Coherent Super Continuum Generation in Photonic Crystal Fibers at Visible and Near Infrared Wavelengths

IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014 7500309

Coherent Super Continuum Generation in PhotonicCrystal Fibers at Visible and Near

Infrared WavelengthsKaisar R. Khan, M. F. Mahmood, and Anjan Biswas

Abstract—Physical mechanisms those interplay in generating su-per continuum from femto-second pulses propagated through pho-tonic crystal fiber (PCF) have been investigated here. We comparespectrums from two distinct PCFs with different group velocitydispersion profiles to determine the most desirable spectral fea-tures such as stronger and ripple free output spectra at wavelengthregions of interest, specifically around near infrared wavelengthwhich we can use for coherent anti-Stokes Raman Scattering mi-croscopy of lipid-rich structures. Coherency of the pulses fromthese two PCFs was also compared. The spectrums from theoreti-cal model will provide us guidance for future experiments.

Index Terms—Photonic crystal fiber (PCF), super continuum,coherent anti-stokes Raman scattering (CARS).

I. INTRODUCTION

THE generation of very broad spectra, called super contin-uum in photonic crystal fiber (PCFs) has attracted much

attention due to its application in bio photonic imaging andfrequency metrology [1]–[3]. It was Ranka and other whodemonstrated the first super continua in PCFs using low powertitanium-sapphire laser pulses [1], [4], [5]. In a PCF, small ef-fective area of the mode leads to high intensities in the fiberseven at low pulse energy (in the order of pJ) [6]–[8]. Sangeetaand other experimentally demonstrate coherent anti-stokesRaman scattering (CARS) microscopy using a single unam-plified femtosecond Ti: sapphire laser and a PCF with twoclosely lying zero dispersion wavelengths (ZDW) for the Stokessource [9]. Unique dispersion characteristics of PCF effectivelydetermine the dynamics of the super continuum generation, oneof the reasons being the possibility to control the phase-matchingof several nonlinear processes [3], [10], [11].

In general, super continuum generation is due to multiple non-linear processes such as four-wave mixing, stimulated Raman

Manuscript received November 28, 2013; revised January 2, 2014; acceptedJanuary 15, 2014.

K. R. Khan is with the Department of Electrical Engineering Tech-nology, State University of New York, Canton, NY 13617 USA (e-mail:[email protected]).

M. F. Mahmood is with the Department of Mathematics, Howard University,Washington, DC 20059 USA (e-mail: [email protected]).

A. Biswas is with the Department of Mathematical Sciences, Delaware StateUniversity, Dover, DE 19901–2277 USA and also with the Department ofMathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSTQE.2014.2302353

scattering (SRS) and other soliton dynamics [10]–[12]. Todaythe generation can be controlled by engineering the dispersionand appropriate choice of input parameters such as pulse width,wavelength and pulse average power etc. [3], [9]–[11]. For aspecific PCF geometry, the input parameters interplay togetherto determine the spectrum of the propagated pulse and alsoidentify which parameter is dominating the particular physicalaspect of pulse spectrum evolution.

Light from a tunable Ti:sapphire laser can produce ∼65 fspulses at 80 MHz repetition rate [9], [13]. These pulses can belaunched to a PCF with two closely lying ZDW s (NL-1.4–775–945, Crystal Fiber A/S, Denmark) for one analysis. In anotheranalysis we consider the similar laser pulse which was launchedto another PCF with widely spaced ZDWs (NL-PM-750, CrystalFiber A/S, Denmark). The group velocity dispersions (GVD) ofthese two PCFs are shown in Fig. 1 [14].

In both cases for a pulse launched at around 800 nm wave-length we observed depletion of pump beam and formation oftwo distinguished continuous lobes (Stoke and anti-Stoke) atboth sides of the pump wavelength. It is mostly the distinct dis-persion characteristics of the PCFs that determine the spectraldifferences for the two femto second pulses launched with sim-ilar input parameters propagating through these two types ofPCFs. We also investigate the phase of the propagated pulses tocheck the coherency of the signals as highly coherent signal isdesirable for CARS microscopy application.

