Submillimeter Wave Generation Through Optical Four-Wave Mixing Using Injection-Locked Semiconductor Lasers

Transcription

1 502 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 Submillimeter Wave Generation Through Optical Four-Wave Mixing Using Injection-Locked Semiconductor Lasers Taraprasad Chattopadhyay, Member, IEEE, Madhumita Bhattacharya Abstract This paper presents a comprehensive analysis of submillimeter wave generation through optical four-wave mixing (FWM) in an injection-locked semiconductor laser. The probe wave introduces pump-probe difference frequency amplitude modulation (AM) phase modulation (PM) of the slave laser injection locked to the pump wave. The AM PM indexes of the locked laser output lightwave modulated at the submillimeter wave frequency have been calculated. The submillimeter wave power generated through this technique has also been calculated theoretically. The analysis predicts a submillimeter wave power of 3.7 dbm at 300-GHz frequency for a free-running slave laser output power of 30 mw. In the presence of amplitude modulation of the probe wave, the same modulation is transferred to the submillimeter wave. The suppression of output lightwave amplitude noise relative to the pump, probe, or free-running slave laser amplitude noise has also been estimated in this analysis. At a submillimeter wave frequency of 300 GHz a probe power equal to the pump power, typical amplitude noise reduction occurs by 7 db. Index Terms Four-wave mixing (FWM), injection locking, modulation, noise, semiconductor laser, submillimeter wave. I. INTRODUCTION THE submillimeter waves are electromagnetic waves which span the frequency b of 300 GHz to 3 THz. In the last decade, a good deal of research activity has been seen on the generation of submillimeter waves. A method of submillimeter wave generation through frequency multiplication in a single barrier varactor (SBV) device has been described in [1], [2]. Theoretically, an output power of 50 W was predicted at a frequency of 750 GHz from an InAs SBV diode tripler assuming an input power of 6 mw at 250 GHz. Resonant-tunneling diode (RTD) [3], [4] impact ionization avalanche transit time (IM- PATT) diode form another class of oscillators capable of generating submillimeter waves. However, IMPATT diodes have higher intrinsic noise a wider linewidth of the output wave. RTDs have lower output power, typically 50 W at 210 GHz. Varactor diode harmonic generators suffer from linewidth multiplication. In the past few years, optical generation of submillimeter waves has attracted much attention in the scientific community. Two important methods of submillimeter-wave generation by optical means are photomixing optical parametric oscilla- Manuscript received June 06, 2001; revised November 26, The authors are with the Department of Physics, Visva-Bharati University, Santiniketan , West Bengal, India ( tara_vb@hotmail.com). Publisher Item Identifier S (02) tion in a nonlinear medium. Recently, submillimeter wave has been generated from an organic nonlinear crystal of 4-dimethylamino-N-4-stilbazolium-tosylate (DAST) by mixing the two wavelengths of a dual wavelength Ti: Sapphire laser [5]. However, the conversion efficiency is poor. In optical parametric oscillation, a pump wave is injected into a nonlinear crystal medium, such as LiNbO, which gives rise to an idler lightwave having a wavelength longer than that of the pump wave a difference-frequency submillimeter wave. Experiments are being conducted to improve the conversion efficiency the output coupling of the submillimeter wave [6], [7]. In this paper, we propose a method of submillimeter wave generation through optical four-wave mixing (FWM) in an injection-locked semiconductor laser. In this method, a slave laser is injection-locked to the pump wave. Another lightwave called the probe wave is injected into the slave laser, which produces pump-probe difference frequency amplitude phase modulation of the output lightwave. We have calculated the amplitude modulation (AM) phase modulation (PM) indexes of the output lightwave studied their dependence on the value of submillimeter wave frequency. The power of the submillimeter wave has been calculated. If the probe wave is amplitude modulated, this modulation gets transferred on the submillimeter wave. This modulation transfer has been theoretically established. The effect of relative intensity noise (RIN) of the pump, probe, the free-running slave laser output wave on the generated submillimeter wave has been calculated. II. ANALYSIS FWM in an injection-locked semiconductor laser is a process which involves the interaction of four lightwaves, viz., a freerunning laser output wave, a pump wave, a probe wave, a wavelength-shifted lightwave. The free running slave laser is injection-locked to the pump wave of frequency. The probe wave, having a frequency, is injected into the injection-locked laser, which produces amplitude phase perturbation of the locked laser. The detuning of the probe wave from the free-running slave laser is much greater than that of the pump wave. Thus, locking is established with the pump wave, even if the probe pump powers are equal. It is well known that, in FWM, the carrier concentration in the active region of the slave laser is modulated by the pump-probe beat frequency [8]. This, in turn, leads to similar beat frequency modulation of gain refractive index of the active region of the slave laser. As a result, the output wave of the slave laser is an /02$ IEEE

