Cavity design and characteristics of monolithic long-wavelength InAs / InP quantum dash passively mode-locked lasers

By extending the net-gain modulation phasor approach to account for the discrete distribution of the gain and saturable absorber sections in the cavity, a convenient model is derived and experimentally verified for the cavity design of two-section passively mode-locked quantum dash (QDash) lasers. The new set of equations can be used to predict functional device layouts using the measured modal gain and loss characteristics as input. It is shown to be a valuable tool for realizing the cavity design of monolithic long-wavelength InAs/InP QDash passively mode-locked lasers. ©2009 Optical Society of America OCIS codes: (140.4050) Mode-locked lasers; (140.5960) Semiconductor lasers; (130.3120) Integrated optics devices. References and links 1. D. A. B. Miller, “Rationale and challenges for optical interconnects to electronic chips,” Proc. IEEE 88(6), 728– 749 (2000). 2. G. A. Keeler, B. E. Nelson, D. Agarwal, C. Debaes, N. C. Helman, A. Bhatnagar, and D. A. B. 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Introduction
Monolithic mode-locked lasers (MLLs) are promising candidates for inter-chip/intra-chip clock distribution as well as high bit-rate optical time division multiplexing, electro-optic sampling, and arbitrary waveform generation due to their compact size, low power consumption, and direct electrical pumping [1,2].Some unique characteristics of quantum dot (QD) materials, such as ultra broad bandwidth, ultra fast gain dynamics, and easily saturated gain and absorption, make them an ideal choice for semiconductor monolithic MLLs.For QD systems, the most impressive results that clearly demonstrate complete mode-locking have been realized for 1.2-1.3µm QD MLLs fabricated on a GaAs substrate [3][4][5][6].Although QD and quantum dash (QDash) MLLs made on InP substrates in the 1.55-µm range have been vigorously pursued, achieving mode-locking in two-section devices using these materials has been more challenging [7,8].In part, it is believed that this is caused by the higher threshold current density and waveguide internal loss in InP-based QDs and QDashes compared to the more mature InAs/GaAs QD material system [9,10].To further improve the development of 1.55-µm passive QD/QDash MLLs, a simple analytical model is needed to provide cavity geometry guidelines that can improve the mode locking performance in two-section devices.
This work extends a previous model based on a microwave photonics perspective that treated passive mode-locking without self-pulsation using a net-gain modulation phasor approach [11,12].The new set of equations presented here includes the influence of the waveguide internal loss and the effect of separate as opposed to distributed gain and loss.We theoretically predict and experimentally confirm the passive MLL geometries using material gain and loss data that are obtained through the segmented contact method [13,14].Compared to our previous delay differential equation model [15] and the work of Vladimirov and Turaev [16], the advantage of the proposed analytical model is the prediction of the functional modelocking device layout through the use of measured static laser parameters on the actual device.Thus, we can construct a simpler analytical model without knowing the material parameters such as the carrier lifetime or the gain/absorber recovery times.The theory is applied to the design of monolithic InAs/InP QDash passive MLLs emitting at 1.59-µm.Mode locking is achieved as predicted, and a repetition rate as high as 18.4 GHz is realized.

