- Email: [email protected]
Observation of the second harmonic generation pumped by microscopic to extraterrestrial incoherent light sources
Optics Communications 284 (2011) 5376–5380
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Observation of the second harmonic generation pumped by microscopic to extraterrestrial incoherent light sources Gintaras Tamošauskas ⁎ Department of Quantum Electronics, Vilnius University, Saulėtekio Ave. 9, Bldg. 3, LT10222 Vilnius, Lithuania
a r t i c l e
i n f o
Article history: Received 24 February 2011 Received in revised form 5 May 2011 Accepted 24 July 2011 Available online 6 August 2011
a b s t r a c t I report on the experimental demonstration of the second harmonic generation in bulk nonlinear crystals excited by light emitting diode, halogen lamp and the Sun. Practical application for measurement of autocorrelation functions of incoherent non-laser driven sources via second order nonlinearity is demonstrated for the first time. © 2011 Elsevier B.V. All rights reserved.
Keywords: Nonlinear optics Frequency conversion Harmonic generation Astronomical Space-research instrumentation Correlators
1. Introduction Recently optical community celebrated 50 years since the first laser was demonstrated in 1960 [1]. Development of coherent powerful source of light also stimulated the development of nonlinear optics and especially the one based on frequency conversions in crystals with second order nonlinearity. The very first experimental demonstration of the process was second harmonic generation in crystalline quartz published in 1961 [2]. Laser-based research of nonlinear optics was soon followed by attempts to implement incoherent sources for second harmonic, sum-frequency generation [3,4] and spontaneous parametric down-conversion [5]. Attempts of researches were focused on at least partial imitation of laser by incoherent sources. Atomic line emission sources and spatial spectra control were exploited in order to keep radiance and spectral radiance as high as possible, achieving parameters closer to the ones of the laser in both cases. Nevertheless these works did not find continuation and application for four decades. Lots of troubles were associated with low efficiency caused by extremely low spectral radiance of incoherent sources comparing with year-by-year improved lasers. Finally, ideas of incoherent excitation in contrast to laser use become inconsistent. Since that time only laser, laser initiated or stimulated
⁎ Tel.: + 370 5 2366023; fax: + 370 5 2366006. E-mail address: [email protected]. 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.07.056
emission (lasing media) sources were used for generation of the second harmonic. An important factor was also the absence of developed theoretical model for incoherent excitation, while, in contrast, all handbooks of nonlinear optics start with the definition of the pump of sinusoidal electromagnetic field. That is a direct attribute of highly coherent radiation. Decrease of the coherence of the pump is used for illustration of limitations and decreased process efficiency in handbooks. There is a well-developed theory and dozens of practical applications and scientific publications related to the process, published during half a century. Nevertheless, there is still no theory and practical application for second harmonic generation in nonlinear crystals excited by originally incoherent light sources. Present work relays on achievements made in experimental physics since the first attempts were made. A very important invention of CCD (charge coupled devices), from the point of view of light sensing, was made in 1971 [6]. It changed scientific methods dramatically and, for example, made a revolution in astronomy and high sensitivity microscopy. Present invention and its technological development took place when incoherent excitation in nonlinear optics had already lost its relevance. Recently, spontaneous parametric frequency down-conversion excited by the LED was investigated, showing high signal to noise contrast [7] as recorded with cooled CCD camera. While running that work, it was estimated that CW (continuous wave) signals resulted from the process with conversion efficiency as low as 10 − 15 could be recorded. The Hawking radiation detection [8] may also be an example of successful application of the CCD for recording signals from extremely low efficient nonlinear process.
