1. Introduction

For many applications in interferometry and spectroscopy, it is desirable to have a laser source with a wavelength continuously tunable over a spectral range without mode hopping [1]. In order to achieve mode-hop-free wavelength tuning, the optical path length of the laser cavity must be adjusted in a synchronized fashion when the wavelength is tuned by a wavelength-selective element. For monolithically integrated lasers, two synchronous tuning electrodes are usually required for continuous tuning [2–4]. To avoid using multi-electrode simultaneous tuning architecture which complicates the tuning algorithms and limits the tuning speed, several single-electrode tuning structures have been proposed. By using a tunable twin guide (TTG) layer structure in a Distributed Feed Back (DFB) laser, one can change the refractive index of the laser cavity without influencing its gain significantly [5]. The drawback of the TTG-DFB laser is that it requires very complex multiple regrowth and etching fabrication process. Another single-electrode tuning approach based on DFB lasers is to employ longitudinally interleaved passive and active segments [6]. However, when the lasing wavelength is tuned, satellite reflection peaks are generated which results in degradation of the side-mode suppression ratio (SMSR). Single-electrode control of the lasing wavelength has also been demonstrated in a Distributed Bragg Reflector (DBR) laser with three different tuning configurations [7–9]: Fujiwara et al. used a very short gain section to achieve quasi-synchronous mode-hop-free tuning [7]. However, a short gain section (several tens of micrometers) results in a large current intensity and may cause heat dissipation problems of the laser. Another way is to use an interdigital tuning electrode which only covers part of the DBR region [8]. The problem of the method is that the interdigital tuning electrode may generate non-uniformly refractive index variation in DBR region. Consequently, a sample grating is formed if a large tuning current is injected by the interdigital electrode, which degrades the single-mode characteristics of the laser. The third method is to apply different confinement factors in DBR and phase control region, respectively [9]. Such technique requires different core layer thickness in different regions and thus complicates the fabrication processes. Besides, coupling loss exists between the two sections.

Recently ring resonator coupled lasers have been investigated by many authors. The state-of-the-art fabricated devices have shown their potential including the tuning of the wavelength [10–13]. However, no attention has been paid for achieving mode-hop-free tuning.

In this paper, a novel single-electrode-controlled mode-hop-free tunable laser is proposed based on a ring coupled cavity. The device comprises of a passive ring resonator coupled to an active Fabry-Perot (FP) cavity. The tuning electrode covers a part of the ring as well as certain passive waveguide segments belonging to the FP cavity. Mode hop free tuning is achieved by properly designing the electrode lengths within the FP cavity and in the ring.

2. Laser structure and principle of mode-hop-free operation

Figure 1 shows the schematic diagram of the mode-hop-free ring coupled laser. It consists of a ring resonator coupled to two straight waveguides WG1 and WG2. The right ends of the two waveguides are terminated by two partially reflecting mirrors M1 and M2, which constitutes a Fabry-Perot cavity with the ring resonator acting as an optical filter inside the cavity. The light propagating to the left ends of the straight waveguides diverges to an absorbing slab waveguide and is lost. However, no energy is lost for the main lasing mode since it corresponds to the resonance of the ring cavity with 100% transmission from one waveguide to the other, theoretically. The waveguide WG1 contains an active waveguide segment of length L_a, and a passive segment of length L_p1, while WG2 is a passive waveguide of length L_p2. The ring is coupled to the two passive waveguides through two coupling regions, respectively. The left half of the ring between the two coupling regions is within the optical path of the Fabry-Perot cavity. It is therefore a common waveguide segment between the ring resonator and the FP cavity and has a length L₁’. The waveguide in the ring resonator is divided into a tuning segment of length L₁ which includes the common waveguide segment (L₁≥L₁’) and a bias segment of length L₂. The tuning electrode covers the tuning segment, and the two passive waveguide segments outside the ring. When a tuning current is applied through the electrode and a ground electrode, all the waveguide segments within the tuning region have the same refractive index variation.

 

Fig. 1 Schematic of the mode-hop-free tunable ring coupled laser. The shaded region is the tuning section under a common tuning electrode.

