## Pump-probe nonlinear phase dispersion spectroscopy |

Optics Express, Vol. 21, Issue 8, pp. 9353-9364 (2013)

http://dx.doi.org/10.1364/OE.21.009353

Acrobat PDF (1524 KB)

### Abstract

Pump-probe microscopy is an imaging technique that delivers molecular contrast of pigmented samples. Here, we introduce pump-probe nonlinear phase dispersion spectroscopy (PP-NLDS), a method that leverages pump-probe microscopy and spectral-domain interferometry to ascertain information from dispersive and resonant nonlinear effects. PP-NLDS extends the information content to four dimensions (phase, amplitude, wavelength, and pump-probe time-delay) that yield unique insight into a wider range of nonlinear interactions compared to conventional methods. This results in the ability to provide highly specific molecular contrast of pigmented and non-pigmented samples. A theoretical framework is described, and experimental results and simulations illustrate the potential of this method. Implications for biomedical imaging are discussed.

© 2013 OSA

## 1. Introduction

1. D. Fu, T. Ye, T. E. Matthews, B. J. Chen, G. Yurtserver, and W. S. Warren, “High-resolution in vivo imaging of blood vessels without labeling,” Opt. Lett. **32**(18), 2641–2643 (2007). [CrossRef] [PubMed]

2. D. Fu, T. E. Matthews, T. Ye, I. R. Piletic, and W. S. Warren, “Label-free in vivo optical imaging of microvasculature and oxygenation level,” J. Biomed. Opt. **13**(4), 040503 (2008). [CrossRef] [PubMed]

3. T. E. Matthews, I. R. Piletic, M. A. Selim, M. J. Simpson, and W. S. Warren, “Pump-probe imaging differentiates melanoma from melanocytic nevi,” Sci. Transl. Med. **3**(71), 71ra15 (2011). [CrossRef] [PubMed]

4. T. E. Matthews, J. W. Wilson, S. Degan, M. J. Simpson, J. Y. Jin, J. Y. Zhang, and W. S. Warren, “In vivo and ex vivo epi-mode pump-probe imaging of melanin and microvasculature,” Biomed. Opt. Express **2**(6), 1576–1583 (2011). [CrossRef] [PubMed]

5. P. Samineni, A. deCruz, T. E. Villafaña, W. S. Warren, and M. C. Fischer, “Pump-probe imaging of historical pigments used in paintings,” Opt. Lett. **37**(8), 1310–1312 (2012). [CrossRef] [PubMed]

6. M. C. Fischer, T. Ye, G. Yurtsever, A. Miller, M. Ciocca, W. Wagner, and W. S. Warren, “Two-photon absorption and self-phase modulation measurements with shaped femtosecond laser pulses,” Opt. Lett. **30**(12), 1551–1553 (2005). [CrossRef] [PubMed]

9. P. Samineni, B. Li, J. W. Wilson, W. S. Warren, and M. C. Fischer, “Cross-phase modulation imaging,” Opt. Lett. **37**(5), 800–802 (2012). [CrossRef] [PubMed]

10. E. O. Potma, W. P. de Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. **80**(6), 3019–3024 (2001). [CrossRef] [PubMed]

^{(3)}(Ω), where Ω is the vibrational frequency [11

11. D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. **92**(12), 123905 (2004). [CrossRef] [PubMed]

12. P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. **70**(23), 9562–9569 (2010). [CrossRef] [PubMed]

13. J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. **463**(4-6), 300–304 (2008). [CrossRef]

14. J. W. Wilson, P. Schlup, and R. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. **33**(18), 2116–2118 (2008). [CrossRef] [PubMed]

15. B. E. Applegate and J. A. Izatt, “Molecular imaging of endogenous and exogenous chromophores using ground state recovery pump-probe optical coherence tomography,” Opt. Express **14**(20), 9142–9155 (2006). [CrossRef] [PubMed]

