a larger nonresonant signal, appears brighter. The image in FIG. 16C demonstrates the ability of the microscope to spectrally resolve the Raman resonant contribution of a single vibrational level. In a practical system, the difference image can be directly measured by lock-in detection, alternating the phase masks of the images shown in FIGS. 16A and 16B at a high frequency.

[0156] It should be appreciated that for materials having more than one vibrational level it is possible to improve the detection selectivity by tailoring shaped pulses to induce constructive quantum interference of these levels.

[0157] As such, those skilled in the art to which the present invention pertains, can appreciate that while the present invention has been described in terms of preferred embodiments, the concept upon which this disclosure is based may readily be utilized as a basis for the designing of other structures, systems and processes for carrying out the several purposes of the present invention.

[0158] Although the example of utilization of the CARS spectrometer technique of the present invention were shown for CARS microscopy, the spectral measurement utilizing the coherent control of the present invention can be easily combined with other nonlinear microscopic methods such as multiphoton fluorescence and third-harmonic generation using the same microscope system.

[0159] Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting.

[0160] It is important, therefore, that the scope of the invention is not construed as being limited by the illustrative embodiments set forth herein. Other variations are possible within the scope of the present invention as defined in the appended claims and their equivalents.