II. DEVELOPED MODEL FOR SUPER CONTINUUM GENERATION

In order to explain super continuum generation in PCF weneed accurate values for the dispersion and nonlinear parame-ters of the fiber for a wide frequency range (at least the range offrequency that covers the generated spectrum) [7], [8], [13]. Weincorporate the measured dispersion values in the model [14].Input pulse power level along with the fiber’s dispersion de-termines the contribution of nonlinear processes [7]–[12]. Bothsolitonic and non-solitonic radiations are observed while thepulses are propagating through the PCF [8]–[10]. At higher in-put power, it is evident that the other frequencies are generateddue to several nonlinear processes such as self phase modula-tion (SPM), wave-mixing and SRS [8]–[11]. One term is moreprominent at one input level over other. As the input param-eters such as power, pulse duration and wavelength change,the different physical mechanism starts to interplay with eachother. Also the dispersion profile and length of the PCF have astrong impact on the shape of the spectrum. Time and frequency

1077-260X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications standards/publications/rights/index.html for more information.

7500309 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 20, NO. 5, SEPTEMBER/OCTOBER 2014

Fig. 1. GVD of (a) PCF with two closely separated ZDW and (b) PCF with two widely separated ZDW (Courtesy Crystal Fiber Inc.).

domain investigation of the pulse phase evolution along its prop-agation distances are necessary to determine the coherency ofthe super continuum signal. From Tsunami laser a soliton likepulse emitted which is reasonably modeled by hyperbolic se-cant function [12]. We can add either up or down chirp using aprism compressor before launching it to the PCF for continuumgeneration. A chirped soliton pulses can be symbolized by thefollowing equation [12]:

q(0, τ) =√

P0 sec h

(τ

τ0

)exp

(− iCτ 2

2τ 20

). (1)

Here P0 is normalized incident peak power; τ0 is 1/e halfwidth of pulse intensity, for an average power Pav and pulserepetition rate f, P0 = Pav /(τ0 ∗ f); C is the chirp parameterwhich can be positive (up chirp) or negative (down chirp). Thepulse propagation equation is described by the generalized non-linear Schrodinger equation (GNLSE) which includes physicalmechanism such as dispersion, SPM, SRS [3], [10]–[12]:

i∂q

∂z− β2

2∂2q

∂τ 2 − iβ3

6∂3q

∂τ 3 +β4

24∂4q

∂τ 4 + γ

(1 + i

1ω

∂

∂τ

)q

∫ ∞

−∞{(1 − fR )δ(t) + fRhR (t)}q(z, τ − t)dt = 0 (2)

where β2 is the GVD and β3 and β4 are the third (3OD) andfourth order dispersion (4OD), respectively. The integral termof the (2) is the Raman response function, where fR = 0.18,

hR =τ1 + τ 2

2

τ1τ 22

e(−t/τ2 ) sin(t/τ1). (3)

Here τ1 = 12.2 fs, τ2 = 32 fs [3], [12]. Also γ is the nonlinearparameter which we chose from the PCF data sheet as 1.8 ×10−3 cm−1 W−1 [14]. The solution of (2) for a balanced disper-sion and nonlinearity provide us with a soliton solution [8]–[12].The constraint condition to have a soliton solution is [15]

γ(κβ3 + β2) > 0 (4a)γ

κβ3 + β2= Constant. (4b)

Here κ represents soliton frequency. These are valid for 3OD.If we consider the 4OD, then the equation permits integrabilityonly for stationary solitons. However intra-pulse Raman scatter-ing is a dissipative perturbation term that accounts for downshiftin soliton frequency [3], [12]. We used split step Fourier methodto numerically solve the above (2) [12]. As the dispersion valuesare quite different in the range of wavelength that the spectrumspread, we consider higher order dispersion term to accuratelymatch the dispersion. We include β2 , β3 and β4 in our model.Inclusion of higher order terms will increase the accuracy of thecalculation.