16. D. Jacob, R. L. Shelton, and B. E. Applegate, “Fourier domain Pump-Probe Optical Coherence Tomography imaging of melanin,” Opt. Express **18**(12), 12399–12410 (2010). [CrossRef] [PubMed]

17. U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. **25**(2), 111–113 (2000). [CrossRef] [PubMed]

18. F. E. Robles, C. Wilson, G. Grant, and A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics **5**(12), 744–747 (2011). [CrossRef] [PubMed]

19. M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. **30**(10), 1162–1164 (2005). [CrossRef] [PubMed]

20. F. E. Robles and A. Wax, “Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry,” Opt. Lett. **35**(17), 2843–2845 (2010). [CrossRef] [PubMed]

21. F. E. Robles, L. L. Satterwhite, and A. Wax, “Nonlinear phase dispersion spectroscopy,” Opt. Lett. **36**(23), 4665–4667 (2011). [CrossRef] [PubMed]

11. D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. **92**(12), 123905 (2004). [CrossRef] [PubMed]

14. J. W. Wilson, P. Schlup, and R. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. **33**(18), 2116–2118 (2008). [CrossRef] [PubMed]

## 2. Experimental system and methods

13. J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. **463**(4-6), 300–304 (2008). [CrossRef]

1. D. Fu, T. Ye, T. E. Matthews, B. J. Chen, G. Yurtserver, and W. S. Warren, “High-resolution in vivo imaging of blood vessels without labeling,” Opt. Lett. **32**(18), 2641–2643 (2007). [CrossRef] [PubMed]

4. T. E. Matthews, J. W. Wilson, S. Degan, M. J. Simpson, J. Y. Jin, J. Y. Zhang, and W. S. Warren, “In vivo and ex vivo epi-mode pump-probe imaging of melanin and microvasculature,” Biomed. Opt. Express **2**(6), 1576–1583 (2011). [CrossRef] [PubMed]

*c*= 4.16 ps, where

*c*is the speed of light in vacuum. The three beams are combined using a dichroic mirror and are sent collinearly to a microscope objective (10X, 0.25 numerical aperture), which focuses the light onto the sample. Then, light is collimated, filtered to remove the pump beam, coupled into a single mode fiber (SMF), and sent to a spectrometer (HR4000, Ocean Optics) for detection. Note that while the pump beam does not interfere with the reference field and it is spectrally resolved on the spectrometer, it must be filtered out to prevent potential nonlinear interactions in the SMF. Further, the reference must precede the pump, otherwise the reference field would experience changes from long-lived exited states induced on the sample by the pump.

_{pr}, where τ

_{pr}is the duration of the probe beam), which ensures that the observed behavior is not a result of thermal effects. This is achieved by introducing a cover glass onto the pump’s path, which produces a delay of 700 fs. The ‘on’/’off’ time delay is fixed at τ ~0 fs for the experimental results discussed in section 4. Both pulses have a duration (full width at half maximum, FWHM) of 140 fs, and are well described by a hyperbolic secant function.

_{2}), pure water, 30 mM rhodamine 6G (R6G) in methanol, and pure methanol, each placed in separate glass cuvettes. Water and CS

_{2}are chosen because their nonlinear properties have been well studied and can be modeled using a classical approach that allows validation of the method (see section 3). In addition, water is a relevant target for biomedical applications. Methanol and R6G are chosen to directly compare the effects of two-photon absorption, since R6G has a large cross section for this type of interaction.

## 3. Theory

*z*

_{r}is the Rayleigh range of the focused beam, and

*φ*, to account for shot-to-shot phase variations arising from instabilities in the interferometer. The effect of

_{r}*φ*will be discussed in more detail below.