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The transmission coefficient of the ring resonator t is given by [12]

If Eq. (8) is not satisfied, the tunings of the ring and the FP modes are no longer synchronous. This results in a limited mode-hop-free tuning range Δλ_MHF, which is defined as the wavelength tuning range when the resonant ring mode is tuned from one FP mode to its adjacent mode due to the asynchronous tuning. From Eqs. (6), (7) and the free spectral range of the FP cavity, Δλ_MHF can be derived as

In practice, Eq. (9) gives the upper limit of the mode-hop-free tuning range since the tuning range Δλ is usually limited by the maximum achievable refractive index change Δn_max with the relationship $\genfrac{}{}{0.1ex}{}{\Delta \lambda }{\lambda }\text{=}\genfrac{}{}{0.1ex}{}{\Delta {\text{n}}_{\max }{\text{L}}_1}{{\text{nL}}_1+n_2{L}_2}$.

Note that the refractive index of the bias segment of the ring can be adjusted by injecting a current into the biased section to make initial alignment between the resonance peak of the ring and that of the FP cavity. However, this bias current does not need to be tuned synchronously to achieve the mode-hop-free operation.

3. Simulation results and discussions

When a tuning current I is applied to the tuning region, the refractive index is changed due to the free carrier dispersion effect [13]. Here, the effective refractive index variation Δn is assumed to be proportional to the carrier density N, i.e. $\Delta n=\Gamma \chi N$, where Γ is the optical confinement factor and χ the ratio between the material index change and the carrier density. In our numerical examples, we have used $\Gamma =0.65$ and χ = −1.63 × 10⁻²⁰cm³ [13].The carrier density N is determined by the steady-state rate equation, i.e. J/(ed) = AN + BN² + CN³, where J is the injection current density, d = 0.3 μm is the thickness of the waveguide core layer, A = 10⁸s⁻¹, B = 4 × 10⁻¹⁰cm³/s and C = 7.5 × 10⁻²⁹cm⁶/s. Figure 2(a) shows the absolute value of the effective refractive index variation as a function of the injection current density J.

 

Fig. 2 (a) Absolute value of the effective refractive index variation as a function of the injection current density. (b) Threshold gain of the FP modes (circles).

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Now let us consider a numerical example with the following parameters: L₁ = 26.67μm, L₂ = 13.5μm, L₁’ = 20μm, L_p = 767.67μm, L_a = 400μm, r₁ = 0.5255, r₂ = 0.8, κ₁ = κ₂ = 0.265, n_a = 3.2. The resonant wavelength is calculated to be 1.55μm. Figure 2(b) shows the threshold gain of the resonance modes (circles) of the FP cavity near the main mode which is aligned to a resonant mode of the ring. We have used n = n_a = 3.2 in this example. The threshold gain margin between the main mode and the closest side modes is about 19cm⁻¹. This value can provide an excellent single mode stability even under high-speed dynamic operation. The free spectral range (FSR) of the ring is calculated to be about 19nm which is large enough to eliminate side modes because of the limited gain spectral width. Such a small ring resonator on the InGaAsP/InP platform has been reported by Park et al [14].

Figure 3(a) shows the threshold gain margin as a function of the refractive index change of the tuning section, calculated by using Eqs. (1)-(3) with L_p equal to 767.67μm (solid line), 514.19 (dashed line) and 260.43 (dash-dotted line). The first case satisfies the mode-hop-free condition determined by Eq. (8). The mode-hop-free tuning range as determined by Eq. (9) for the second and the third case is 2.9nm and 1.4 nm, respectively. If the refractive index n is assumed to be varied from 3.21 to 3.19, corresponding to a tuning current of 0-100mA for an injection width w = 3.0μm, the tuning range limited by Δn_max is about 6.4nm. The corresponding variations of the lasing wavelength for the three cases are plotted in Fig. 3(b), 3(c) and 3(d), respectively. When the length L_p satisfies the condition of mode-hop-free operation, i.e. L_p = 767.67μm, the threshold gain margin within the whole tuning range is a constant at about 19 cm⁻¹. The unchanged threshold gain margin indicates that the wavelength shifts of the ring filter and of the FP cavity modes are rigorously synchronized during the wavelength tuning. No mode hoping happens. If L_p departs from this value, however, the threshold gain margin varies as the refractive index changes and may reaches zeros at certain refractive index values where the mode hoping occurs. The larger the deviation from the condition of Eq. (8), the more mode hoping points exist, as can be seen in Figs. 3(c) and 3(d).

 

Fig. 3 (a) Threshold gain margin as a function of the absolute value of the refractive index change |Δ n| with L_p equal to 767.67μm (solid line), 514.19(dashed line) and 260.43(dash dot line). The corresponding lasing wavelength is plotted in (b), (c) and (d), respectively.

