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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 21 — Oct. 17, 2005
  • pp: 8555–8564
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Efficient broadband emission from condensed media irradiated by low-intensity, unfocused, ultrashort laser light

A.K. Dharmadhikari, F. A. Rajgara, D. Mathur, H. Schroeder, and J. Liu  »View Author Affiliations


Optics Express, Vol. 13, Issue 21, pp. 8555-8564 (2005)
http://dx.doi.org/10.1364/OPEX.13.008555


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Abstract

We report here measurements of the efficiencies of broadband emission in different optical media using an unfocused, ultrashort (~40 fs) laser beam. Two different measurements have been carried out by placing a wire mesh in the path of the incident laser radiation. The wire mesh introduces a periodic intensity distribution in the x-y plane and also in the direction of the laser beam propagation. We measure both on-axis and off-axis components of the broadband emission and also observe modulation in broadband generation as the distance between the mesh and the sample is varied. The experimentally measured locations of broadband emission maxima are in agreement with simulations based on Fresnel diffraction integrals. The off-axis emission efficiencies lie in the range of 16–87%.

© 2005 Optical Society of America

1. Introduction

Supercontinuum production, or the generation of broadband emission due to the propagation of intense, ultrashort light pulses through optical media, continues to excite considerable interest in the laser physics and nonlinear optics community even though it has been the topic of exploration for many decades after it was first demonstrated by Alfano and Shapiro in the early 1970’s [1–3

1 . R.R Alfano and S.L. Shapiro , “ Emission in the region 4000 to 7000 Å via four-photon coupling in glass ,” Phys. Rev. Lett. 24 , 584 – 587 ( 1970 ). [CrossRef]

]. The physics governing such emission is of intrinsic interest [4

4 . S.L. Chin , S.A. Hosseini , W. Liu , Q. Luo , F. Théberge , N. Aküzbek , A. Becker , V.P. Kandidov , O.G. Kosareva , and H. Schroeder , Can. J. Phys. 83 , 863 – 905 ( 2005 ). [CrossRef]

] and of importance in that ultra-broadband coherent radiation sources [5

5 . J.K. Ranka , R.S. Windler , and A.J. Strenz , “ Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm ,” Opt. Lett. 25 , 25 – 27 ( 2000 ). [CrossRef]

,6

6 . A.L. Gaeta , “ Nonlinear propagation and continuum generation in microstructured optical fibers ,” Opt. Lett. 27 , 924 – 926 ( 2002 ). [CrossRef]

] are of obvious utility in the generation of ultrashort, sub-femtosecond light pulses [7

7 . M. Nisoli , S. Stagira , S. De Silvestri , O. Svelto , S. Sartania , Z. Cheng , M. Lenzner , Ch. Spielmann , and F. Krausz , “ A novel-high energy pulse compression system: generation of multigigawatt sub-5-fs pulses ,” App. Phys. B 65 , 189 – 196 ( 1997 ). [CrossRef]

,8

8 . A. Baltuska , Z.Y. Wei , M.S. Pschenichnikov , and D.A. Wiersma , “ Optical pulse compression to 5 fs at a 1 Mhz repetition rate ,” Opt. Lett. 22 , 102 – 104 ( 1997 ). [CrossRef] [PubMed]

]. Such sources will open new vistas of high field science in the ultrashort, few optical cycle regime, with diverse applications in the physical and biological sciences.