G. Tamošauskas / Optics Communications 284 (2011) 5376–5380
On the other hand, it is not clear how efficient the process of second harmonic generation is and how to simulate frequency upconversion of incoherent radiation. The existing theory [4] cannot simulate truly both incoherent frequency and spatially broadband pump such as tungsten bulb lamp. Modern widely accepted theory [9] and existing experimental demonstration [3,4] suggest that efficient coupling of incoherent CW light into ordinary nonlinear crystal is complicated, if not impossible. This is determined by either narrow frequency-spatial acceptance of a centimeter-long crystal or undetectable power conversion in a few microns long crystal. Simulations of spatial and frequency bandwidths of incoherent pump exceeding acceptance bandwidths of the centimeter-long crystal by hundreds of times and phase noise of the pump are rather complicated. This might be the reason why attempts to develop a general theory were not made until recently [10]. These conditions resulted in the decision to investigate the second harmonic generation (which is a threshold-less process) of truly incoherent CW sources experimentally, omitting theoretical analysis. The aim of the present work is to demonstrate well detectable generation of the second harmonic by various incoherent continuous wave sources in order to renew interest in this area of nonlinear optics. Practical application for adoption and development of correlation type [11] light characterization methods utilizing nonlinear transformations of incoherent light in bulk crystals are discussed and supported by demonstration of second order intensity autocorrelation measurements. Progress in this field may be important taking into account that majority of natural and artificial light sources are non-lasing incoherent. 2. Second harmonic generation Three different continuous wave sources of light were chosen for investigation: infrared light emitting diode (LED), halogen lamp and the Sun. All sources emit near infrared, therefore, second harmonics are expected to be in green-blue visible area. Mass production LED SFH4550 consists of miniature light emitting object with 300 μm edge
L1
length, relatively narrow emission bandwidth of 42 nm and low power. Original plastic collimator of the LED was polished out to decrease spherical distortions. Halogen lamp (Halostar 64440 S from OSRAM GmbH) is probably the best available analog to black body emission in the near infrared. The Sun is of highest spectral radiance among the used sources and its distant location makes it attractive for demonstration purpose. Named sources, compared to lasers, are of low spectral radiance and, for example, milliwatt laser exceeds them by a few orders of magnitude. These sources demonstrate a large variety of incoherent emitters available for investigation. The presented results were obtained by using mobile experimental setup designed to be capable to record the second harmonic generation of the introduced light sources. Simplified scheme of the setup for measurements of the Sun are presented in Fig. 1a and photo Fig. 1c. Setup consisted of objective L1 (different for various investigated sources), long wave pass filter F1, nonlinear crystal mounted on the rotation stage, long wave cut-off filter F2, imaging optics L2 and CCD camera ANDOR iDus420-OE as a light sensor. Reflection of the pump from the filter F2 is send to the guiding camera which is focused at the center of the nonlinear crystal. Guiding camera was used to visualize position of the light source and record images at approximately 0.9 μm wavelength shown in Fig. 2 a, c, e. Detection band approximately from 390 nm to 550 nm was set by filter F2 made of two blue glass filters CЗC-21 of 1.5 mm thickness and CЗC-22 of 2.5 mm thickness mounted at a 45° angle to the incident beam and transmittance of optics L2. The pump band of 0.73-1.2 μm was formed by the filter F1 made of two RG715 glass filters of 3 mm thickness mounted at a 45° angle to incident beam from the short wave side and the limit of reflection of the mirror M1 from the long wave side. Two nonlinear crystals were used. Most of the results were obtained using Lithium Iodate (LiIO3) crystal. Potassium Dihydrogen Phosphate (KDP) crystal was used for comparative measurements. Both crystals were 20 mm long and cut for Type I (o — ordinary polarized pump and e — extraordinary polarized second harmonic) interaction. Average wavelength acceptance bandwidth for the coherent second harmonic generation in the LiIO3 crystal is 0.45 nm and 5.3 nm in KDP. The setup worked as follows: objective imaged an object into the crystal where
Light source
a F1
Nonlinear crystal F2
L2
M2 Guiding camera
BS F1
Nonlinear crystal
F2
300 m
c
0
d
L2
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10
1 mm
e
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30 20
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c
0.8
0.4
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b
b
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f
200
Photoelectrons/s mm2 x1000
M1
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L1 100
CCD camera Guiding camera
Fig. 1. Simplified scheme of experimental setup: for second harmonic generation (a); modification for recording of autocorrelation traces (b); and photo of the setup (c).
