Saturated Gain-Induced Non-Reciprocal Transmission and Broadband On-Chip Optical Isolator

Abstract

To overcome the limitation of dynamic reciprocity, a new method for designing broadband on-chip optical isolators is proposed and demonstrated based on saturated gain, which is able to support simplex and duplex operation modes. By connecting a saturated gain waveguide to an appropriate linear loss waveguide, broadband isolation is predicted and proved theoretically through saturated gain-induced non-reciprocal transmission. The proposed isolator is numerically demonstrated with an operating band of 59 nm and an isolation ratio of −20 dB at the central wavelength of 1550 nm. It is noteworthy that when the current pump changes, the isolator still works well and keeps the high isolation ratio at a different input power. The footprint of the whole device is 465 μm × 0.35 μm which satisfies the requirement of photonic integrated circuits. The proposed isolator, with the combined advantages of compact footprint, broadband, duplex operation and high isolation, can enable on-chip unidirectional transmission and complex topological routing designation.

1. Introduction

Non-reciprocity is a remarkable physical phenomenon, which provides abundant applications in the photonics industry [1,2,3,4,5,6,7,8], especially on-chip photonics. The photonic isolator is one of the biggest concerns in non-reciprocal on-chip photonic devices due to wide applications of integrated backscatter eliminating and complex communication topology construction in photonics. To implement on-chip isolation, three well-known non-reciprocal phenomena have been investigated extensively as solutions, including nonlinear optical (NLO) effects [9,10,11,12,13], magneto-optical (MO) effects [14,15,16,17,18,19,20,21,22] and the time-dependent optical (TDO) system [23,24,25]. The NLO effects usually provide two schemes, which are optically induced transparency [8] and optical bistability [9,10]. The former exploits four-wave mixing in micro-ring which leads to the narrow operation band. The latter is seriously limited by dynamic reciprocity [26], and hence, the isolator function cannot be constructed when a forward signal transmits through the system, which means the duplex operation modes cannot be supported. The MO effects are also actualized by two schemes. One is an MO micro-ring [12], which is not only a narrow operation band device but also requires complex manufactured technology. The other is the MO-induced reciprocal loss waveguide [14,18], which is limited by its large size for on-chip photonics. The TDO system demands a very high modulation frequency. Therefore, although numerous pieces of research focus on optical isolators, there is still a lack of a small-sized scheme holding not only a wide operating band but also supporting duplex workings and keeping a high isolation rate.

In this paper, we propose and demonstrate that saturated gain can be a new solution to implement non-reciprocal transmission, which is a fabrication-friendly, duplex work supporting, wide operating band and relatively small-sized scheme.

Table 1. Characteristics of the current schemes and proposed scheme.

	Fabrication	Duplex Working	Operating Band	Size
NLO	Easy	No	Narrow (~1 nm)	~100 μm
MO micro-ring	Very Hard	Yes	Narrow (<1 nm)	~100 μm
Normal MO	Easy	Yes	Wide (>50 nm)	>1 mm
TDO	Hard	Yes	Narrow (<10 nm)	~100 μm
Saturated gain	Easy	Yes	Wide (>50 nm)	~500 μm

shows the comparison between current schemes and the saturated gain-induced non-reciprocal transmission proposed in this paper.

In this work, we utilize the broadband saturated gain of a semiconductor optical amplifier (SOA) waveguide to construct a non-reciprocal propagation area, and then compensate the power change with an appropriate linear loss waveguide which is designed as a hybrid surface plasmon polariton (SPP) waveguide [27]. The designed isolator supports duplex operation mode in a 59 nm operating band, and the isolation rate is as high as −20 dB, while the whole size of the device is as small as 465 μm × 0.35 μm.

2. Non-Reciprocal Transmission in Saturated Gain Waveguide

There is an important property of non-reciprocal transmission in a saturated gain waveguide. When light only inputs to one port of the waveguide with different powers (simplex operation mode), the output powers are identical after propagating over a long enough distance. The model of saturated gain is described in [28,29,30,31] as

$$G=\frac{G_0}{1+P/P_{\mathrm{s}}}-\alpha$$

(1)

where P is the power of light propagating in the saturated gain waveguide, P_s is the saturated parameter, G₀ is the gain coefficient for small signals, and α is the linear loss of the waveguide. Figure 1 shows the relationship between G and P. The zero point of the G–P curve is defined as cut-off power P_c, which can be expressed as

$$P_{\mathrm{c}}=(\frac{G_0}{\alpha }-1)P_{\mathrm{s}}$$

(2)

When the power of the input light P is higher (lower) than P_c, the gain coefficient G is smaller (greater) than zero, and then P is going to decrease (increase) to P_c. It can be found that the gain coefficient G convergences to zero as shown in Figure 2a,b after a long enough propagating distance, and the output power P convergences to P_c which corresponds to the zero-gain coefficient.