At high values of incident laser intensity, it has been demonstrated that when focused, intense, ultrashort (~45 fs duration) laser pulses propagate through high-bandgap bulk optical media like barium fluoride, a nearly flat spectrum of white light is produced that spans the wavelength region from 400 nm to 1000 nm [9

9 . A. K. Dharmadhikari , F. A. Rajgara , N. C. Reddy , A. S. Sandhu , and D. Mathur , “ Highly efficient white light generation from barium fluoride ,” Opt. Express 12 , 695 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695 . [CrossRef] [PubMed]

]. High conversion efficiencies, of the order of 40% to 70%, have been shown to be the norm in such experiments [9

9 . A. K. Dharmadhikari , F. A. Rajgara , N. C. Reddy , A. S. Sandhu , and D. Mathur , “ Highly efficient white light generation from barium fluoride ,” Opt. Express 12 , 695 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695 . [CrossRef] [PubMed]

]. The flatness of the spectra that are produced appears to depend on the duration of the incident laser pulse; measurements indicate that tenfold-longer pulse durations (~300 fs) at similar incident peak powers do not produce broadband light with nearly the same flatness of spectrum [10

10 . A. K. Dharmadhikari , F. A. Rajgara , and D. Mathur , “ Systematic study of highly efficient white light generation in transparent materials using intense femtosecond laser pulses ,” App. Phys. B 80 , 61 – 66 ( 2005 ). [CrossRef]

]. The efficiency of broadband light generation was also shown to depend on parameters like the focal position inside the medium, and the polarization state and pulse duration of the incident radiation [10

10 . A. K. Dharmadhikari , F. A. Rajgara , and D. Mathur , “ Systematic study of highly efficient white light generation in transparent materials using intense femtosecond laser pulses ,” App. Phys. B 80 , 61 – 66 ( 2005 ). [CrossRef]

].

Although the use of very high intensity light pulses can yield very high values of broadband light conversion efficiency and impressively flat broadband spectra, damage to the optical medium is a major problem when the incident intense light beam is tightly focused. We describe here a new set of measurements on broadband light generation that we have carried out in two different laboratories using various transparent materials without focusing the incident ultrashort laser beam with a lens. The new methodology that we adopt in these experiments involves the use of a wire mesh, and is based on the following premise.

It is known that the spatial profile of a train of femtosecond laser pulses is not expected to possess a perfectly smooth envelope but will contain small amplitude irregularities. During propagation through a nonlinear medium these amplitude irregularities break up into separate filaments. Koechner [11

11 . W. Koechner , “ Solid-state laser engineering, 2 nd edition ,” Springer-Verlag, Berlin ( 1988 ).

] has described this physical process as interference between a strong beam and weak beams, producing index variations due to the intensity-dependent refractive index. The diffraction of the strong beam by the resulting phase grating “spills” energy into the weak beams. The filament formation is random in nature and cannot be controlled. However, Schroeder and coworkers have recently shown [12

12 . H. Schroeder , J. Liu , and S.L. Chin , “ From random to controlled small-scale filamentation in water ,” Opt. Express 12 , 4768 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768 . [CrossRef] [PubMed]

] that by placing a wire mesh in the path of the incident laser radiation, such filamentation may, indeed, be controlled and the mesh, thus, aids the “spilling” of the energy into weak beams. A wire mesh not only introduces a strongly modulated intensity distribution in the x-y plane but also in the z-direction, that is, in the direction of the laser beam propagation. This intensity distribution is caused by interferences which locally give rise to intensity minima and intensity maxima. These maxima are the seed for nonlinear processes in the optical medium.

The mesh simulates the normal case of beam propagation, where multiple filamentation is observed due to small-scale inhomogeneities in the incident laser beam. Because of diffraction and interference, these inhomogeneities give rise to complicated hot spot distributions along the propagation axis. The diffraction due to the mesh can be understood by assuming that the ‘normal’ beam is superimposed by a stronger but controlled inhomogeneity pattern. Moreover, treating the mesh as a local focusing element (also known as a diffraction optical element) permits us to accurately measure the efficiency of conical (off-axis) emission. The incident beam remains essentially parallel at low intensities, in contrast to the situation when a focusing geometry is used. Only beyond a certain threshold value of incident laser power does the beam exhibit extra divergence (conical emission), thus reducing the on-axis intensity. The fact that quantitative data on conical emission has hitherto not been available in the literature suggests that our mesh approach provides a unique method to measure efficiencies for the off-axis emission. In particular, we demonstrate in the following that conical emission is the major loss channel that counterbalances catastrophic self focusing in optical media.

