1. Introduction

Deterministic quantum light sources delivering single photons and entangled photon pairs on demand are key resources in photonic quantum technologies. They enable the implementation of complex quantum communication networks [1–3] and photonic quantum processors [4,5]. While triggered single-photon emission is well established for many types of quantum emitters, including defect centers in solid state materials [6,7], discrete emitters in transition metal dichalcogenide monolayers [8], and self-assembled semiconductor quantum dots (QDs) [9], it is still a great challenge to produce quantum light sources that meet all requirements of advanced quantum photonics applications. Among them is the photon extraction efficiency $\eta _{ext}$, which states the probability of transferring a photon generated by a single quantum emitter into a usable photon in the target application. To maximize $\eta _{ext}$, especially of QD-based quantum light sources, different light extraction strategies have been developed relying on micropillars [10–14], microdisks [15], photonic crystals [16–18], photonic wires [19], microlenses [20], and circular Bragg gratings (CBGs) [21–24]. Today, CBGs are widely applied thanks to the fact that they combine excellent broadband photon extraction efficiency $\eta _{ext}$ and decay rate enhancement $F_{P}$. Moreover, they can be fabricated deterministically with marker-based or in-situ lithography [22,25], and can be implemented in different material systems and wavelength ranges [23,24,26]. Theory also predicts that they can emit with high coupling efficiency into single-mode fibers [27,28].

Note that the working principle of hybrid CBGs is based on resonant grating waveguide structures (GWS) [29,30], which have been discovered in 1985 and have served as bandstop and bandpass filters [31,32], mirrors [33,34], and an element of sensors [35], etc.. By carefully designing the geometry of the structures, the circular grating could lead to either vertical diffraction or in-waveguide backscattering of the light, which contributes to high $\eta _{ext}$ and $F_{P}$, respectively [36]. However, when one attempts to analytically design a valid CBG with the stated concepts, further intensive numerical optimization would always be necessary. Many numerical design studies of CBG-based quantum light sources in different wavelength ranges have been published including 780 nm [23], 900-960 nm [37], 1300 nm [27,28], and 1550 nm [28,38]. Such optimizations are often based on multi-dimensional finite-difference time-domain method (FDTD) and finite element method (FEM) simulations, which are computationally demanding and costly because of the comparatively large parameter space describing the geometry of the CBG devices. Although for simple designs without electrical contact bridges, one could still adopt cylindrical rotational symmetry to accelerate the optimization [39], the lack of an efficient and systematic optimization approach poses a challenge to designing electrically-contacted CBGs with contact bridges as illustrated in Fig. 1, where rotational symmetry can no longer be exploited. Moreover, the optimized design is mostly valid only for one specific emission wavelength and does not provide insight into the underlying physics defining for instance the photon loss channels. This hinders the progress in the development of CBG quantum light sources, and it would be crucial to develop an efficient optimization scheme for these devices which is applicable to different material combinations and emission wavelengths.

 

Fig. 1. Illustration of an electrically-contacted CBG with contact bridges in labyrinth geometry [40].

Download Full Size | PDF

To overcome the described limitations in the numerical optimization, we propose and demonstrate a simple yet robust scaling approach, which adapts and generalizes an already-optimized CBG design to a broad wavelength range in a highly flexible and efficient way. The scaling approach allows us to efficiently optimize high-performance hybrid CBG designs over a broad wavelength ranges from 900 to 1600 nm with and without electrical contact bridges. Furthermore, such a scaling approach highly enhances the CBG design flexibility, allowing one to easily design CBGs for various wavelengths, layer thicknesses, or layer materials, and further enables an in-situ design tuning to account for all the emitters within an inhomogeneously broadened ensemble on the same chip.

2. Results and discussion

To efficiently design high-performance CBG structures, we explore three scaling methods, namely, wavelength scaling, optical path-length scaling, and effective optical path-length scaling as depicted in Fig. 2. The wavelength scaling method utilizes constant refractive indices at the target wavelength and scales the whole CBG geometry in all dimensions according to the wavelength variation while leaving the aspect ratio of the structure unchanged. It is useful for compensating the mode energy shift in order to initialize a design at a target wavelength, where the refractive index dispersion can be omitted. The optical path-length scaling method additionally rescales the initial CBG dimensions according to the refractive index dispersion, in order to adapt an initial design to another wavelength while maintaining the performance. Finally, the effective optical path-length scaling method rescales the center mesa radius and the grating period according to the layer design variation, which gives one the flexibility to change the layer design efficiently.