2 CHATTOPADHYAY AND BHATTACHARYA: SUBMILLIMETER WAVE GENERATION THROUGH OPTICAL FWM 503 Fig. 1. A schematic diagram of the submillimeter wave generation process. HM: Half mirror. AM PM wave that contains pump-probe difference frequency modulation in its amplitude phase. This is also predicted from the theory of laser synchronization [9]. The output amplitude modulation can be detected in a wideb photo detector [10] [12]. A schematic diagram of the submillimeter wave generation process is shown in Fig. 1. The complex amplitude of the composite wave injected into the slave laser can be written as is the direct current (dc) phase error, are the phase angles. Substituting (4) (5) in (2) (3) applying the principle of harmonic balance under the slowly varying amplitude phase approximation, we obtain (5) (1) are arbitrary phase angles of the pump probe respectively, is the magnitude of the pump wave amplitude, is the ratio of amplitudes of the probe wave pump wave, is the pump-probe difference angular frequency, are the angular frequencies of the pump probe waves, respectively. Let be the complex amplitude of the output lightwave from the locked laser. Here, is the phase angle of the output wave. The amplitude phase equations of the injected laser is given by [9], [13] Re (2) is the phase error of the pump wave the output wave from the slave laser. Here, Re sts for real part of Im sts for imaginary part of., is the refractive index of the active region, is the linear gain, is the cavity length, is the output power, is the saturation power of the free-running slave laser. Taking, cm, m,, we get. ; is the external -factor of the slave laser cavity, is the free-running angular frequency, is the wavelength, is the linewidth enhancement factor of the slave laser. is the vacuum velocity of light. is the pump wave injection power into the slave laser. In presence of the probe wave, the output of the locked laser is an AM PM wave, the modulation being at the pump-probe difference frequency. Thus, the solutions of (2) (3) are expected in the form (3) (4) are the upper-side lower-side locking bs, respectively, of the slave laser. Here The AM index the PM index of the output lightwave from the locked laser are numerically calculated plotted in Fig. 2(a) (b) as functions of the generated submillimeter wave frequency with the relative amplitude of the probe wave as a parameter. From Fig. 2(a), it is seen that the AM index decreases with the increase in submillimeter wave frequency. It also decreases with the decrease in probe wave amplitude. Thus, higher power of the probe wave will be preferred for submillimeter wave generation subject to the condition that locking of the slave laser to the pump wave is not destroyed. From Fig. 2(b), it is apparent that decreases with the decrease in relative probe amplitude. The photodetector (PD) current is proportional to the optical power input to the PD. Again (6) (7) (8) (9) (10) Neglecting the 2 component, which is small, we can write (11) is the free-running power of the slave laser. Power of the generated submillimeter wave signal is given by (12)

3 504 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 with 10-mW output power is 8.6 GHz. In view of (6), the value of depends upon the factor, has a typical value of 20 GHz for db,, Hz. The relaxation resonance frequency [15] of the injection-locked slave laser increases with the increase in.for (, hence, ), submillimeter wave power generation decreases with the increase in. (a) (b) Fig. 2. (a) Calculated AM index of the locked laser output lightwave as a function of submillimeter wave frequency ( ) with the relative amplitude (x) of the probe wave as a parameter. P =P = 010 db, k =0:1, Q = 3000, = 1:55 m, = 3, (! 