When light signals are input into both of the two ports of a waveguide (duplex operation mode), Equation (1) is changed as

$$G(L)=\frac{G_0}{1+[P_1(L)+P_2(L)]/P_{\mathrm{s}}}-\alpha$$

(3)

where P₁ and P₂ are the power of light signals input from the right and left ports, respectively. In addition, P₁ and P₂ satisfy the following relations and conditions:

$$\begin{array}{cc}\frac{d{P}_1}{dL}=G{P}_1,& \frac{d{P}_2}{dL}=-G{P}_2\end{array}$$

(4)

$$\begin{array}{cc}\frac{d{P}_1}{dL}{|}_{L\to \infty }=0,& \frac{d{P}_2}{dL}{|}_{L\to \infty }=0\end{array}$$

(5)

Assuming that L_w is long enough to meet the boundary conditions, the solutions can be obtained by combining Equations (3)–(5) as

$$\begin{array}{cc}{P}_1(L_w)+P_2(L_w)=P_{\mathrm{c}},& P_2(0)+P_1(0)=\end{array}{P}_{\mathrm{c}}$$

(6)

Evidently, the sum of the input power at the right port and the output power at the left port is equal to the sum of the output power at the right port and the input power at the left port, and the value is exactly equal to P_c.

3. Isolator Model

Using the saturated gain model, we propose a sketchy model, supporting both the simplex and duplex operation modes, and then investigate the relationship between device size and performance. Exploiting the preceding demonstrations of Equations (1)–(6), the property of a saturated gain waveguide can be summed up as the illustration in Figure 3a. P_o1 is the output power of P_H, and P_o2 is the output power of P_L, where P_H >> P_L, and P_o1 ≈ P_o2 ≈ P_H ≈ P_c. Connecting a linear loss element to the saturated gain waveguide, the isolator model is obtained as shown in Figure 3b.

In the simplex operating mode, only one of the two ports of the device allows for the input of light signals. As shown in Figure 3b, when the light transmits from the left side to the right side, and its power is as high as P_H ≈ P_c, the power can only be gained a little and becomes P_o1 because of the saturated gain property; then, it decays to P_L << P_H after transmitting through the additional loss element. By contrast, if light with power P_H is input from the right side, its power will decay to P_L first, and then grow to P_o2 which is very close to P_H.

In the duplex operating mode, both of the two ports are inputs as shown in Figure 3c, it can be understood that P_H1 + P_o2 = P_L2 + P_o1 = P_c in terms of Equation (6). If P_H1 = P_c, it is clear that P_o2 = P_c/2 >> P_L1. The isolation for backward signals is kept when the forward signals are transmitted through it. It should be noted that the operating power of duplex mode is half that of simplex in the same device.

The above discussion is based on the theory demonstrated in Equations (4) and (5), a theory that demands enough waveguide length. Here, a more detailed analysis is given to demonstrate how long that required length is. The design isolation ratio of the isolator r is defined as

$$r=\frac{T_{\mathrm{L}}}{T_{\mathrm{R}}}$$

(7)

where T_L is the transmission of input from the left and T_R is the transmission of input from the right. Firstly, we discuss the simplex operation mode. The P–L curve of a saturated gain waveguide for small signal input is plotted in Figure 4a in accordance with the numerical solution of

$$\frac{P+P_{\mathrm{s}}}{P}dP=(P_{\mathrm{s}}{G}_0-\alpha P_{\mathrm{s}}-\alpha P)dL$$

(8)

and the “enough amount of length” of the saturated gain waveguide can be found in Figure 4a as L_t1, which considers the output power tolerance as t × P_c. Connecting a linear loss waveguide which decays the input power from P_c to r_sP_c (r_s is the isolation ratio of simplex operation mode), the asymmetric transmission phenomenon can be observed in Figure 4b,c.

Next, we discuss the duplex operation mode. Similar to the simplex operation mode, the P–L curve of the saturated gain waveguide is also needed to find the “enough amount of length” L_t2 as shown in Figure 5a. Further, connecting a linear loss waveguide which decays the input power from P_c to r_dP_c/2 (r_d is the isolation ratio of duplex), the P–L curve becomes Figure 5b for different propagating directions, and the asymmetric transmission can be observed. It should be noted that the main difference between simplex and duplex is the operation power. The operation power of duplex is half of that in simplex. Comparing simplex operation mode with duplex operation mode in the same system, it can be found that their operation powers are different. The operation power of duplex changed to P_c/2, which is half that of the simplex operation mode.

