An optical parametric Bragg amplifier on a CMOS chip

2.1 Principles of the optical parametric Bragg amplifier

FWM is a nonlinear process that occurs in third-order nonlinear media, requiring both energy conservation and phase matching. Nondegenerate FWM involves two different pump photons at different frequencies (ω _p1,p2) generating a signal and idler photon at frequencies ω _s and ω _i, respectively. Degenerate FWM utilizes two pump photons at the same frequency ω _p being annihilated to generate a single signal and idler photon at frequencies ω _s and ω _i, respectively, according to the equation, 2ω _p = ω _s + ω _i. Pump and signal photons co-propagating in nonlinear media can lead to signal amplification and generation of idler photons (Figure 1a). The signal gain and idler conversion efficiency depend on the phase-mismatch, Δk _t = 2γ _eff·P _in + Δk _L, where γ _eff and P _in are the effective nonlinear parameter and input peak power, respectively. Δk _L = k _s + k _i − 2k _p is the linear phase mismatch, where k _p, k _s, and k _i are the pump, signal, and idler wavenumbers, respeectively. The linear phase mismatch may alternately be described in terms of the effective index of the pump, signal, and idler (n _p, n _s, n _i), according to, Δ k L = 1 c n s ⋅ ω s + n i ⋅ ω i − 2 n p ⋅ ω p . High parametric gain is achieved if Δk _t is close to zero, indicating that Δk _L ∼ −2γ _eff·P _in.

Figure 1:

(a) Energy conservation in degenerate FWM process. Two pump photons are converted into signal and idler photons. In a stimulated case, the signal wave is amplified while idler waves are generated. Momentum conservation (phase-matching) should be satisfied to fulfill amplification of signal waves and generation of idler waves. (b) Effective index near the band edges of photonic bandgap in the CMBGs structure. The slopes of red solid and black dashed lines depict effective indices in respective CMBGs and photonic nanowire waveguide (WG), where Λ is the period pitch of a grating.

In photonic WGs where the GVD, β ₂ (and therefore n _eff) varies slowly with wavelength, Δk _L is approximately β _2·(ω _p − ω _s)² for small pump-signal detuning [24]. The phase matching is therefore dependent on anomalous dispersion existing in the WG. In the regime of high peak power and large nonlinear parameter, small magnitudes of anomalous dispersion typically present in WGs are insufficient to cancel out the nonlinear contribution. In other words, achieving high parametric gain and strong idler conversion efficiencies requires anomalous dispersion magnitudes significantly larger than that available simply through geometry-based engineering of WG dispersion or that available through bulk material dispersion [21], [22], [23].

On-chip Bragg gratings possess strong band edge dispersion, useful for triggering soliton fission and the enhancement of supercontinuum generation [25], [26], [27]. As a result of the interaction between the forward and backward coupled waves located close to the grating stopband, the group index increases (decreases) rapidly as the wavelength is increased on the blue (red) side of the stopband. The GVD, β 2 = λ 3 2 π c 2 ⋅ d 2 n eff d λ 2 = − λ 2 2 π c 2 d n g d λ , where n _g is the group index of the propagating mode. Therefore, it may be seen that a rapid increase in the group index corresponds to a similar rapid increase in the effective index of the propagating mode, as well as a large β ₂. This large increase in the effective index may therefore be strategically leveraged for phase matching (Δk _t = 0) in the regime of large pump power and strong nonlinear parameter. In this paper, we shed light on nonlinear gratings for optical parametric Bragg amplification; this is achieved by applying the strong effective index variation introduced in a nonlinear ultra-silicon-rich nitride (USRN) grating design toward enhanced phase matching.