0! )=1! = 00:5. (b) Calculated PM index of the locked laser output lightwave as a function of submillimeter wave frequency ( ) with the relative amplitude (x) of the probe wave as a parameter. Other parameter values are the same as in Fig. 2(a). A. Transfer of Probe Modulation Let us now consider the modulation transfer from the probe wave to the generated submillimeter wave. We consider the amplitude modulation of the probe wave. In this case, (1) can be rewritten as (13) is the AM index is the modulating signal frequency of the probe wave. When there is a single probe wave, the locked laser output is amplitude phase modulated at the pump-probe difference frequency. Now, when the probe wave is amplitude modulated, there are three frequency components, viz.,, in the probe spectrum. Hence, the amplitude phase modulation of the locked laser output will occur at frequencies. Under this condition, the solution of the amplitude (2) can be written as (14) Substituting (13) (14) in (2) applying the principle of harmonic balance as before, we obtain (15) assuming. Also, because,. In view of this solution, (14) can now be recast as (16) Fig. 3. Theoretical variation of generated submillimeter wave power with the submillimeter wave frequency using free-running slave laser power (P ) as a parameter. = 0:8 A/W, R = 50. Other parameters have same values as in Fig. 2(a). is the responsivity of the photodetector is the load resistance of the PD. Calculated variation of submillimeter wave power with the submillimeter wave frequency using the free-running slave laser power as a parameter is shown in Fig. 3. The submillimeter wave power decreases with the increase in submillimeter wave frequency. also increases with the increase in free-running slave laser power. Thus, higher slave laser power is desired for submillimeter wave generation. Also, the submillimeter wave power increases with the square of the AM index of the lightwave output from the slave laser. Because we are dealing with submillimeter wave generation, the frequencies of interest are much higher than the relaxation resonance frequency of the slave laser. Typical value of relaxation resonance frequency [14] for a free-running slave laser Equation (16) indicates that the submillimeter wave having a frequency is amplitude modulated with the same index. III. EFFECT OF LASER RIN ON THE GENERATED SUBMM WAVE The relative intensity noise (RIN) of the lightwaves taking part in the FWM process in the injection-locked laser can introduce amplitude noise in the output lightwave of the locked laser. In this section, we attempt to find a relation between the power spectral densities (PSDs) of the amplitude noises associated with the mixing lightwaves the locked laser output lightwave. Let,,, be the normalized amplitude noises of the pump wave, probe wave, free-running slave laser output wave, the locked laser output lightwave respectively. Then, we can write (1) as Now, we can write (17) (18)

4 CHATTOPADHYAY AND BHATTACHARYA: SUBMILLIMETER WAVE GENERATION THROUGH OPTICAL FWM 505 (19) is the free-running amplitude of the slave laser. In absence of free-running slave laser noise,. While calculating the effect of RIN, we neglect the amplitude phase modulations of the output lightwave. Substituting (17) (19) in the amplitude (2) equating noise terms from both sides, we construct the following noise equation: (20),,. Taking Fourier transform of both sides of (20) then the complex conjugate, we can obtain When there is no pump no probe, we set. Then,,,. Equation (23), in this case, yields. This result tells that the output noise of the slave laser is the same as that of the free-running slave laser in absence of pump probe. In absence of the probe wave, the situation reduces to the case of an injection-locked laser. Then, putting, (23) reduces to (22). Taking,, db,, GHz, rad, we obtain,,. The free-running slave laser wavelength is 1.55 m. While calculating,wehaveassumed that the pump wave frequency is located at the middle of the lower side lockb of the slave laser. In this case, (22) indicates that is considerably reduced compared with. As an example, if we take, we get db. Because we desire submillimeter wave generation, we are interested in the output lightwave amplitude noise PSD evaluated at the submillimeter wave frequency. The PSD of RIN is given by [14] RIN (21) Here,,,, are the PSDs of the amplitude noises of the locked laser output wave, pump wave, probe wave, the free-running slave laser output wave, respectively. To find out in (21), we make a zeroth-order approximation by taking, i.e., the case of no probe. Then,. Under this condition (22) We can now find out from (22). Substituting these expressions in (21), we can obtain from (21) to a first-order approximation. Following this process, we can find out a relation (23) (24) (25),, are the laser linewidth according to Schawlow Townes formula, resonance frequency, the damping factor, respectively. For when RIN (26) RIN (27). is the inverse recombination lifetime of the carrier is a factor related with damping. As an example [14], GHz, ns, GHz is in milliwatts. Now,,,, for. Taking, we calculate the ratio at numerically using the aforesaid parameter values. The ratio as a function of submillimeter wave frequency with the relative probe-wave amplitude as a parameter is plotted in Fig. 4. The plot shows a clear suppression of output lightwave amplitude noise in comparison with the pump, probe, or free-running slave laser amplitude noise. Fig. 4 implies that the amplitude noise of the locked laser is higher for higher probe amplitude. The output lightwave amplitude noise suppression occurs due to the inherent amplitude limiting action [13] of the injection-locked semiconductor laser. When the probe amplitude increases, the power of the generated submillimeter wave increases. However, we cannot increase the probe power arbitrarily because higher probe power will lead to a destruction of locking of the slave laser to the pump wave. Moreover, amplitude noise of the submillimeter wave at

