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Empty waves do not induce stimulated emission in laser media
Volume 127,number 8,9
PHYSICSLETTERSA
14 March 1988
EMPTY WAVES DO NOT INDUCE STIMULATED E M I S S I O N IN LASER M E D I A W. MUCKENHEIM, P. LOKAI and B. BURGHARDT Lambda Physik, P.O. Box 2663, D-3400 G6ttingen, FRG
Received 18 November 1987;acceptedfor publication 11 January 1988 Communicatedby J.P. Vigier
Due to dispersion in a 20 m longquartz fiber an empty light wave (movingwith phase velocity) arrives 1.3 ns earlier than the photons. Using a short dye laser pulse the effect of the separated empty wave on a laser medium has been investigated with negative results.
postulated by Bohr. Thus, they are capable of pro-
1. Introduction In 1923 de Broglie postulated that each massive particle should be associated with a matter wave propagating with the phase velocity vp = E / p = ~ / F o > Co,
(1)
with E and p relativistic energy and momentum of the particle, and Co the speed of light a~. The particle's velocity is given by the group velocity of the corresponding wave packet VG = d E / d p = p / m .
(2)
According to special relativity matter waves cannot contain energy or momentum, and they cannot be utilized as a medium for transmitting signals. Otherwise, the foundations of special relativity would be severely weakened. The resulting superluminal signals then could be utilized to synchronize clocks, and Einstein's famous gedankenexperiment involving "long trains" would break down. Therefore, these waves have been called "empty waves" or "ghost waves" #2 On the other hand, the wavelength of these ernpy waves, 2 = h/p, has been measured (first by Davisson and Germer), and they deliver a plausible explanation of the integer angular momentum 1= nh, e.g. of electrons in stable atomic orbits, which had to be ~ For an introduction and a bibliographysee ref. [ 1]. ~2An overviewof this topic gives Selleri [ 2].
ducing effects which can be detected by means of physical processes. A reasonable explanation is to assume that the amplitude of the empty wave, due to interference, is always zero except at the particle's position. But the Broglie's idea is that empty waves have to be understood as guiding the particle and being responsible for that kind of physically observable interference effects which, up to now, prohibit (or, at least cause a lot of struggle about) a satisfactory combination of relativity and quantum mechanics. According to de Broglie, there is not a dualism but a coexistence of particle and wave. The particle is guided by the phase ~ of the wave such that the particle's velocity is determined by v= - m - IV tp [3]. "On con~oit alors l'onde continue comme guidant le mouvement de la particule. C'est une onde pilote" [4], and there are "physical phenomena that seem to us unexplainable unless the idea of a permanent localization of the corpuscle is accepted" [ 5 ]. In virtue of this problem, it would be interesting to look for a observable action of empy waves, for instance whether these waves might be capable of inducing stimulated emission because this would not require energy or momentum transfer between wave and particle. Although it is beyond o u r present experimental facilities to do so with empty matter waves, a related effect can be investigated by means of common experimental equipment, namely stimulated photon emission in laser media induced by
0375-9601/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
387
Volume 127, number 8,9
PHYSICS LETTERS A
empty light waves. Empty light waves are not propagating with superluminal velocity, but effects induced by them may be expected from empty matter waves too. In analogy to massive particles photons can be described as wave packets, and it can be expected that these waves play a dominant role in inducing stimulated emission, if empty matter waves do. De Broglie and Andrade e Silva used the action of empty light waves to interprete an experiment by Pfleegor and Mandel [ 6 ] who observed interference between two different laser beams: "There exist interference fringes in the apparatus even if there is no photon that permits one to detect them" [7]. They arrived at a plausible interpretation. An observation supporting this line was reported by Blake and Scarl [8]. They found that there is (whithin 1 ns) no temporal correlation between an incident photon and a photon induced by this via the process of stimulated emission in a HeNe laser gain tube. Henoe, this process should be generated by the wave, rather than by the photon. In order to investigate this possible effect, it is sufficient to separate a part of the empty wave from the photons. This can be done in refractive media. For n(2), the index of refraction, and dn(X)/dg, its variation with the wavelength, the phase velocity cp of the waves and the group velocity co of the photons can be derived from eqs. (1), (2). Conveniently expressed as a function of the wavelength 2 we obtain (3)
cp = co/ n
14 March 1988
and co=cp(l+-2-~)n "
(4)
In media with normal dispersion d n / d ) t is negative. Therefore the empty waves propagate faster than the photons and can be separated via long distances, e.g. in quartz fibers. After passing through, the effect of the empty wave can be observed in a laser amplifier. Such an experiment has been performed.