Figure 1b illustrates how the phase-matching condition is satisfied in cladding modulated Bragg gratings (CMBGs), on which the optical parametric Bragg amplifier is based, compared to photonic nanowire WGs. Photonic bandgaps in CMBGs intrinsically possess two band edges where rapid, wavelength-dependent variations in the effective index and group index exist. Compared to photonic WGs where the effective index changes slowly, the variation of the effective index with the wavelength in CMBGs is larger close to the stopband: When the frequency approaches Bandedge1 (blue edge), the wavenumber (k) in CMBGs is smaller than that in WG at the same frequency (ω). Equivalently, n _eff decreases as k decreases at Bandedge1. Therefore, n _eff in CMBGs is smaller than that in WGs close to Bandedge1. Conversely, when the frequency approaches Bandedge2 (red edge), k is larger than that in a photonic WG at the same frequency. This implies that n _eff increases as k increases and n _eff in CMBGs is larger than that in WGs close to Bandedge2. Consequently, a wider range of effective indices is available in CMBGs for the purpose of phase matching, achieved through a judicious selection of the operating frequency close to the photonic band edges. Furthermore, this feature circumvents the typical requirement of operating in the anomalous dispersion region associated with FWM in photonic WGs.

The optical parametric gain of signal, G _s may be described according to the equation,

where the parametric gain coefficient, g = ( γ eff P in ) 2 − ( ( 2 γ eff P in + Δ k L ) 2 ) 2 , and L _eff is the effective length. In the limit where Δk _t approaches zero, Δk _L = −2γ _eff·P _in resulting in the maximum value of G _s [10, 15]. The effective nonlinear parameter, γ eff = 2 π n 2 λ A eff ⋅ ( n g n 0 ) 2 , where P _in is the input peak power, n ₂ is the nonlinear refractive index of the material, A _eff is the effective area and n ₀ is the material refractive index. In USRN, the linear and nonlinear refractive indices are 3.1 and 2.8 × 10⁻¹³ cm²/W, respectively. When λ = 1526 nm, n _g = 4.0 and P _in = 1.6 W, the quantities within Equation (1) equate to: γ _eff = 800 W⁻¹/m and −2γ _eff·P _in ∼ −2560 m⁻¹. The contribution to Δk _L from the pump is −2n _p·ω _p/c (negative sign). Conversely, contributions to Δk _L from the signal and idler frequency terms is (n _s·ω _s + n _i·ω _i)/c (positive sign). In light of these quantities, phase matching within the grating may be further described according to the two regimes:

1. Regime dominated by grating dispersion: If pump wavelength is located at a position closer to Bandedge2 relative to that of signal and idler wavelengths, we can achieve perfect phase matching.

2. Regime dominated by WG dispersion: If the pump, signal, and idler wavelengths are far from the grating band edge, phase matching approaches the case of a conventional photonic WG. In this case, perfect phase matching will be difficult to achieve (in the limit where 2γ _eff·P _in is large), due to the small magnitude of GVD (β ₂) relative to a large pump peak power and nonlinear parameter. The linear phase mismatch in a photonic WG is defined as β ₂ Ω ², where Ω is the frequency detuning between pump and signal. The largest magnitude of anomalous GVD in high index contrast WGs is on the order of −1 ps²/m [14]. Whereas β ₂ Ω ² is small, 2γ·P _in possesses a large value due to large nonlinear parameter of 500 W⁻¹/m of the USRN WG, where γ is the nonlinear parameter in WG. Perfect phase matching in the WG is, therefore, hard to achieve even if the pump-signal detuning is small.

It may further be inferred from Equation (1) that the achievable gain in the FWM process relies on γ _eff. Another intrinsic advantage of performing FWM in nonlinear Bragg gratings is the elevated group index (and therefore γ _eff) that resides close to the grating band edge. As the USRN platform possesses a strong nonlinear refractive index, the advantages conferred by appropriately designed nonlinear gratings may provide enhancements in FWM processes both from augmented nonlinear parameters and advantageous phase-matching.

