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Self-pulsing and instabilities in a unidirectional ring dye laser with intracavity frequency shift
15April 1995 OPTICS COMMUNICATIONS I-,l_SEVIl-X
Optics Communications 116 (1995) 136-142
Self-pulsing and instabilities in a unidirectional ring dye laser with intracavity frequency shift Stefan Balle, Klaas Bergmann Fachbereich Physik der Universitiit, Posrfnch 3049. 676S3 Kaiserslautern, Germany
Received 4 October 1994; revised version received I5 December I994
Abstract We study the dynamics of a ring dye laser that contains a frequency shifting intracavity element as well as a bandwidth limiting filter. The laser emits a train of pulses with a repetition rate corresponding to K pulses per cavity round trip. The integer number K increases with increasing pump power P. The transition K u K + 1 exhibits a pronounced hysteresis as P is changed. Numerical simulations show that this behaviour of a dye laser with intracavity frequency shift results from a characteristic time variation of the instantaneous frequency which is converted into time dependent losses by the intracavity etalon. The pulsed operation at a given K is sustained by the concerted action of these frequency dependent losses and the nonlinear coupling between the photon number in the cavity and the inversion of the active medium.
1. Introduction Controlling and shaping the spectral characteristics of the output of a laser is of practical interest in order to adapt the radiation to special tasks. Shifting the frequency of the intracavity field of a dye laser before fed back into the active medium has proven successful in realizing a broadband spectrum [ 11. As was demonstrated in Ref. [2] a smooth and stationary spectral profile forms the envelope for a comb of evenly spaced chirped modes. This envelope describes a uniform distribution of spectral energy, if temporally averaged over many round trip cycles. For small shift frequencies the formation of modes as well as their chirp can be understood by analyzing the characteristics of a passive frequency shifted feedback (fsfb) cavity [ 23. Previous experimental [ I] and theoretical [ 3,4] work on lasers with intracavity frequency shift were mostly concerned about the width and frequency posi0030-4018/95/$l9.50
tion of the spectral envelope. Applications of the fsfb broadband laser include electronic frequency control for pulsed lasers [ 51, the generation of a frequency comb and amplification of weak optical signals via injection seeding [ 61, the cooling of the longitudinal velocity distribution of a beam of metastable Ne atoms [ 71, and spatial separation of Rb-isotopes in a cell by white light induced drift [ 81. In Ref. [ 91 a diode laser with frequency shifted optical feedback was studied for weak feedback levels. In the following, we investigate the rather interesting properties of a unidirectional fsfb ring dye laser. This laser emits a train of pulses with a repetition rate VR = K/TKI. where K is zero (for a noisy output) or an integer number and 7~ is the cavity round trip time. The value of K increases with pump laser power P and transitions K H K + 1 are associated with a pronounced hysteresis when P increases and then decreases. In sections 2 and 3 we describe the experimental
@ 1995 Elsevier Science B.V. All rights reserved
SSDIOO30-4018(95)00059-3
S. Balle, K. Bergmann /Optics
Opt. Diode
AOM 1
Communications
137
116 (1995) 136-142
6-"""""""""""'(a) K = 0 -
543-
7
Fig. I. Experimental setup with a schematic representation of the laser system. The photodiode has a bandwidth of 3.5 GHz, the digital oscilloscope has an analogue bandwidth of 2 GHz and a real-time sampling rate of 8 GSa/s. The rf-spectrum analyzer has a maximum scan bandwidth of 2.6 GHz
setup and the observed phenomena. Section 4 offers a qualitative explanation of the laser behaviour which is based on time domain numerical simulations.
2. Experiment Frequency shifted feedback is realized by closing the ring of a conventional dye laser via the first frequency-shifted diffraction order of a high efficiency acousto-optic bragg cell, see Fig. 1. A Faraday rotator together with a half-wave plate forms an optical diode that guarantees unidirectional ring operation. An etalon of reflectivity R = 4% in combination with a birefringent filter provides a passband filter. In this work we impose a frequency shift of VFs = 80 MHz. The dye is DCM pumped by a multi-line argon ion laser. The performance and in particular the emission bandwidth of this system for various shift frequencies and filter bandwidths is discussed in Ref. [lo]. The laser intensity is recorded by a power meter as well as by a fast P-I-N photo diode that is connected to a fast digital oscilloscope and a radio frequency spectrum analyzer. The laser is enclosed in a box to reduce air turbulence. Care was taken to obtain a mechanically stable dye jet though small fluctuations could not be avoided. In particular it is known that air bubbles, crossing the
0
10
20
30
40
50
60
70
60
90
100 110 120
Time [ ns ] Fig. 2. Time-dependent intensity of the laser output as recorded by the photodiode, see Fig. 1, for K = 0, 1, 2 and 3. The cavity round trip time is 5.6 ns
pump focus, can switch off the laser for a few pus. Slow power fluctuations of the multimode pump laser did not exceed 0.5%.