2. Experiment The experimental set-up is shown in fig. 1. A dye laser, pumped by an excimer laser (EMG 103 MSC, FL 3002, Lambda Physik) produces pulses of 16 ns duration and 0.2 cm-~ bandwidth at 589 nm, the central wavelength of the dye Rhodamine 6G. Part of its output is directed onto the entrance of a 20 m long hard-clad silica fiber with 1 m m core-diameter (HCN-M 1000T-12, Laser Components) such that 0.1 mJ pulse energy arrives at the end of the fiber (specified attenuation of the fiber at this wavelenth is 20 dB/km). After leaving the fiber the pulse is used as a seed pulse for a dye laser amplifier, i.e. a 20 m m long dye cell pumped by an EMG 103 MSC excimer laser (of 20 ns pulse duration) 10 ns before the seed pulse arrives. 20m FIBER
A
B
BS
DYE CELL
k2
1
EXCIMER LASER
1
/PuMp
~AM
Fig. 1. Experimental arrangement. L: piano-convex lens, BS: beam splitter (quartz flat), A: attenuator, VA: variable attenuator, B: block, VB: variable block.
388
Volume 127, number 8,9
PHYSICS LETTERS A
The seed pulse had a divergence of ~ 5 ° when leaving the fiber. It was focused by a piano-convex lens and fed through the dye cell, the optical axis of which was tilted by ~ 10 ° with respect to the pulse direction, such that the super-fluorescence induced by the dye cell's windows did not interfere with the experiment. A small fraction of the pulse impinging onto a photodiode (FD 125 M 20 U V G 48, ITL) was recorded with an oscilloscope (7834, Tektronix). This measurement was performed when the dye cell was pumped and when the dye cell was not pumped. As the recorded energies with and without amplification were very different (10 p.J and 1.2 ~tJ, respectively), a variable attenuator was inserted into the beam path, in order to get comparable pulse heights at the oscilloscope. A possible time jitter of + 2 ns caused by the excimer laser pumping the dye laser was eliminated by directing a part of the seed pulse before entering the fiber onto the photodiode and utilizing its leading edge as trigger signal for the oscilloscope. A corresponding time jitter of the excimer laser pumping the amplifier dye cel was uncritical.
3. Analysis of data and result
14 March 1988
Fig. 2. Seed pulse without amplification in the dye cell (pump beam blocked). Time scale is 2 ns per small division.
look different. In particular, the leading part of the amplified pulse is pronounced. But this is a wellknown effect, related to gain depletion in the amplifier. The time difference at the lower part of the leading edges is about 0.3 ns. The experiment has been repeated 40 times, continuously switching between both alternatives. The result is a time difference At = 0.1 + 0.2 ns, which has to be compared to an expected value of At= 1.3 + 0.2 ns.
