Quasi-phase-matching [1] makes it possible even for high-order nonlinear processes in ${\chi ^{(2)}}$ materials to access substantial effective nonlinear coefficients. Early work in periodically poled lithium niobate (PPLN) demonstrated that this facility, when combined with the high intensities available within guided-wave devices, enabled a form of supercontinuum generation that exploited multiple cascaded and high-order three-wave interactions to generate supercontinua [2]. This approach has since been refined both theoretically [3] and experimentally [4] to deliver greater control of such processes, but it has remained limited to waveguide devices, and principally to the material lithium niobate. Engineerable phase matching in semiconductors like orientation-patterned gallium arsenide (OPGaAs) [5] and orientation-patterned gallium phosphide (OPGaP) [6] has enabled the demonstration of highly efficient ultra-broadband or extremely tunable femtosecond optical parametric oscillators [7,8]. In particular, OPGaP combines transparency extending well into the visible region with a high nonlinear coefficient (${d_{14}} = 70.6\;{{\rm pm}\,{\rm V}^{ - 1}}$) [9] that results in a nonlinear figure of merit ($d_{\rm eff}^2/{n^3}$) 3 times that of PPLN [9]. When such a high nonlinear coupling is available along with a strong driving field, many high-order processes become relatively efficient in quasi-phase-matched media; for example, the first report of optical parametric oscillation in OPGaP observed ninth-order visible light generation using narrow-linewidth nanosecond pump pulses [9].

Here we report broadband supercontinuum generation in OPGaP pumped by 1040 nm pulses from a sub-100 fs Yb:fiber laser operating at 100 MHz (Chromacity 1040). As illustrated in Fig. 1, the pulses are tightly focused into a 27 µm period crystal of length 1 mm, achieving intensities in excess of ${20}\;{\rm GW}\,{{\rm cm}^{ - 2}}$ in the crystal. Spectra were recorded using a visible spectrometer (Ocean Optics QEPro) to cover 400–900 nm and an optical spectrum analyzer (Ando AQ6317B) for longer wavelengths. Various reflective and transmissive color filters were used to isolate wavebands near 1040 nm (pump, measured at low power), 450–650 nm (all visible outputs), $ \lt {500}\;{\rm nm}$ (blue/green supercontinuum), near 520 nm [pump second-harmonic generation (SHG) and green supercontinuum], and $ \gt {600}\;{\rm nm}$ (red supercontinuum), allowing their spatial distributions to be recorded with a beam profiling camera. The purpose of these measurements was to examine the beam quality and structure of the supercontinuum components; comparison of the relative beam sizes in Fig. 1 is not possible due to the varying profiling camera positions necessitated by the different filtering arrangements used.

 

Fig. 1. Supercontinuum generation experiment. Stretched pulses from an Yb:fiber laser were de-chirped in a grating compressor before being focused into an OPGaP crystal (X). The resulting supercontinuum was measured using a visible spectrometer and optical spectrum analyzer (OSA), and also with a beam profiling camera. Intense pump light was rejected using two attenuators (A), and beam profiling employed different color filters (C) to isolate: (a) pump light at 1040 nm; (b) all visible outputs; (c) wavelengths $ \lt {500}\;{\rm nm}$; (d) wavelengths at ${520}\;{\rm nm}{\rm \pm }{10}\;{\rm nm}$; and (e) wavelengths $ \gt {600}\;{\rm nm}$. Profiles were measured at different observation planes, so their relative sizes are not comparable.

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The evolution of the supercontinuum spectrum is presented in Fig. 2(a) for average pump powers increasing linearly to 3.2 W, corresponding to an intensity of around ${20}\;{\rm GW}\,{{\rm cm}^{ - 2}}$. At the highest pump intensity, the spectral coverage extends from the blue/green to the red, from approximately 450–600 nm, and then in the infrared from 950–1250 nm. The broad visible coverage can be readily seen from the photograph in Fig. 2(b), which was recorded after dispersing the visible components of the spectrum using a diffraction grating and imaging the spectrum with a lens. The generation is only observed when the pump pulses, which are produced by an Yb:fiber master-oscillator power-amplifier system, are fully compressed to their minimum durations of around 100 fs.

 

Fig. 2. (a) Upper panels: output spectra at maximum pump power, recorded using a visible spectrometer and an optical spectrum analyzer. Lower panels: evolution of the supercontinuum for average pump powers from zero to 3.2 W. (b) Photograph of the visible output corresponding to approximately 450–600 nm. A weak violet color is visible at the short-wavelength edge of the image.