A. Physical Processes Involved in SuperContinuum Generation

The physical processes that govern the super continuum gen-eration in PCFs can be very different, depending particularlyupon the chromatic dispersion, length of the fiber as well asthe input parameters. When femtosecond pulses are used, thespectral broadening can be dominantly caused by SPM [8]–[11].In the anomalous dispersion regime, the combination of SPMand dispersion can lead to soliton dynamics, including the split-up of higher-order soliton into multiple fundamental soliton(soliton fission) [3], [8], [10], [11]. In some cases, when SPM isdominant and dispersion is normal, the process is very determin-istic, and the phase coherence of the generated super continuumpulses can be very high, even under conditions of strong spec-tral broadening [3], [10], [11]. Temporal and spectral coherencyis determined by the deterministic nature of the signal outputintensity and phase. With known dispersion and at relativelylower power the signal shows better coherency. In other cases(e.g., involving higher-order soliton effects), the process canbe extremely sensitive to the slightest fluctuations (includingquantum noise) [3], [16]. This situation occurs at higher inputpower when nondeterministic process such as Raman scatteringstarts contributing with the presence of higher order soliton. Thequantum noise does break the coherency and is discussed in theliterature [17]. Considering additive random noise in equation

KHAN et al.: COHERENT SUPER CONTINUUM GENERATION IN PHOTONIC CRYSTAL FIBERS 7500309

(1) the impact of noise can be observed. For intensity randomnoise term should be added with power P0 and for phase noisethe term should be added with chirp C. The random noise doesaggravate the coherency and causes the output signal more non-deterministic. Experimentally reported CARS signal at extremepressure and temperature was also previously reported for chem-ical detection [18]. The strong nonlinear nature of super contin-uum generation makes it difficult to intuitively understand all thedetails of the interaction, or to predict relations with analyticaltools. Therefore, numerical pulse propagation modeling (oftenwith special precautions due to the extreme optical bandwidth)is required for the analysis of such processes [3], [8], [10], [11].Some of the physical process has been discussed in this sectionare interrelated to each other and exist simultaneously in the su-per continuum. Intuitive pictures or analytical guidelines can betested by comparison with results from such numerical modelsas well as from the experiments.

Optical field experiences self-induced phase shift while prop-agating through optical fibers. Magnitude of the phase shift is

φ = nk0L = nk0L + n2 |E|2 k0L (5)

where k0 = 2π/λ, n is the refractive index of the glass, n2 is thenonlinearity constant, E is the electric field and L is the fiberlength [12]. The second term of above equation is nonlinearphase induced due to SPM. SPM is responsible for spectralbroadening for the ultra-short pulses and formation of solitonin the anomalous dispersion regime of fiber (β2 < 0) [12]. Athigher power SPM is more and causes wider broadening of thespectrum. So it is expected that the spectrum will be widen athigher input power. The results were previously reported in [8]for dual core PCF. Simulation results shown in the later sectionsfor these types of PCF also confirm it.

A four wave mixing (FWM) is one of the process whichdetermine the coherency of the signal. Degenerate FWM pro-duces two photons from a pump beam with frequency ωP areconverted into a signal photon with frequency ωS and an idlerphoton with frequency ωI . Phase-matching is achieved whenboth energy (6) and momentum (7) conserve:

Δω = ωS + ω| − 2ωP = 0 (6)

Δβ = β(ωS) + β(ω|) − 2β(ωP) + ΔβNL = 0. (7)

For example the SC used for CARS microscopy, the PCFs arepumped using a fs Ti:Sapphire laser at center wavelength closeto 800 nm. When this wavelength is used as either the Stokesor the pump beam, we suggest an optimum PCF candidate togenerate the second wavelength needed for lipid imaging ateither 648 nm or 1027 nm, respectively. This enables a compactsystem where the generated super continuum can be used eitheras Stokes or pump beam, and the Ti:Sapphire laser can be usedas the other wavelength [3], [9]–[11]. In our calculation we haveused 800 nm as pump and 1040 nm as signal wavelength.

The nonlinear contribution to the propagation constantΔβN L = 2γP0 originates from self-phase and cross-phase mod-ulation [3], [10]–[12]. The phase-matching condition can alsobe expressed in terms of the even terms in the Taylor expansion

Fig. 2. Soliton number with average power for the 280 fs pulse propagatedthrough PCFs having GVD profile shown in Fig. 1 at 800 nm pump wavelength.

of the propagation constant [10]–[12]:

2∞∑

n=1

β2n

(2n)!Ω2n + 2γP0 = 0 (8)

where Ω is the frequency difference between the pump andthe signal/idler frequencies. If the intensities are sufficientlyhigh FWM occur between the soliton and the non-solitonicradiation (NSR) contributing to the generation of new frequencycomponents in the spectrum. NSR can be associated with thepresence of higher order soliton represented by soliton number,

N =

√γτ0Pav

|β2 | f. (9)

With the PCF having GVD showed in Fig. 1 and average laserpower between 200–480 mW with 80 MHz repetition rate, thevalue of N = 170–270 for first PCF with two closely separatedZDW and around half for the second PCF with two widelyseparated ZDW. Fig. 2 shows the soliton number for the twoPCFs at pump wavelength of 800 nm. The values have beenselected from the PCF data sheet [14].