3. Results In Fig. 2 we show the laser intensity as recorded by the fast photo diode and the digital oscilloscope. The cavity round trip time is 5.6 ns and the time base is chosen to cover about 2 1 round trips. Parts (a) to (d) of the figure show pulse trains with K = 0,1, 2 and 3 pulses per round trip, respectively. The pump power was P = 4.6 W which is only slightly above the threshold pump power of P = 3.5 W. For this low pump power the laser appears to be very sensitive to mechanical or acoustical perturbations. The state of oscillation is not very stable and switches between different values of K with K 5 3. However, operation of the laser with a well defined pulse repetition rate occurs sufficiently frequently for periods of a few seconds to record the traces shown in Figs. 2a-d. Fig. 2a shows a
S. Balle, K. Bergmann/Optics
138
I
1
I””
”
1
Communications 116 (1995) 136-142
I
250
.j
-
..
.':.. . .. iii
200
-
150
-
.:.: .*
3
: _. ...
a" 3 a
-.:I .i!.?
Fig. 3. Evolution of the signal repetition rate ~a = K/rar with pump power. Full dots were recorded for increasing, open dots for decreasing pump power. The values for increasing pump power are slightly displaced for purposes of presentation. The shift frequency was 80 MHz and the reflectivity of the etalon was R = 4
noisy signal (K = 0) that is structured on a time scale which is related to the cavity round trip time. For a pump power that is even closer to threshold the laser will operate only with a value of K = 0, see Fig. 2a. For K > 3, and a constant pump power P, stable operation of the laser is observed with only rare excursions to a mode of operation with K’ = K f 1. The variation of the pulse repetition rate and the output power with pump power P is shown in Figs. 3 and 4. While recording this data unidirectional operation of the dye laser in a single passband of the intracavity etalon, see Fig. 1, was assured. The pump power is changed by computer controlled variation of the driving power applied to the acousto-optic modulator AOM 2, see Fig. 1. With increasing driving power, a larger percentage of the laser power is diverted into the first diffraction order of the modulator and directed to a beam stop. The laser power transmitted through the zeroth order is used to pump the dye laser. A small fraction of that power is extracted by a beam splitter to monitor the pump power. After calibration, this signal provides an accurate measure of the pump power delivered to the dye laser. For each value of the pump power, the pulse repetition rate is obtained by extracting the fundamental frequency of the intensity spectrum, va = K/rw, from the data transferred from the radio frequency spectrum analyzer to the computer. As seen from Fig. 3, a pronounced hysteresis for transitions K + K’ = K f 1 is observed as P is changed. In that figure the data for increasing P is slightly dis-
%
100
-
i.. ...a\. . .
82
8.4
8 6
8.8
9 0
Pump Power
9.2
9 4
9.6
9.8
[W ]
Fig. 4. Variation of the output power with pump power P. The dam were recorded for decreasing pump power. The pump power intervals for which specific values of the repetition rate are observed are indicated at the bottom of the figure
placed downwards for better visibility. According to Figs. 3 and 4 both the pulse repetition rate and the output power vary, as a trend, linearly with the pump power P. However, closer inspection of Fig. 4 and comparison with Fig. 3 shows a stepwise decrease of the output power with P associated with a change of K, as is clearly resolved for K 5 5. The threshold pump power in Fig. 4 is higher than that reported above, because of a degradation of the spatial profile of the pump beam due to a thermal lens induced in the acousto-optic modulator (AOM 2).
4. Discussion Results of a theoretical investigation of a laser with intracavity frequency shift were recently presented by Cutler [ 111. The author specifies a noise signal over a period of length rm and numerically determines its evolution as it is frequency shifted and propagated
S. Balle, K. Bergmann / Optics Communications 116 (1995) 136-142
through the various intracavity elements. A specific pulse shape M(r) evolves over many round trips and dynamic gain saturation was found to synchronize M(t) with the feedback rate 1/QT. A change of the pulse repetition rate was not observed. In Ref. [ 121 Kowalski et al. reported autocorrelation signals for the dye laser output indicating the formation of ps-pulses when the frequency shift of the AOM matched the cavity mode spacing, i.e. for @s = l/rm. Furthermore, Kowalski observed a change of the repetition rate of the pulses as the diffraction efficiency of the intracavity AOM was changed. Selflocking of the longitudinalmodes of a HeNe laser with intracavity frequency shift introduced by the uniform motion of a cavity mirror was reported by Smith [ 131. In the following we present preliminary results from numerical simulations of the dynamics of the laser system. For a complete cavity round trip, the traveling wave electric field at a fixed position within the cavity is described by E(t)
= iE( t) exp( -iwJ)
+ c.c.,
where E(t)
= JMoexp[-icu(t)]
is the slowly varying complex envelope with M(t) being the photon flux and v,i = 0421r is the resonance frequency of the etalon passband that supports the oscillation. The deviation v(t) of the instantaneous frequency from vet is given by v(t)
1 dcu(r) = -27r dt ’
The laser field is numerically relation @i)(t)
= ~{&(‘--l)(r
_ rKr)},
determined
from the
i= l,...,imax,
where the operator 0 formally represents the transformation of the field by the intracavity elements. The integer number i counts the round trips. The lasing process evolves from spontaneous emission noise represented by E(O) ( t) . The maximum number of round trips i,, is large enough for the average output power to have settled to its steady state. The gain medium of the dye laser is treated as a homogeneously broadened two level system. Signal
propagation
139
through the laser medium is described by