2. Experimental details

Our experiments were carried out with unfocused laser pulses of ~40 fs duration and 810 nm wavelength of 600 μJ maximum energy in one set of experiments (at Mumbai), and with a maximum of 2 mJ energy, 50 fs pulse duration and 810 nm wavelength light in the other (at Garching). We measured broadband emission and monitored the energy profiles of the emitted light as the distance between the wire mesh and the medium was varied. In contrast to the usual situation that would be obtained if a focusing lens were used, where the fundamental beam would first converge and then diverge, the overall beam in our case remained essentially parallel. The beam diameter was 3 mm in both sets of experiments, and the active area of the detectors used was ~1 cm2. The stainless steel mesh that we used was of dimension 200 μm × 200 μm, with wire thickness of 95 μm and 50% light transmission in the one case. In other experiments, the mesh was of dimensions 443 μm × 443 μm, with wire thickness of 54 μm. In both instances, the introduction of the wire mesh introduced amplitude irregularities and created a symmetric diffraction pattern [12

12 . H. Schroeder , J. Liu , and S.L. Chin , “ From random to controlled small-scale filamentation in water ,” Opt. Express 12 , 4768 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768 . [CrossRef] [PubMed]

].

By spatially scanning the mesh in a direction perpendicular to the laser propagation direction (Fig. 1), we were able to expose the sample to different laser intensity profiles along the light propagation. Such a spatially modulated beam was used to irradiate diverse optical media in our experiments, such as BaF2 (a crystal of length 75 mm), blocks of acrylic (50 mm thickness) and glass (16 mm thickness) as well as doubly distilled water contained in a 50 mm length cuvette. Other media that were used in our experiments were organic liquids like perfluorooctane, methanol, ethanol, acetone, toluene, benzene and carbon disulphide as well as 1 cm long crystals of some fluorides, SiO2, sapphire and YAG. The generation of broadband light was observed in each instance and the conversion efficiency measured.

In a typical set of measurements the mesh-to-sample distance was increased from 1 cm to 40 cm in steps of 1 cm, with the minimum distance being when the mesh was actually in contact with the sample. This refers to the zero on the horizontal axis of data shown in Fig. 2 which depicts the white light intensity variation as a function of mesh-sample distance for various samples. The energy meter that we used had a nearly flat and wide spectral response that covered the range 400–1100 nm. The same energy meter was used to measure both the incident energy as well as energy of the generated continuum.

Fig. 1. Schematic depiction of the experimental arrangement used in the present experiments. Emission was detected in the far field, at a distance of 60 cm downstream of the sample. z=0 corresponds to the mesh in physical contact with the front face of the sample.

3. Results and discussion

Figure 2 shows measured energy profiles of broadband emissions from different media (BaF2, acrylic, BK-7 glass, and water) when an unfocused, low intensity, parallel laser beam (600 μJ) fell on the mesh and, thence on different samples. Changing the distance between the mesh and the sample along the direction of light propagation exposed the samples to different intensity profiles of the incident light, thus resulting in varying amounts of broadband emission due to non-linear propagation effects. Correspondingly, we observed modulation in the intensity of the broadband light that was generated: positions of low intensity (minimum or no white light) and high intensity (maximum white light) were observed, as shown in Fig. 2. When the ultrashort pulses were incident on the mesh in the absence of any sample in the diffracted beam path, such intensity modulation was not observed as the mesh was scanned along the laser beam propagation direction.

