1. Introduction
In this paper, we have analyzed correlated photon pair generation in Ge_{11.5} nanowire waveguides as a function of detuning from the pump frequency. Our analysis includes the effects of dispersion, nonlinearity and both the real and imaginary parts of response function for SpRS. We show that the best figure of merit, defined as the ratio of pair generation rate from SFWM to the noise generated by SpRS, is achieved for frequency shifts greater than 17 THz above the pump. In this region a photon pair correlation >100 is achievable in theory, together with a figure of merit >10 at a pair generation rate >8 × 10^{8} pairs/s.
In order to access this region we have developed designs for Ge_{11.5} nanowires with near-zero anomalous dispersion for the fundamental TM mode that have a high tolerance to fabrication errors. Because the nonlinear parameter of these nanowires is large, a short waveguide can be used, which means the GVD needs to lie between zero and 7 ps∙km^{−1}nm^{−1} as we discuss later. Since it is important that the correlated photons are generated at frequencies where high detection efficiency is available from an InGaAs single photon detector, the pump wavelength was chosen to be 1420 nm and this leads to the generation of photon pairs at wavelengths of 1314 nm (signal) and 1544 nm (idler).
From our analysis of the waveguide design, we found that low dispersion Ge
_{11.5} nanowires can have a high tolerance to errors in the waveguide width, but are then very sensitive to waveguide thickness. As a result, we developed a cladding design that uses a dual-layer to compensate for fabrication errors in the waveguide thickness. This design employs a thin layer of SiO
_{2} or Al
_{2}O
_{3} between the waveguide and a top cladding with a refractive index of 1.52. The implementation requires the exact waveguide thickness to be determined post fabrication using highly accurate metrology, such as optical profilometry, with nm precision. The dual layer cladding then allows the GVD to be tuned to become near-zero by depositing a layer whose thickness can be controlled with high accuracy using a process such as atomic layer deposition (ALD) [
1616. S. M. George, “Atomic Layer Deposition: An Overview,” Chem. Rev. 110(1), 111–131 (2010). [CrossRef] [PubMed]
].
2. Correlated photon-pair generation with CW pump
In order to analyze the quality of correlated photon-pair generation by SFWM in Ge
_{11.5} nanowires, we need to treat the influence of SpRS on the SFWM carefully because this contributes not only Raman gain, arising from the imaginary part of Raman response function, but also affects the nonlinear phase modulation for SFWM via the real part of the response function [
1111. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express 15(13), 8104–8114 (2007). [CrossRef] [PubMed]
,
1717. X. Gai, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Interplay between Raman scattering and four-wave mixing in As_{2}S_{3} chalcogenide glass waveguides,” J. Opt. Soc. Am. B 28(11), 2777–2784 (2011). [CrossRef]
]. As very low pump power is used for correlated photon pair generation, the undepleted pump approximation can be used in the analysis. In addition, the power of idler has a negligible influence on the pump. We, therefore, deduced
Eqs. (1),
(2) and
(3) shown below from Refs. [
1111. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express 15(13), 8104–8114 (2007). [CrossRef] [PubMed]
,
1717. X. Gai, D.-Y. Choi, S. Madden, and B. Luther-Davies, “Interplay between Raman scattering and four-wave mixing in As_{2}S_{3} chalcogenide glass waveguides,” J. Opt. Soc. Am. B 28(11), 2777–2784 (2011). [CrossRef]
,
1818. Q. Lin, J. Zhang, P. M. Fauchet, and G. P. Agrawal, “Ultrabroadband parametric generation and wavelength conversion in silicon waveguides,” Opt. Express 14(11), 4786–4799 (2006). [CrossRef] [PubMed]
] and these describe the interaction between the pump, signal and idler including SpRS:
Here the subscripts
p,
s and