The time delay between trigger pulse and seed pulse was about 100 ns in accordance with the refractive index of fused silica n = 1.45845 [9] at 589 nm. From dn/d2= ( - 3 . 3 + 0 . 3 ) × 104 m - t , interpolated from ref. [ 9], it can be calculated that broadening of the seed pulse due to dispersion in the fiber is negligible ( < 1 ps) because of the narrow bandwidth. But the group velocity calculated according to (4) is 1.3% smaller than the phase velocity co/n. Hence, the photons propagating with cG should arrive by At= 1.3 +0.2 ns after the leading edge of the empty wave. If the latter were capable of inducing stimulated emission, this effect should be indicated by a corresponding time difference between the leading edges of the pure seed pulse (observed when the amplifier dye cell was not pumped) and the amplified seed pulse. Two pulses exhibiting maximum time difference are shown in figs. 2 and 3. Their intensities were attenuated to the same peak power. The pulse shapes
Hence, it can be excluded that empty photon waves induce stimulated emission in laser media.
Fig. 3. Amplified seed pulse. Same time scale as in fig. 2. Attenuation o f the variable attenuator increased by a factor of 10.
389
Volume 127, number 8,9
PHYSICS LETTERS A
References
[ 1 ] G. Lochak, De Broglies initial conception of de Broglie waves, in: The wave-particle dualism, eds. S. Diner et al. (Reidel, Dordrecht, 1984) p. 1. [2] F. Selleri, Gespensterfelder, in: The wave-particle dualism, eds. S. Diner et al. (Reidel, Dordrecht, 1984) p. 101. [3] L. de Broglie, J. Phys. Radium 20 (1959) 963. [4] L. de Broglie, J. Phys. Radium (VI) 8 (1927) 225.
390
14 March 1988
[5] L. de Broglie, G. Lochak, J.A. Beswick and J. VassaloPereira, Found. Phys. 6 (1976) 3. [ 6 ] R.L. Pfleegor and L. Mandel, Phys. Rev. 159 ( 1967 ) 1084. [7] L. de Broglie and J. Andrade e Silva, Phys. Rev. 172 (1968) 1284. [8] G.D. Blake and D. Scarl, Phys. Rev. A 19 (1979) 1948. [9] Handbook of chemistry and physics, 64th Ed. (CRC Press, Boca Raton, 1984) p. E-364.
PHYSICSLETTERSA
14 March 1988
EMPTY WAVES DO NOT INDUCE STIMULATED E M I S S I O N IN LASER M E D I A W. MUCKENHEIM, P. LOKAI and B. BURGHARDT Lambda Physik, P.O. Box 2663, D-3400 G6ttingen, FRG
Received 18 November 1987;acceptedfor publication 11 January 1988 Communicatedby J.P. Vigier
Due to dispersion in a 20 m longquartz fiber an empty light wave (movingwith phase velocity) arrives 1.3 ns earlier than the photons. Using a short dye laser pulse the effect of the separated empty wave on a laser medium has been investigated with negative results.
postulated by Bohr. Thus, they are capable of pro-
1. Introduction In 1923 de Broglie postulated that each massive particle should be associated with a matter wave propagating with the phase velocity vp = E / p = ~ / F o > Co,
(1)
with E and p relativistic energy and momentum of the particle, and Co the speed of light a~. The particle's velocity is given by the group velocity of the corresponding wave packet VG = d E / d p = p / m .
(2)
According to special relativity matter waves cannot contain energy or momentum, and they cannot be utilized as a medium for transmitting signals. Otherwise, the foundations of special relativity would be severely weakened. The resulting superluminal signals then could be utilized to synchronize clocks, and Einstein's famous gedankenexperiment involving "long trains" would break down. Therefore, these waves have been called "empty waves" or "ghost waves" #2 On the other hand, the wavelength of these ernpy waves, 2 = h/p, has been measured (first by Davisson and Germer), and they deliver a plausible explanation of the integer angular momentum 1= nh, e.g. of electrons in stable atomic orbits, which had to be ~ For an introduction and a bibliographysee ref. [ 1]. ~2An overviewof this topic gives Selleri [ 2].