[ 141
where Mi, and M,,r is the photon flux at the input and output of the amplifying medium, respectively, N(t) the inversion, ys is the spontaneous emission rate, P the pump rate and (Yis proportional to the cross section for stimulated emission. Spontaneous emission is retained during the calculations as a stochastic noise source S(t). Filtering by the frequency selective intracavity elements is described in the time domain by a recursive digital filter algorithm and round trip losses by a power reflection coefficient R. The frequency shift operation is performed by the prescription cu(i)(t) = (y(i-l) (t -
TRT)
+
fiFS tt
where the first term would be the only one when considering a laser without frequency shift (imposing conventional cavity boundary conditions) while the second term is due to the frequency shift. The time dependence of the inversion N(t) as well as the photon number M(t) and instantaneous frequency v(t) of the evolving laser field are shown in Fig. 5 for one cavity round trip. They give a qualitative explanation of the formation of the pulses and the pump power dependence of the repetition rate. We find that the observed behaviour does not depend on any specific ratio of the shift frequency and the modespacing. A more detailed investigation, based on extensive experimental and numerical data, will be the subject of a forthcoming publication. We first consider parts (a) and (b) of Fig. 5. As the pulses pass through the gain medium they deplete the inversion by stimulated emission. Between pulses, the inversion recovers at a rate that depends on the pump rate P. With increasing P recovery is faster, the inversion will sooner reach threshold after depletion and be ready for the amplification of the next pulse. On the average, the repetition rate will therefore increase with increasing P. The cavity boundary conditions restrict the evolution of signals to temporal structures that are related to the cavity round trip time. This is observed even when the laser is not pulsing, see Fig. 2a. For pulsed operation, the repetition rate must assume discrete values
140
S. Balle, K. Bergmann / Opfics Communications 116 (I 995) 136-142
Time [ ns ] Fig. 5. Temporal behaviour of (a) the inversion N(r), (b) the photon flux M(t) and (c) the instantaneous frequency V(I) for a pump power that leads to K = 5. The overall structure is periodic with the cavity round trip time of 5 ns. This value derives from a cavity length of L = I.5 m. The dashed vertical line marks the time at which the photon number passes through a minimum, i.e. where gain equals loss. The results are obtained for a shift frequency of 8 MHz per round trip and an etalon reflectivity of R = 40%. The time dependence of the quantities shown does not change qualitatively when another set of parameters is used
K/rm. Due to the high Q-value of the resonator and the interdependence of the inversion and the photon number, the intracavity pulse tram will be maintained at a given K even if the pump power is varied. A transition from K to K’= K f 1 occurs only if a pump rate is reached for which the repetition rate K’/T~ allows laser oscillation with a higher power extraction efficiency. This is illustrated by the change in output power shown in Fig. 4. Part (c) of Fig. 5 shows that the pulsation is associated with a pronounced saw-tooth like frequency structure. The frequency shift direction is positive, i.e. from negative to positive frequency values. Because of the frequency-selective response of the intracavity filter, the time dependent frequency structure of the intracavity field leads to a time dependent loss. At a time pre-
ceeding the build-up of the pulses, the instantaneous frequency v(t) approaches the resonance frequency of the etalon, and the losses decrease. At the same time the inversion recovers. Decreasing losses and increasing gain combine to form a sharp leading edge of the laser pulses. The dashed vertical line shown in Fig. 5 marks a time when gain equals losses. The trailing edge of the pulses decay at a somewhat slower rate while the instantaneous frequency increases giving again rise to higher losses. Obviously, the pulses are not transform-limited. When the function y(t) approaches the resonance frequency of the etalon, irregular deviations from a saw-tooth like dependence are observed. A comprehensive explanation of this frequency structure is presently not available. The state of oscillation shown in Fig. 5 evolved from a simulation after 3 x lo4 cavity round trips have been completed. Choosing different numbers of round trips, we obtained different patterns for y(t). The saw-tooth like structure is encountered in any case. The essence of the above discussion is, however, not affected by the seemingly irregular deviations. Alternatively we may discuss the observed behaviour in the frequency domain with the laser field being described as a comb of chirped modes. The response of the gain medium is taken account of by invoking nonlinear coupling between the modes via four wave mixing. As the AOM induces a frequency shift to higher frequencies it drives the spectral components away from the transmission maximum of the etalon and thus imposes increasing losses. The modes will eventually die out at the high frequency side of the spectral envelope. A chirped comb of modes can be sustained, however, if spectral components develop at the low frequency side of the spectrum. The mechanism which stimulates the growth of those spectral components is four wave mixing. At the low frequency side of the spectral envelope these components experience positive net gain. The components will compete successfully with broadband spontaneous emission and provide the seed for the modes which then accumulate power as they are chirped towards the maximum of the spectral profile. The process of four wave mixing generates these seed components coherently, with the frequency intervals and phases determined by the modes that lead to their formation. The comb of modes will thus oscillate