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Now let us consider the effect when the current injected into the gain section or the bias section is slightly off from the ideal values. Assume that as a result, the refractive index n_a (or n₂) departs from its designed value as determined by Eq. (8) by Δn_a (or Δn₂). From Eq. (9), to obtain a certain mode-hop-free tuning range Δλ_MHF, the maximum deviation must satisfy $\left|\Delta {\text{n}}_{\text{a}}\right|\text{<}{\lambda }^2\text{/(2}\Delta {\lambda }_{MHF}{\text{L}}_{\text{a}})$ or $\left|\Delta {\text{n}}_{\text{2}}\right|\text{<}{\lambda }^2{\text{L}}_{\text{1}}/\left[\text{2(}{\text{L}}_{\text{p}}\text{+}{\text{L}}_{\text{1}}{\text{')L}}_{\text{2}}\Delta {\lambda }_{MHF}\right]$. To achieve a mode-hop-free tuning range of 20nm, the refractive index change tolerance is 0.15 for both n₂ and n_a in our numerical example. This is an order of magnitude larger than the refractive index change that can be caused by current injection. Therefore, the variation of current injection in the gain or bias section has little effect on the mode-hop-free tuning of the device.

For practical applications, the fabrication tolerances also need to be considered. Here we consider a cavity length error caused by the misalignment of device cleaving (we assume both of the mirrors M1 and M2 use the same cleaved facet). Figure 4 depicts the threshold of the main mode and the threshold margin as a function of Δn when the misalignment of the cleaved facet are 10μm (solid line). Due to the misalignment of the ring and FP cavity peaks, the threshold of the main mode increases from 20 cm⁻¹ to about 25 cm⁻¹ and the threshold margin decreases from 19 cm⁻¹ to only a few cm⁻¹. To compensate the error, n₂ is tuned to 3.20492 by a bias current of 0.75mA (2.07 kA/cm²) in the bias section. The threshold gain is then reduced to about 21 cm⁻¹ (dashed line in Fig. 4(a)), while the threshold margin is restored to above 18cm⁻¹ for the whole tuning range (dashed line in Fig. 4(b)).

 

Fig. 4 Main mode threshold gain (a) and side-mode threshold margin (b) as a function of the refractive index variation in the tuning section when the misalignment of the cleaved facet are 10μm with (dashed line) and without (solid line) the bias current compensation.

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Propagation loss is another important parameter affecting the performance of a coupled ring laser [12]. Hence, the influence of the free carrier absorption effect also needs to be considered. Here we denote the loss in the passive waveguides due to the free carrier absorption effect by α_n and the loss caused by the waveguide sidewall roughness by α₀. The total loss α in the following simulation is equal to α₀ + α_n. α_n is assumed to be proportional to the carrier density N, i.e. α_n = γN, and α₀ is set to be a constant of 20 cm⁻¹. The absorption in the active waveguide is also assumed to be 20 cm⁻¹.

Figure 5(a) shows the threshold gain margin as a function of injection current with different values of the optical loss coefficient γ = 1.06 × 10⁻²¹cm² (dash-dotted line) and γ = 2.12 × 10⁻²¹cm² (solid line). When the current is increased from 0 to 100mA (J = 0~4kA/cm²), the refractive index is changed from 3.21 to 3.19 while the absorption α_n varies from 0 to 20cm⁻¹ for γ = 1.06 × 10⁻²¹cm² and to 40cm⁻¹ for γ = 2.12 × 10⁻²¹cm². The threshold margin degrades from 12cm⁻¹ to about 3.5cm⁻¹ for γ = 2.12 × 10⁻²¹cm. The SMSR is shown in Fig. 5(b), which is calculated by the formula given in [15] assuming an output power of 5mW. One can see that even for the worst case α = 60 cm⁻¹, the SMSR is still above 36dB.

 

Fig. 5 (a)Threshold gain margin and (b) SMSR as a function of the tuning current with the optical loss coefficients γ of 1.06 × 10⁻²¹cm² (dash-dotted line), and 2.12 × 10⁻²¹cm²(solid line)

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4. Conclusions

In summary, a novel mode-hop-free tunable laser based on a ring coupled laser is proposed. Mode-hop-free operation is achieved without multi-electrode synchronized tuning. Simulation shows that by properly designing the laser structure, a large mode-hop-free tuning range (>6nm, only limited by achievable refractive index change) can be obtained with an injection current less than 100mA. A good SMSR is maintained during the wavelength tuning operation. The proposed laser can be tuned at high speed (in the nanosecond range) and can have important applications for lidar sensing and interferometry.