ducing effects which can be detected by means of physical processes. A reasonable explanation is to assume that the amplitude of the empty wave, due to interference, is always zero except at the particle's position. But the Broglie's idea is that empty waves have to be understood as guiding the particle and being responsible for that kind of physically observable interference effects which, up to now, prohibit (or, at least cause a lot of struggle about) a satisfactory combination of relativity and quantum mechanics. According to de Broglie, there is not a dualism but a coexistence of particle and wave. The particle is guided by the phase ~ of the wave such that the particle's velocity is determined by v= - m - IV tp [3]. "On con~oit alors l'onde continue comme guidant le mouvement de la particule. C'est une onde pilote" [4], and there are "physical phenomena that seem to us unexplainable unless the idea of a permanent localization of the corpuscle is accepted" [ 5 ]. In virtue of this problem, it would be interesting to look for a observable action of empy waves, for instance whether these waves might be capable of inducing stimulated emission because this would not require energy or momentum transfer between wave and particle. Although it is beyond o u r present experimental facilities to do so with empty matter waves, a related effect can be investigated by means of common experimental equipment, namely stimulated photon emission in laser media induced by
0375-9601/88/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
387
Volume 127, number 8,9
PHYSICS LETTERS A
empty light waves. Empty light waves are not propagating with superluminal velocity, but effects induced by them may be expected from empty matter waves too. In analogy to massive particles photons can be described as wave packets, and it can be expected that these waves play a dominant role in inducing stimulated emission, if empty matter waves do. De Broglie and Andrade e Silva used the action of empty light waves to interprete an experiment by Pfleegor and Mandel [ 6 ] who observed interference between two different laser beams: "There exist interference fringes in the apparatus even if there is no photon that permits one to detect them" [7]. They arrived at a plausible interpretation. An observation supporting this line was reported by Blake and Scarl [8]. They found that there is (whithin 1 ns) no temporal correlation between an incident photon and a photon induced by this via the process of stimulated emission in a HeNe laser gain tube. Henoe, this process should be generated by the wave, rather than by the photon. In order to investigate this possible effect, it is sufficient to separate a part of the empty wave from the photons. This can be done in refractive media. For n(2), the index of refraction, and dn(X)/dg, its variation with the wavelength, the phase velocity cp of the waves and the group velocity co of the photons can be derived from eqs. (1), (2). Conveniently expressed as a function of the wavelength 2 we obtain (3)
cp = co/ n
14 March 1988
and co=cp(l+-2-~)n "
(4)
In media with normal dispersion d n / d ) t is negative. Therefore the empty waves propagate faster than the photons and can be separated via long distances, e.g. in quartz fibers. After passing through, the effect of the empty wave can be observed in a laser amplifier. Such an experiment has been performed.
2. Experiment The experimental set-up is shown in fig. 1. A dye laser, pumped by an excimer laser (EMG 103 MSC, FL 3002, Lambda Physik) produces pulses of 16 ns duration and 0.2 cm-~ bandwidth at 589 nm, the central wavelength of the dye Rhodamine 6G. Part of its output is directed onto the entrance of a 20 m long hard-clad silica fiber with 1 m m core-diameter (HCN-M 1000T-12, Laser Components) such that 0.1 mJ pulse energy arrives at the end of the fiber (specified attenuation of the fiber at this wavelenth is 20 dB/km). After leaving the fiber the pulse is used as a seed pulse for a dye laser amplifier, i.e. a 20 m m long dye cell pumped by an EMG 103 MSC excimer laser (of 20 ns pulse duration) 10 ns before the seed pulse arrives. 20m FIBER
A
B
BS
DYE CELL
k2
1
EXCIMER LASER
1
/PuMp
~AM
Fig. 1. Experimental arrangement. L: piano-convex lens, BS: beam splitter (quartz flat), A: attenuator, VA: variable attenuator, B: block, VB: variable block.