S. Balle. K. Bergmann /Optics Communications 116 (1995) 136142
in a self-locked spectra1 configuration. Self-locking is evident from the hysteresis shown in Fig. 3. The components generated by nonlinear mixing will be created with the same frequency intervals as established for the oscillating modes. Thus, the system is stabilized against the break up of a spectra1 configuration, and the transition from K to K’ = K h I occurs at a different pump power P when P is increased or decreased. Further consequences of four wave mixing related to spectral properties such as the frequency position of the maximum of the spectra1 envelope, as well as the width and an asymmetry of the spectral profile will be discussed elsewhere. The behaviour of our laser may be compared to passive Q-switching where sustained spiking is induced by an intracavity saturable absorber. Passive Qswitching, however, relates to the photon number of a single cavity mode and is found for lasers with a decay rate of the inversion smaller than the cavity decay rate (class-B lasers such as diode or solid state lasers). In contrast, this paper deals with multimode operation of a dye laser (class-A laser) and the dynamical variable is the complex intracavity field amplitude. Furthermore, the data shown in Fig. 5 do not result from the solution of an initial value problem but emerge from the interplay between the field and the active and passive intracavity elements over a large number of round trips. In Ref. [ I] the output of the fsfb dye laser was viewed as resulting from incoherent, regeneratively amplified spontaneous emission. In fact, close to threshold the laser emits a noisy radiation field, see Fig. 2a. Near threshold, the intracavity field is obviously too weak to generate nonlinear mixing components, and laser action is driven solely by spontaneous emission. However, sufficiently far above threshold, nonlinear mixing is important, mode locking occurs and the laser seeks a mode of operation with highest lasing efficiency. This is evidenced by a jump in the output power associated with transitions K = 0 ++ K’ > 0, see Fig. 4. It is interesting to compare the behaviour of fsfb lasers with gain media, possessing a widely differing lifetime of the upper laser level. For dye molecules, the lifetime is of the order of ns, while it is on the order of ps for titanium sapphire. In fact, quite interesting and distinctly different phenomena have ‘been observed for a titanium sapphire laser with intracav-
141
ity frequency shift [ 151. For pump powers exceeding threshold by no more than 705% the output of such a laser consists of intensity pulsations with a repetition rate that increases linearly from 310 to 490 kHz with increasing P. Similar observations are reported in Ref. [ 161. The temporal evolution of the intensity is associated with a shift of the instantaneous spectral envelope toward the transmission profile of the etalon (see also Ref. [ 41 where a similar behaviour is discussed for the build-up transient of a fsfb dye laser). The resulting loss modulation and the character of the coupling between the photon number and the inversion (class-B type) sustain the pulsations. At high pump power, the spectra1 broadening associated with the short-time response of the inversion leads to a new kind of mode-locking in such a laser [ 171. Recent investigations exploiting the effects of self-phase modulation in other solid state laser media are given in Refs. [ 18-201.
5. Summary In summary, we have shown that the combined action of intracavity frequency shifting and frequency filtering substantially modifies the output of a conventional dye laser. A train of pulses with pulse-to-pulse intervals smaller than the cavity round trip time can be formed. The cavity boundary conditions enforce a pUk repetition rate that is restricted to values Va = K/rm, where K is an integer number which increases with the pump rate. Values up to K = 8 are documented in this paper, but values as large as K = 11 have been observed without placing an AOM in the pump beam. The variation of K exhibits a pronounced hysteresis as the pump power is increased or decreased. More detailed experimental data and results from a numerical simulation study, which lead to a quantitative understanding of the dye laser with intracavity frequency shift, will be presented in a subsequent publication.
Acknowledgements This work was done in the “Zentrum fur LasermeBtechnik und Diagnostik” (supported by the Stiftung Rheinland-Pfalz fur Innovation) at the Uni-
S. Balle. K. Bergmann / Optics Communications
142
versity of Kaiserslautern. Forschungsgemeinschaft acknowledged.
Support by the Deutsche under Be 623/ 16 is also
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[lOI I. Litter, S. Balle and K. Bergmann, Optics Comm. 88 ( 1992) 514.
IIll CC. Cutler IEEE J. Quantum Electron. QE-28 ( 1992) 60; 282.
1121 EV. Kowalski, S.J. Shattil and P.D. Hale Appl. Phys. Lett. References Ill F.V. Kowalski, PD. Hale and S.J. Shattil, Optics Lett. 13 (1988) 622; I. Littler, S. Balle and K. Bergmann, J. Opt. Sot. Am. B 8 (1991) 1412. 121S. Balle, I.C.M. Littler, K. Bergmann and E Kowalski, Optics Comm. 102 (1993) 166. 131W. Streifer and J. R. Whinnery, Appl. Phys. Lett. 17 ( 1970) 335; P Saltz and W. Streifer, IEEE J. Quantum Electron. QE-8 ( 1972) 893; W. Streifer and I? Saltz IEEE J. Quantum Electron. QE-9 ( 1973) 563. 141 I.C.M. Littler and J.H. Eschner, Optics Comm. 87( 1.2) (1991) 44. 151 D.J. Taylor, S.E. Harris, S.T.K. Nieh and T.W. Hansch, Appl. Phys. Len. 19 (1971) 269. 161 I. Littler and K. Bergmann, Optics Comm. 88 ( 1992) 523: 1. Littler, K. Bergmann and R. Roy, Optics Comm. 87 ( 1992)
s3. 171 I.C.M. Littler,
H.-M. Keller, U. Gaubatz and K. Bergmann,
Z. Phys. D 18 (1991) 307. 181 D. Mugglin, A. &eater, S. BaIle and K. Bergmann, Optics Comm. 104 (1993) 165. 191 I. Martin, Y. Zhao, S. Balle, M.P Fewell and K. Bergmann, Optics Comm. I12 ( 1994) 109.