 

Fig. 2. Cross-section of CBGs with 2 rings for the illustration of various scaling strategies including (a) an initial design optimized at $\lambda$ wavelength, (b) the wavelength scaling method, (c) the optical path-length scaling method, (d) the effective optical path-length scaling method. Here, R, $\Lambda$, W, H, and T are the center mesa radius, grating period, trench width, membrane thickness, and SiO$_{2}$ thickness, respectively. $\alpha$, $\beta$, and $\gamma$ are the scaling variables detailed in the text.

Download Full Size | PDF

Following the demonstration of each scaling method in individual sections, we show that the combination of all methods allows designing CBGs efficiently for exemplary wavelengths ranging from 900 nm to 1600 nm with an excellent $F_P$ and $\eta _{ext}$. We demonstrate the applicability of the approach to CBGs with electrical contact bridges in the labyrinth geometry [40] as well, relieving the strong needs for computationally intensive 3D simulations which would otherwise pose a significant burden.

Throughout the article, to evaluate the adapted designs’ performance, namely, the photon extraction efficiency and the Purcell factor, numerical simulations are carried out via a commercial FEM software, JCMsuite [41,42]. Unless specified in the article, the refractive index dispersion, including the one of low temperature GaAs, is being taken into accounts [43–46]. All the presented extraction efficiencies are calculated for a numerical aperture of 0.8. The detailed numerical simulation setup is available in the supporting information.

2.1 Wavelength scaling method

To begin with, we apply the wavelength scaling method to initialize a quantum dot CBG device for high $\eta _{ext}$ and $F_P$ at 1300 nm in the telecom O-band. The key of the method is to set a constant refractive index at the target wavelength so that any CBG mode shift could be compensated easily by scaling all the lengths according to the wavelength shift. The considered layer and device design is depicted in Fig. 2 (a).

Recall that CBGs act as resonant structures between a TE slab waveguide and a circular grating. Such resonance at wavelength $\lambda _{0}$ can be described analytically by the following equation [36,47]:

We start by simulating the TE slab waveguide at 1300 nm via a 1-D transfer matrix method utilizing scattering matrices [48,49] with initial layer thicknesses {H, T} = {240, 300} nm with reference to L. Rickert et al. [27] to obtain $n_{eff} = 2.8684$ as presented in Fig. 3 (a). A more detailed explanation on the calculation of $n_{eff}$ is available in the supporting information. Afterward, we set the initial mesa radius $R = \Lambda = 1300$ nm$/n_{eff}$ surrounded by a 5-ring circular grating with a fill factor of 0.68 as in L. Rickert et al. [27] to fully define the CBG geometry. A QD emitter is simulated as an in-plane dipole emitter positioned at the TE fundamental mode maximum, which is 117 nm above the SiO$_{2}$ layer, near the center of the GaAs membrane. However, such a design does not lead to the expected enhanced $\eta _{ext}$ and $F_{P}$ at the target wavelength of 1300 nm. In fact, by toggling off the material dispersion and numerically simulating $\eta _{ext}$ and $F_{P}$ over a broad wavelength range, we observe that the CBG resonant mode with high $\eta _{ext}$ and $F_{P}$ actually locates at 1136.2 nm as shown in Fig. 3 (b), which is strongly blue shifted in comparison to the target wavelength of 1300 nm. This could be attributed to the fact that the grating equation approximates the case of shallow gratings, treating the etching as a small perturbation.

 

Fig. 3. Illustration of the wavelength scaling method. (a) 1-D TE slab waveguide simulation. (b) A CBG designed solely based on the grating equation, which shows a strong blueshift of the mode. (c) A wavelength-rescaled CBG design to shift the mode to the target 1300 nm. (d) Optimized CBG design at 1300 nm after slight adjustment of the thickness and the fill factor. Note that in (b) and (c), the material refractive indices are set constants corresponding to 1300 nm to fully exploit the wavelength scaling method. The simulation in (d) however has the dispersion toggled on again.

