Short duration, intense pulses of light can experience dramatic spectral broadening when propagating through lengths of optical fibre. This continuum generation process is caused by a combination of nonlinear optical effects including the formation of dispersive waves. Optical analogues of Cherenkov radiation, these waves allow a pulse to radiate power into a distant spectral region. In this work, efficient and coherent dispersive wave generation of visible to ultraviolet light is demonstrated in silica waveguides on a silicon chip. Unlike fibre broadeners, the arrays provide a wide range of emission wavelength choices on a single, compact chip. This new capability is used to simplify offset frequency measurements of a mode-locked frequency comb. The arrays can also enable mode-locked lasers to attain unprecedented tunable spectral reach for spectroscopy, bioimaging, tomography and metrology.
Continuum generation in microstructured optical fibre1 gained importance with the generation of broad spectra2 for application in optical frequency combs. There, a mode-locked laser is broadened as a precurser to f-2f measurement of the comb offset frequency3 and self-referencing4. The advent of frequency microcombs5 and most recently the demonstration of femtosecond pulse generation in microcavities6,7,8,9 has focused attention on techniques for supercontinuum generation on a chip. Beginning with studies of Raman and four-wave-mixing effects in monolithic waveguides10, there has been steady progress towards supercontinuum generation using a variety of on-chip waveguide materials11,12,13,14,15,16,17. Low pulse energies for efficient broadening have been demonstrated on account of large nonlinear coefficients combined with nano-scale waveguide cross sections14,15, and devices operating in the mid-infrared18,19 are possible. Moreover, self-referencing has been achieved using a silicon nitride based, monolithic waveguide on silicon20.
However, while there has been remarkable progress on visible21,22 and ultraviolet band23,24,25 continuum generation in microstructured optical fibres, as well as harmonic ultraviolet and deep ultraviolet generation in gas-filled fibres26,27, there have been no reports of chip-based ultraviolet generation. Furthermore, widely tunable emission in a single device is a feature of monolithic arrays that has no parallel in optical fibres. Arrays enable precisely targeted wavelength emission for optimal self-referencing. As shown here, their compactness also eliminates the need for delay lines in these systems. Finally, this class of devices can be combined with microcombs and compact mode-locked lasers to provide user-designed coherent, short pulse light for optical clocks28, laser cooling29, quantum manipulation of atoms and ions30, and bioimaging31.
After describing the silicon ridge waveguide array fabrication process, measurements of dispersive-wave generation are presented that include a study of the phase matching wavelength dependence upon the waveguide geometry. Application of the waveguide array to optimized self-referencing of a mode-locked Yb fibre laser is then presented. Here, the dispersive wave phase matching wavelength is precisely matched to the 2f frequency so as to provide maximum signal-to-noise in the frequency-comb offset-frequency measurement. Also, the approach eliminates the delay line used in the standard self-referencing method. Finally, the continuum spectra produced by the waveguide arrays are analysed and modelled in detail.
Silica ridge waveguide arrays
Continuum generation in waveguides results from a combination of nonlinear processes10,32. Self-phase modulation in combination with second-order anomalous dispersion induces temporal compression of an input pulse. As the pulse spectrally broadens, higher-order dispersion and Raman interactions become important and the pulse undergoes soliton fission. The resulting series of fundamental solitons experiences Raman self-frequency shifting towards longer wavelengths. If the soliton spectrum has significant overlap with spectral regions that feature normal dispersion, then it can radiate energy into a dispersive wave that phase matches to the soliton phase33. The dispersive wave, which can also be understood in terms of an analogy to Cherenkov radiation34, provides a powerful way to both engineer the spectral extent of the resulting optical continuum and to also spectrally concentrate optical power in new bands22,35. The waveguides demonstrated here apply lithographic control to engineer the generation of coherent ultraviolet to visible dispersive-wave radiation.
The waveguide geometry is shown in Fig. 1a,b and features a silica ridge design that is air-clad on three sides. The air-cladding enables a high level of optical confinement to both increase the optical nonlinearity and shift the wavelength for zero group velocity dispersion towards visible wavelengths. The fabrication of the waveguides is an adaptation of the process used for dispersion engineering in high-Q resonators36. The process flow is presented in Fig. 2. More detail on the fabrication process is provided in Supplementary Note 1. The waveguides support both transverse electric (TE) and transverse magnetic (TM) polarizations. The TM-polarization provides dispersive wave generation at shorter wavelengths.