53 (1988) 734: PD. Hale and F.V. Kowalski IEEE J. Quantum Electron. QE-26 (1990) 1845. 1131 P.W. Smith Appl. Phys. Lett. IO (1967) 51. r141 A.E. Siegman, Lasers (Univ. Science Books, Mill Valley, CA, 1986) Ch. 10.1. 1151 S. Balle, G. Bonnet, T. Kraft and K. Bergmann, Oscillation behaviour of a titanium-sapphire laser with intracavity frequency shift, European Quantum Electronics Conference ‘94, paper number QTuB3. 1161 I.R. Perry, R.L. Wang and J.R.M. Barr, Optics Comm. 109 (1994) 187. 1171 G. Bonnet, S. Balle, K. Kraft and K. Bergmann, Investigation of a Titanium Sapphire Laser with Intracavity Frequency Shift, Optics Comm., to be submitted. 1181 Q. Wu, J.Y. Zhou, X.G. Huang, 2.X. Li and Q.X. Li, J. Opt. Sot. Am. B 10 (1993) 2080. I191 H. Sabert and E. Brinkmeyer, Electron. Lett. 29 (1993) 2122. 1201Y. Kodama, M. Romagnoli and S. Wabnitz, Electron. Len. 30 (1994) 261; E Fontana, L. Bossalini, P France, M. Midrio, M. Romagnoli and S. Wabnitz, Electron. Lett. 30 (1994) 321; M. Romagnoli, S. Wabnitz, P. France, M. Midrio, EFontana and G.E. Town, European Quantum Electronics Conference ‘94, paper number QTuB4.
Optics Communications 116 (1995) 136-142
Self-pulsing and instabilities in a unidirectional ring dye laser with intracavity frequency shift Stefan Balle, Klaas Bergmann Fachbereich Physik der Universitiit, Posrfnch 3049. 676S3 Kaiserslautern, Germany
Received 4 October 1994; revised version received I5 December I994
Abstract We study the dynamics of a ring dye laser that contains a frequency shifting intracavity element as well as a bandwidth limiting filter. The laser emits a train of pulses with a repetition rate corresponding to K pulses per cavity round trip. The integer number K increases with increasing pump power P. The transition K u K + 1 exhibits a pronounced hysteresis as P is changed. Numerical simulations show that this behaviour of a dye laser with intracavity frequency shift results from a characteristic time variation of the instantaneous frequency which is converted into time dependent losses by the intracavity etalon. The pulsed operation at a given K is sustained by the concerted action of these frequency dependent losses and the nonlinear coupling between the photon number in the cavity and the inversion of the active medium.
1. Introduction Controlling and shaping the spectral characteristics of the output of a laser is of practical interest in order to adapt the radiation to special tasks. Shifting the frequency of the intracavity field of a dye laser before fed back into the active medium has proven successful in realizing a broadband spectrum [ 11. As was demonstrated in Ref. [2] a smooth and stationary spectral profile forms the envelope for a comb of evenly spaced chirped modes. This envelope describes a uniform distribution of spectral energy, if temporally averaged over many round trip cycles. For small shift frequencies the formation of modes as well as their chirp can be understood by analyzing the characteristics of a passive frequency shifted feedback (fsfb) cavity [ 23. Previous experimental [ I] and theoretical [ 3,4] work on lasers with intracavity frequency shift were mostly concerned about the width and frequency posi0030-4018/95/$l9.50
tion of the spectral envelope. Applications of the fsfb broadband laser include electronic frequency control for pulsed lasers [ 51, the generation of a frequency comb and amplification of weak optical signals via injection seeding [ 61, the cooling of the longitudinal velocity distribution of a beam of metastable Ne atoms [ 71, and spatial separation of Rb-isotopes in a cell by white light induced drift [ 81. In Ref. [ 91 a diode laser with frequency shifted optical feedback was studied for weak feedback levels. In the following, we investigate the rather interesting properties of a unidirectional fsfb ring dye laser. This laser emits a train of pulses with a repetition rate VR = K/TKI. where K is zero (for a noisy output) or an integer number and 7~ is the cavity round trip time. The value of K increases with pump laser power P and transitions K H K + 1 are associated with a pronounced hysteresis when P increases and then decreases. In sections 2 and 3 we describe the experimental
@ 1995 Elsevier Science B.V. All rights reserved
SSDIOO30-4018(95)00059-3
S. Balle, K. Bergmann /Optics
Opt. Diode
AOM 1
Communications
137
116 (1995) 136-142
6-"""""""""""'(a) K = 0 -
543-
7
Fig. I. Experimental setup with a schematic representation of the laser system. The photodiode has a bandwidth of 3.5 GHz, the digital oscilloscope has an analogue bandwidth of 2 GHz and a real-time sampling rate of 8 GSa/s. The rf-spectrum analyzer has a maximum scan bandwidth of 2.6 GHz
setup and the observed phenomena. Section 4 offers a qualitative explanation of the laser behaviour which is based on time domain numerical simulations.