i refer to the pump, signal, and idler, respectively; Ω =
ω_{s}-ω_{p} is the frequency detuning from signal to pump;
β_{2} is the second order dispersion;
α is the linear loss,
γ is the nonlinear parameter;
f_{R} = 0.13 is fractional Raman factor of Ge
_{11.5}; and
h_{R}(Ω) is the Fourier transform of the Raman response function
h_{R}(
t). From examination of
Eqs. (1),
(2) and
(3), we find that Im[
h_{R}(Ω)] appears in real part of the equation and contributes a term representing loss or gain and thus determines the production of SpRS noise during the generation of correlated photon pairs. At the same time, the term containing Re[
h_{R}(Ω)] contributes to the imaginary part of the equation and modifies the nonlinear coefficient for cross-phase modulation (XPM) and energy conversion between the pump, signal and idler waves. The SFWM efficiency depends not only on the phase mismatch term between the propagation constants of the pump, signal and idler waves, but also on the effects of self-phase modulation [SPM] and XPM. As a result, we need to treat Re[
h_{R}(Ω)] carefully in SFWM whilst Im[
h_{R}(Ω)] is not so critical as it contributes to Raman gain appearing in all of the terms affecting SFWM. Furthermore, the phase matching condition for SFWM no longer contains only the dispersion and nonlinear parameters but also the real part of Raman function Re[
h_{R}(Ω)]. Thus, the phase matching condition which can be directly deduced from Ref. [
1111. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express 15(13), 8104–8114 (2007). [CrossRef] [PubMed]
] has the form
In
Fig. 1
Fig. 1 Fourier transform of the Raman response function h_{R} of Ge_{11.5}, As_{2}S_{3} and SiO_{2}. (a) The imaginary part Im[h_{R}(Ω)]. (b) The real part Re[h_{R}(Ω)].
, we plot Im[
h_{R}(Ω)] and Re[
h_{R}(Ω)] for Ge
_{11.5}, As
_{2}S
_{3} and silica deduced from the Raman gain spectrum for these materials via the Kramers-Kronig relations. The Raman gain spectrum of Ge
_{11.5} and As
_{2}S
_{3} were measured by Raman spectroscopy whilst that for SiO
_{2} was obtained from Ref. [
1212. G. P. Agrawal, Nonlinear Fiber Optics, 3rd. ed. (Academic, 2001).
]. The main peak of Im[
h_{R}(Ω)] for Ge
_{11.5} has the lowest frequency shift of these three materials making it the best choice for photon pair generation using SFWM in a region of the spectrum beyond the Raman peak where SpRS noise should be absent. In addition, there are large negative values of Re[
h_{R}(Ω)] for all three materials which decrease the SFWM conversion efficiencies at detunings just beyond the Raman gain peak. However Re[
h_{R}(Ω)] for Ge
_{11.5} recovers at the lowest detuning and thus offers the greatest potential for broad bandwidth SFWM beyond ≈10 THz.
As mentioned above, SFWM in Ge
_{11.5} nanowires involves not only the phase mismatch and the nonlinear phase modulation, but also the real part of Raman response function Re[
h_{R}(Ω)]. Thus the expression for the spectral density of the photon flux
G_{i}(
υ) should include Re[
h_{R}(Ω)] and can be calculated according to [
1111. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express 15(13), 8104–8114 (2007). [CrossRef] [PubMed]
]:
where
R=K(2q−K);
q(Ω) = 1 –
f_{R} +
f_{R}Re[
h_{R}(Ω)]; K = –
∆k/(2
γP) is the ratio of the phase mismatch term arising from dispersion to the nonlinear term;
∆k(Ω) =
β_{2}Ω
^{2} +
β_{4}Ω
^{4}/12, where
β_{4} is the fourth order dispersion of the waveguide; and where
γ≈140 W
^{−1}m
^{−1} for a Ge
_{11.5} nanowire [
1414. X. Gai, S. Madden, D.-Y. Choi, D. Bulla, and B. Luther-Davies, “Dispersion engineered Ge_{11.5}As_{24}Se_{64.5} nanowires with a nonlinear parameter of 136 W⁻¹m⁻¹ at 1550 nm,” Opt. Express 18(18), 18866–18874 (2010). [CrossRef] [PubMed]
]. The waveguide length
L was chosen to be 0.5 cm because of the very high value of
γ can supply enough nonlinearity in this short length for photon-pair generation. In addition, such a short waveguide also leads to broader SFWM bandwidth for the same dispersion.