We have simulated fluctuations in the emitted light intensity using Fresnel’s diffraction integrals to calculate the local intensities [EP(x0,y0z)]2 at any point downstream of the mesh. For a two-dimensional aperture, the electric field at a point (x0,y0) on the image plane is given by the Fresnel-Kirchoff diffraction integral (in rectangular Cartesian coordinates):

EPx0y0=A0iλzHxyexp(ikr)dxdy,
(1)

where A0 is the intensity at a unit length from the source, z is the distance between the aperture and the image screen, and H(x,y) is the aperture function. The variable r=r(x,y) is the distance between the point of interest on the aperture plane (x,y) and the point of interest on the image plane (x0y0). This distance can be expressed as:

r=z+(xx0)2+(yy0)22z+O(3)+.....
(2)

Considering terms upto the second order, the integral becomes

EPx0y0=A0eik2ziλzHxyexp{i(k2z)[(xx0)2+(yy0)2]}dxdy.
(3)

For the case of a two-dimensional grid, the aperture function can be accurately specified and the electric field for a test point (x0,y0) on the axis becomes

EPx0y0=A0eik2ziλznmEn,m(12)a+n(a+α)(12)a+n(a+α)exp{i(k2z)[(xx0)2]}dx×
(12)a+m(b+β)(12)a+m(b+β)exp{i(k2z)[(yy0)2]}dy.
(4)

Here, α and β are the wire thickness of the grid in the x- and y-directions, respectively. Similarly, a and b are the dimensions of the open rectangles that define our wire mesh. The variables n and m are used to label the cells in the grid. En,m is the electric field amplitude in the (n,m)th cell. Since the cells are small compared to the beams radius in our case, the amplitude can be taken to be constant within that cell. It should also be noted that Gaussian laser beams have a radial variation in phase that has been neglected here to simplify calculations.

Fig. 2. Variation of the far field energy produced at different distances between the mesh and sample. The physical length of each sample is indicated. Note that prominent peaks and dips that are observed in all cases. The solid lines are a guide to the eye.

Figure 3 shows the z-scan data for the off-axis part (conical emission) of broadband intensity in the forward direction, in contrast to the on-axis data depicted in Fig. 2. In the latter case of far-field data, it is clear that the intensity modulation is most prominent for the shortest sample length, and appears to be washed out for longer sample lengths. For longer sample lengths, more intensity loci are expected to become active; the net effect would be a higher yield of broadband emission. In Fig. 3 we record the continuum energy (λ<600 nm) and again observed rapid intensity modulation. The solid curve shows the corresponding simulation. We assume that the z-dependence of the continuum generation is linked to the maximum laser intensity locally present in the x-y plane. We deduced the maximum local intensity by taking a number of test points (typically, we used 21 test points) while shifting the z-position in increments of 4 mm. The correspondence between experiments and simulations is clearly reasonable. It should also be noted that for this particular case (11 × 11 mesh), the local maximum increase is about a factor of 7.

Fig. 3. Variation of relative continuum energy at different mesh-sample distances. Top panel: experimental scheme. The mesh used was 11 × 11, 443 μm × 443 μm, wire thickness of 54 μm, throughput energy of 190 μJ. Bottom panel: comparison between the experimental variation (shaded) and results of simulations (see text).

We now discuss the spectral composition of the broadband emission generated in materials like BaF2, BK7 glass and water when the mesh was placed close to each sample. The spectral measurements were made using a fiberoptic-coupled spectrometer. Typical data that we obtained are shown in Fig. 4. From our measured data it is observed that the spectrum of the broadband emission is significantly broader in the case of water than for either BaF2 or BK7. In case of water, emission on the blue side is considerably enhanced when compared to that in BaF2 and BK7.

Fig. 4. Wavelength spread that is generated when the mesh is placed close to different samples. The spectrum of the incident laser light is also depicted (Amplifier). Normalization of peaks has been made at 800 nm. The spectra were measured using a fiber-optic spectrometer.