2. Experiment Frequency shifted feedback is realized by closing the ring of a conventional dye laser via the first frequency-shifted diffraction order of a high efficiency acousto-optic bragg cell, see Fig. 1. A Faraday rotator together with a half-wave plate forms an optical diode that guarantees unidirectional ring operation. An etalon of reflectivity R = 4% in combination with a birefringent filter provides a passband filter. In this work we impose a frequency shift of VFs = 80 MHz. The dye is DCM pumped by a multi-line argon ion laser. The performance and in particular the emission bandwidth of this system for various shift frequencies and filter bandwidths is discussed in Ref. [lo]. The laser intensity is recorded by a power meter as well as by a fast P-I-N photo diode that is connected to a fast digital oscilloscope and a radio frequency spectrum analyzer. The laser is enclosed in a box to reduce air turbulence. Care was taken to obtain a mechanically stable dye jet though small fluctuations could not be avoided. In particular it is known that air bubbles, crossing the
0
10
20
30
40
50
60
70
60
90
100 110 120
Time [ ns ] Fig. 2. Time-dependent intensity of the laser output as recorded by the photodiode, see Fig. 1, for K = 0, 1, 2 and 3. The cavity round trip time is 5.6 ns
pump focus, can switch off the laser for a few pus. Slow power fluctuations of the multimode pump laser did not exceed 0.5%.
3. Results In Fig. 2 we show the laser intensity as recorded by the fast photo diode and the digital oscilloscope. The cavity round trip time is 5.6 ns and the time base is chosen to cover about 2 1 round trips. Parts (a) to (d) of the figure show pulse trains with K = 0,1, 2 and 3 pulses per round trip, respectively. The pump power was P = 4.6 W which is only slightly above the threshold pump power of P = 3.5 W. For this low pump power the laser appears to be very sensitive to mechanical or acoustical perturbations. The state of oscillation is not very stable and switches between different values of K with K 5 3. However, operation of the laser with a well defined pulse repetition rate occurs sufficiently frequently for periods of a few seconds to record the traces shown in Figs. 2a-d. Fig. 2a shows a
S. Balle, K. Bergmann/Optics
138
I
1
I””
”
1
Communications 116 (1995) 136-142
I
250
.j
-
..
.':.. . .. iii
200
-
150
-
.:.: .*
3
: _. ...
a" 3 a
-.:I .i!.?
Fig. 3. Evolution of the signal repetition rate ~a = K/rar with pump power. Full dots were recorded for increasing, open dots for decreasing pump power. The values for increasing pump power are slightly displaced for purposes of presentation. The shift frequency was 80 MHz and the reflectivity of the etalon was R = 4
noisy signal (K = 0) that is structured on a time scale which is related to the cavity round trip time. For a pump power that is even closer to threshold the laser will operate only with a value of K = 0, see Fig. 2a. For K > 3, and a constant pump power P, stable operation of the laser is observed with only rare excursions to a mode of operation with K’ = K f 1. The variation of the pulse repetition rate and the output power with pump power P is shown in Figs. 3 and 4. While recording this data unidirectional operation of the dye laser in a single passband of the intracavity etalon, see Fig. 1, was assured. The pump power is changed by computer controlled variation of the driving power applied to the acousto-optic modulator AOM 2, see Fig. 1. With increasing driving power, a larger percentage of the laser power is diverted into the first diffraction order of the modulator and directed to a beam stop. The laser power transmitted through the zeroth order is used to pump the dye laser. A small fraction of that power is extracted by a beam splitter to monitor the pump power. After calibration, this signal provides an accurate measure of the pump power delivered to the dye laser. For each value of the pump power, the pulse repetition rate is obtained by extracting the fundamental frequency of the intensity spectrum, va = K/rw, from the data transferred from the radio frequency spectrum analyzer to the computer. As seen from Fig. 3, a pronounced hysteresis for transitions K + K’ = K f 1 is observed as P is changed. In that figure the data for increasing P is slightly dis-
%
100
-
i.. ...a\. . .
82
8.4
8 6
8.8
9 0
Pump Power
9.2
9 4
9.6
9.8
[W ]
Fig. 4. Variation of the output power with pump power P. The dam were recorded for decreasing pump power. The pump power intervals for which specific values of the repetition rate are observed are indicated at the bottom of the figure
placed downwards for better visibility. According to Figs. 3 and 4 both the pulse repetition rate and the output power vary, as a trend, linearly with the pump power P. However, closer inspection of Fig. 4 and comparison with Fig. 3 shows a stepwise decrease of the output power with P associated with a change of K, as is clearly resolved for K 5 5. The threshold pump power in Fig. 4 is higher than that reported above, because of a degradation of the spatial profile of the pump beam due to a thermal lens induced in the acousto-optic modulator (AOM 2).