The photon pair generation rate can be calculated according to [
1010. C. Xiong, L. G. Helt, A. C. Judge, G. D. Marshall, M. J. Steel, J. E. Sipe, and B. J. Eggleton, “Quantum-correlated photon pair generation in chalcogenide As_{2}S_{3} waveguides,” Opt. Express 18(15), 16206–16216 (2010). [CrossRef] [PubMed]
] as
S_{SFWM}(
υ)≈Δ
υ∙
G_{i}(
υ) where
υ = Ω/
2π is the frequency detuning. We chose Δ
υ≈0.12 THz corresponding to a 1 nm wide band-pass filter.
Shown in
Fig. 2
Fig. 2 Photon pair generation rate with γPL = 0.1 and GVD of 15, 5 and 1.5 ps∙km^{−1}nm^{−1}Blue curve is for SFWM including Re[h_{R}(Ω)]. Red curve is for pure SFWM. The frequency detuning is for pump-idler detuning ω_{i}-ω_{p} = ω_{p}-ω_{s}. G/s is for 1 × 10^{9} pairs per second.
is the calculated photon generation rate (PGR) for pure SFWM and SFWM including Re[
h_{R}(Ω)] with different values of GVD of 15, 5 and 1.5 ps∙km
^{−1}nm
^{−1} and
γPL = 0.1 (
P≈0.14 W). From
Fig. 2, we can see that below 5 THz pure SFWM and SFWM including Re[
h_{R}(Ω)] have similar PGR. This is because Re[
h_{R}(Ω)]≈1 in this region as shown in
Fig. 1(b). Between 5 and 7.5 THz, there is a dramatic increase in PGR because Re[
h_{R}(Ω)] increases in this region and this enhances the nonlinear phase modulation. From 7.5 to 12 THz, Re[
h_{R}(Ω)] becomes large and negative which reduces the nonlinear phase modulation leading to a dramatic decrease in the PGR. Beyond 12 THz Re[
h_{R}(Ω)] recovers towards zero and remains constant for higher frequencies. The PGR spectrum becomes flat at a level of 66%–75% of the PGR obtained from pure SFWM. This region has very small Raman noise according to
Fig. 1(a) and thus has great potential as a source of correlated photon pairs. The bandwidth over which the PGR spectrum remains flat is mainly controlled by the waveguide dispersion. With GVD of 1.5, 5 and 15 ps∙km
^{−1}nm
^{−1}, the bandwidth is ≈30, 20 and 8 THz respectively. This indicates the importance of obtaining near-zero anomalous dispersion to achieve correlated photon pairs at frequencies beyond the Raman noise. We choose the 5 ps∙km
^{−1}nm
^{−1} GVD in the following calculations as a value that is realistic for the double clad dispersion engineered waveguides discussed later.
In order to analyze the quality of the correlated photon pair source we need to calculate the spectral density of the photon flux originating from Raman gain as this is the main noise source when generating correlated photon pairs by SFWM. The spectral density of the Raman photon flux can be calculated according to [
1010. C. Xiong, L. G. Helt, A. C. Judge, G. D. Marshall, M. J. Steel, J. E. Sipe, and B. J. Eggleton, “Quantum-correlated photon pair generation in chalcogenide As_{2}S_{3} waveguides,” Opt. Express 18(15), 16206–16216 (2010). [CrossRef] [PubMed]
] as
where
g_{R}(
υ) = 2
γf_{R}Im[
h_{R}(2
πυ)] is the Raman gain spectrum of Ge
_{11.5};
n_{th} = 1/exp(
hυ/
k_{B}T) – 1 is photon population at frequency
υ and temperature
T following the Bose-Einstein distribution;
h is the Planck’s constant;
k_{B} is the Boltzmann constant; and the photon generation rate
S_{SpRS}(
υ)≈Δ
υ∙
f_{SpRS}(
υ) where Δ
υ≈0.12 THz corresponds to a 1 nm band-pass filter. Another important criterion related to the quality of the correlated photon pair source is the figure of merit F which is defined by comparing the PGR from SFWM (signal) to PGR from SpRS (noise) as
In addition, uncorrelated photons due to multi-pair generation at high power stop us from improving the PGR and F by increasing the power. Assuming ideal filters are used for the signal and idler and pair correlation this can be calculated according to [
1010. C. Xiong, L. G. Helt, A. C. Judge, G. D. Marshall, M. J. Steel, J. E. Sipe, and B. J. Eggleton, “Quantum-correlated photon pair generation in chalcogenide As_{2}S_{3} waveguides,” Opt. Express 18(15), 16206–16216 (2010). [CrossRef] [PubMed]
] as
where
η = 1-
f_{R} +
f_{R}h_{R}(Ω).
