Microwave-Photonic Links Based on Transistor-Lasers ... - IEEE Xplore

IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 2, JANUARY 15, 2014

183

Microwave-Photonic Links Based on Transistor-Lasers: Small-Signal Gain Analysis Stavros Iezekiel, Senior Member, IEEE

Abstract— The link gain for a directly modulated microwavephotonic link based on a transistor-laser (TL) is derived by making use of signal flow graph techniques. In contrast to conventional laser diodes, the three-terminal TL introduces an extra microwave port for impedance tuning of link parameters. Gain contour simulations using a small-signal equivalent circuit model for the TL indicate the potential for increased link gain compared with links that are terminated in 50 at all ports. Index Terms— Transistor-laser, analog links, microwavephotonic link, radio-over-fiber.

I. I NTRODUCTION

M

ICROWAVE-photonic links are used in systems such as remote antennas, radio-over-fiber and radar, where the transmission of analog microwave signals over optical fiber benefits from the advantages of wide bandwidth, low fiber loss and electromagnetic immunity [1]. Externally modulated links based on lithium niobate Mach-Zehnder modulators tend to predominate. Directly modulated laser diode-based links offer a cheaper alternative, but are performance-limited compared to externally modulated schemes, especially with regard to bandwidth [2]. With the advent of the transistor-laser [3], there is now an alternative optical source for future microwave-photonic links. The transistor-laser has many advantages, including: a. Enhancement of the modulation bandwidth and increased damping compared to conventional laser diodes [4]–[5] b. Option for common-emitter or common-base operation, with the latter showing increased bandwidth [6]. c. Option for direct collector current feedback control, thereby eliminating the need for monitor photodiodes and simplifying power stabilization circuits [7]–[8]. d. Relative intensity noise close to the shot-noise limit [9]. e. Reduction of third-order intermodulation distortion using collector current feedback [8]. Edge-emitting transistor-lasers based on HBT designs have demonstrated intensity modulation bandwidths up to 22 GHz [10], and bandwidths up to 50 GHz have been predicted by simulations [11]. With the potential for low cost fabrication offered by vertically-emitting versions [12]–[14], the transistor-laser now merits evaluation for its potential use Manuscript received October 4, 2013; revised November 8, 2013; accepted November 13, 2013. Date of publication November 18, 2013; date of current version December 31, 2013. The author is with the Department of Electrical and Computer Engineering, University of Cyprus, Nicosia 1678, Cyprus (e-mail: [email protected]). Digital Object Identifier 10.1109/LPT.2013.2291411

Fig. 1. (a) Microwave-photonic link based on transistor-laser. (b) Corresponding signal flow graph. Superscripts TL, P and F are associated with the transistor-laser, photodiode and interconnecting optical fiber respectively.

in microwave-photonic links. This will require the development of models to predict important link parameters such as gain, noise figure and spurious free dynamic range [15]. In this letter we take a first step towards this by deriving an expression for the gain of a microwave-photonic link based on a directly modulated transistor-laser in order to examine the impact of terminating impedances. A small-signal equivalent circuit model is then developed and parameter values are fitted to published data [16]. The model is subsequently used in gain contour simulations in order to evaluate the potential for increased link gain. II. G AIN A NALYSIS OF M ICROWAVE P HOTONIC L INK BASED ON T RANSISTOR L ASER The block-diagram of a microwave-photonic link based on a directly-modulated transistor-laser and direct-detection photodiode is shown in Fig. 1(a) for the common-emitter configuration; Fig. 1(b) is the associated signal flow graph.