Theory
A frequently cited condition for passive mode-locking requires that the stability parameter, S, must be greater than 1: where E sat , abs is the saturation energy of the absorber, E sat,g is the saturation energy for the gain section, h is Planck's constant, ν is the optical frequency, G g is the differential gain in the gain section multiplied by the group velocity, G a is the differential loss in the absorber multiplied by the group velocity and A is the optical mode cross-sectional area, which is equal in the absorber and gain sections of the monolithic semiconductor laser [17].However, this requirement is not stringent and rarely used to guide semiconductor MLL cavity design.Using a net-gain modulation phasor approach, Lau and Paslaski derived a more useful guideline for obtaining passive mode-locking instead of self-pulsation in the region near lasing threshold where the two processes typically compete and the pulse width is typically the shortest [11,12].This model, however, was based on the assumption that the gain and the saturable absorber are distributed uniformly in the optical cavity, not in separate electrically-isolated sections as common done, and the internal loss was not considered.In the QDash material system, the gain and absorption per unit length are much smaller compared to those of a quantum well or bulk semiconductor system.Thus, we can approximate the actual lumped gain and absorber sections of the optical waveguide as an average gain and loss that are distributed uniformly.It is also important to include the internal loss effect in QDash material system due to the comparable value to the unsaturated absorption.Based on these approximations, we have extended Lau and Paslaski's model to a two-section MLL device geometry that includes a gain section of length L g and an absorber section of length L a , and have accounted for the internal loss, α i , in the optical waveguide.
To understand the region of mode locking without self-pulsation, we employ the net-gain modulation phasor analysis [11,12].In this approach, the photon intensity oscillation is represented by , where s is the real amplitude of the oscillation.ω = Ω MLL = the longitudinal mode spacing or mode-locking frequency.The net gain modulation represents the difference between the average gain and the average loss modulation in the gain and absorber media.Following Lau and Paslaski's model and accounting for the distribution of the gain and absorption in separate sections of the cavity, we write the modified net gain modulation equation for a two-section passive MLL as [12]: ˆnet g is a phasor quantity which is responsible for driving the optical modulation.In Eq. ( 2), g is the modal gain in the gain section and a 0 is the unsaturated absorption in the absorber region.L is the cavity length and L=L a +L g ; v g and n are the group velocity and the carrier density, respectively.1/Tg is the carrier recombination rate in the gain section consisting of the sum of the spontaneous rate, 1/τ g , and the stimulated rate G g S 0 .1/T a is the carrier removal rate in the absorber consisting of the sum of the spontaneous rate, 1/τ a , and the stimulated rate, G a S 0 .τ g and τ a `are the spontaneous carrier lifetimes in the gain and absorber regions, respectively, and should not be confused with the recovery times.The first quantity in { } in Eq. ( 2) is related to the average gain modulation, and the second quantity represents the average loss modulation.
The s in Eq. ( 2) is related to the modulation depth which is assumed to be 100% so that s = S 0 / 2. S 0 is the average photon density in the cavity: where m α is the mirror loss, P is the peak optical power, hv is the photon energy, W is the lateral mode width, and Γ is the optical confinement factor.The necessary conditions for mode-locking without self-pulsation are that the repetition rate should be much faster than the stimulated rate, i.e., ω and the stimulated rates are much greater than the spontaneous recombination rates in the gain and absorber section, i.e., G g S 0 >>1/τ g and G a S 0 >>1/τ a [12].In this work, we further require that the real part of the net gain modulation must exceed the internal loss, α i , of the waveguide: then: Inequality (5) gives the necessary operating condition for a two-section passive MLL and highlights the interdependence of the material parameters and the device's 2-section structure.To apply Eq. ( 5) to the design of an MLL cavity, we make approximations under two different conditions.First, we assume that the differential gain is much smaller than the differential absorption: G a >>G g or, equivalently, that the gain section is biased under strong population inversion.Since it is difficult to measure the differential gain and absorption with respect to the carrier density in practice, dg 0 /dn is replaced with dg 0 /dJ and Eq. ( 5) can be approximated by [19]: Here J is the current density, τ is the carrier lifetime, and η i is the injection efficiency of the laser.We also conservatively approximate that 0 0 0 0 / / g da dn dg dn = ≈ .The left-hand-side of Eq. ( 6) emphasizes that a high contrast between the unsaturated absorption, a 0 , and the internal loss, α i , is favorable for mode-locking.In addition, upon measuring the various device and material parameters, we can use Eq. ( 6) to predict cavity designs (L a and L g ) for twosection mode-locked lasers of a desired repetition rate using novel active region materials.This is the situation described below for the QDash lasers.Alternatively, we can rearrange Eq. ( 6) to estimate the minimum required peak power level according to the following expression: Equation ( 7) reinforces the idea that the internal loss is detrimental to mode-locking in a semiconductor laser by requiring a high power for the onset of operation.
Although it is possible to measure the variables in Eq. ( 6)-( 7) for the actual mode-locked laser or test structures associated with it, the carrier lifetime is frequently difficult to obtain.Thus, a further assumption can be made to obtain a simpler analytical guideline.The second approximation assumes that the power is sufficiently large that the right-hand-side of Eq. ( 6) is negligible.In this case, the following condition analogous to that found in [11,12] is obtained: From Eq. ( 8) it is found that a longer absorber is desirable for realizing mode-locking, especially when the differential gain is not much smaller than the differential absorption.Similar to Eq. ( 1), Eq. ( 8) also suggests that the design strategy of a passive MLL is to minimize the ratio of the differential gain to differential absorption.
The threshold condition in the laser cavity, Eq. ( 9), is another constraint on the system and is applied to determine the modal gain, g 0 .0 0 ( ) ) Therefore, provided that the measured modal gain and loss data is also available from the segmented test structure that is integrated into the MLL, possible cavity designs can be explored using Eq. ( 8) before even fabricating them.These analytical guidelines have been successfully applied previously [18][19][20], but the range of designs and analysis is expanded in this work verifying the broad applicability of the theory.

Material structure
The QDash active region investigated in this work was grown on an n + -InP substrate [21].