2.2 Optical properties of USRN CMBGs

The USRN platform was engineered to possess a strong optical nonlinearity of n ₂ = 2.8 × 10⁻¹³ cm²/W while simultaneously possessing negligible nonlinear loss near 1550 nm of wavelength [28], [29], [30]. CMBGs are periodic photonic structures that implement the periodic modulation of the effective index using cylinders placed at a fixed distance, G ₂, from a central WG as shown in the schematic of Figure 2a. Apodization may be achieved by adiabatically decreasing G from the ends of the grating toward the center. The CMBGs utilize a 600 nm (width, W) by 300 nm (height, H) USRN core with SiO₂ under- and over-cladding. The CMBGs parameters are pillar radius (r) of 100 nm, grating pitch (Λ _B) of 339 nm, and gap distance between the WG to pillar at the center (G ₁) and ends (G ₂) of the CMBGs are 50 and 150 nm, respectively. The 3 mm CMBG is designed with a 200 μm apodized section (L _A) on each end of the grating. Apodization is applied in order to minimize the transmission and group delay ripple, in particular, to ensure smooth transmission at the band edges of the photonic bandgap. The apodization profile is adopted by continuously increasing the gap distance from the center (G ₁ = 50 nm) to each end (G ₂ = 150 nm) over an apodization length (AL) according to the following relation [25],

where

Figure 2:

(a) The schematic and scanning electron micrograph of a fabricated CMBGs. (b) Group (blue line) and effective (red line) indices on wavelength near the band edges of the photonic bandgap. Black dashed line depicts effective index in USRN WG. The light green line shows the linear transmission of the CMBGs with a 10 dB bandwidth of 12 nm.

The apodization profile impacts the modulation of the coupling coefficients, allowing a gradual transition from the effective index of the WG to the grating region. Consequently, appropriately implemented apodization will generate a smooth effective/group index profile, as well as smooth transmission at the band edges [25, 31, 32].

The CMBGs structure is adopted to allow greater control over the apodization since the coupling coefficient of the grating can be controlled by the distance of the cylinders to the central WG. The use of effective apodization is important to minimize phase distortions in the grating band edge, enabling enhanced parametric amplification. Width or height modulated Bragg gratings are an important class of Bragg gratings in their own right. However, height corrugation is difficult to achieve in a single lithographic step, and WG width variation requires very small amplitude modulation at the apodized regions which could be difficult to accurately implement lithographically. For example, sidewall corrugated Bragg gratings have previously been reported to induce spectral distortion due to fluctuations in the WG dimension [33], [34], [35], [36], [37]. For these reasons, we had used the CMBGs to implement the optical parametric Bragg amplifier.

Fabrication of the USRN CMBGs was performed by first performing a 320 nm deposition of the USRN film using inductively coupled chemical vapor deposition at a temperature of 250 °C. Patterning of the structures was performed using electron-beam lithography, inductively coupled reactive ion etching, and plasma-enhanced chemical vapor deposition of the SiO₂ overcladding. A scanning electron micrograph is shown in Figure 2a. The CMBG stopband is centered at 1535 nm and possesses a 10 dB bandwidth of 12 nm as shown in the transmission spectrum (light green line) of Figure 2b. The total CMBG insertion loss outside of the stopband is −15 dB (fiber-WG coupling loss = 6.5 dB, propagation loss = 2 dB). The n _g of the CMBGs as a function of wavelength was measured with a dispersion analyzer as shown in Figure 2b (blue line). The effective index (n _eff) was derived from the relation, n _g = n _eff − λ·(dn _eff/dλ) (red line). It is further observed from Figure 2b that n _eff decreases at the blue side of the band edge and increases at the red side of the band edge, as compared to that in the USRN WG. When λ is far from the photonic band edges, n _eff and n _g are the same as that in the USRN photonic WG without the periodic pillars. n _g is symmetric about the center of the photonic bandgap, a characteristic that allows perfect phase matching to be implemented toward enhanced parametric gain.

2.3 Theoretical analysis of phase-mismatch and group velocity mismatch in USRN CMBGs

The optical parametric Bragg amplifier operates in transmission mode, specifically in the wavelength region of the grating where the transmissivity is high and the Bragg grating induced effective index varies rapidly (for phase matching). Operating in the transmission is essential as it allows us to take advantage of the high dispersion at the band edge induced by the Bragg grating structure.