_{r}*t = ± T*. If only one of the two non-DC terms is considered, then the signal (in the spectral-domain) may be described as,Similarly, when the pump is ‘off,’ the signal is described asTherefore, the nonlinear amplitude change—described by

*ñ*—may be directly assessed using Eqs. (4) and (5),Pump-probe methods, however, measure the probe’s transmission change due to nonlinear effects, thus we also define the fractional transmission change as,For small

_{NL}*K*, Eq. (7) reduces to −2

*Φ(ω,τ)*, which describe the real part of the nonlinear RI, is more challenging due to the random phase term,

*φ*. In the linear regime, this term is eliminated by unwrapping the phase and subtracting a straight line, which isolates the wavelength-dependent (dispersive) terms of the linear RI [20

_{r}20. F. E. Robles and A. Wax, “Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry,” Opt. Lett. **35**(17), 2843–2845 (2010). [CrossRef] [PubMed]

*Φ(ω,τ)*may contain linear components, thus this approach would only assess second and higher order terms of

*Φ(ω,τ)*with respect to

*ω*. Here, a different approach is taken to avoid this problem, where the random phase term is eliminated by subtracting the average phase as a function of wavelength from both the ‘on’ and ‘off’ signals. This process yields Eq. (8)where denotes the phase angle and the bar denotes the average over

*ω*. The end parameter,

*Φ’(ω,τ),*retains the spectral shape of

*Φ(ω,τ),*including linear components, and significantly reduces the noise on the measured signal. Experimentally, the phase deviation (noise) per wavelength on

*Φ’(ω,τ)*is two orders of magnitude lower than

*Φ(ω,τ)*, due to the elimination of

*φ*(see section 4). This enables experimental evaluation of the small wavelength-dependent phase changes resulting from nonlinear interactions that are typically obscured by noise.

_{r}*Φ(ω,τ)*and

*K(ω,τ)*are modeled. To achieve this, it is convenient to switch from the frequency-domain to the time-domain, where the probe field may now be described as,where

*κ*and

*ϕ*denote the time-domain intensity and phase changes, respectively, resulting from nonlinear interactions. For non-absorbing samples, the phase changes may be described using a phenomenological model of the OKE dynamics [22

22. D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. **24**(2), 443–454 (1988). [CrossRef]

*c*is a proportionality constant,

_{1}*I*is the pump intensity, and ⊗ denotes a convolution. The terms in brackets represent the sample’s OKE response: the delta function describes the instantaneous electronic response and the second term describes the dynamic nuclear response. For the latter, typically three terms (

_{pu}*m*= 3) are used, which describe (1) intermolecular interactions, (2) librational motion, and (3) free rotation [22

22. D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. **24**(2), 443–454 (1988). [CrossRef]

_{2}and water, we refer the readers to refs [23

23. I. A. Heisler, R. R. B. Correia, T. Buckup, S. L. S. Cunha, and N. P. da Silveira, “Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures,” J. Chem. Phys. **123**(5), 054509 (2005). [CrossRef] [PubMed]

24. Y. J. Chang and E. W. Castner, “Femtosecond dynamics of hydrogen-bonding solvents. Formamide and N-methylformamide in acetonitrile, DMF, and water,” J. Chem. Phys. **99**(1), 113 (1993). [CrossRef]

_{2}and water do not exhibit any time-domain intensity changes, since they are non-absorbing, thus κ = 0. For samples that do exhibit intensity changes in the time-domain, more complete models that take quantum mechanics into account must be employed [25

25. E. Tokunaga, A. Terasakiy, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B **12**(5), 753–771 (1995). [CrossRef]

22. D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. **24**(2), 443–454 (1988). [CrossRef]

23. I. A. Heisler, R. R. B. Correia, T. Buckup, S. L. S. Cunha, and N. P. da Silveira, “Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures,” J. Chem. Phys. **123**(5), 054509 (2005). [CrossRef] [PubMed]

*Φ’(ω,τ)*and

*K(ω,τ)*, consider a non-absorbing sample with a quadratic temporal phase change, given by