Figure 3
Fig. 3 Criteria for correlated photon pair generation for γPL = 0.07, 0.1 and 0.15. (a) The photon pair generation rate of SFWM and SpRS. (b) Figure of merit F = S_{SFWM}/S_{SpRS}. (c) Photon pair correlation. G/s is for 1 × 10^{9} pairs per second.
shows the PGR of SFWM and Raman noise, the figure of merit and pair correlation at
γPL of 0.07, 0.1 and 0.15 respectively. From
Figs. 3 (b) and (c), we find that the figure of merit and pair correlation show opposite trends as a function of
γPL since higher
γPL values lead to stronger photon pair brightness but also increases the generation of uncorrelated multiple photon pairs. As a result, we focus on
γPL = 0.1 as a compromise between the figure of merit and photon pair correlation. Because photons generated from Raman gain are the main noise source in our system, we can identify four interesting regions where Raman noise is relatively low. Region A lies below 0.4 THz. The PGR of SFWM in this region is the same as pure SFWM at about 1.2 G/s because Re[
h_{R}(Ω)] ≈1 as indicated above. The figure of merit and the pair correlation are ≈10 and ≈80 at maximum but drop rapidly below 5 and 60 for just by 0.3 THz frequency shift. Region B is the first low Raman gain window extending from 4.5 THz to 5.5 THz. This region has the highest SFWM PGR as the high value of Re[
h_{R}(Ω)] enhances the nonlinear phase modulation in this region but the figure of merit and pair correlation is only about 2.5 and 50 at maximum. Region C is the second low Raman gain window between 10 and 13 THz. The SFWM PGR has recovered from the dip of large negative values of Re[
h_{R}(Ω)] and remains constant at 0.8–0.9 G/s. The figure of merit is of 5 at maximum while the pair correlation is about 100 and remains constant in the region. Region D is defined between 17 THz and 35 THz. In this region, the PGR remains at 0.9 G/s over more than 15 THz bandwidth. The highest figure of merit and photon correlation is achieved here, the values being 20 and 130 respectively, and these remain constant across the whole detuning range. Region D is only accessible using ultra-low dispersion waveguide design and gives us a broad bandwidth photon pair source with best quality for a glass waveguide. Accessing this region, however, places the most demanding restrictions on dispersion and hence waveguide design.
3. Near-zero anomalous dispersion waveguides
In order to produce a design for a nanowire with near-zero anomalous dispersion with a high tolerance to fabrication errors, we need to firstly consider the fabrication process and identify where the main errors occur.
Figure 4(a)
Fig. 4 (a) A standard single clad Ge_{11.5} waveguide structure. (b) The GVD for a 0.625 µm wide waveguide. Dark blue curve is the contour for GVD of 7 ps∙km^{−1}nm^{−1}; light blue curve is the zero-dispersion contour; the black line shows the pump wavelength at 1.42 µm. (c) the GVD for a 0.58 µm film thickness and 0.61, 0.625 and 0.64 µm waveguide width.
shows a standard waveguide structure and its refractive index profile. In the fabrication process a Ge
_{11.5} film is deposited onto an oxidized silicon wafer by thermal evaporation at a rate ~0.2–0.3 nm/s to a thickness of 500–650 nm with an uncertainty of ~±10–15 nm. The precise film thickness can be measured after deposition to better accuracy (±5 nm) using a dual angle spectroscopic reflectometer (SCI Filmtek 4000) or post etching with an optical profiler to an accuracy of ±2 nm. The width of the waveguides is determined by the lithography and etching processes. In those processes the waveguides are first patterned onto 250 nm ZEP by electron-beam lithography (EBL) with 20 µm aperture and 30 kV acceleration voltage. The fixed beam moving stage (FBMS) method was applied to remove all the stitching errors between different write-fields. Following this inductively coupled plasma etching is used to transfer the waveguide patterns into the Ge
_{11.5} films. At the end of process, an inorganic polymer glass (IPG) is spin-coated onto the waveguides as a top cladding with a refractive index of 1.52 at 1420 nm. During fabrication, the widths of waveguides can vary from the design values due to errors in the pattern width introduced during EBL and due to process bias during ICP etching. These create an uncertainty of ~±15–20 nm in the waveguide width. Hence the fabrication errors that affect dispersion arise from errors in both the thickness of the deposited film and the width of the nanowires.