Figure 3 shows the phase mismatch (Δk _t) and group velocity mismatch in the CMBGs. We utilize a 5 ps pulsed pump centered at 1550 nm with a peak power, P _in = 1.6 W. We used the CMBGs’ dispersive behavior to counterbalance the large, positive nonlinear phase to achieve perfect phase matching. The total phase mismatch versus the signal wavelength is shown in Figure 3a, where the pump wavelength is fixed at 1550 nm and the continuous wave (CW) signal wavelength is varied. Vanishing phase mismatch is obtained at 1525 and 1574 nm. The dashed line denotes the phase mismatch for a WG where it is observed that conditions for vanishing phase mismatch do not exist. This phenomenon arises because the magnitude of anomalous dispersion is insufficient to cancel the nonlinear contribution.

Figure 3:

(a) Phase mismatch (Δk _t) in the CMBGs (red solid line) and WG (blue dashed line) as a function of signal wavelength. The pump wavelength is 1550 nm and the signal wavelengths are varied between 1510–1528 and 1573–1595 nm. For the Δk _t curve at a shorter signal wavelength of 1510–1528 nm, the signal wavelength is located close to Bandedge1 to optimize the phase mismatch. For the Δk _t curve at a longer signal wavelength of 1573–1595 nm, generated idler wavelengths are tuned close to Bandedge1 to optimize the phase mismatch. The pump is located near Bandedge2 to minimize Δk _t. The 5 ps pump peak power is 1.6 W. (b) The group velocity matching length (L _gvm) is defined as τ/|1/v _p − 1/v _s,i|, where τ is pulse width and v _p, v _s,i are velocities for pump, signal, and idler beam. L _gvm is larger than the device length of 3 mm (green dashed). Gray lines depict linear transmission in the dB scale as a function of wavelength.

On one hand, we leverage the grating-induced dispersion toward improved phase matching. On the other hand, the grating-induced modification in the group index profile could impede the temporal overlap of pump, signal, and idler pulses. Therefore, the effect of the altered group index (or equivalently, the group velocity) profile is another important element to analyze. The input CW beam serves only as a stimulating source. The generated signal, idler, and input pump assume a pulsed form, particularly since the amplified signal and idler are generated only at temporal instances when the pump pulses co-propagate with the signal. We may derive further insight from the nonlinear Schrödinger equation for FWM. Equations (2) and (3) are coupled equations describing the generated idler amplitude A ₄ [24]:

where A _i, v _i are the field amplitude and group velocity of fields, and subscript 1, 2 refer to the degenerate pump photons. Subscript 3 and 4 are for signal and idler photons, respectively. The source term is a direct product of three photons, namely two pump photons and one signal photon. It follows from Equations (2) and (3) that the temporally nonoverlapped source term will be zero. In the absence of the source term, the idler cannot increase in amplitude. The group velocity matching length (L _gvm) is defined as τ/|1/v ₁ − 1/v _3,4|, where τ is the temporal pulse width. For FWM to take place efficiently through the entire device length, the group velocity matching length should exceed the device length. In our USRN CMBGs, our analysis shows that this condition is indeed satisfied: The L _gvm is larger than the device length of 3 mm as shown in Figure 3b [24].

2.4 Experimental results of gain in the optical parametric Bragg amplifier

Experiments are performed using a 5 ps pulsed pump with a repetition rate of 20 MHz centered at 1550 nm. A tunable CW laser is used as a signal source. The input peak power of the pump is fixed at 1.6 W. Both pump and signal lasers are combined using a 3 dB coupler and coupled into the USRN CMBGs via a tapered fiber. The output spectra coupled out from a tapered fiber are measured by an optical spectrum analyzer (OSA). In our experiments, the experimentally measured FWM spectra are shown in Figure 4a and b as the signal wavelengths tuned from 1512–1526 and 1570–1579 nm, respectively, where the pump, amplified signal, generated 1st and 2nd idlers at each signal wavelength are observed. The signal wavelength is tuned from 1512 to 1526 nm at the blue side of the grating stopband (Bandedge1), in order to experimentally determine the maximum gain as shown in Figure 4a. The generated idlers wavelengths are tuned closing to Bandedge1 to optimize phase mismatch, thus obtain maximum gain by tuning from 1570 to 1579 nm of signal wavelength as shown in Figure 4b. Figure 4c shows the measured and theoretical on/off signal gains as a function of signal wavelength. On/off signal gain is defined as P _sig,peak/P _signal,out, where P _sig,peak is calculated using P sig,peak = 1 R τ ( ∫ P sig,avg ( λ ) d λ ) , and R and τ are the repetition rate of the pulse and the pulse width, respectively. P _sig,avg (λ) represents the average output power spectrum of the signal measured using the OSA. The power of the CW signal line is subtracted from P _sig,avg (λ) to obtain P _sig,peak. P _signal,out is the CW signal power at the output of the device with the pump off [11], [12], [13], [14], [15]. By tuning the signal wavelength to the blue side of the band edge, the maximum signal gains of 20 dB are obtained at a signal wavelength of 1524 nm. The maximum on/off signal gain is obtained to be 20 dB at a signal wavelength of 1576 nm where the phase-matching condition is optimally satisfied.