1041-1135 © 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

184


Ports 1 and 2 of the transistor-laser are terminated with impedances Z S and Z L respectively, with corresponding reflection coefficients S and L . While both these ports could in principle be driven simultaneously, here we assume a single microwave source driving port 1. Port 2 of the photodiode is terminated with Z P ( P ). The convention described in [16]–[18] is adopted for the scattering-parameter representation of the transistor-laser, optical fiber and photodiode: ⎡ TL ⎤ ⎡ TL ⎤ ⎡ TL ⎤ TL b1 S11 S12 0 a1 ⎣ bT L ⎦ = ⎣ ST L ST L 0 ⎦ ⎣ a T L ⎦ 2 21 22 2 TL TL S31 b3T L S32 0 a3T L F F F b1 a1 0 S12 = F b2F S21 0 aF 2P P 0 0 a1 b1 = . (1) P P S21 S22 b2P a2P x is the reflection coefficient at port n and Here Snn represents transfer from port n to port m of device x while the variables anx and bnx are incident and reflected traveling power waves at port n. In particular, the waves at ports 1 and 2 of the transistor-laser, port 2 of the photodiode and the source power wave b S are traveling power waves as in purely microwave devices, while the remaining a and b variables are modulated optical power waves using the definition in [18]. It is assumed that there are no optical reflections between the fiber and the optical ports of the transistor-laser and photodiode. The transducer power gain of the link is defined as the ratio of the power delivered to the link’s load (i.e. Z P ) to the power available from the source. Using standard techniques from microwave two-port theory to account for mismatches [19], this is given by: P 2

b 1 − | P |2 2

. (2) GT = |b S |2 / 1 − | S |2 x Smn

Applying Mason’s non-touching loop rule [19] to obtain and substituting into (2) yields: TL T L 2 1 − | S |2 T L S21 L S32 · S31 + GT = T L |1 − S I N |2 1 − S22 L 2 2 2 1 − | P | F P · S21 (3) · S21 · 1 − S P P 2 22

b2P /b S

where TL IN = S11 +

TL S TL S12 21 TL 1 − S22 L

is the input reflection coefficient at port 1 of the transistorlaser. The main point to note from (3) is that if port 2 of T L also the transistor-laser is mismatched, the S-parameter S32 contributes to link gain. Here it is assumed that the three-port formalism for the transistor-laser developed in [16] is compatible with the two-port photodiode formalism developed in [17], in that the optical powers generated by signals that are simultaneously present at both ports 1 and 2 of the transistorlaser add in a linear fashion. (This is not to be confused with the issue of coherent/incoherent optical signal addition, since

Fig. 2. Small-signal equivalent circuit model of transistor-laser. The elements within the dotted box are associated with light emission from the base region and are a circuit representation of the linearized rate equations.

the transistor-laser has a single optical cavity.) Moreover, it is assumed that the microwave modulating signal is sufficiently small-signal such that the mixing effects reported in [20] are avoided. III. S MALL -S IGNAL E QUIVALENT C IRCUIT In order to investigate the impact of terminating impedances on overall link gain, a small-signal equivalent circuit model was derived. Given that the fundamental structure of the transistor-laser is an HBT (heterojunction bipolar transistor) in which light emission occurs in the base, the standard T-model of the HBT [21] forms the core structure of the equivalent circuit. This is extended with the inclusion of the equivalent circuit representation of the transistor-laser rate equations [22]: Q N dN = − − G (N − N0 ) (1 − εS) S dt τC τQ W dS βN S = G (N − N0 ) (1 − εS) S − + dt τP τQ W dQ Q = i Bi − dt τB

(4) (5) (6)

where N and S are carrier and photon populations, N0 is the value of N at transparency, Q is the base charge, i Bi is the intrinsic base current, τC is the electron capture time normalized to the quantum well geometry factor, τ Q W is the spontaneous emission recombination lifetime, τ P is

IEZEKIEL: MICROWAVE-PHOTONIC LINKS BASED ON TLs

185

TABLE I E QUIVALENT C IRCUIT E LEMENT VALUES

Fig. 4. Electrical scattering parameters for the frequency range 0.1 GHz to 20 GHz (increasing frequency is in a clockwise direction for each trace).

Fig. 3. Forward and reverse intensity modulation response, with the forward response normalized to 0 dB at 0.1 GHz.

the photon lifetime, τ B is the base charge lifetime, G is optical gain, and β is the spontaneous emission coefficient. Here, a gain compression term ε has also been included. In Fig. 2, the elements R Q and C Q represent equation (6), where R Q C Q = τ B and the voltage v Q is an analog of the base charge Q. This then serves as the drive term in equation (4) via the current source gv Q . Rate equations (4) and (5) have the same form as the standard rate equations of a diode laser, hence these are represented by the corresponding model of Tucker and Pope [23], in which the resonance frequency is determined by (L L C L )−1/2 and the damping factor by (R L + R S )/L L . The voltage μv S is an analog of S. This part of the equivalent circuit is within the dotted box in Fig. 2. In the absence of raw measured data from [16], identical values to those from [16] were chosen for the bias-independent elements (as listed in the left hand column of Table 1) along with α and R BC x . The elements R Q and C Q correspond in value to R B and C Q W in [16]. The remaining bias-dependent elements (including those of the rate equation portion of the model) were tuned individually until the generated modulation responses (Fig. 3) and electrical S-parameters (Fig. 4) matched the qualitative behavior reported in the corresponding figures in [16] for a bias point of VC E = 1.25 V, I B = 60 mA. These values are listed in the right hand column of Table 1. It should be noted that when the intensity modulation response of a laser is modeled or measured, the phase response is not normally included because link gain will not depend on

Fig. 5.