Download Full Size | PDF

The observed blueshift can however be easily compensated with the wavelength scaling method. We define the wavelength scaling parameter $\alpha$ to be a ratio of the target wavelength to the current wavelength:

Thanks to the fact that the material refractive indices have been set constant at 1300 nm in the simulation of Fig. 3 (b), we could simply shift the design from one wavelength to another without changing any design performance by rescaling the overall CBG geometry uniformly with $\alpha =$ 1300 nm/1136.2 nm as depicted in Fig. 2 (b). For comparison, we present the new design at 1300 nm in Fig. 3 (c) with the material dispersion remaining off. We remark that without the refractive index dispersion, the simulated $F_{P}$ and $\eta _{ext}$ can deviate from the real ones at wavelengths other than 1300 nm in Fig. 3(b) and (c). However, they provide a precise information on how much the CBG mode has been shifted for the wavelength scaling approach.

Before proceeding to further generalize the design, we performed a slight tuning of the design to optimize the fill factor and layer thickness with the help of the effective optical path method, which will be explained in the following section. Figure 3 (d) presents the optimized CBG design, exhibiting high $F_{P} = 28$ and $\eta _{ext} = 0.93$ at 1300 nm with the following 5-ring CBG geometry parameters: {$R, \Lambda, W, H, T$} = {533.4, 533.4, 154.7, 240, 300} nm. Note that the geometry is similar to the one numerically optimized [27].

Despite the power of the wavelength scaling method to tune the CBG mode wavelength without changing any performance, it does not consider the material dispersion. It is therefore useful to initialize a design by compensating the known wavelength shift due to, for instance, structural perturbation, where the material dispersion could and should be omitted.

2.2 Optical path-length scaling method

To further adapt and generalize one initial design to a broad range of wavelengths without numerically re-optimizing the design, further care must be taken to compensate for the refractive index dispersion. The optical path-length scaling method, in addition to the wavelength, also scales the CBG dimensions with the refractive indices to maintain the design performance.

To show the impact of refractive index dispersion, we firstly apply the wavelength scaling method to the above-optimized 1300 nm CBG to generate new CBG designs at different wavelengths ranging from 900 to 1600 nm. Figure. 4 (a) depicts the wavelength scaling parameter $\alpha$ and Fig. 4 (c) depicts the numerical simulation of $\eta _{ext}$ and $F_{P}$ of each corresponding CBG at each wavelength. Thanks to its broadband nature, $\eta _{ext}$ remains above 0.9 for all the new designs. Nevertheless, $F_{P}$ falls off quickly away from the optimized 1300 nm due to the material dispersion. To avoid confusion, we clarify that in Fig. 4 each wavelength corresponds to a newly adapted CBG design. A total number of 500 CBG designs are generated by each scaling approach and then numerically simulated to obtain $\eta _{ext}$ and $F_{P}$.

 

Fig. 4. (a) and (b) displays the scaling parameters for the wavelength scaling method and optical path-length scaling method, respectively. (c) and (d) displays numerical simulation of $F_{P}$ and $\eta _{ext}$ with the wavelength scaling method and optical path-length scaling method, respectively. Each wavelength corresponds to an individual CBG design with a newly adapted CBG geometry.

Download Full Size | PDF

To compensate for the material dispersion, an intuitive and simple solution is to scale the CBG geometry with the optical path considering the dispersion of each material as shown in Fig. 2 (c). An additional scaling factor, namely, $\beta _{i}$, is introduced:

Remark that the strong difference in $F_{P}$ between the two scaling approaches away from 1300 nm can be attributed to the Lorentzian-like curve of the Purcell factor enhancement, as can been seen in Fig. 3 (d). Since an inaccurate scaling of the CBG design could easily shift the CBG mode away from the target wavelength and out of the enhancement bandwidth with a FWHM of approximately 5 nm, $F_{P}$ could be greatly reduced in such case. Similarly, a strong decrease in $F_P$ observed at shorter wavelength even with the optical path-length scaling approach is resulted from the variation of the TE waveguide propagation constant and the optimized fill factor. The issues will be addressed in the following sections.

2.3 Effective optical path-length scaling method

The obtained results of the optical path-length scaling method mentioned above are already highly promising and can simplify the CBG device design and optimization for a wide range of emission wavelengths significantly. In practice, there are additional constraints originating from, for instance, technological limitations or already grown sample layer structures. As an example, one might have a QD-heterostructure with a layer design and layer thicknesses that differ from the ideal parameter set obtained from the design optimization. Additionally, due to the inhomogeneous broadening of self-assembled QDs, a single optimized design with a narrow bandwidth of Purcell enhancement as shown in Fig. 3(c) limits the available and often desired range to a small subset of the available QDs whose emission wavelength is aligned with the $F_P$ enhancement curve.