Waveguide arrays of varying mode area (0.76–2.22 μm2) were fabricated on the silicon chip. The effective mode areas are determined by input of waveguide cross sections (measured in a scanning electron microscope, SEM) into a finite-element-method (FEM) solver. The wavelength dependence of the second-order dispersion is also calculated using the FEM solver. The Sellmeier equation was used to include the wavelength dependence of the silica refractive index37. While bulk silica features anomalous dispersion only for wavelengths beyond 1,270 nm, the geometrical dispersion introduced by the strong optical confinement of the ridge waveguide enables anomalous dispersion at much shorter wavelengths. In particular, the zero crossing of the dispersion (λZDW) can be engineered to occur over a wide range of wavelengths from 557 to 731 nm as is apparent in Fig. 1c,d. Importantly, these lie well below the pumping wavelengths of 830 and 1,064 nm that we employ.
The phase matching condition for the dispersive wave generation satisfies the following equation38:
where β(ωDW) and β(ωp) are the propagation constants at the dispersive wave frequency (ωDW) and the pump frequency (ωp), respectively, and vg is the group velocity at the pump frequency. Pp is the peak power of the pulse when the dispersive wave is generated. γ is the nonlinearity of the waveguide at the pump frequency and is given by γ=ωpn2/(cAeff) where n2 is the Kerr coefficient and Aeff is the effective mode area. Defining Δβ(ω)=β(ω)−β(ωp)−(ω−ωp)/vg, the dispersive wave phase matching condition is given by Δβ(ωDW)=γPp/2 and is plotted in Fig. 1d for an 830 nm pump. At this pump wavelength, the phase matching wavelength can be engineered to vary from 310 to 576 nm. Discussion on the range of phase matching wavelengths can be found in Supplementary Fig. 2.
Imaging dispersive waves in the array
Photographs of pumped waveguides on a single chip are combined in Fig. 1e. The laser pulse in these images is provided by a mode-locked titanium-sapphire laser (830 nm emission, 60 fs pulse width measured on an autocorrelator, and 81 MHz repetition frequency) and is coupled into the silica ridge waveguides using a × 60 objective lens. The coupling efficiency is measured to be 25–35%. As the laser pulse propagates along a given waveguide (left-to-right in image), the infrared pulse is initially invisible. The pulse undergoes temporal compression and spectral broadening because of the self phase modulation and anomalous second-order dispersion. As broadening occurs, portions of the pulse’s spectrum becomes visible. Solition fission and dispersive wave generation occur at the bright orange spot. Waveguide areas are larger for upper waveguides in the photograph and decrease towards the lower portion of the plot. Decreasing mode areas shift the phase matching condition to shorter wavelengths so that the dispersive wave generation transitions from the visible to ultraviolet. For wavelengths below 400 nm the dispersive wave is not visible in the photograph.
More details about the pulse propagation in the waveguide are provided in Fig. 3. Here, calculated spectra are plotted versus propagation length for pulse energies of 330 pJ (Fig. 3a) and 1,100 pJ (Fig. 3c). The pulse initially propagates as a higher-order soliton that undergoes temporal compression and spectral broadening until experiencing soliton fission and dispersive wave generation at a fission length, Lf, that depends upon the pulse energy (330 pJ: Lf=0.39 cm; 1,100 pJ: Lf=0.16 cm). As the input pulse energy increases, the calculated fission length decreases. This behaviour is observable in Fig. 3b where a composite of photographs of the waveguide is shown at coupled pulse energies from 330 to 1,100 pJ. Soliton fission is observable as the reddish-orange emission. The observed soliton fission length agrees well with a numerical simulation shown as the grey line.
The dispersive wave initially overlaps with the soliton pulse but walks off from the soliton with continued propagation because of group velocity mismatch (see Fig. 3d,e). Also, the dispersive wave is temporally stretched as it propagates in the waveguide because of the normal dispersion it experiences. Walk-off is a typical feature of fibre broadeners and requires a delay line to spatially overlap the octave wave (2f) and dispersive wave. However, as shown in the next section, the waveguide length can be adjusted to optimize overlap between 2f and dispersive-wave pulses. Moreover, the array, itself, provides the user with the ability to optimize the dispersive wave efficiency around a specific laser source.