The phase mismatch plot in Fig. 3 obtained by solving equa-tion (3) demonstrates that both PCFs show similar phase match-ing near the pump wavelength but at longer wavelength thesecond PCF with widely separated ZDWs shows more phasemismatch.

In super continuum, SRS act as a non-parametric processwhere energy is lost due to the vibration excitation of the ma-terial. Raman scattering is the origin of a self-frequency shiftincreasing with propagation length of solitons to longer wave-lengths. Raman scattering can be explained as scattering of lighton the optical phonons and 1/τ 1 gives the optical phonon fre-quency. 1/τ 2 gives the bandwidth of the Lorentzian line [3], [12].The self-steepening effect given through the time derivative ofthe nonlinearity in the nonlinear Schrodinger equation is signif-icant for short pulses. This is prominent at higher input pulse


Fig. 3. Phase mismatch for the 280 fs pulse propagated through two different PCFs at an average power of (a) 20 mW and (b) 200 mW.

Fig. 4. Spectrum at the output of a 12.5 cm long two closely separated ZDW, PCF at different input pulse power: (a) 200 mW average power and (b) 480 mWaverage power.

power. The term represents the frequency dependent rate ofchange of SPM. Similar to SPM it is prominent at higher inputpower [12], [19], [20].

III. RESULTS AND DISCUSSIONS

A. Spectral Features of Pulse Through Two Closely SeparatedZDW PCF

The super continuum generation experiment that involve twoclosely separated ZDW PCFs, shows two distinct lobes at bothside of the pump wavelength and also spectrum is broadenedas the input pulse power increases. The fundamental reasonof complete depletion of the pump wave and generating twodistinct lobe is due to FWM which is perfectly phase matchedaround those wavelength. The dispersion profile of this PCFplays a significant role in the spectrum. SPM is the primary

cause of the spectral broadening and which is power dependent.Results in Fig. 4 confirm these characteristics of the spectrum.In the figure we observe depletion of the spectrum for an inputpulse launched at 800 nm.

As the input power increases the depletion grows. This is be-cause at higher input power phase matching is more pronounced.The results were in good agreement with the experimental re-sults reported in [9], [13]. We also conducted simulation toobserve the effect of individual term of GNLSE (2) on the spec-tral profile. We start removing each term of the equation (2)such as the shock and Raman term. In Fig. 5 we are comparingthe spectrums of a 280 fs pulse with different input power. Thispulse at femto second range demonstrates some interesting non-linear phenomena that were not visible for longer pulse width.Also, there were some CARS experiments previously reportedfor 200 to 300 fs [9], [13], [16]. The figures demonstrate that


Fig. 5. Spectral profile at the output of a 12.5 cm long PCF with two closely separated ZDW showing the effect of different terms of GNLE: (a) 200 mW averagepower and (b) 480 mW average power.

Fig. 6. 3-D view of the 280 fs pulse propagation through the 12.5 cm PCF with two closely separated ZDW at different average input power: (a) 200 mW and(b) 480 mW.

the IR lobe is more affected by these terms. The self steepening(shock) term demonstrates negligible effect on the IR lobe andon the other hand Raman term shows significant effect on the IRpart of the spectrum. This effect is more visible at higher inputpower.

Three-dimensional (3-D) view of the spectrum in Fig. 6 showsthat the pump wave split shortly after it starts propagating. Theseparation of the two lobes is wider as the pulse propagates withdistance and also at higher input power as well. At higher powerthe spectral lobes gets broadened as expected. It is accountedfor stronger SPM at higher input power. Splitting of solitonicpulse spectrum is mainly due to comparable GVD and higherorder dispersion while pulse starts propagating.