The mentioned issues significantly reduce the device yield when using conventional nano-fabrication techniques such as electron beam lithography, which do not account for the random spectral and spatial distribution of the self-assembled QDs for device processing. Even when using advanced deterministic nanofabrication techniques, for instances, in-situ electron-beam lithography (iEBL) [20,25] or marker-based lithography approaches [22], one has to identify QDs emitting at the target design wavelength to ensure high Purcell enhancement. This complicates the device processing and still does not overcome the problem that only a subset of QDs can be integrated into devices.

Ideally, if there is enough wavelength flexibility in the target application scenario, one would like to have full wavelength flexibility in the CBG designs to integrate all the quantum emitters on the same chip independent of their emission energy and still get optimum performance of the CBG device. To study this case, we firstly apply the optical path-length scaling method with fixed layer thicknesses, {H,T} = {240, 300} nm, optimized for 1300 nm emission wavelength, only varying the CBG parameters. Figure 5 (a) shows the corresponding $\eta _{ext}$ and $F_{P}$ as a function of the wavelength. It is clearly seen that only a small range of designs around the initial optimized wavelength of 1300 nm shows promising performances with $\eta _{ext} > 0.9$ and the Purcell enhancement is again narrow-band-like with a FWHM of (31.9 $\pm$ 0.1) nm.

 

Fig. 5. (a) The optical path-length scaling method with a fixed layer thickness. (b) Scaling factors for the effective optical path-length scaling method. (c) $\eta _{ext}$ and $F_{P}$ obtained by the effective optical path-length scaling method with a fixed layer thickness. Each wavelength corresponds to an individual CBG design with a newly adapted CBG geometry under fixed layer thickness.

Download Full Size | PDF

The solution to overcome the strong wavelength dependency and to design CBGs even with non-optimized layer designs in this scenario is to recall the basis that a CBG cavity is composed of a TE slab waveguide in resonance with the surface grating. Therefore, any layer design and thickness variation will result in a change in the waveguide propagation constant, and consequently lead to a shift in the waveguide-grating resonance wavelength. Such tuning behavior in resonant waveguide-grating structures has been proposed to be applied in chemical refractive index sensors [50].

Here, based on Eq. (1), we define a scaling factor $\gamma$ to compensate for the non-optimized layer design and thickness:

It is noteworthy that even with a fixed layer thickness, we are able to obtain a wide range of CBG designs around the initially optimized 1300 nm O-band not only with $\eta _{ext} > 0.9$ but also with $F_P > 27$. Considering a QD ensemble emission centered at 1300 nm, due to the nature of self-assembled QD growth, the QDs’ emission is inhomogeneously broadened and can be found anywhere in the O-band from 1260 nm to 1360 nm [51]. The effective scaling method will allow one to adapt the CBG design individually to integrate any emitter within the O-band, regardless of the inhomogeneous broadening. Such broadband scaling will highly increase the flexibility in fabrication and could ultimately enable multi-channel quantum communication on the same chip, where telecom O-band and C-band quantum emitters are all integrated all together.

We also remark that although the layer thickness is fixed to the pre-determined values in this example, the results actually prove the flexibility of CBG designs even when deviating from the initial material and thickness. The approach enables one to optimize and change the layer design effectively, since the in-plane CBG geometry always adapts accordingly. On the other hand, by revisiting the waveguide nature of CBG structures, one could identify the loss channel of the TE slab waveguide. For instance, a thinner SiO$_{2}$ cladding layer could lead to optical absorption of the light from the Au, which would be reflected in the complex propagation constant and a potentially lower performance. In such inevitable cases of complex effective refractive index, despite of the small quantity of the imaginary component compared to the real component, the waveguide loss can potentially lead to a tradeoff between $F_{P}$ and $\eta _{ext}$: the more in-plane resonance the CBG brings, the more light being lost by the absorbing layer and not being extracted. In this case, one could also use the scaling approaches as a starting point for further numerical optimization based on, for instance, Bayesian optimization, with the specified goals balanced between $F_{P}$ and $\eta _{ext}$ [28].