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The fundamental origin of the supercontinuum generation can be understood by considering the main image of Fig. 3, which presents the phase-matching efficiency map ${{\rm sinc}^2}( {\Delta kL/2} )/{m^2}$ for $m$th-order difference-frequency mixing between wavelengths in the range 500–650 nm. It shows that the second harmonic of the laser at 520 nm (marked as the white dashed line on Fig. 3) can act as a pump to parametrically amplify neighboring longer wavelengths from around 550–600 nm. Shorter wavelengths are amplified by lower-order processes than higher wavelengths, and so they experience stronger conversion because of the $1/{m^2}$ dependence of the parametric gain coefficient. While the high-order phase-matching loci occupy very narrow bands, they lie diagonally on the phase-matching map, which means that the spectral bandwidth of a broadband pump wave can be translated into the parametric signal wavelength. To illustrate this, the right panel of Fig. 3 shows the spectrum of a few-nanometer (nm)-wide 520 nm pump wave, whose product with the phase-matching map is shown in the top panel of Fig. 3 and compared with the experimental supercontinuum. Good agreement is seen in the positions of the first few peaks, corresponding to $m = 5$, 7, and 9. The positions of the higher-order peaks agree less well, but this is not surprising since even tiny errors in the refractive index data used for the calculation [10] are amplified by a factor of $m$ and can result in noticeable changes to the phase-matching loci.

 

Fig. 3. Fundamental and high-order ($m={3 - 17}$) phase-matching loci for difference-frequency mixing in a 27 µm period OPGaP crystal of length 1 mm. Interaction efficiency, proportional to ${{\rm sinc}^2}( {\Delta kL/2} )/{m^2}$, is represented by the color map. Strong second-harmonic light centered at 520 nm (dashed line) acts as a pump to amplify neighboring longer wavelengths that satisfy a high-order phase-matching condition. The bandwidth of the 520 nm pump pulses is transferred into these signal pulses, which have sufficient spectral width to form a supercontinuum. This process is illustrated by considering how a narrow 520 nm pump spectrum (right axis) is mapped into multiple signal pulses (top axis, green). For comparison, the top axis shows in red the experimentally measured spectrum, whose maxima agree well with those predicted for $m = 5$, 7, and 9. At higher values of $m$, the experimental and calculated behaviors are more sensitive to uncertainties in the OPGaP fabrication and in the Sellmeier equations, leading to differences in the positions of the conversion maxima.

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The above analysis assumes that some seed light already exists at wavelengths longer than 520 nm. By using a numerical simulation to solve a combined ${\chi ^{( 2 )}}$ and ${\chi ^{( 3 )}}$ nonlinear envelope equation (NEE), we show that frequency-doubled self-phase modulation (SPM) sidebands of the pump light are the origin of this seed light. Our NEE model provides a rigorous means of analyzing ultra-broadband pulse evolution in a medium possessing both an engineered ${\chi ^{( 2 )}}$ nonlinearity in the form of a quasi-phase-matched grating and an intrinsic ${\chi ^{( 3 )}}$ nonlinearity. Unlike the coupled-wave equations, such an approach makes no prior assumptions about the number of interacting fields or the processes involved. A similar method has already been successfully applied to predict the structure of an octave-spanning supercontinuum generated in a PPLN waveguide [3,4].

The intra-crystal focus has a Rayleigh range of 6.5 mm at 1040 nm, meaning that linear diffraction is insignificant over the crystal length of 1 mm, so our approach follows the $ 1 +1{\rm D}$ formalism in [11–15], which leads to a NEE with the form

The refractive index of GaP was taken from a new temperature-dependent Sellmeier equation [10], which has validity from 700 nm to 12.5 µm and was expected to provide more accurate short-wavelength values than the more commonly used expression in [16]. Wavelength-dependent linear absorption at wavelengths close to the band edge was included using data from [17]. Using the NEE and data for ${\chi ^{( 2 )}}$ and ${\chi ^{( 3 )}}$ in OPGaP from [9] and [18], respectively, we modeled the supercontinuum generation, taking as the input a transform-limited pulse with a spectrum matching that measured experimentally at 1040 nm. We then normalized the pulse peak power so that the energy matched the experimental values and calculated the intensity according to the experimental focal-spot radius of 25 µm. The confocal parameter for this focal spot size is 13 mm, so linear diffraction can be neglected; however, spatio-temporal effects are not included in the model but do manifest themselves experimentally, as explained later.

In Fig. 4 we present the propagation modeling results for a 27 µm OPGaP grating. Powers are chosen to match the range examined experimentally in Fig. 2. Using the NEE model allows us to separately investigate the contributions from the ${\chi ^{( 2 )}}$ and ${\chi ^{( 3 )}}$ nonlinearities. The color maps show the calculated evolution of the visible and infrared spectra as the laser power is increased from zero to 3.2 W, with the upper axes showing the maximum-power spectra when both nonlinearities are present, or when just ${\chi ^{( 2 )}}$ or ${\chi ^{( 3 )}}$ is present. With both nonlinearities present, Fig. 4 shows that SPM broadens the input laser spectrum to span from 950–1250 nm; SHG then converts the most intense central components into the light at 520 nm that will act as a pump, while the weaker longer wavelengths seed the high-order parametric gain process. With ${\chi ^{( 2 )}} = 0$, no frequency-doubled light is observed, while with ${\chi ^{( 3 )}} = 0$, the input laser spectrum remains unbroadened, and no second-harmonic light of sufficiently long wavelength is available to seed the supercontinuum process.