In previous work, the waveguide dispersion was designed by varying the film thickness assuming the waveguide width was known. Under this assumption, we calculated the GVD for a 0.625 µm wide Ge
_{11.5} waveguide as a function of film thickness using the finite difference method [
1919. A. B. Fallahkhair, K. S. Li, and T. E. Murphy, “Vector finite-difference mode solver for anisotropic dielectric waveguides,” J. Lightwave Technol. 26(11), 1423–1431 (2008). [CrossRef]
,
2020. P. Lüsse, P. Stuwe, J. Schüle, and H. G. Unger, “Analysis of vectorial mode fields in optical waveguides by a new finite difference method,” J. Lightwave Technol. 12(3), 487–494 (1994). [CrossRef]
].
The results are shown in
Fig. 4(b) where the vertical black line indicates a wavelength of 1420 nm and the light and dark blue curves are the contours for zero-dispersion and a GVD of 7 ps∙km
^{−1}nm
^{−1} respectively. From
Fig. 4(b), we find that the zero-dispersion contour intercepts the 1420nm line at thicknesses of 0.56 and 0.6 µm and the maximum GVD is 5 ps∙km
^{−1}nm
^{−1} at 1420 nm at a thickness of 0.58 µm. This shows that if there was no error in the waveguide width, the tolerance on film thickness is ±20 nm and this is larger than the ±15 nm fabrication tolerance associated with film deposition making a GVD < 5 ps∙km
^{−1}nm
^{−1} achievable.
As a result, to identify a structure with better tolerance to fabrication errors, we have to study the GVD as a function of both waveguide width and thickness. This is shown in
Fig. 5(a)
Fig. 5 (a) GVD at 1.42 µm as a function of film thickness and waveguide width. (b) GVD as a function of film thickness in region I. (c) GVD as a function of waveguide width in region II.
. Here the dark and light blue curves indicate 7 ps∙km
^{−1}nm
^{−1} and zero dispersion respectively and black curves are for 20, −10 and −20 ps∙km
^{−1}nm
^{−1} as indicated. From
Fig. 5(a), there are two regions of interest. Region I is located at film thicknesses between 0.56 and 0.6 µm and waveguide width between 0.6 and 0.65 µm. In this region, we observed a slow dependence of GVD on film thickness. More details are shown in
Fig. 5(b), where for the 0.625 µm wide waveguide, a >40 nm change in film thickness from 0.56 to 0.6 µm leads to only 5 ps∙km
^{−1}nm
^{−1} variation on GVD from 0 to 5 ps∙km
^{−1}nm
^{−1}. In fact, this is the same structure as studied in
Fig. 4 that was very sensitive to waveguide width. However, an interesting observation from
Fig. 5(b) is that the GVD curves contain a local maximum and their shape is only weakly dependent on width, although the maximum GVD value shifts quite rapidly. This presence of this local maximum explains the insensitivity to film thickness and results in the GVD varying by <7 ps∙km
^{−1}nm
^{−1} from the peak value for >50 nm change in thickness.