Figure 4:

Experimentally measured FWM spectra for the optical parametric Bragg amplifier at the signal wavelength of (a) 1512–1526 nm and (b) 1570–1579 nm. (c) On/off signal gains (pink dots) are compared with theoretical curves in the CMBGs (red line) and WG (blue dashed). The grating transmission is presented as the grayline. 1st/2nd idler gains corresponding to the FWM spectra in (a) and (b) are shown in (d) and (e), respectively.

Theoretical on/off signal gain is defined as P _sig,peak/P _signal,out, where P _sig,peak and P _signal,out are the amplified signal peak power and CW signal power at the device output, respectively. G _s is defined as the amplified signal power at the device output divided by input signal power. Consequently, the on/off signal gain is given by, G _s·e ^α·Leff, where L eff = 1 α [ 1 − e − α L ] and α is the loss coefficient. The figure shows the trend of measured on/off signal gains (pink dots) agrees well with the theoretical calculations (red solid line).

The comparison of the on/off signal gain between the CMBGs and WG is also presented in Figure 4c. The maximum gain achieved in the CMBGs is around 20 dB, occurring at a signal wavelength of around 1524 and 1576 nm where the phase-matching condition is satisfied. We may observe from Figure 3 that as the signal wavelength closes to Bandedge1 increasing beyond 1524 nm and approaches Bandedge2 decreasing below 1576 nm, phase matching and group velocity matching become worse. Thus as expected, it is observed from Figure 4c that the gains drop sharply. A decrease in gain is observed as the signal wavelength shifts away from the stopband as a result of the worsening phase matching. The slow decreases in gains decreasing below 1524 nm and increasing beyond 1574 nm are also to be expected since variations in both group index and dispersion vary much less rapidly in regions far from the grating stopband. Conversely, in the WG case, it is observed that the gain remains fairly constant at around 13 dB in the wavelength of interest wavelength even if perfect phase matching is not satisfied (blue dashed). Consequently, it is theoretically and experimentally predicted that the enhanced phase matching conferred by CMBGs allows a significant increase in the achievable parametric gain compared to WGs. We note further that far from the grating stopband, the parametric gain approaches that achievable in a USRN WG without the grating structure. In our experiment, 12 nm of working bandwidth with on/off parametric gain exceeding 8 dB is achieved at each band edge and the parametric gain exceeds that achieved in the WG across an 8 nm bandwidth. Summarily, the optical parametric Bragg amplifier provides augmented parametric gain from enhanced phase matching close to the grating stopband, and similar gain as a USRN WG when operating far from the grating stopband.