We now address the question of the conversion efficiency for broadband emission that is obtained in different media. We recall that by spatially scanning the wire mesh we are basically exposing the irradiated sample to different intensity profiles. In the far field the diffraction angle is determined by the outer mesh contour. Our energy detector covered an area of 1 cm2. The detected energy remained constant when we placed the detector as far as 2m downstream of the mesh (the far field position) and, subsequently, increased the distance by another 40 cm (without a sample in the beam path). The energy also remained constant when we inserted the sample cell but, at the same time, we decreased the input power by a factor of 100 (by temporal stretching of the laser pulse length to 4ps). Only the transmitted energy was somewhat reduced (by 8%) due to the window reflectivities in such cases. The trace that was thus recorded is taken as a baseline for the series of efficiency measurements that are presented in the data set depicted in Fig. 6. The base line characterizes the case when there is no conical emission as a result of non-linear propagation effects. We also obtained a nearly constant energy signal when we again applied the full intensity but placed the detector as close as possible to the exit window of the cell. This indicates that the emission that is generated is only emitted in the forward direction, and that there are no other detectable losses, such as those due to thermal effects or effects due to plasma formation. Moreover, this is a simple manifestation of the conservation of energy in the case of non-linear propagation. In this context we note that on using the same mesh and identical sample sizes, an energy dip in measurements of the type shown in Fig. 2 would be expected to correspond to a peak in the conical emission of the type depicted in Fig. 3.

Fig. 5. Spectra obtained from water for different values of incident laser energy.
Fig. 6. Determination of conversion efficiency for broadband emission for different liquid samples (see text).

Now, by placing the energy meter back into the far field position and performing the scans of mesh-sample distance we obtain a strongly modulated energy signal whose morphology is, indeed, the mirror image of the broadband light intensity variations depicted in Fig. 3. This simply means that a major part of the broadband emission fails to hit the detector area. We can now quantify the conversion efficiency for broadband emission, as it is clearly determined by the energy loss with respect to the base line.

The results obtained with eight liquid samples are presented in Fig. 6. Although all measured liquids exhibited a similar intensity variation as the mesh-sample distance was varied, they are found to be remarkably different with respect to their conversion efficiencies. Our results indicate that perfluorooctane is the least efficient liquid (15.8%) for emission while CS2 is the most efficient. We also noted that the relative intensity modulation that we obtained for perfuorooctane was considerably larger compared to that obtained with CS2.

A compilation of the off-axis broadband emission conversion efficiencies that we measured is presented in Table 1 for a range of crystalline solids (1 cm length) and liquids.

Table 1:. Conversion efficiency values for conical emission from different samples measured in the present experiments. Values of nonlinear refractive index, n2 [13], and the ionization energy, IE (or bandgap, Eg), for each sample are also tabulated. Values of conversion efficiency were measured, in each instance, at an intensity of ~4.7 × 1011 W cm-2.

table-icon
View This Table

The table also lists the nonlinear index of refraction, n2, which has been calculated for a wavelength of 800 nm [13

13 . R. Adair , L.L. Chase , and S.A. Payne , “ Nonlinear refractive index of optical crystals ,” Phys. Rev. B 39 , 3337 – 3350 ( 1989 ). [CrossRef]

] and the gas phase ionization energy, IE, or bandgap, Eg, for each sample. It appears clear to us that our conversion efficiency values correlate rather well with n2, and not so well with IE or Eg.

The far field spectra for perfluooctane, benzene, and water as well as the reference spectrum of the incident beam are displayed in Fig. 7. They confirm the different conversion yields. It is also important to realize that the on-axis part (the non-conical part) does not contain any new spectral features. Furthermore, the spectra are very asymmetric, as has been noted in earlier experiments with focused beams [4

4 . S.L. Chin , S.A. Hosseini , W. Liu , Q. Luo , F. Théberge , N. Aküzbek , A. Becker , V.P. Kandidov , O.G. Kosareva , and H. Schroeder , Can. J. Phys. 83 , 863 – 905 ( 2005 ). [CrossRef]

]. It can be shown that this blue/red asymmetry can be altered by chirping the laser pulse, but further work along this direction is still in progress.