From the phase diagram at the Fig. 7 we observe that thephase relative to the phase of input pulse peak at 200 mW is less

variable than that at 480 mW. It is expected that at higher inputpower as the SPM is intense which results less matching thanat lower power. Again that is also depends on the dispersionprofile of the PCF. It is also noticed that the phase variation isminimum at the depleted region and increases toward both lobe.

Fig. 8 displays the pulse spectrum at the output of the PCFwith variable input power. As discussed earlier, the power de-termines the nature of energy radiation of the pulse. The figureshows solitonic radiation at a relatively low power (less than20 mW) for the same PCF with dispersion shown in Fig. 1(a).Our soliton solution with the constrain condition mentioned inequation (4) his point. Beyond 20 mW spectrum demonstratesNSR due multiple nonlinear processes such as FWM, SRS etc.The constrain conditions in equation (4) do not hold any more.Splitting of the spectrum is primarily due to FWM and we also


Fig. 7. 3-D view of the 280 fs pulse phase while propagating through the PCF with two closely separated ZDW (a) at 200 mW and (b) at 480 mW.

Fig. 8. Evolution of output (at 12.5 cm) spectrum at different power level forPCF with two closely separated ZDW.

observe that as the power increases the separation between thetwo lobes also increases earlier and then at higher power regionthis separation remain almost same. This implicates that FWMis efficient and prominent in this PCF for moderate input powerbut beyond a certain power level it was no longer an efficientcoherent (FWM) process. Rather it is the higher order solitonicradiation (soliton fission) that dominates at these power levels.It is soliton fission that causes multiple split in both lobes (morein infrared).

B. Spectral Features of Pulse Through Two Widely SeparatedZDW PCF

Similar as the spectrum generated from the other PCF, the twowidely separated ZDW PCF demonstrates two distinct spectrallobes in visible and near infrared but this time the pump waveis not completely depleted. It was predicted earlier that becauseof the different dispersion profile, this PCF will show differ-ent spectral features. Fig. 9 shows the simulated spectrum. Wealso observe similar spectral broadening with increase of powerwhich due to stronger SPM again. Another notable contrast

Fig. 9. Spectrum at the out put of two widely separated ZDW, PCF at differentinput pulse power (a) 200 mW average power and (b) 480 mW average power.


Fig. 10. Spectrum at the out put of a 12.5 cm long PCF with two widely separated ZDW showing the effect of different terms of GNLE (a) 200 mW averagepower and (b) 480 mW average power.

Fig. 11. 3-D view of the 280 fs pulse propagation through the PCF with two widely separated ZDW (a) at 200 mW and (b) at 480 mW.

between the spectrum generated from the other type of PCFand this spectrum is the incomplete depletion of the pump sig-nals. Less efficient FWM due to different dispersion profile ofthe PCFs is the primary cause of this difference. In the pumpwavelength of 800 nm this PCF demonstrate 10 time higherGVD.

For this type of PCF with two widely separated ZDW, weagain turn on and off different terms of the GNLSE and ob-serve the contribution of different physical process which wasrepresented by individual terms of the equation on the spectrumgenerated by the femto second pulse propagated through thisPCF. Unlike the spectrum generated from the other type of PCF,we observed in the Fig. 10 that the Raman term does not havethat much effect in the IR lobe.

Fig. 11 shows the 3-D view of the spectrum of the 280 fs pulsepropagated through the two widely separated ZDW PCF. Similarto the spectrum generated from the other PCF we observe that

separation of the two lobes increases as the pulse propagate.Also higher input power causes wider separation. The GVDaround pump wavelength (700 nm–900 nm) for a two widelyseparated ZDW PCF is much below the zero dispersion line thanthat of a two closely separated ZDW PCF (about 10 times less).This actually leads to less phase matching in PCF with GVDshown in Fig. 1(b) than that in the other PCF with GVD shownin Fig. 1(a).

We also observe the phase changes in the phase diagramshown in Fig. 12. Phase of two widely separated ZDW PCF,is much away from the zero phase line than the other PCF’sphase around same wavelength region. Also it shows similarless coherence as the power increases. We compare the co-herency of the signal from these two PCFs. Both PCF showssimilar coherency around 1.0–1.1 um which is our targeted fin-ger print region for the bio photonic imaging of lipid reachcompounds.