Walk-off-free dispersive-wave-enhanced octave generation
Beyond the generation of broadly tunable visible light, precise dispersive-wave engineering in a monolithic waveguide can be applied both to enhance the signal-to-noise ratio as well as simplify the setup for detection of the carrier-envelope offset frequency of a laser frequency comb3. As a demonstration, f-2f offset frequency generation of a Yb fibre laser comb is performed using a silica ridge waveguide. The waveguide having a mode area of 3.13 μm2 and length of 1.50 cm is dispersion engineered so as to enhance dispersive wave formation at twice the frequency of the Yb laser comb. The experimental setup is shown in Fig. 4a. The Yb laser emits 90 fs pulses with centre wavelength of 1,064 nm (100 MHz repetition rate). Before waveguide coupling, a halfwave plate rotates the Yb laser polarization so that 80% of the total coupled pulse energy (2,300 pJ) is transmitted in the TE mode and 20% is transmitted in the TM mode of the waveguide.
The TE wave forms a dispersive wave near 532 nm. A photograph of the spectrum of the continuum is shown in Fig. 4b and a spectral scan is provided in 4c. Both the TE and TM waves are subsequently coupled to a potassium niobate (KNbO3) crystal where the TM component is phase matched for second harmonic generation. The phase-matching condition generates the second-harmonic beam that is rotated by 90° relative to the TM fundamental so that the second-harmonic polarization is aligned with the TE polarized dispersive wave. The measured doubled spectrum and the dispersive-wave spectrum are shown in Fig. 4d. After spectral filtering around 532 nm the two waves are mixed on a photodiode for offset frequency (fceo) beatnote generation. In this final step, the enhanced dispersive wave comb lines increase the beatnote strength. The electrical spectrum of the beatnotes at fceo,1=25.8 MHz and fceo,2=frep−fceo,1=73.8 MHz are shown in Fig. 4e. Both signals have a signal-to-noise ratio >34 dB at an electrical resolution bandwidth of 300 kHz. This establishes the coherent nature of the dispersive wave and is more than sufficient for subsequent self-referenced servo control of the comb.
Beyond the enhanced signal-to-noise provided by the ability to select an optimal waveguide in the array for matching to the 2f frequency, there is a key simplification enabled by colinear generation of dispersive and second harmonic waves. The overall group velocity dispersion between the TE dispersive wave and the TM wave at 1,064 nm in both the waveguide array and the KNbO3 crystal is such that both the dispersive wave and the second-harmonic pulses emerge from the doubling crystal with a high degree of spatial overlap (that is, walk-off-free). As a result, a major simplification is possible by eliminating the traditional step of path-length balancing using a Michelson interferometer. Instead, the two pulses (the dispersive wave and the second-harmonic pulse) can be directly coupled to the photodetector39.
To further probe the behaviour of the dispersive wave generation process, spectral measurements were performed at varying waveguide cross sectional areas. For these measurements, the titanium sapphire laser was used (see earlier discussion) and the experimental setup included an attenuator to vary the input pulse energy, as well as a half-wave plate to control polarization. The light output from the waveguides is endfire-coupled to a multimode fibre for the measurement on a spectrometer. To cover the entire spectral range of interest two spectrometers were used: a Yokogawa (AQ6370D, 600–1,700 nm) and an Ocean Optics (HR4000, 200–900 nm).
Measured supercontinuum spectra are shown in Fig. 5a for TM and TE polarized pulses launched into waveguides of varying mode area in the waveguide array shown in Fig. 1e. Conversion of pump light in the near infrared to visible and ultraviolet wavelength dispersive waves is apparent in each spectrum. A summary of measured dispersive wave emission wavelengths λDW versus mode area is provided in Fig. 5b. Controlled tuning of the dispersive wave from 310 to 576 nm with an average 8 nm interval is demonstrated in the TM mode and from 475 to 613 nm in the TE mode. Also included in Fig. 5b is the predicted dispersive wave emission wavelength using the phase matching condition (equation (1)). The measurement result agrees well with the calculation.
To investigate the conversion efficiency of the input pulse from the near-infrared into ultraviolet–visible wavelengths (300–650 nm), a ultraviolet fused silica aspheric lens (transmission 200–2,000 nm) was used to collect the light exiting the waveguides. The optical power in the ultraviolet–visible wavelengths was then filtered out with a bandpass filter and measured by a thermopile power metre (nearly uniform spectral response). The power was calibrated using the wavelength-dependent transmission curves of the bandpass filter and the measured supercontinuum spectra. The scatter plot of measured conversion efficiency (and average dispersive wave power) plotted versus dispersive wave peak wavelength for both polarizations is shown in Fig. 5c. For this measurement, conversion efficiency is defined as the dispersive wave power at the waveguide output divided by the total collected spectral power at the waveguide output. The spectral extent of the dispersive wave was defined by selecting wavelengths where the power spectral density of the dispersive wave had fallen to 5% of the maximum value.