4. Device Designing

Then, we give a practical design of an on-chip optical isolator in accordance with the model described in Figure 3. The design is made up of an SOA waveguide covered by metal, which provides saturated gain with a linear loss α fitting the mathematical model in Equation (1). Figure 6a exhibits the schematic of our design. The isolator consists of two parts, the gain part and the loss part. The cross-sections of the two parts are the same, shown in Figure 6b, while the lengths and pump currents are different. For the gain part, the length is L_SOA = 450 μm, and the pump current is 90 mA, corresponding to the parameters P_s = 3.41 mW and G₀ = 0.3 μm⁻¹ at 1.55 μm operation wavelength [19,20,21,22]. For the loss part, the length is only L_D = 15 μm, and no pump is utilized in it. Figure 6b shows the layer structure of the cross-section of the proposed design. It can be seen that the SOA waveguide is an SPP waveguide consisting of a metal layer (exploited as an electrode), a p-type InP layer, an n-type InP layer and an InGaAsP quantum well layer [18]. It should be noted that the parameters P_s and G₀ are of the material, not of the SPP mode employed as shown in Figure 6c. The effective index of the SPP mode is 3.03 + i0.0176, and the decayed coefficient α is 0.1426 μm⁻¹ in terms of the imaginary effective index 0.0197. Meanwhile, the P_s and G₀ become 3.5365 mW and 0.1687 μm⁻¹, respectively, and the cut-off power P_c is 643 μW. Accordingly, it can be calculated using Equation (8) and the FDTD method or the Runge–Kutta method that 15 μm L_D provides a bidirectional 20 dB decay to make the 643 μW input power decay to 6.43 μW; additionally, the 450 μm L_SOA ensures the 6.43 μW low-power signal increases back to 643 μW, and the 643 μW signal maintains its power, which realizes non-reciprocal transmission.

According to Equation (8) and the parameters (α, P_s and G₀), the solid blue line in Figure 7a can be calculated numerically. It is clear that a 6.43 μW signal increases to 642.5 μW (99.92% of P_c) after propagating a 450 μm distance. The finite-difference time-domain (FDTD) [32,33] result (the red dashed line) also fits the analytical solution (calculated using Equations (4) and (5) with original code) as shown in Figure 7a. Meanwhile, if a signal with a power of 643 μW is input, the P–L curve changes to Figure 7b. Connecting a 15 μm loss waveguide with the SOA mentioned above, the function of an isolator can be realized; the P–L curves (signal inputs from the left and right), similar to Figure 4b,c, are given in Figure 8a,b, respectively.

Our design also supports broadband operation. Exploiting the broadband gain spectrum of the SOA, we have calculated the broadband transmission characteristics of the SOA when the input power is 643 μW and 6.43 μW in Figure 9a. Combining with the transmission spectrum of the loss part, Figure 9 can be obtained to illustrate the output power spectrum of both directions of the isolator and the spectrum of the isolating factor, F, expressed by P_out/P_in. Further, considering F > 99 as a criterion, the bandwidth of the isolator is calculated to be as broad as 59 nm. All the results are simulated.

It has already been pointed out in Figure 5 that duplex operation mode exhibits lower operation power compared to simplex, so it is important to find an effective way to adjust operation power. The pump current is the key to controlling operation power. The operation power varies with the pump current of the gain part. Figure 10a gives the relation between P and L of the SOA with different pump currents at 1.55 μm, and the corresponding operation power can be calculated in Figure 10b. If we change the operation mode from simplex to duplex, and hope to maintain operation power, we can increase pump currents to fit it.

5. Conclusions

In summary, we have proposed a novel method of designing the broadband optical isolator based on nonlinear gain, and the fundamental theory of the isolator is completely demonstrated. With the guidance of this theory, we have designed a broadband optical isolator working at a wide wavelength scope, from 1.500 μm to 1.559 μm. In addition, the isolator works at different powers with the same isolated factor, 100, when the current pump is changed. Moreover, the length of the whole device is only 465 μm, and the footprint area is as small as 465 μm × 0.35 μm. The size of the device satisfies the requirement of the application of photonic integrated circuits, and in particular, it can be applied to eliminate integrated backscatter, protect the source and construct complex communication topology in photonic integration.