Fig. 12. 3-D view of the 280 fs pulse phase while propagating through the PCF with two widely separated ZDW (a) at 200 mW and (b) at 480 mW.

IV. CONCLUSION

We numerically showed the evolution of coherent super con-tinuum spectra generated from a femtosecond pulses propagat-ing through two distinct PCFs with different dispersion profiles.For a typical PCF with widely separated ZDWs supporting fem-tosecond pulses pumped in the anomalous dispersion regime,the dynamics of super continuum generation is due to the com-bined effect of phase matched parametric process and decay ofhigher order solitons emitting radiations. On the other hand fora fiber with dispersion profile with two closely separated ZDWphase matched FWM process cover a wide range of frequencies.In general the importance of phase-matched processes such asFWM increases with decreasing bandwidth of the pulses, cor-responding to increasing length of the pulses. This two closelyseparated ZDW PCF shows better coherence of the propagatedpulses than the two widely separated ZDW PCF. The nonlinearresponses grow with increasing intensity and it is consequentlyeasier to address various nonlinear effects at higher intensities.

ACKNOWLEDGMENT

The authors would like acknowledge the help of R. Ramsyof Cristal Wave Inc. for providing the dispersion data of thePCFs. Also special thanks go to Dr. G. P. Agrawal for valuabletechnical discussions.

REFERENCES

[1] A. Bjarkiev, J. Broeng, and A. S Bjarkiev, Photonic Crystal Fibers.Norwell, MA, USA: Kluwer, 2003.

[2] J. C. Knight, “Photonic crystal fibres,” Nature, vol. 424, pp. 847–51, 2003.[3] J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in

photonic crystal fiber,” Rev. Mod. Phys., vol. 78, pp. 1135–1184, 2006.[4] J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum gener-

ation in air silica microstructure optical fibers with anomalous dispersionat 800 nm,” Opt. Lett., vol. 25, no. 1, pp. 25–27, 2000.

[5] C. M. Bowden and A. M. Zheltikov, “Nonlinear optics of photonics crys-tals, feature issue,” J. Opt. Soc. Amer. B., vol. 19, pp. 2046–2296, 2002.

[6] A. Betlej, S. Suntsov, K. G. Makris, L. Jankovic, D. N. Christodoulides,G. I. Stegeman, J. Fini, R. T. Bise, and D. J. DiGiovanni, “All-optical

switching and multi-frequency generation in a dual core photonic crystalfiber,” Opt. Lett., vol. 31, pp. 1480–1482, 2006.

[7] K. R. Khan and T. Wu, “Short pulse propagation in wavelength selectiveindex guided photonic crystal fiber coupler,” IEEE J. Sel. Topics QuantumElectron., vol. 14, no. 3, pp. 752–757, May/Jun. 2008.

[8] K. R. Khan, T. X. Wu, D. N. Christodoulides, and G. I. Stegeman, “Solitonswitching and multifrequency generation in nonlinear photonic crystalfiber,” Opt. Exp., vol. 16, no. 13, pp. 9417–9428, 2008.

[9] S. Murugkar, C. Brideau, A. Ridsdale, M. Naji, P. K. Stys, and H. Anis,“Coherent anti-stokes Raman scattering microscopy using photonic crystalfiber with two closely lying zero dispersion wavelengths,” Opt. Exp.,vol. 15, no. 21, pp. 1428–1437, 2007.

[10] K. Hilligsoe, T. Andersen, H. Paulsen, C. Nielsen, K. Molmer, S. Keiding,R. Kristiansen, K. Hansen, and J. Larsen, “Supercontinuum generation ina photonic crystal fiber with two zero dispersion wavelengths,” Opt. Exp.,vol. 12, pp. 1045–1054, 2004.

[11] M. H. Frosz, P. Falk, and O. Bang, “The role of the second zero-dispersionwavelength in generation of supercontinua and bright-bright soliton-pairsacross the zero-dispersion wavelength,” Opt. Exp., vol. 13, pp. 6181–6192,2005.

[12] G. P Agrawal, Nonlinear Fiber Optics, 3rd ed. New York, NY, USA:Academic Press, 2001.