The FWM spectrum in Figure 4a and b both show evidence of cascaded FWM, where a 1st and 2nd idler is generated during the parametric process. The on/off nth idler gain is calculated as P _{idler(n),peak}/P _signal,out, where n represents the idler number. The power within the nth idler is calculated using the expression, P idler ( n ) ,peak = 1 R τ ( ∫ P idler ( n ) ,avg ( λ ) d λ ) , where P _idler(n),avg (λ) is the average output power spectrum of the nth idler measured using the OSA [11], [12], [13], [14], [15]. As the signal wavelength is tuned closer to the blue side of the band edge, the effective index decreases at a faster rate compared to the WG. Therefore, the total phase matching eventually goes to zero. We can further observe a 2nd idler gain of close to 1 dB at a signal wavelength of 1525 nm, corresponding to when the signal gain exceeds 16 dB as shown in Figure 4d. The 1st and 2nd idlers are generated at two wavelength regions: from 1570–1594 nm, and close to 1600 nm as shown in Figure 4a. The generated 1st idler is tuned near the blue side of the band edge, the 1st and 2nd idlers are generated from 1520–1530 nm, and 1600–1610 nm, respectively, as shown in Figure 4b. Second idlers are observed with conversion efficiencies varying between −4 and 1 dB, corresponding to when the signal gain exceeds 12 dB as shown in Figure 4e. We observe similar parametric gain values in both Figure 4c–e because the signal (idler) wavelengths are tuned at the blue (red) side of the band edge by switching the location of the signal/idler wavelengths with each other. The output pump shows self-phase-modulation-induced broadening due to the large nonlinear parameter in the CMBGs.

To further analyze how parametric gain is facilitated with the enhanced phase matching conferred by the grating, we investigate the FWM process when the pump is located at the blue side of the band edge. In other words, this particular placement of the pump and signal does not lead to ideal phase matching. In this case, situating the pump wavelength at the red side of the band edge is ideal for achieving a negative Δk _L value. However, the smaller effective index when the pump is at the blue side of the band edge makes it difficult to obtain negative Δk _L and results in significantly less effective phase matching. In the next set of experiments, a USRN CMBGs with the stopband centered at 1575 nm is used (gray line in Figure 5a). The signal wavelength is varied from 1556 to 1563 nm, on the blue side of the band edge. We note here that the effective index is smallest at 1563 nm. As the pump wavelength is also located at the blue side, the on/off signal and idler gains are measured to be around 10 dB at a signal wavelength of 1563 nm (Figure 5b), which is smaller than that achieved in Figure 4 where the pump wavelength is located at the red side. No visible 2nd idler is observed due to the smaller overall parametric conversion efficiency in this configuration.

Figure 5:

FWM spectra (a) and their on/off signal and 1st idler gains (b) at signal wavelength of 1556–1563 nm. FWM spectra (c) and their on/off signal and 1st idler gains (d) at signal wavelength of 1520–1529 nm. Black dashed lines in (b) and (d) show the theoretical on/off signal gains which agree well with the experiments. Gray lines depict linear transmission in the dB scale as a function of wavelength. Input peak power is 1.6 W.

Next, the parametric gain is measured in the CMBGs far from the band edge. When the pump wavelength is far from the band edge in the CMBGs, pump, signal, and idler waves evolve similarly to the WG case. The gray line in Figure 5c represents the transmission vs. wavelength for a CMBG that does not have a photonic bandgap in the wavelength range of interest between 1520 and 1610 nm. We use a pump wavelength of 1547 nm and tune the signal wavelength between 1520 and 1529 nm. The measured on/off signal and 1st idler gains are 12 dB at a signal wavelength of 1525 nm (Figure 5d). The measured on/off signal gains agree well with the values in the theoretical simulation (black dashed lines).

A further set of experiments is conducted to confirm the role of the CMBGs-induced phase matching. Poor phase matching is observed when the pump is located at the red side of Bandedge2 and the signal wavelength is tuned to close to the Bandedge2 as shown in Figure 6a. As the signal frequency term, n _s ω _s in Δk _L has the largest magnitude with positive sign close to the band edge, the discrepancy between Δk _L and the quantity, −2γ _eff·P _in is large and poor phase matching is expected. When the pump wavelength is located at the blue side of Bandedge1, the pump frequency term, −2n _p ω _p/c from Δk _L possesses a smaller magnitude with a negative sign, again resulting in poor phase-matching (Figure 6b). Therefore, idlers are not observed in Figure 6a and b.

Figure 6:

FWM spectra at a signal wavelength of (a) 1540–1545 nm using the CMBGs as that used in Figure 4a and b signal wavelength of 1583–1589 nm using the CMBGs as that used in Figure 5a. No idlers are observed in either case due to poor phase matching.