Fig. 7. Far-field wavelength spectra measured for different liquid samples. The integrating sphere was placed 2 m downstream of the sample cell in these measurements. The mesh-sample distance was optimized for maximum intensity of the white light signal.

4. Concluding remarks

In summary, we have reported results of experiments on broadband emission from various condensed media upon irradiation by an unfocused, low-intensity, ultrashort laser beam. We have used a wire mesh to introduce a periodic intensity distribution in the x-y plane, and also in the direction of the laser beam propagation. Using such a beam we observe broadband emission due to non-linear propagation. Two different types of measurements have been performed by us: measuring the on-axis and off-axis broadband emission. We measure significant modulation in broadband emission generated as the distance between the mesh and the sample is varied in both types of measurements. These modulations are reduced in the case of longer samples.

We have also measured the efficiency of off-axis broadband emission. We interpret the measured efficiency values using the conservation of energy during the nonlinear propagation of ultrashort laser pulses through condensed media in the presence of a wire mesh. These efficiencies vary in the range of 16–87 % for different media. We know of no other values for conical emission efficiencies in the literature.

References and Links

1 .

R.R Alfano and S.L. Shapiro , “ Emission in the region 4000 to 7000 Å via four-photon coupling in glass ,” Phys. Rev. Lett. 24 , 584 – 587 ( 1970 ). [CrossRef]

2 .

R.L. Fork , C.V. Shank , C. Hirlimann , R. Yen , and W.J. Tomlinson , “ Femtosecond white light continuum pulses ,” Opt. Lett. 8 , 1 – 3 ( 1983 ). [CrossRef] [PubMed]

3 .

A.L. Gaeta , “ Catastrophic collapse of ultrashort pulse ,” Phys. Rev. Lett. 84 , 3582 – 3585 ( 2000 ). [CrossRef] [PubMed]

4 .

S.L. Chin , S.A. Hosseini , W. Liu , Q. Luo , F. Théberge , N. Aküzbek , A. Becker , V.P. Kandidov , O.G. Kosareva , and H. Schroeder , Can. J. Phys. 83 , 863 – 905 ( 2005 ). [CrossRef]

5 .

J.K. Ranka , R.S. Windler , and A.J. Strenz , “ Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm ,” Opt. Lett. 25 , 25 – 27 ( 2000 ). [CrossRef]

6 .

A.L. Gaeta , “ Nonlinear propagation and continuum generation in microstructured optical fibers ,” Opt. Lett. 27 , 924 – 926 ( 2002 ). [CrossRef]

7 .

M. Nisoli , S. Stagira , S. De Silvestri , O. Svelto , S. Sartania , Z. Cheng , M. Lenzner , Ch. Spielmann , and F. Krausz , “ A novel-high energy pulse compression system: generation of multigigawatt sub-5-fs pulses ,” App. Phys. B 65 , 189 – 196 ( 1997 ). [CrossRef]

8 .

A. Baltuska , Z.Y. Wei , M.S. Pschenichnikov , and D.A. Wiersma , “ Optical pulse compression to 5 fs at a 1 Mhz repetition rate ,” Opt. Lett. 22 , 102 – 104 ( 1997 ). [CrossRef] [PubMed]

9 .

A. K. Dharmadhikari , F. A. Rajgara , N. C. Reddy , A. S. Sandhu , and D. Mathur , “ Highly efficient white light generation from barium fluoride ,” Opt. Express 12 , 695 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695 . [CrossRef] [PubMed]

10 .

A. K. Dharmadhikari , F. A. Rajgara , and D. Mathur , “ Systematic study of highly efficient white light generation in transparent materials using intense femtosecond laser pulses ,” App. Phys. B 80 , 61 – 66 ( 2005 ). [CrossRef]

11 .

W. Koechner , “ Solid-state laser engineering, 2 nd edition ,” Springer-Verlag, Berlin ( 1988 ).

12 .