Contours for increase in link gain GT in the L plane at 4 GHz.

this. However, the second term on the RHS of (3) requires T L and S T L is known if one is to evaluate that the phase of S31 32 link gain for non-zero values of S and L . The rate-equation part of the model in Fig. 2 is predominantly responsible for these two parameters, and since it is based on device physics then there is a high degree of confidence that the correct phase T L and S T L is being calculated. As far difference between S31 32 as the magnitude of these parameters is concerned, there is a deviation between the two at low frequencies in line with measured results [24]. IV. E FFECT OF L OAD ON L INK G AIN The equivalent circuit model described in Section III was used to investigate the potential for increased link gain with the configuration in Fig. 1(a). The terminations Z S , Z L and Z P were initially set to 50 . The input to the transistor-laser T L ∗ ); since was then conjugately matched to Z S (i.e. S = S11 the input reflection coefficient of the transistor laser shows little frequency dependence and is approximately real at 5, a quarter-wave transformer was used to transform the 50

186


source impedance to 5. Gain contour simulations were then performed using the AWR Microwave Office program in order to examine the effect on link gain G T for varying values of Z L . Fig. 5 shows the gain contours for Z L at a frequency of 4 GHz, which is close to resonance for the particular transistor laser being modeled here. These show the potential increase in link gain for the case in which all parameters in the link are kept unchanged apart from Z S , which is transformed to 5 and Z L which is swept across the passive impedance part of the Smith chart. Since the aim is to show the combined impact of these two impedances on link gain, the fiber and photodiode F and S P were normalized to unity. For this S-parameters S21 21 particular case, the link gain can be increased to approximately 5 dB compared to its value for a link with 50 terminations.