Device Design and Characterization
According to the model from the previous section, we examined InAs QDash passive MLLs with a total cavity length of 2.3-mm, 3.5-mm, and 4-mm, respectively.For the 2.3-mm cavity length with an absorber of 0.3-mm, the gain section must provide a modal gain, g 0 , of 21.8 cm −1 at 1.59-µm according to the threshold condition.This value is near to the maximum modal gain value with a corresponding current density of 2750 A/cm 2 .The differential gain is 0.0008 cm/A, which is much smaller than the differential loss value.After calculation, the 2.3-mm and 3.5-mm devices satisfy the condition stated in Eq. ( 8), and it is noteworthy that the 2.3-mm device has a ratio of over 60 comparing the left-and right-hand sides of Eq. ( 8).
In contrast, the 4-mm cavity length MLL does not satisfy Eq. ( 8).The 2.3-mm and 3.5-mm QDash MLLs are predicted to work under mode-locking operation without self-pulsation and the 4-mm device should not mode-lock at all.The device parameter values and the modelocking analysis results are summarized in Tables 1 and 2. A 4-mm cavity length device with a 0.5-mm absorber and a 3.5-mm gain section is abbreviated as A 0.5 G 3.5 .According to Eq. ( 7), the minimum peak power required can be estimated as well.Using a carrier lifetime of 170 ps, injection efficiency of 81%, and an optical confinement factor equal to 0.096 [22], the estimated value for the minimum peak power is about 0.6 W for the 3.5-mm QDash MLL.This is a high estimate because of the conservatively low value that is used for the differential absorption, but is reasonable considering typical peak operating powers in quantum dot MLLs [3].No Yes Yes The figures below show data for the 2.3-mm and 3.5-mm cavity length passive QDash MLLs. Figure 6 is the Light-Current (LI) curve of the laser for various absorber biases of the 2.3-mm device.The maximum slope efficiency is 0.05 W/A with 0 V applied to the absorber.The inset of Fig. 6 demonstrates the optical spectrum under 170 mA DC bias on the gain section and −2 V applied to the absorber.The peak lasing wavelength is around 1.59-µm as described above.Figure 7 confirms that the mode-locked repetition rate is 18.4 GHz for the 2.3-mm device and shows the first two harmonics without any undesirable self-pulsation.Figure 8 corroborates that the fundamental mode-locked repetition rate is 12.3 GHz for the 3.5-mm device and shows that at least three harmonics are observed, again without selfpulsation.Both diagrams show at least two harmonics in the RF spectrum, which gives us confidence that the devices of 2.3-mm and 3.5-mm length are mode-locked as was established in [15,17].The RF spectral analysis is relied upon to characterize the mode-locking because it is very difficult to build a second harmonic generation autocorrelator with the required sensitivity at 1.59 µm wavelength.From the measurement results of the RF spectrum (not shown), we confirm that the 4-mm device does not mode-lock, which substantiates our prediction from the cavity design guidelines derived above and described in Table 2.

Conclusion
Guidelines for mode-locking in two-section passive MLLs that have separate gain and saturable absorber regions and significant internal loss have been derived through the net-gain modulation phasor approach and applied to a variety of cavity designs for long-wavelength QDash MLLs.It has been shown that the new set of equations can be used to predict functional device layouts using measured modal gain and loss characteristics that are obtained through the segmented contact method on the actual device.After the modal gain and total loss measurement, the MLL was built by reconfiguring this same linear array of diodes.Equation ( 8) was found to be most useful when designing the two-section passive MLL cavities since it does not include the peak power, carrier lifetime and waveguide internal loss.
From Table 2, it has been confirmed that Eq. ( 1) is not particularly instructive for designing two-section semiconductor MLLs.The experimental results corroborated the theoretical predictions, which should be an invaluable tool for future realization of long-wavelength passive QDash MLLs that are generally difficult to achieve.

Figure 1
shows the structural diagram of the epitaxial layers.The dashes-in-a-well (DWELL) active region consists of 5 layers of InAs quantum dashes embedded in compressivelystrained Al 0.20 Ga 0.16 In 0.64 As quantum wells separated by 30-nm undoped tensile-strained Al 0.28 Ga 0.22 In 0.50 As spacers.A lattice-matched 105-nm thick layer of undoped Al 0.30 Ga 0.18 In 0.52 As is added on each side of the active region.The p-cladding layer is stepdoped AlInAs with a thickness of 1.5-µm to reduce free carrier loss.The n-cladding layer is 500-nm thick AlInAs.The laser structure is capped with a 100-nm heavily p-type doped InGaAs layer.

Fig. 1 .
Fig. 1.The layer structure of the InAs QDash laser

Fig. 3 .
Fig. 3.The side view of the two-section passive QDash MLL.

Fig. 4 .Fig. 5 .
Fig. 4. Qualitative comparison of the left-and right-hand sides of Eq. (9) and the determination of thethreshold wavelength

Fig. 6 .
Fig. 6.L-I curve with reverse voltage from 0V to 2V of the 2.3-mm passive MLL.Inset: Optical spectrum with a DC gain current of 170 mA on the 2-mm gain section and a reverse voltage of 2V on the 0.3-mm absorber.

Fig. 7 .
Fig. 7.The full span of the RF spectrum at 170mA and 2V reverse voltage of the 2.3-mm twosection passive QDash MLL device.The fundamental repetition frequency is 18.4 GHz.The RF spectrum clearly shows the first two harmonic components.

Fig. 8 .
Fig. 8.The full span of the RF spectrum at 400mA and 1V reverse voltage of the 3.5-mm twosection passive QDash MLL device.The fundamental repetition frequency is 12.3 GHz.The RF spectrum clearly shows the first three harmonic components.