Another interesting feature in Fig. 5(c) is the 2-fold increase of $F_{P}$ to a value beyond 57 and the strong decrease of $\eta _{ext}$ around 1500 nm. This could potentially be attributed to the interaction between the TE slab waveguide mode and the grating. Although Eq. (1) has been used to describe the resonant condition, it does not necessarily provide information on the ratio of light in each diffraction order, namely the back-scattering and the out-coupling diffractions. When the back-scattering ratio enhances, the in-plane resonance can become stronger, leading to a higher Q-factor and $F_{P}$, while decreasing the $\eta _{ext}$ in this case. On the other hand, the coupling between the QDs and the fundamental TE slab waveguide mode also plays an important role. Even though the layer thickness is fixed in this case, by changing the wavelength, the optical thickness is also changing. Reducing the optical thickness of the GaAs layer can effectively increase the coupling efficiency and therefore the $F_{P}$ as well. The same behavior has also been observed when reducing the GaAs layer thickness with the effective optical path-length scaling approach in design initialization as presented in the supporting information. Despite the high $F_{P}$ beyond 57 around 1500 nm, such design is not experimentally preferred due to the accompanying $\eta _{ext}$ decrease and enhancement linewidth narrowing. On the other hand, for shorter wavelength where the optical thickness increases, QDs could more easily couple to higher order TE slab waveguide modes, which therefore decreases the CBG performance. The observed dip around 1100 nm can possibly be attributed to the resonance of a higher order mode.

2.4 Combined scaling methods for CBG designs with and without electrical contact bridges

Even better overall performance can be achieved by combining all the scaling methods. In this context, it is important to note that the methods are complementary in the following sense: The effective optical path-length scaling method is good at scaling $R$ and $\Lambda$ with a pre-determined layer thickness, while not directly optimizing the layer thickness. On the other hand, the optical path-length scaling method scales the layer thickness as well, with however less accuracy and flexibility in scaling $R$ and $\Lambda$. Finally, the wavelength scaling method is useful in initializing a design and in compensating the mode energy shift due to, for instance, the electrical contact bridges, yet it requires the material dispersion to be toggled off in the first place.

As a first demonstration, we optimize high-performance CBG designs for a broad wavelength range spanning from 900 nm to 1600 nm by scaling the layer thickness with the optical path-length scaling method: $H' = \alpha \beta _{1} H$ and $T' = \alpha \beta _{2} T$. $R$ and $\Lambda$ scale accordingly with the effective optical path-length scaling method as illustrated in Fig. 2 (d). We further note that the proposed scaling methods are not intended to totally replace the numerical simulation, but to greatly reduce the computational efforts. So far, the scaling methods leave, for instance, the fill factor $F = (\Lambda -W)/\Lambda$ of the gratings out of consideration. This can be improved with a minimal number of numerical optimizations by introducing a parameter $\delta$:

To not overuse the numerical calculation in this demonstration, here we consider a set of five values for the parameter $\delta$, comprising the values {0.92, 0.96, 1, 1.04, 1.08}, for each adapted design. In other words, we limit ourselves here to only perform 5 numerical simulations at each target wavelength to optimize the fill factor.

Figure 6 presents in total 200 optimized designs with wavelengths spanning from 900 nm to 1600 nm with the corresponding scaling parameters. All the optimized CBG designs show an $F_{P}$ exceeding 26 and a high $\eta _{ext}$ above 0.92. Remark that the optical path-length scaling factor $\beta _{1}$ of GaAs and the effective optical path-length scaling parameter $\gamma$ in Fig. 6 (a) have a very similar value in this case, explaining why the optical path-length scaling method in Fig. 4 could yield an acceptable yet lower performance over a broad wavelength range. We also note that although a 5-value set is chosen for optimizing the fill factor, only 3 of them within $\delta$ = {1, 1.04, 1.08} are adopted in the presented wavelength range and could effectively compensate for the performance fall-off at shorter wavelengths when no fill factor optimization is performed. The optimized $\delta$ are plotted in Fig. 6 (a) along with other scaling parameters.

 

Fig. 6. (a) Scaling parameters for the combined scaling method. (b) The Purcell factor and the extraction efficiency of the combined scaling method with and without fill factor optimization. Each wavelength corresponds to an individual CBG design with a newly adapted CBG geometry.