[5] M. Feng, H. W. Then, N. Holonyak, G. Walter, and A. James, “Resonance-free frequency response of a semiconductor laser,” Appl. Phys. Lett., vol. 95, no. 3, pp. 033509-1–033509-3, Jul. 2009. [6] B. Faraji, W. Shi, D. L. Pulfrey, and L. Chrostowski, “Common-emitter and common-base small-signal operation of the transistor laser,” Appl. Phys. Lett., vol. 93, no. 14, pp. 143503-1–143503-3, Oct. 2008. [7] E. W. Iverson and M. Feng, “Transistor laser power stabilization using direct collector current feedback control,” IEEE Photon. Technol. Lett., vol. 24, no. 1, pp. 4–6, Jan. 1, 2012. [8] H. W. Then, F. Tan, M. Feng, and N. Holonyak, “Transistor laser optical and electrical linearity enhancement with collector current feedback,” Appl. Phys. Lett., vol. 100, no. 2, pp. 221104-1–221104-3, May 2012. [9] F. Tan, W. Xu, X. Huang, M. Feng, and N. Holonyak, “The effect of ground and first excited state transitions on transistor laser relative intensity noise,” Appl. Phys. Lett., vol. 102, no. 8, pp. 081103-1–081103-3, 2013. [10] H. W. Then, G. Walter, M. Feng, and N. Holonyak, “Optical bandwidth enhancement of heterojunction bipolar transistor laser operation with an auxiliary base signal,” Appl. Phys. Lett., vol. 93, no. 16, pp. 163504-1–163504-3, Oct. 2008. [11] B. Faraji, S. Wei, D. L. Pulfrey, and L. Chrostowski, “Analytical modeling of the transistor laser,” IEEE J. Sel. Topics Quantum Electron., vol. 15, no. 3, pp. 594–603, Jun. 2009. [12] M. K. Wu, M. Feng, and N. Holonyak, “Voltage modulation of a vertical cavity transistor laser via intra-cavity photon-assisted tunneling,” Appl. Phys. Lett., vol. 101, no. 8, pp. 081102-1–081102-3, Aug. 2012. [13] M. K. Wu, M. Liu, F. Tan, M. Feng, and N. Holonyak, “Selective oxidization cavity confinement for low threshold vertical cavity transistor laser,” Appl. Phys. Lett., vol. 103, no. 1, pp. 011104-1–011104-4, Jul. 2013. [14] X. Yu, et al., “Room-temperature operation of transistor vertical-cavity surface-emitting laser,” Electron. Lett., vol. 49, no. 3, pp. 208–210, Jan. 2013. [15] A. S. Daryoush, E. Ackerman, N. R. Samant, S. Wanuga, and D. Kasemset, “Interfaces for high speed fiber-optic links: Analysis and experiment,” IEEE Trans. Microw. Theory Tech., vol. 39, no. 12, pp. 2031–2044, Dec. 1991. [16] H. W. Then, M. Feng, and N. Holonyak, “Microwave circuit model of the three-port transistor laser,” J. Appl. Phys., vol. 107, no. 9, pp. 094509-1–094509-7, May 2010. [17] B. Stockbroeckx, P. Dellisse, and A. Vander Vorst, “S-matrix definition for microwave-optical transducers,” Microw. Opt. Technol. Lett., vol. 7, no. 17, pp. 803–806, Dec. 1994. [18] S. Iezekiel, “Measurement of microwave behavior in optical links,” IEEE Microw. Mag., vol. 9, no. 3, pp. 100–120, Jun. 2008. [19] D. M. Pozar, Microwave Engineering. Hoboken, NJ, USA: Wiley, 2009. [20] M. Feng, N. Holonyak, R. Chan, A. James, and G. Walter, “Signal mixing in a multiple input transistor laser near threshold,” Appl. Phys. Lett., vol. 88, no. 6, pp. 063509-1–063509-3, Feb. 2006. [21] U. Schaper and B. Holzapfl, “Analytical parameter extraction of the HBT equivalent circuit with T-like topology from measured S-parameters,” IEEE Trans. Microw. Theory Tech., vol. 43, no. 3, pp. 493–498, Mar. 1995. [22] L. Zhang and J.-P. Leburton, “Modeling of the transient characteristics of heterojunction bipolar transistor lasers,” IEEE J. Quantum Electron., vol. 45, no. 4, pp. 359–366, Apr. 2009. [23] R. S. Tucker and D. J. Pope, “Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser,” IEEE J. Quantum Electron., vol. 19, no. 7, pp. 1179–1183, Jul. 1983. [24] H. W. Then, private communication, Oct. 2013.

V. C ONCLUSION The first analysis of link gain in a microwave-photonic link using a transistor-laser has been achieved via signal flow graph techniques and the use of the S-parameter formalism for photonic devices [17]–[18]. This allows the impact of various small-signal link parameters (and in particular the terminating impedances) on link gain to be evaluated. To this end, a smallsignal equivalent circuit model of the transistor-laser has been developed. A unique feature of the transistor-laser (compared to laser diodes) is that two ports are available for microwave modulating signals. Hence reflections off a mismatch on the collectoremitter (port 2) will also contribute to the optical modulation response (and thereby the link gain). This property has been investigated using the equivalent circuit and gain contour simulations to show that link gain can be increased. It is anticipated that the overall modeling approach described here will prove useful (when combined with parameter extraction techniques) in the design and characterization of future microwave photonic links based on transistor-lasers. R EFERENCES [1] C. H. Cox, Analog Optical Links. Cambridge, U.K.: Cambridge Univ. Press, 2004. [2] C. H. Cox, E. I. Ackerman, G. Betts, and J. L. Prince, “Limits on the performance of RF-over-fiber links and their impact on device design,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 2, pp. 906–920, Feb. 2006. [3] G. Walter, N. Holonyak, M. Feng, and R. Chan, “Laser operation of a heterojunction bipolar light-emitting transistor,” Appl. Phys. Lett., vol. 85, no. 20, pp. 4768–4770, Nov. 2004. [4] M. Feng, N. Holonyak, H. W. Then, and G. Walter, “Charge control analysis of transistor laser operation,” Appl. Phys. Lett., vol. 91, no. 5, pp. 053501-1–053501-3, Jul. 2007.