[13] M. Naji, S. Murugkar, K. Khan, and H. Anis, “Coherent anti stokes Ramanscattering (CARS) microscopy using photonic crystal fiber,” presented atthe Photon. West, San Fransisco, CA, USA, Jan. 2010.

[14] Data sheet, Crystal Fiber Inc. (now NKT photonics Inc.), Blokken,Denmark, 2008.

[15] P. D. Green and A. Biswas, “Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media,” Commun. Nonlinear Sci.Numer. Simul., vol. 15, pp. 3865–3873, 2010.

[16] K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams,K. Weber, and R. S. Windeler, “Fundamental noise limitations to super-continuum generation in microstructure fiber,” Phys. Rev. Lett., vol. 90,pp. 113904-1–113904-4, 2003.

[17] J. M. Dudley and S. Coen, “Coherence properties of supercontinuumspectra generated in photonic crystal and tapered optical fibers,” Opt.Lett., vol. 27, pp. 1180–1182, 2002.

[18] A. F. Goncharov, D. A. Dalton, R. Stewart McWilliams, andM. F. Mahmood, “Development of ultrafast spectroscopic techniques tostudy rapid chemical and physical changes in materials under extremepressure and temperature conditions,” in Mater. Res. Soc. Symp. Proc.,vol. 1405, 2012. [Online]. Available: http://www.fpl.fs.fed.us/documnts/pdf2012/fpl_2012_melgarejo001.pdf.

[19] D. N. Christodoulides and R. I. Joseph, “Femtosecond solitary waves inoptical fibers,” Electron. Lett., vol. 20, pp. 559–660, 1984.

[20] E. Bourkoff, W. Zhao, R. I. Joseph, and D. N. Christodoulides, “Evo-lution of femtosecond pulses in single mode fibers having higher-ordernonlinearity and dispersion,” Opt. Lett., vol. 12, pp. 272–273, 1987.


Kaisar R. Khan received the Ph.D. degree in elec-trical engineering from the University of CentralFlorida, Orlando, FL, USA, in 2008. He then wenton to join the University of Ottawa as a Postdoc-toral Fellow. Currently, he is with State Univer-sity of New York Canton, Canton, NY, USA, as anAssistant Professor of Electrical Engineering. He wasinvolved in several industry collaborative, multidis-ciplinary research projects on computational electro-magnetic, nonlinear optics, and nano photonics. Priorto resuming his graduate study in the USA, he was

working as an Engineer in the nationalized telecommunication service providerin Bangladesh from where he completed his electrical engineering undergrad-uate education. His current research interests include applied electromagneticand meta-material, nanophotonics, and femto second-pulse propagation throughoptical waveguides.

M. F. Mahmood received the Ph.D. degree in physicsfrom Howard University, Washington, DC, USA, in1988. He is both an Experimental Laser Physicist andan Applied Mathematician. His Postdoctoral work isin material science. He is a Professor in the Depart-ment of Mathematics, Howard University. He is alsoa Visiting Scientist at the Geophysical Laboratory,Carnegie Institution of Washington, Washington andworks on a funded research project on energetic mate-rials under extreme conditions using Broad Band Op-tical and Coherent Antistokes Raman Spectroscopy.

His theoretical research interests include solitons in optical fibers and metama-terials. He advises both Ph.D. students and postdoctoral fellows.

Anjan Biswas received the B.Sc. (Hons.) degreefrom Saint Xavier’s College in Calcutta, India. Sub-sequently, he received the M.Sc. and M. Phil. de-grees in applied mathematics from the University ofCalcutta, Calcutta. Then, he received the M.A. andPh.D. degrees in applied mathematics from the Uni-versity of New Mexico in Albuquerque, New Mexico,USA. After that he carried out his Postdoctoral stud-ies in applied mathematics from the University ofColorado, Boulder, CO, USA. He was then an As-sistant Professor of Mathematics at Tennessee State

University, Nashville, Tennessee. Currently, he is working as an Associate Pro-fessor of Mathematics at Delaware State University, Dover, DE, USA. Hisresearch interest is on theory of solitons.

Documents

Coherent Super Continuum Generation in Photonic Crystal Fibers at Visible and Near Infrared Wavelengths