4. Discussion Results of a theoretical investigation of a laser with intracavity frequency shift were recently presented by Cutler [ 111. The author specifies a noise signal over a period of length rm and numerically determines its evolution as it is frequency shifted and propagated
S. Balle, K. Bergmann / Optics Communications 116 (1995) 136-142
through the various intracavity elements. A specific pulse shape M(r) evolves over many round trips and dynamic gain saturation was found to synchronize M(t) with the feedback rate 1/QT. A change of the pulse repetition rate was not observed. In Ref. [ 121 Kowalski et al. reported autocorrelation signals for the dye laser output indicating the formation of ps-pulses when the frequency shift of the AOM matched the cavity mode spacing, i.e. for @s = l/rm. Furthermore, Kowalski observed a change of the repetition rate of the pulses as the diffraction efficiency of the intracavity AOM was changed. Selflocking of the longitudinalmodes of a HeNe laser with intracavity frequency shift introduced by the uniform motion of a cavity mirror was reported by Smith [ 131. In the following we present preliminary results from numerical simulations of the dynamics of the laser system. For a complete cavity round trip, the traveling wave electric field at a fixed position within the cavity is described by E(t)
= iE( t) exp( -iwJ)
+ c.c.,
where E(t)
= JMoexp[-icu(t)]
is the slowly varying complex envelope with M(t) being the photon flux and v,i = 0421r is the resonance frequency of the etalon passband that supports the oscillation. The deviation v(t) of the instantaneous frequency from vet is given by v(t)
1 dcu(r) = -27r dt ’
The laser field is numerically relation @i)(t)
= ~{&(‘--l)(r
_ rKr)},
determined
from the
i= l,...,imax,
where the operator 0 formally represents the transformation of the field by the intracavity elements. The integer number i counts the round trips. The lasing process evolves from spontaneous emission noise represented by E(O) ( t) . The maximum number of round trips i,, is large enough for the average output power to have settled to its steady state. The gain medium of the dye laser is treated as a homogeneously broadened two level system. Signal
propagation
139
through the laser medium is described by
[ 141
where Mi, and M,,r is the photon flux at the input and output of the amplifying medium, respectively, N(t) the inversion, ys is the spontaneous emission rate, P the pump rate and (Yis proportional to the cross section for stimulated emission. Spontaneous emission is retained during the calculations as a stochastic noise source S(t). Filtering by the frequency selective intracavity elements is described in the time domain by a recursive digital filter algorithm and round trip losses by a power reflection coefficient R. The frequency shift operation is performed by the prescription cu(i)(t) = (y(i-l) (t -
TRT)
+
fiFS tt
where the first term would be the only one when considering a laser without frequency shift (imposing conventional cavity boundary conditions) while the second term is due to the frequency shift. The time dependence of the inversion N(t) as well as the photon number M(t) and instantaneous frequency v(t) of the evolving laser field are shown in Fig. 5 for one cavity round trip. They give a qualitative explanation of the formation of the pulses and the pump power dependence of the repetition rate. We find that the observed behaviour does not depend on any specific ratio of the shift frequency and the modespacing. A more detailed investigation, based on extensive experimental and numerical data, will be the subject of a forthcoming publication. We first consider parts (a) and (b) of Fig. 5. As the pulses pass through the gain medium they deplete the inversion by stimulated emission. Between pulses, the inversion recovers at a rate that depends on the pump rate P. With increasing P recovery is faster, the inversion will sooner reach threshold after depletion and be ready for the amplification of the next pulse. On the average, the repetition rate will therefore increase with increasing P. The cavity boundary conditions restrict the evolution of signals to temporal structures that are related to the cavity round trip time. This is observed even when the laser is not pulsing, see Fig. 2a. For pulsed operation, the repetition rate must assume discrete values
140
S. Balle, K. Bergmann / Opfics Communications 116 (I 995) 136-142
Time [ ns ] Fig. 5. Temporal behaviour of (a) the inversion N(r), (b) the photon flux M(t) and (c) the instantaneous frequency V(I) for a pump power that leads to K = 5. The overall structure is periodic with the cavity round trip time of 5 ns. This value derives from a cavity length of L = I.5 m. The dashed vertical line marks the time at which the photon number passes through a minimum, i.e. where gain equals loss. The results are obtained for a shift frequency of 8 MHz per round trip and an etalon reflectivity of R = 40%. The time dependence of the quantities shown does not change qualitatively when another set of parameters is used
K/rm. Due to the high Q-value of the resonator and the interdependence of the inversion and the photon number, the intracavity pulse tram will be maintained at a given K even if the pump power is varied. A transition from K to K’= K f 1 occurs only if a pump rate is reached for which the repetition rate K’/T~ allows laser oscillation with a higher power extraction efficiency. This is illustrated by the change in output power shown in Fig. 4. Part (c) of Fig. 5 shows that the pulsation is associated with a pronounced saw-tooth like frequency structure. The frequency shift direction is positive, i.e. from negative to positive frequency values. Because of the frequency-selective response of the intracavity filter, the time dependent frequency structure of the intracavity field leads to a time dependent loss. At a time pre-