The second interesting region II has similar features, but this time the GVD varies only slowly with waveguide width. According to
Figs. 5(a) and
5(c), we find that for a film thickness of 0.625 µm, the GVD varies between zero and 7 ps∙km
^{−1}nm
^{−1} for a 170 nm change in waveguide width from 0.67 to 0.85 µm. The tolerance to waveguide width is much larger than the estimated fabrication errors making them negligible. However, the GVD is now sensitive to film thickness as shown in
Fig. 5(c), where the peak GVD for a 0.61 µm wide waveguide increases to 18 ps∙km
^{−1}nm
^{−1} and that for the 0.64 µm wide waveguide decreased to −6 ps∙km
^{−1}nm
^{−1} which is far larger than can be tolerated. As was the case of
Fig. 5(b) the existence of a local maximum explains the insensitivity to width and all structures have over 170 nm tolerance to waveguide width for <7 ps∙km
^{−1}nm
^{−1} variation from the peak value of GVD. Region II is of more interest because of its much bigger tolerance to fabrication errors in the width. This can be understood because the continuity conditions for the fundamental TM mode mean that the effective index is mainly determined by the position of the horizontal surfaces in the structure and hence varies rapidly with film thickness. On the other hand the TM mode index is much less sensitive to the positions of the vertical surfaces leading a low sensitivity to waveguide width.
By studying
Fig. 5(a), we can see there is no region that lies close to the zero-dispersion contour that is sufficiently tolerant to fabrication errors in both film thickness and waveguide width to allow the reliable manufacture of a low dispersion structure. As a result we need a new approach. We started by choosing region II for our initial structure. What is now needed is a method to compensate fabrication errors in film thickness and which allows the maximum GVD to be tuned post fabrication to between zero and 7 ps∙km
^{−1}nm
^{−1}.
When the waveguide is too thin, for example 0.61 µm corresponding to −15 nm error relative to the targeted film thickness of 0.625 µm, the peak value of GVD far exceeds the maximum of 7 ps∙km
^{−1}nm
^{−1}. According to
Figs. 6(d) and (e), however, inserting a layer of Al
_{2}O
_{3} whose refractive index is higher than that of the IPG cladding again allows the TM mode index to be tuned but in this case the GVD decreases as the thickness of the Al
_{2}O
_{3} layer increases thereby compensating the errors caused by the thinner waveguide film. From
Fig. 6(f), using 30 nm of Al
_{2}O
_{3} reduced the peak dispersion to 4 ps∙km
^{−1}nm
^{−1} and achieves over 130 nm tolerance to waveguide width.
Although this method can be used to compensate the fabrication error in Ge
_{11.5} waveguide thickness, this additional layer also has an error tolerance in its thickness. According to
Figs. 6(b) and (e), we found that SiO
_{2} and Al
_{2}O
_{3} layers need to be controlled to a tolerance of 15 nm and 8 nm respectively. The reason that Al
_{2}O
_{3} has poorer fabrication error tolerance than SiO
_{2} is because the refractive index contrast between Al
_{2}O
_{3} and IPG is much larger than that between SiO
_{2} and IPG leading a more rapid change of GVD with Al
_{2}O
_{3} layer thickness. In fractional terms the thickness of either film has to be controlled to 20–30% which is technologically feasible using various different deposition processes.
For example, although the fabrication tolerance on the thickness of the SiO
_{2} or Al
_{2}O
_{3} layers is small in absolute terms, they can be realized using atomic layer deposition (ALD). This technology allows film thickness to be controlled on the atomic scale and produces conformal coatings on structured surfaces [
1616. S. M. George, “Atomic Layer Deposition: An Overview,” Chem. Rev. 110(1), 111–131 (2010). [CrossRef] [PubMed]
]. ALD is available for a variety of materials including Al
_{2}O
_{3}, SiO
_{2}, ZnO, etc. It is a surface self-limiting process where film growth terminates after deposition of a single layer of atoms. Hence it allows the growth of thin amorphous layers with nanometer precision. ALD, therefore, allows us to add a layer of SiO
_{2} or Al
_{2}O
_{3} with accurately controlled thickness to modulate the refractive index profile of waveguide cladding as illustrated in
Fig. 6. This should allow us to fabricate a waveguide with near-zero anomalous dispersion insensitive to the waveguide width by compensating the fabrication errors in film thickness with a high precision process. This method relies on accurate measurement of the waveguide thickness post deposition and the choice of a target thickness that allows either SiO
_{2} or Al
_{2}O
_{3} be deposited by ALD to tune the dispersion in the appropriate direction. In our experience optical profilometry can achieve the required measurement accuracy in films after processing.