5 506 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 20, NO. 3, MARCH 2002 Fig. 4. Calculated variation of the ratio of amplitude noise power spectral densities, S (! )=S (! ), with the submillimeter wave frequency ( ) using relative probe amplitude (x) as a parameter. Values of other parameters are the same as in Fig. 2(a). higher probe power is higher than the same for lower probe power. When the probe power is lower, the generated submillimeter wave power is smaller. On the other h, the amplitude noise of the generated submillimeter wave is smaller for lower probe power. Thus, there exists a tradeoff in the power of the generated submillimeter wave its amplitude noise. The optimum probe power level should be chosen depending upon the system requirement. IV. CONCLUSION A detailed analysis of submillimeter wave generation through FWM in an injection-locked semiconductor laser has been presented. The AM PM indexes of the locked laser output lightwave have been calculated. The amplitude phase modulation indexes decrease with the increase in submillimeter wave frequency. The power of the generated submillimeter wave, which can be obtained at the output of a photodetector, has been numerically estimated. The submillimeter wave power decreases with the increase in submillimeter wave frequency. The theory shows that any amplitude modulation of the probe wave gets transferred to the submillimeter wave with the same index of amplitude modulation. The RIN of the mixing lightwaves introduces noise in the generated submillimeter wave. The noise power associated with the submillimeter wave is considerably reduced compared with the input noise. REFERENCES [1] A. Rydberg, H. Gronqvist, E. Kollberg, Millimeter submillimeter-wave multipliers using quantum-barrier-varactor (QBV) diodes, IEEE Electron Device Lett., vol. 11, pp , July [2] S. M. Nilsen, H. Gronqvist, H. Hjelmgren, A. Rydberg, E. 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Streetman, J. C. Campbell, Resonant-cavity InGaAs-InAlAs Avalanche photodiodes with gain bwidth product of 290 GHz, IEEE Photon. Technol. Lett., vol. 11, pp , Sept [13] M. Bhattacharya T. Chattopadhyay, A method for generation of optical FM signal through injection locking, J. Lightwave Technol., vol. 16, pp , Apr [14] T. Fukushima, R. Nagarajan, J. E. Bowers, R. A. Logan, T. Tanbun-Ek, Relative intensity noise reduction in InGaAs/InP multiple quantum well lasers with low nonlinear damping, IEEE Photon. Technol. Lett., vol. 3, pp , Aug [15] L. Li, Static dynamic properties of injection-locked semiconductor lasers, IEEE J. Quantum Electron., vol. 30, pp , Aug Taraprasad Chattopadhyay (M 98) received the Ph.D. degree from the University of Burdwan, West Bengal, India, in He joined the Department of Physics at Visva-Bharati University, Santiniketan, West Bengal, India, as a Lecturer in Currently, he is a Reader in the same department. From 1988 to 1989, he carried out research at Kyoto University, Kyoto, Japan, in optical communication with a scholarship from the Ministry of Education, Government of Japan. From 1991 to 1992, he was an invited researcher of the Japan Research Development Corporation, he carried out research on the design of a high-frequency light modulator. In 1996, he was a Researcher with the Association of International Education, Japan. From 1991 to 1993, he was a Visiting Associate of Council of Scientific Industrial Research (CSIR), New Delhi, India. He has published 48 papers in national international conferences refereed journals. He has been a reviewer for international journals, including Electronics Letters Proceedings of the IEE (part H). Dr. Chattopadhyay is a member of the IEEE Lasers Electro-Optics Society (LEOS) Institution of Electronics Telecommunications Engineers (IETE). Madhumita Bhattacharya received the M.Sc. degree in physics, with a specialty in radio physics electronics, from University of Burdwan, West Bengal, India, in 1988 the Ph.D. degree from Visva-Bharati University, Santiniketan, West Bengal, India, in From 1996 to 2001, she was a Research Associate of the Council of Scientific Industrial Research, New Delhi, India. Her research interests include optical communications. She has published 23 papers in conferences national international journals.