Download Full Size | PDF

Eventually, we proceed to CBG designs with electrical contacts bridges in a 4-long-ways (4-LW) labyrinth geometry, as depicted in Fig. 7 (a). Among several designs studied by Q. Buchinger et al., including straight contact bridges, such 4-LW design shows the least perturbation caused by the contact bridges, which could otherwise form leaky waveguides and affect the far field pattern of the emission [40]. Similar to the case without contact bridges previously, we start by turning off the material dispersion and then adding 200-nm-wide contact bridges in the 4-LW geometry to an initial 5-ring CBG design at 1300 nm. A redshift of around 14 nm of the CBG mode is immediately observed and then shifted back to 1300 nm with the wavelength scaling method. After an initial numerical optimization of the fill factor, the 5-ring design exhibits $F_{P} = 28$ and $\eta _{ext} = 0.87$ at 1300 nm with {$R, \Lambda, W, H, T$} = {527.8, 527.8, 136.2, 237.5, 296.9} nm and 197.9-nm-wide bridges. A more detailed optimization process with and without contact bridge is available in the supporting information, where we also conduct an in-depth analysis of the scaling approach’s effectiveness in maintaining both the local and global optimum.

 

Fig. 7. (a) CBG with electrical contact bridges in 4-LW labyrinth geometry. The dark area indicates the etched gaps. (b) Scaling parameters for the combined scaling method. (c) The Purcell factor and the extraction efficiency of the combined scaling method with and without fill factor optimization. Each wavelength corresponds to an individual CBG design with a newly adapted CBG geometry.

Download Full Size | PDF

Finally, we adapt the 4-LW design at 1300 nm to other wavelengths with the combined scaling methods. Here, we scale the layer thickness with the optical path method, the in-plane CBG geometry including the contact bridges with the effective optical path method. We also perform an optimization of the fill factor with a 5-value set for $\delta$ as before. With computation-intensive 3D numerical simulations, we show in Fig. 7 that all adapted CBG designs with fill factor optimization have a high $F_{P}$ exceeding 26 and $\eta _{ext}$ above 0.86. Interestingly, from Fig. 6 (a) and Fig. 7 (b) we also observe that the optimized fill factor scales roughly inversely with the effective refractive index, which is not surprising as the fill factor can be related to the weight between the waveguide section and the etched section.

We would also like to remark on the experimental aspect that the smallest feature in the short-wavelength CBGs is the trench width between the rings. The trench width can shrink to around 60-70 nm at 900 nm, which are well compatible with the feasible feature sizes when employing state-of-the-art EBL [52]. In the case of EBL fabrication issues, one could always decrease the fill factor from the optimized value without sacrificing much the CBG performances as shown in the supporting information.

To highlight the saved computation resources with the scaling approach, we remark that a single full 3-D simulation of the bridgeless CBGs performed on our high-performance computing cluster [53] would take approximately 4 hours, depending on the size of the simulated structures. If one adopts the conventional blind-searching optimization approach, which requires thousands of trials to optimize a single CBG design [28], the computation time would easily reach weeks and months even with parallel computing. On the other hand, with the scaling approach, we greatly reduce the number of computations to less than 5 trials and therefore making the optimization task possible within one day even without parallel computing.

3. Conclusion and outlook

To conclude, we proposed and demonstrated that the design of high-performance hybrid CBG structures can be much more efficient and versatile than in conventional numeric design optimizations by exploiting the nature of resonant grating waveguide structures. With the wavelength scaling method, we are able to initialize quickly a design at the target wavelength by compensating the CBG mode shift due to, for instance, structural perturbation. The optical path-length scaling method preserves the CBG performance while varying the wavelength to a significant degree. Finally, the effective optical path-length scaling method adapts the in-plane geometry according to the layer design. With a combination of all three methods, we presented 5-ring CBG designs covering emission wavelengths from 900 nm to 1600 nm with $F_{P} > 26$ and $\eta _{ext} > 0.92$ without electrical contact bridges and $F_{P} > 26$ and $\eta _{ext} > 0.86$ for the bridged counterpart in 4-LW labyrinth geometry.

The proposed approach is highly flexible, allowing one to adapt the CBG designs according to reality constraints, such as preset layer thicknesses. With deterministic fabrication approaches, this further opens the possibility to integrate all the quantum emitters within an inhomogeneously broadened ensemble on the same chip. Furthermore, it is noteworthy that the approach would even allow one to change the material system, for instance, from GaAs to InP, which represents a refractive index change that could be compensated as material dispersion. Additionally, the cryo-temperature refractive indices are often not readily accessible in the literature, which may result in a deviation of the experimental mode energy from the optimized design. The presented work complements the ambiguity by offering the insights into tuning and correcting the experimental CBG mode energy. Finally, by revisiting the waveguide nature of CBGs, one also gains insights in the photon loss channel, including optical absorption during propagation. This physical understanding enables a more rational design of structures. The work represents a significant step forward in enhancing the fabrication and integration of single-photon emitters within high-performance quantum devices.