388
Volume 127, number 8,9
PHYSICS LETTERS A
The seed pulse had a divergence of ~ 5 ° when leaving the fiber. It was focused by a piano-convex lens and fed through the dye cell, the optical axis of which was tilted by ~ 10 ° with respect to the pulse direction, such that the super-fluorescence induced by the dye cell's windows did not interfere with the experiment. A small fraction of the pulse impinging onto a photodiode (FD 125 M 20 U V G 48, ITL) was recorded with an oscilloscope (7834, Tektronix). This measurement was performed when the dye cell was pumped and when the dye cell was not pumped. As the recorded energies with and without amplification were very different (10 p.J and 1.2 ~tJ, respectively), a variable attenuator was inserted into the beam path, in order to get comparable pulse heights at the oscilloscope. A possible time jitter of + 2 ns caused by the excimer laser pumping the dye laser was eliminated by directing a part of the seed pulse before entering the fiber onto the photodiode and utilizing its leading edge as trigger signal for the oscilloscope. A corresponding time jitter of the excimer laser pumping the amplifier dye cel was uncritical.
3. Analysis of data and result
14 March 1988
Fig. 2. Seed pulse without amplification in the dye cell (pump beam blocked). Time scale is 2 ns per small division.
look different. In particular, the leading part of the amplified pulse is pronounced. But this is a wellknown effect, related to gain depletion in the amplifier. The time difference at the lower part of the leading edges is about 0.3 ns. The experiment has been repeated 40 times, continuously switching between both alternatives. The result is a time difference At = 0.1 + 0.2 ns, which has to be compared to an expected value of At= 1.3 + 0.2 ns.
The time delay between trigger pulse and seed pulse was about 100 ns in accordance with the refractive index of fused silica n = 1.45845 [9] at 589 nm. From dn/d2= ( - 3 . 3 + 0 . 3 ) × 104 m - t , interpolated from ref. [ 9], it can be calculated that broadening of the seed pulse due to dispersion in the fiber is negligible ( < 1 ps) because of the narrow bandwidth. But the group velocity calculated according to (4) is 1.3% smaller than the phase velocity co/n. Hence, the photons propagating with cG should arrive by At= 1.3 +0.2 ns after the leading edge of the empty wave. If the latter were capable of inducing stimulated emission, this effect should be indicated by a corresponding time difference between the leading edges of the pure seed pulse (observed when the amplifier dye cell was not pumped) and the amplified seed pulse. Two pulses exhibiting maximum time difference are shown in figs. 2 and 3. Their intensities were attenuated to the same peak power. The pulse shapes
Hence, it can be excluded that empty photon waves induce stimulated emission in laser media.
Fig. 3. Amplified seed pulse. Same time scale as in fig. 2. Attenuation o f the variable attenuator increased by a factor of 10.
389
Volume 127, number 8,9
PHYSICS LETTERS A
References
[ 1 ] G. Lochak, De Broglies initial conception of de Broglie waves, in: The wave-particle dualism, eds. S. Diner et al. (Reidel, Dordrecht, 1984) p. 1. [2] F. Selleri, Gespensterfelder, in: The wave-particle dualism, eds. S. Diner et al. (Reidel, Dordrecht, 1984) p. 101. [3] L. de Broglie, J. Phys. Radium 20 (1959) 963. [4] L. de Broglie, J. Phys. Radium (VI) 8 (1927) 225.
390
14 March 1988
[5] L. de Broglie, G. Lochak, J.A. Beswick and J. VassaloPereira, Found. Phys. 6 (1976) 3. [ 6 ] R.L. Pfleegor and L. Mandel, Phys. Rev. 159 ( 1967 ) 1084. [7] L. de Broglie and J. Andrade e Silva, Phys. Rev. 172 (1968) 1284. [8] G.D. Blake and D. Scarl, Phys. Rev. A 19 (1979) 1948. [9] Handbook of chemistry and physics, 64th Ed. (CRC Press, Boca Raton, 1984) p. E-364.