ceeding the build-up of the pulses, the instantaneous frequency v(t) approaches the resonance frequency of the etalon, and the losses decrease. At the same time the inversion recovers. Decreasing losses and increasing gain combine to form a sharp leading edge of the laser pulses. The dashed vertical line shown in Fig. 5 marks a time when gain equals losses. The trailing edge of the pulses decay at a somewhat slower rate while the instantaneous frequency increases giving again rise to higher losses. Obviously, the pulses are not transform-limited. When the function y(t) approaches the resonance frequency of the etalon, irregular deviations from a saw-tooth like dependence are observed. A comprehensive explanation of this frequency structure is presently not available. The state of oscillation shown in Fig. 5 evolved from a simulation after 3 x lo4 cavity round trips have been completed. Choosing different numbers of round trips, we obtained different patterns for y(t). The saw-tooth like structure is encountered in any case. The essence of the above discussion is, however, not affected by the seemingly irregular deviations. Alternatively we may discuss the observed behaviour in the frequency domain with the laser field being described as a comb of chirped modes. The response of the gain medium is taken account of by invoking nonlinear coupling between the modes via four wave mixing. As the AOM induces a frequency shift to higher frequencies it drives the spectral components away from the transmission maximum of the etalon and thus imposes increasing losses. The modes will eventually die out at the high frequency side of the spectral envelope. A chirped comb of modes can be sustained, however, if spectral components develop at the low frequency side of the spectrum. The mechanism which stimulates the growth of those spectral components is four wave mixing. At the low frequency side of the spectral envelope these components experience positive net gain. The components will compete successfully with broadband spontaneous emission and provide the seed for the modes which then accumulate power as they are chirped towards the maximum of the spectral profile. The process of four wave mixing generates these seed components coherently, with the frequency intervals and phases determined by the modes that lead to their formation. The comb of modes will thus oscillate
S. Balle. K. Bergmann /Optics Communications 116 (1995) 136142
in a self-locked spectra1 configuration. Self-locking is evident from the hysteresis shown in Fig. 3. The components generated by nonlinear mixing will be created with the same frequency intervals as established for the oscillating modes. Thus, the system is stabilized against the break up of a spectra1 configuration, and the transition from K to K’ = K h I occurs at a different pump power P when P is increased or decreased. Further consequences of four wave mixing related to spectral properties such as the frequency position of the maximum of the spectra1 envelope, as well as the width and an asymmetry of the spectral profile will be discussed elsewhere. The behaviour of our laser may be compared to passive Q-switching where sustained spiking is induced by an intracavity saturable absorber. Passive Qswitching, however, relates to the photon number of a single cavity mode and is found for lasers with a decay rate of the inversion smaller than the cavity decay rate (class-B lasers such as diode or solid state lasers). In contrast, this paper deals with multimode operation of a dye laser (class-A laser) and the dynamical variable is the complex intracavity field amplitude. Furthermore, the data shown in Fig. 5 do not result from the solution of an initial value problem but emerge from the interplay between the field and the active and passive intracavity elements over a large number of round trips. In Ref. [ I] the output of the fsfb dye laser was viewed as resulting from incoherent, regeneratively amplified spontaneous emission. In fact, close to threshold the laser emits a noisy radiation field, see Fig. 2a. Near threshold, the intracavity field is obviously too weak to generate nonlinear mixing components, and laser action is driven solely by spontaneous emission. However, sufficiently far above threshold, nonlinear mixing is important, mode locking occurs and the laser seeks a mode of operation with highest lasing efficiency. This is evidenced by a jump in the output power associated with transitions K = 0 ++ K’ > 0, see Fig. 4. It is interesting to compare the behaviour of fsfb lasers with gain media, possessing a widely differing lifetime of the upper laser level. For dye molecules, the lifetime is of the order of ns, while it is on the order of ps for titanium sapphire. In fact, quite interesting and distinctly different phenomena have ‘been observed for a titanium sapphire laser with intracav-
141
ity frequency shift [ 151. For pump powers exceeding threshold by no more than 705% the output of such a laser consists of intensity pulsations with a repetition rate that increases linearly from 310 to 490 kHz with increasing P. Similar observations are reported in Ref. [ 161. The temporal evolution of the intensity is associated with a shift of the instantaneous spectral envelope toward the transmission profile of the etalon (see also Ref. [ 41 where a similar behaviour is discussed for the build-up transient of a fsfb dye laser). The resulting loss modulation and the character of the coupling between the photon number and the inversion (class-B type) sustain the pulsations. At high pump power, the spectra1 broadening associated with the short-time response of the inversion leads to a new kind of mode-locking in such a laser [ 171. Recent investigations exploiting the effects of self-phase modulation in other solid state laser media are given in Refs. [ 18-201.
5. Summary In summary, we have shown that the combined action of intracavity frequency shifting and frequency filtering substantially modifies the output of a conventional dye laser. A train of pulses with pulse-to-pulse intervals smaller than the cavity round trip time can be formed. The cavity boundary conditions enforce a pUk repetition rate that is restricted to values Va = K/rm, where K is an integer number which increases with the pump rate. Values up to K = 8 are documented in this paper, but values as large as K = 11 have been observed without placing an AOM in the pump beam. The variation of K exhibits a pronounced hysteresis as the pump power is increased or decreased. More detailed experimental data and results from a numerical simulation study, which lead to a quantitative understanding of the dye laser with intracavity frequency shift, will be presented in a subsequent publication.
Acknowledgements This work was done in the “Zentrum fur LasermeBtechnik und Diagnostik” (supported by the Stiftung Rheinland-Pfalz fur Innovation) at the Uni-
S. Balle. K. Bergmann / Optics Communications
142
versity of Kaiserslautern. Forschungsgemeinschaft acknowledged.
Support by the Deutsche under Be 623/ 16 is also
116 (1995) 136-142
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