*ϕ(t) = -*ϕ " ⋅(t + τ), which yields a simple analytical solution (see appendix). This form of the temporal phase provides a good approximation for Eq. (10) at pump-probe time-delays near the temporal phase maximum, at

^{2}*t*= 50 fs and 165 fs for water and CS

_{2}, respectively, as well as

*t*= 0 for a purely electronic response. The analytical solution (detailed in the appendix) shows that the phase changes in the spectral-domain exhibit a quadratic dependence with respect to

*ω*given by

*Φ’(ω,τ)∝*ϕ " ⋅(ω - ω, where

_{0})^{2}*ω*is the center frequency. Thus the concavity (up or down) of the spectral phase depends on the sign of or, more generally, on the second derivative of

_{0}*ϕ(t)*. In comparison, the transmission changes are given by

*K(ω,τ)∝τ⋅(ω - ω*, which has a linear dependence with respect to

_{0})*ω*that deviates about the center frequency (i.e., no transmission change at

*ω*). An intuitive way of viewing the transmission changes is that even though no intensity changes take place in the time-domain, the Fourier transform of the time-varying phase produces real and imaginary terms, where the imaginary term will manifest itself as spectral intensity changes. In addition, the spectrum must be an odd function about

_{0}*ω*, to ensure that the net effect disappears in the conjugate domain. It is also worth noting that the slope of

_{0}*K(ω)*at a given time-delay,

*τ*, changes signs when the temporal phase,

*ϕ(t)*, reaches a maximum (

*ϕ(τ*= 0) in this case).

## 4. Results and discussion

20. F. E. Robles and A. Wax, “Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry,” Opt. Lett. **35**(17), 2843–2845 (2010). [CrossRef] [PubMed]

21. F. E. Robles, L. L. Satterwhite, and A. Wax, “Nonlinear phase dispersion spectroscopy,” Opt. Lett. **36**(23), 4665–4667 (2011). [CrossRef] [PubMed]

*c*in Eq. (10) is adjusted to qualitatively match the amplitude of the experimental phase changes—we find that values of 0.02 and 0.035 provide good agreement for water and CS

_{1}_{2}, respectively. The modeled OKE responses [Eq. (10)] are illustrated in Fig. 2(d). Figures 3 -4 show the experimental results of 10 independent measurements from water and CS

_{2}along with the theoretical simulated signals.

*Φ’*(solid red curves in Figs. 3-4) are in excellent agreement, where both show the same concavity (up or down) and slight asymmetry in the parabolic shape for each sample. These results can be understood by using the approximation provided in section 3 (and appendix): Specifically, the difference in concavity between the two samples results from the fact that the OKE response of CS

_{2}peaks at a later time compared to water, which causes the second derivatives to have opposite signs at τ = 0. These are drastic changes that reflect important features of the OKE response, and highlights how

*Φ’*can readily reveal the diffusive motions of molecules. We also note that the average standard deviation of

*Φ’*per wavelength (spectral phase noise) is ~0.1 mrads. In comparison, the spectral phase noise of

*Φ*, which does not take the random phase term (

*φ*) into account, is ~20 mrads, and thus this parameter significantly obscures the spectral features of interest. This result underscores the importance of accounting for the random phase noise term using the spectral information [as described by Eq. (8)]. Figure 3(c) shows

_{r}*Φ*for CS

_{2}, where the influence of

*φ*is clearly visible.

_{r}*c*in Eq. (10), also provides good agreement between the amplitude of the transmission changes (i.e., both experiment and simulation span a range of ~ ± 1%). The discrepancy in the slope of the water transmission spectrum at τ = 0 can be attributed to error in the pump-probe time delay. For example, according to our OKE model for water [24

_{1}24. Y. J. Chang and E. W. Castner, “Femtosecond dynamics of hydrogen-bonding solvents. Formamide and N-methylformamide in acetonitrile, DMF, and water,” J. Chem. Phys. **99**(1), 113 (1993). [CrossRef]

