Supercontinuum generation in water by intense, femtosecond laser pulses under anomalous chromatic dispersion

We report efficient generation of a broadband supercontinuum (SC) in water upon irradiation by intense, near-infrared, femtosecond laser pulses. The SC spectra generated when the pump wavelength lies in the anomalous chromatic dispersion region are characterized by largely blueshifted peaks in the visible range. These SC spectral features are rationalized within the framework of a phenomenological self-phase-modulation model, taking into account higher-order group velocity dispersion. Our model provides an intuitive explanation for the relation between the observed pump-wavelength dependence of the blueshifted SC peaks and the anomalous chromatic dispersion.

Figure 1

Supercontinuum (SC) spectra generated in undoped water by 55 fs pulses at ${\lambda }_{pu}=1300$ nm ($P_{pu}=90$ MW, green) and ${\lambda }_{pu}=1350$ nm ($P_{pu}=500$ MW, red). Even though both the pump wavelengths are within the anomalous chromatic dispersion range (appreciable absorption) of water, the SC spectra are surprisingly broad, spanning more than two octaves. They are characterized by well-separated peaks in the visible range. Note the blueshift and the narrowing of the visible peak with increasing ${\lambda }_{pu}$.

Figure 2

(a) Normalized SC spectra generated in undoped water by femtosecond pulses centered at ${\lambda }_{pu}=800$ nm ($P_{pu}=55$ MW, violet), 1200 nm ($P_{pu}=55$ MW, magenta), 1250 nm ($P_{pu}=55$ MW, blue), 1300 nm ($P_{pu}=55$ MW, green), and 1350 nm ($P_{pu}=90$ MW, red). Vertical dash-dotted line marks the spectral ranges of the two spectrometers used. The two spectral ranges are normalized separately and spectra are shifted vertically for clarity. Gray dashed lines mark the shift in the SC peaks with ${\lambda }_{pu}$. Pump pulse spectrum (black dotted lines) for each case is also shown for comparison. (b) Spectral position of the visible peak (${\lambda }_{vis}^c$, symbol) and IR ($▵{\lambda }_{ir}$, red) as well as visible ($▵{\lambda }_{vis}$, blue) spectral extents of the SC as a function of ${\lambda }_{pu}$. Blueshifted peak is seen only when pumped under the anomalous GVD range ($>$1100 nm). As in Fig. 1, the visible peaks shift to blue and get narrower with increasing ${\lambda }_{pu}$.

Figure 3

(a) Refractive index ($n$, black) and measured absorbance (red) in undoped water. The refractive index is calculated using the Sellmeier equation given in the literature [41, 42]. (b) Second- ($k^{\prime \prime }$) and third- ($k^{\prime \prime \prime }$) order GVD coefficients calculated using $n$ shown in (a). The GVD in water changes sign at $\sim$1100 nm. For longer wavelengths, the anomalous chromatic regime is characterized by rapidly increasing $k^{\prime \prime \prime }$ due to increasing absorbance. (c) Normalized intensity spectrum (red) of a Gaussian pulse centered at 1300 nm, having FWHM of 100 nm, and its spectral phase in the presence of (i) no dispersion (black dotted), (ii) only second-order GVD (quadratic, black dashed), and (iii) second- and third-order GVD (quadratic + cubic, black solid). (d) Normalized temporal intensity profiles of the Gaussian pulse shown in (c) considering GVD of different orders. $P^n\left(\varphi \right)$ represents the order of the spectral phase polynomial used to obtain the intensity profile. The temporal profiles are shifted vertically for clarity.

Figure 4

(a) Comparison between the observed (dotted) and simulated (solid) SC spectra after accounting for absorption in undoped water. Vertical dash-dotted line marks the spectral ranges of the two spectrometers used. The two spectral ranges are normalized separately and the spectra are shifted vertically for clarity. Gray dashed lines mark the shift in the SC peaks with ${\lambda }_{pu}$. The SC spectra are simulated using a phenomenological SPM model considering second- and third-order GVD. (b) Effect of various GVD terms on the SC spectrum (${\lambda }_{pu}=1300$ nm). Odd-order GVD (third being the lowest) is essential for the occurrence of the blueshifted peak. Adding higher-order GVD terms to the spectral phase polynomial $P^n\left(\varphi \right)$ improves the match between simulated and observed spectra.

Figure 5

(a) Comparison of normalized undoped-water SC spectra recorded at $P_{pu}\sim 110$ MW (solid) and $P_{pu}\sim 55$ MW (dotted) for ${\lambda }_{pu}=1200$ nm (bottom) and ${\lambda }_{pu}=1300$ nm (top). There is marginal narrowing of the IR as well as the visible component at higher pump power, possibly due to the competing nonlinear absorptive processes. (b) Enhancement in SC spectral extent by adding metal nanorods to water shown for two pump wavelengths ${\lambda }_{pu}=1200$ nm (bottom) and ${\lambda }_{pu}=1300$ nm (top) at $P_{pu}\sim 55$ MW. SC spectra for undoped water (dotted) are shown for comparison. Vertical dash-dotted line marks the spectral ranges of the two spectrometers used. The two spectral ranges are normalized separately and spectra are shifted vertically for clarity.

Figure 6

(a) Linear extinction spectrum of the gold-nanorod-doped water showing prominent longitudinal SPR peak at 626 nm and transverse SPR peak at 515 nm. (b),(c) Transmission electron microscope images of gold nanorods (25 nm diameter, 55 nm length) used in our experiments. (d) Size distribution deduced from (b).