 

Fig. 4. Simulated evolution of the visible and near-infrared spectra after propagation through a 1 mm long OPGaP crystal fabricated with a grating period of 27 µm. The upper panels show the spectra obtained at maximum pump power (3.2 W) and the effect on these of switching off either the ${\chi ^{( 2 )}}$ or ${\chi ^{( 3 )}}$ nonlinearity.

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The NEE model, while elucidating the processes responsible for supercontinuum generation, exhibits power distributions within the fundamental and supercontinuum spectra that differ from those observed experimentally by showing stronger SPM. Beam-profile data for the fundamental wavelength are presented in Fig. 5, revealing a power-dependent defocusing effect that cannot be explained by either Kerr self-focusing or thermal lensing, both of which imply positive lensing in GaP and would result in a tighter focus and stronger SPM than we observe. Instead, we attribute the weaker SPM to self-defocusing of the fundamental beam due to cascaded second-order effects [19]. Using the analysis presented in Ref. [20], it can be shown that ${\chi ^{( 2 )}}( {\omega ;2\omega , - \omega } ):{\chi ^{( 2 )}}( {2\omega ;\omega ,\omega } )$ cascading causes the fundamental beam to experience a peak nonlinear phase shift of $ - 19\;{\rm rad} $, corresponding to $n_2^{{\rm eff}} \approx - 6.2 \times {10^{ - 13}}\;{{\rm cm}^2}\,{{\rm W}^{ - 1}}$, opposite in sign and nearly ${10} \times $ larger than ${n_2}$ (Kerr) $ = 6.5 \times {10^{ - 14}}\;{{\rm cm}^2}\,{{\rm W}^{ - 1}}$. Strong negative defocusing is associated with this nonlinearity, leading to a self-limiting behavior that suppresses further SPM-driven spectral broadening. Extending the existing NEE model to a spatio-temporal simulation including thermal, Kerr, cascaded-${\chi ^{( 2 )}}$, and even photorefractive effects [21,22] would be needed to adequately capture the full dynamics of the supercontinuum process, but its accuracy would ultimately be limited by uncertainties in experimental and material parameters, e.g., grating nonuniformity.

 

Fig. 5. Profiles of the fundamental beam after the OPGaP crystal, showing a power-dependent self-defocusing effect, which we attribute to cascaded second-order effects. Panels (a) and (b) show, respectively, the $x$ and $y$ beam profiles at minimum (blue) and maximum (red) powers. The corresponding color maps show the beam intensity on a linear scale, indicating a divergence that approximately doubles as the power is increased from 60 mW to 3.38 W.

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Fig. 6. Full-spectrum NEE simulation, showing long-wave infrared generation above 7 µm, corresponding to idler radiation from difference-frequency mixing between 520 nm and wavelengths shorter than 562 nm.

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Our assertion that parametric gain in the green is responsible for the supercontinuum generation process is further confirmed in Fig. 6, which illustrates the long-wave infrared generation observed in the NEE model above powers where SPM broadens the spectrum to a range sufficient to generate the necessary seed wavelengths. Infrared generation occurs above 7 µm, corresponding to peak parametric gain below 562 nm, as observed experimentally. The exceptional properties of OPGaP, which combines a phase-matchable ${\chi ^{( 2 )}}$ nonlinearity with a high ${\chi ^{( 3 )}}$ nonlinearity and simultaneous transmission in the visible and long-wave infrared, make it uniquely suitable for such an intra-pulse supercontinuum process. Indeed, optical parametric oscillation pumped at 1.04 µm has been reported at wavelengths extending to 13.5 µm [23], and OPGaP’s transparency extends to 17 µm, with the exception of an absorption around 14 µm.

In summary, we have reported the first example of supercontinuum generation in a bulk nonlinear crystal pumped by a high-repetition-rate femtosecond laser oscillator. Visible light generation is a result of 520 nm pumped parametric gain, which amplifies weak SPM sidebands while simultaneously generating long-wavelength idler light. A power-dependent defocusing effect observed in tandem with supercontinuum generation is attributed to cascaded second-order effects in the OPGaP crystal, and it serves to self-limit the amount of SPM-induced spectral broadening in the crystal. With the ready possibility of using engineered quasi-phase-matching to enhance the high-order effects responsible for supercontinuum generation, it may be possible to reduce the average power needed to levels where greater spectral broadening is achieved along with reduced parasitic effects.