21. F. E. Robles, L. L. Satterwhite, and A. Wax, “Nonlinear phase dispersion spectroscopy,” Opt. Lett. **36**(23), 4665–4667 (2011). [CrossRef] [PubMed]

_{2}and an instantaneous electronic response [delta term in Eq. (10)]. The results are shown in Fig. 5 , where in general the phase behavior shows a parabolic shape as a function of wavelength, and the transmission changes show a linear dependence. Moreover, the concavity (up or down) of the spectral phase corresponds to the sign of the second derivative of the temporal OKE response, thus the points of inflection give an indication of the time when the spectral phase changes concavity. Similarly, these inflection points correspond to when the slope of the spectral-transmission-changes reach a maximum, which is in good agreement with spectral shifting methods [8

8. J. W. Wilson, P. Samineni, W. S. Warren, and M. C. Fischer, “Cross-phase modulation spectral shifting: nonlinear phase contrast in a pump-probe microscope,” Biomed. Opt. Express **3**(5), 854–862 (2012). [CrossRef] [PubMed]

_{2}, also shown in Fig. 5. The nuclear repose of OKE causes this imbalance. Thus, the rich structure of the spectral phase and transmission changes offer a wealth of information that provides molecular contrast of non-pigmented samples.

## 5. Conclusion and future work

*τ*, and should help mitigate setup errors. Backscattering geometries will also be explored to enable in-vivo applications. Finally, the pump beam will be modulated to reduce low frequency noise from the source. This is expected to provide better SNR, in addition to potentially enabling assessment of the average phase as a function of time-delay (i.e.,

*Φ(ω,τ)*instead of

*Φ’(ω,τ)*).

## Appendix

*a*describes the width of the Gaussian pulse and

*n = n*. As the probe field propagates through the perturbation, it acquires a time-dependent phase modulation, which may be express as a Tyler series,where the primes denote a derivative with respect to time,

_{0}+ δn*t*(constants are ignored for simplicity). Because the method described in this work is insensitive to phase offsets,

*ϕ*can be ignored. Further, if we consider the electronic response near time delays when the pump and probe are temporally overlapped, then

_{0}*ϕ*’~0 since the response can be well represented by a second order function. Higher order terms are assumed to be negligible. The resulting temporal phase change experienced by the probe field is described by,where

*ϕ”*is a positive constant that depends on the sample. Note that we have explicitly accounted for the pump-probe time delay, τ. This form of the temporal phase provides a good approximation for Eq. (10) at pump-probe time-delays near the temporal phase maximum at

*t*= 50 fs and 165 fs for water and CS

_{2}, respectively, as well as

*t*= 0 for a purely electronic response. Following Eq. (9), the field in the Fourier domain is now given by, To separate the real and imaginary parts, we multiply the terms in the exponential by the complex conjugate of the denominator, which yields:Therefore, Eq. (16) can be expressed as,where

8. J. W. Wilson, P. Samineni, W. S. Warren, and M. C. Fischer, “Cross-phase modulation spectral shifting: nonlinear phase contrast in a pump-probe microscope,” Biomed. Opt. Express **3**(5), 854–862 (2012). [CrossRef] [PubMed]

*τ*are small constants) we finally obtain,Here

*τ*, which means that when the pump beam is temporally overlapped with the probe (

*τ*= 0) the amplitude is unmodulated. This is in agreement with the experiments and numerical simulations shown in Figs. 3-5. This analytical treatment gives an accurate description of the frequency-dependent phase and amplitude changes observed for non-absorbing samples.