We reconsider the pump-probe setup used in Figure 4a and investigate the impact of changing the pump wavelength. When the pump wavelength is changed from 1550 to 1554 nm while utilizing the same experimental condition of Figure 4a, the maximum signal gain is blue-shifted from 1524 to 1522 nm as shown in Figure 7. This phenomenon arises from the smaller resultant effective index associated with the blue-shifted pump. In order to fulfill the phase-matching condition, Δk _L ∼ −2γ _eff P _in, n _s ω _s is decreased as −2n _p ω _p/c is decreased in Δk _L = (n _s ω _s + n _i ω _i − 2n _p ω _p)/c. Therefore, the impact of the signal wavelength on the trend observed in the on/off signal gain in Figure 7 further confirms the effectiveness of the optical parametric Bragg amplifier in conferring improved phase matching.

Figure 7:

Comparison of on/off signal gains between pump wavelength (λ _pump) of 1550 and 1554 nm. The blue triangular line is the same as the pink dots at the shorter wavelength region in Figure 4c.

The performance of the optical parametric Bragg amplifier may be evaluated with respect to the gain, device length (L), and input peak power (P _in) used. We utilize the figure of merit G P L = 10 × log 10 G sig P in 2 ⋅ L 2 , where G sig = P sig , peak P signal , out , is the on/off parametric gain, to compare the performance of various on-chip parametric amplifiers. G _PL accounts for the fact that the FWM process increases with the square of input peak power × device length [38]. This comparison plot is included in the revised manuscript as Figure 8 [11], [12], [13], [14, 39]. G _PL for our device is 26, which is the largest among other on-chip parametric amplifiers including silicon and amorphous silicon photonic WGs. It indicates that parametric amplification in USRN CMBGs benefits from enhanced phase-matching and the augmented group index at the grating band edge.

Figure 8:

Comparison of on/off parametric gains among on-chip parametric amplifiers of Ref. [11], [12], [13], [14, 39], and our work.

Brillouin scattering has been used to generate large amplification of >20 dB [40, 41]. However, the bandwidth of Brillouin amplification is inherently limited by the phonon lifetime which is typically tens of Megahertz [24]. Wider gain bandwidth has been demonstrated by broadening the stimulated Brillouin scattering pump but is still limited to gigahertz bandwidth, considerably smaller than the parametric amplification bandwidth achieved in our work which approximates terahertz bandwidth.

Efficient, on-chip FWM processes have also been implemented with much success using high-Q silicon nitride and Hydex micro-ring resonators, enabling wideband frequency comb generation [22, 42, 43]. Noting that optical parametric amplification in silicon nitride ring resonators has not been demonstrated, as far as we are aware, the fundamental difference with the approach demonstrated in our work is the bandwidth constraint imposed by the resonant response of the rings. Another possible reason is the weaker Kerr nonlinearity in Silicon nitride (100× smaller than in USRN).

In the optical parametric Bragg amplifier, aside from the high parametric amplification, the gain may be conferred to signals over a continuous wavelength range, albeit within the operating bandwidth of the band edge. Indeed, there is a bandwidth over which perfect phase matching may be achieved, which perhaps can be extended in the future through further design optimizations. In addition, the footprint of a typical silicon nitride ring resonator (100 μm radius) is about 3.1 × 10⁻⁸ m², larger compared to the footprint of the optical parametric Bragg amplifier (5 × 10⁻⁹ m²).

We note that this amplification strategy may be implemented for any wavelength region and is especially useful for achieving phase matching when the background WG dispersion is normal. When a strong nonlinear phase is expected either from a high-powered pump or strong device nonlinearity, the Bragg-induced improvement in phase matching would most certainly facilitate more efficient parametric processes. High pump powers reduce the coherent length for FWM in the presence of nonperfect phase matching. Because the device length should be less than the coherence length, strong pump powers place a limit on the usable device length. Therefore, perfect phase matching induced by the CMBG structure enables a longer coherence length and therefore, a longer device length can potentially be used for optical parametric amplification once group velocity matching is satisfied.