Using the Yb laser emission at 1,064 nm, it was also possible to investigate even deeper ultraviolet dispersive wave generation below 300 nm. This observation is consistent with the phase-matching condition for dispersive wave generation (Supplementary Fig. 2). Figure 5d shows supercontinuum spectra measured in the TM mode of two waveguides having cross-sectional areas of 1.09 and 1.12 μm2 using a coupled pulse energy of approximately 2,000 pJ. The spectra feature multiple peaks because of soliton breathing and subsequent dispersive wave emission. The shortest wavelength edge of the spectrum is nearly 265 nm for the case of the waveguide with mode area 1.09 μm2.
A silicon chip based waveguide array has been applied to generate ultraviolet to visible light by conversion of an input pulse into a dispersive wave. The dispersive wave emission wavelength is precisely tuned from ultraviolet to visible by lithographic control of the waveguide dimensions. Generation of ultraviolet emission as short as 265 nm has been demonstrated. The measured and predicted dispersive wave emission wavelengths are in excellent agreement. Arrays-on-a-chip containing hundreds of waveguides are easily fabricated and provide ready access to a range of emission wavelengths using a single pump laser. This chip-based tuning control allows for optimization of emission for spectroscopy and metrology using a single device. As a demonstration, offset frequency generation in a Yb mode-locked laser frequency comb was demonstrated by designing a waveguide to generate a dispersive wave that is optimally matched to the second harmonic of the original 1 μm comb. Significantly, this demonstration also confirms the high coherence of the dispersive wave generated by these waveguides. Moreover, the ability to tailor the chip length to provide walk-off-free self-referencing was demonstrated. Monolithic waveguide arrays for wide-band coherent optical generation (up to two octaves) provide a new capability for integration with other optical elements on a chip and can also find application in other areas including bioimaging.
To verify that the waveguide exhibits anomalous dispersion near the value predicted by the FEM simulations in Fig. 1d, the group velocity dispersion is characterized using a Mach-Zehnder interferometer having one arm with an adjustable delay40. In the dispersion measurement, a probe pulse is attenuated to a low enough pulse energy (<30 pJ) so as to prevent significant nonlinear phase shifts in the waveguide. The pulse is split using a beamsplitter and propagates into two arms of a Mach-Zehnder interferometer. One pulse is coupled to the waveguide and the other one propagates through the adjustable delay line in the air. The light emitted from the waveguide is collimated and the pulses from the two arms are combined using a second beamsplitter. The combined beams are then focused into a single mode fibre and sent to a spectrometer. The time delay between the two pulses is calculated using the Fourier-transform of the measured spectrum which shows spectral fringes41. By tuning the laser wavelength from 770 to 810 nm, the dispersion of the waveguide is then measured from the observed wavelength-dependence of the group delay in the waveguide arm. The measured dispersion is plotted in Fig. 1d and agrees well with the FEM simulation. The error bars in Fig. 1d are derived from the standard deviation of group delay from 10 spectral measurement at each wavelength.
Numerical simulations of pulse propagation in the waveguides were performed using a generalized nonlinear Schrödinger equation. To model the frequency dependence of the nonlinear response, the following equation is used42.
Here, is the complex spectral envelope of the pulse at waveguide position z, is defined as , α(ω) is the linear loss and R(T) is the Raman response function. is the parameter related to the nonlinear response defined as:
The frequency-dependent propagation constant (β(ω)), effective mode index (neff(ω)) and mode area (Aeff(ω)) of the waveguides were calculated using FEM simulations and imported into the pulse propagation simulations.
The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.
How to cite this article: Oh, D. Y. et al. Coherent ultra-violet to near-infrared generation in silica ridge waveguides. Nat. Commun. 8, 13922 doi: 10.1038/ncomms13922 (2017).
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We gratefully acknowledge the Defense Advanced Research Projects Agency (DARPA) under the PULSE (W31P4Q-14-1-0001) and QuASAR (W911NF-14-1-0284) programs, the National Aeronautics and Space Administration (NASA) (KJV.JPLNASA-1-JPL.1459106), the Kavli Nanoscience Institute, and the Institute for Quantum Information and Matter, a National Science Foundation (NSF) Physics Frontiers Center (PHY-1125565) with support of the Gordon and Betty Moore Foundation, NIST and the National Science Foundation (AST-1310875).
Supplementary Notes and Supplementary Figures
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