## Acknowledgments

## References and links

1. | D. Fu, T. Ye, T. E. Matthews, B. J. Chen, G. Yurtserver, and W. S. Warren, “High-resolution in vivo imaging of blood vessels without labeling,” Opt. Lett. |

2. | D. Fu, T. E. Matthews, T. Ye, I. R. Piletic, and W. S. Warren, “Label-free in vivo optical imaging of microvasculature and oxygenation level,” J. Biomed. Opt. |

3. | T. E. Matthews, I. R. Piletic, M. A. Selim, M. J. Simpson, and W. S. Warren, “Pump-probe imaging differentiates melanoma from melanocytic nevi,” Sci. Transl. Med. |

4. | T. E. Matthews, J. W. Wilson, S. Degan, M. J. Simpson, J. Y. Jin, J. Y. Zhang, and W. S. Warren, “In vivo and ex vivo epi-mode pump-probe imaging of melanin and microvasculature,” Biomed. Opt. Express |

5. | P. Samineni, A. deCruz, T. E. Villafaña, W. S. Warren, and M. C. Fischer, “Pump-probe imaging of historical pigments used in paintings,” Opt. Lett. |

6. | M. C. Fischer, T. Ye, G. Yurtsever, A. Miller, M. Ciocca, W. Wagner, and W. S. Warren, “Two-photon absorption and self-phase modulation measurements with shaped femtosecond laser pulses,” Opt. Lett. |

7. | P. Samineni, Z. Perret, W. S. Warren, and M. C. Fischer, “Measurements of nonlinear refractive index in scattering media,” Opt. Express |

8. | J. W. Wilson, P. Samineni, W. S. Warren, and M. C. Fischer, “Cross-phase modulation spectral shifting: nonlinear phase contrast in a pump-probe microscope,” Biomed. Opt. Express |

9. | P. Samineni, B. Li, J. W. Wilson, W. S. Warren, and M. C. Fischer, “Cross-phase modulation imaging,” Opt. Lett. |

10. | E. O. Potma, W. P. de Boeij, and D. A. Wiersma, “Femtosecond dynamics of intracellular water probed with nonlinear optical Kerr effect microspectroscopy,” Biophys. J. |

11. | D. L. Marks and S. A. Boppart, “Nonlinear interferometric vibrational imaging,” Phys. Rev. Lett. |

12. | P. D. Chowdary, Z. Jiang, E. J. Chaney, W. A. Benalcazar, D. L. Marks, M. Gruebele, and S. A. Boppart, “Molecular histopathology by spectrally reconstructed nonlinear interferometric vibrational imaging,” Cancer Res. |

13. | J. W. Wilson, P. Schlup, and R. A. Bartels, “Synthetic temporal aperture coherent molecular phase spectroscopy,” Chem. Phys. Lett. |

14. | J. W. Wilson, P. Schlup, and R. Bartels, “Phase measurement of coherent Raman vibrational spectroscopy with chirped spectral holography,” Opt. Lett. |

15. | B. E. Applegate and J. A. Izatt, “Molecular imaging of endogenous and exogenous chromophores using ground state recovery pump-probe optical coherence tomography,” Opt. Express |

16. | D. Jacob, R. L. Shelton, and B. E. Applegate, “Fourier domain Pump-Probe Optical Coherence Tomography imaging of melanin,” Opt. Express |

17. | U. Morgner, W. Drexler, F. X. Kärtner, X. D. Li, C. Pitris, E. P. Ippen, and J. G. Fujimoto, “Spectroscopic optical coherence tomography,” Opt. Lett. |

18. | F. E. Robles, C. Wilson, G. Grant, and A. Wax, “Molecular imaging true-colour spectroscopic optical coherence tomography,” Nat. Photonics |

19. | M. A. Choma, A. K. Ellerbee, C. Yang, T. L. Creazzo, and J. A. Izatt, “Spectral-domain phase microscopy,” Opt. Lett. |

20. | F. E. Robles and A. Wax, “Separating the scattering and absorption coefficients using the real and imaginary parts of the refractive index with low-coherence interferometry,” Opt. Lett. |

21. | F. E. Robles, L. L. Satterwhite, and A. Wax, “Nonlinear phase dispersion spectroscopy,” Opt. Lett. |