H. Schroeder , J. Liu , and S.L. Chin , “ From random to controlled small-scale filamentation in water ,” Opt. Express 12 , 4768 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768 . [CrossRef] [PubMed]

13 .

R. Adair , L.L. Chase , and S.A. Payne , “ Nonlinear refractive index of optical crystals ,” Phys. Rev. B 39 , 3337 – 3350 ( 1989 ). [CrossRef]

OCIS Codes
(190.4180) Nonlinear optics : Multiphoton processes
(320.2250) Ultrafast optics : Femtosecond phenomena

ToC Category:
Research Papers

History
Original Manuscript: August 5, 2005
Revised Manuscript: October 6, 2005
Published: October 17, 2005

Citation
A. Dharmadhikari, F. Rajgara, D. Mathur, H. Schroeder, and J. Liu, "Efficient broadband emission from condensed media irradiated by low-intensity, unfocused, ultrashort laser light," Opt. Express 13, 8555-8564 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-21-8555


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References

  1. R.R Alfano & S.L. Shapiro, �??Emission in the region 4000 to 7000 �? via four-photon coupling in glass,�?? Phys. Rev. Lett. 24, 584-587 (1970). [CrossRef]
  2. R.L. Fork, C.V.Shank, C.Hirlimann, R. Yen, & W.J. Tomlinson, �??Femtosecond white light continuum pulses,�?? Opt. Lett. 8, 1-3 (1983). [CrossRef] [PubMed]
  3. A.L. Gaeta, �??Catastrophic collapse of ultrashort pulse,�?? Phys. Rev. Lett. 84, 3582-3585 (2000). [CrossRef] [PubMed]
  4. S.L. Chin, S.A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V.P. Kandidov, O.G. Kosareva, & H. Schroeder, Can. J. Phys. 83, 863-905 (2005). [CrossRef]
  5. J.K. Ranka, R.S. Windler, & A.J. Strenz, �??Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800 nm,�?? Opt. Lett. 25, 25-27 (2000). [CrossRef]
  6. A.L. Gaeta, �??Nonlinear propagation and continuum generation in microstructured optical fibers,�?? Opt. Lett. 27, 924-926 (2002). [CrossRef]
  7. M. Nisoli, S. Stagira, S. De Silvestri, O. Svelto, S. Sartania, Z. Cheng, M. Lenzner, Ch. Spielmann, & F. Krausz, �??A novel-high energy pulse compression system: generation of multigigawatt sub-5-fs pulses,�?? App. Phys. B 65, 189-196 (1997). [CrossRef]
  8. A. Baltuska, Z.Y.Wei, M.S. Pschenichnikov, & D.A. Wiersma, �??Optical pulse compression to 5 fs at a 1 Mhz repetition rate,�?? Opt. Lett. 22, 102-104 (1997). [CrossRef] [PubMed]
  9. A. K. Dharmadhikari, F. A. Rajgara, N. C. Reddy, A. S. Sandhu, & D. Mathur, �??Highly efficient white light generation from barium fluoride,�?? Opt. Express 12, 695 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-4-695</a> [CrossRef] [PubMed]
  10. A. K. Dharmadhikari, F. A. Rajgara, & D. Mathur, �??Systematic study of highly efficient white light generation in transparent materials using intense femtosecond laser pulses,�?? App. Phys. B 80, 61-66 (2005). [CrossRef]
  11. W. Koechner, �??Solid-state laser engineering, 2nd edition,�?? Springer-Verlag, Berlin (1988).
  12. H. Schroeder, J. Liu, & S.L. Chin, �??From random to controlled small-scale filamentation in water,�?? Opt. Express 12, 4768 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4768</a> [CrossRef] [PubMed]
  13. R. Adair, L.L. Chase, & S.A. Payne, �??Nonlinear refractive index of optical crystals,�?? Phys. Rev. B 39, 3337-3350 (1989). [CrossRef]

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