22. | D. McMorrow, W. T. Lotshaw, and G. A. Kenney-Wallace, “Femtosecond optical Kerr studies on the origin of the nonlinear responses in simple liquids,” IEEE J. Quantum Electron. |

23. | I. A. Heisler, R. R. B. Correia, T. Buckup, S. L. S. Cunha, and N. P. da Silveira, “Time-resolved optical Kerr-effect investigation on CS2/polystyrene mixtures,” J. Chem. Phys. |

24. | Y. J. Chang and E. W. Castner, “Femtosecond dynamics of hydrogen-bonding solvents. Formamide and N-methylformamide in acetonitrile, DMF, and water,” J. Chem. Phys. |

25. | E. Tokunaga, A. Terasakiy, and T. Kobayashi, “Femtosecond phase spectroscopy by use of frequency-domain interference,” J. Opt. Soc. Am. B |

26. | R. W. Boyd, |

**OCIS Codes**

(120.3180) Instrumentation, measurement, and metrology : Interferometry

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(190.3270) Nonlinear optics : Kerr effect

(300.6420) Spectroscopy : Spectroscopy, nonlinear

(180.4315) Microscopy : Nonlinear microscopy

**ToC Category:**

Spectroscopy

**History**

Original Manuscript: February 13, 2013

Revised Manuscript: April 1, 2013

Manuscript Accepted: April 4, 2013

Published: April 9, 2013

**Virtual Issues**

Vol. 8, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Francisco E. Robles, Prathyush Samineni, Jesse W. Wilson, and Warren S. Warren, "Pump-probe nonlinear phase dispersion spectroscopy," Opt. Express **21**, 9353-9364 (2013)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-21-8-9353

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### References

- D. Fu, T. Ye, T. E. Matthews, B. J. Chen, G. Yurtserver, and W. S. Warren, “High-resolution in vivo imaging of blood vessels without labeling,” Opt. Lett.32(18), 2641–2643 (2007). [CrossRef] [PubMed]
- D. Fu, T. E. Matthews, T. Ye, I. R. Piletic, and W. S. Warren, “Label-free in vivo optical imaging of microvasculature and oxygenation level,” J. Biomed. Opt.13(4), 040503 (2008). [CrossRef] [PubMed]
- T. E. Matthews, I. R. Piletic, M. A. Selim, M. J. Simpson, and W. S. Warren, “Pump-probe imaging differentiates melanoma from melanocytic nevi,” Sci. Transl. Med.3(71), 71ra15 (2011). [CrossRef] [PubMed]
- T. E. Matthews, J. W. Wilson, S. Degan, M. J. Simpson, J. Y. Jin, J. Y. Zhang, and W. S. Warren, “In vivo and ex vivo epi-mode pump-probe imaging of melanin and microvasculature,” Biomed. Opt. Express2(6), 1576–1583 (2011). [CrossRef] [PubMed]
- P. Samineni, A. deCruz, T. E. Villafaña, W. S. Warren, and M. C. Fischer, “Pump-probe imaging of historical pigments used in paintings,” Opt. Lett.37(8), 1310–1312 (2012). [CrossRef] [PubMed]
- M. C. Fischer, T. Ye, G. Yurtsever, A. Miller, M. Ciocca, W. Wagner, and W. S. Warren, “Two-photon absorption and self-phase modulation measurements with shaped femtosecond laser pulses,” Opt. Lett.30(12), 1551–1553 (2005). [CrossRef] [PubMed]
- P. Samineni, Z. Perret, W. S. Warren, and M. C. Fischer, “Measurements of nonlinear refractive index in scattering media,” Opt. Express18(12), 12727–12735 (2010). [CrossRef] [PubMed]
- J. W. Wilson, P. Samineni, W. S. Warren, and M. C. Fischer, “Cross-phase modulation spectral shifting: nonlinear phase contrast in a pump-probe microscope,” Biomed. Opt. Express3(5), 854–862 (2012). [CrossRef] [PubMed]
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