106 km
0
Fig. 2. Images recorded in infrared by the guiding camera of the LED (a), halogen lamp (c) and the Sun (e). Second harmonic images of the LED (b), halogen lamp (d) and the Sun (f) recorded within 16 × 14 mm LiIO3 crystal area. Color bars indicate number of photoelectrons per second excited by the second harmonic radiation emitted from 1 mm2 area of the crystal.
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frequency doubling appeared, and newly generated radiation was imaged onto the CCD sensor. Such double imaging technique allowed not only to record the fact of frequency conversion, but also produced second harmonic images of the light emitting objects in acceptable quality. The main results of measured signal up-conversion are shown in Fig. 2. Images of the second harmonic, generated in LiIO3 crystal pumped by the LED, halogen lamp and the Sun (Fig. 2 b, d, f) are 16 × 14 mm in size. Spatial bandwidth of the pump is 0.05 rad for the LED, 0.14 rad for the halogen lamp and 0.04 rad for the Sun. Color bars indicate the number of photoelectrons per second excited by light emitted from 1 mm 2 area of the crystal recorded with approximately 25% quantum efficiency of detection. Images of the second harmonic are blurred in θ plane due to the spatial walk-off of the e polarized wave caused by the birefringence of the crystal. Second harmonic images, including the one made with only a few milliwatts power from the LED, are of similar shape as the images are recorded in infrared by the guiding camera and well recognizable. The presence of the second harmonic well recordable signal with pump irradiance of incoherent light well below 1 W/cm 2 is a promising result for application. Measurements of the Sun were performed by mounting optical-mechanical setup on an amateur altitude-azimuth astronomical mount. Sunlight, as the most powerful used, produced the strongest second harmonic signal (see Fig. 2f and 3). Power conversion efficiency is in order of 10− 11 (3· 10− 12 for the LED, 4.9 · 10 − 12 for the halogen lamp and 2.4 · 10− 11 for the Sun), but still can be effectively recorded with modern equipment. There are several experimental facts to prove that observed radiation is namely the second harmonic and not the other type of radiation. First of all, measurements without the crystal were performed and no light of similar power passing through optical filters was observed. Filters F1 and F2 provide sufficient power attenuation of straight light down to 5 · 10 − 15 as measured with halogen lamp. Also, the signal obtained in the crystal strongly depends on the polarization of the pump and can be canceled by rotating film polarizer mounted after the objective. This complies with the requirement of o polarized pump for Type I interaction. Also the power of the signal depends on nonlinear crystal orientation in phase matching θ plane. The narrow spatial spectrum of the signal excited by the LED was recorded by mounting the crystal close to the second lens L2 and placing CCD camera in the focal plane. This result confirmed that obtained signal was not a multi-photon absorption fluorescence with random directivity pattern. Finally, Raman anti-stokes generation should be excluded due to several reasons mentioned above. 10
10
7
The Sun (LiIO3) 6
Photoelectrons/s
2
y~x 10
10
10
10
Halogen lamp (LiIO3)
5
4
LED (LiIO3) Halogen lamp (KDP)
3
2
1
10
100
1000
Pump power,m W Fig. 3. Second harmonic signal dependence on pump power as recorded with various sources in LiIO3 (the Sun ■; halogen lamp ○; LED □) and KDP (halogen lamp ◊) crystals.
Listed arguments confirm that only the second harmonic generation occurred. Main properties of the second harmonic radiation excited by incoherent light source can be described in addition to the generation as experimental fact alone. Dependence of the second harmonic signal on pump power of halogen lamp, which was attenuated by neutral density glass filters, is presented in Fig. 3. LiIO3 and KDP crystals show good agreement with the second order dependence (lines in Fig. 3) on the pump power. The LED provided relatively the highest conversion efficiency compared to other sources taking into account lowest power and irradiance. This could be caused by narrow wavelength spectrum which relatively increases spectral radiance. Second harmonic conversion efficiency for the halogen lamp pump depends almost linearly on crystal length as recorded with various length KDP crystals starting from 4 mm up to 40 mm. An example of simplified numerical simulation for LiIO3 crystal was made to compare how a simple model based on theory of coherently pumped second harmonic generation matches experimental results. The pump was split into portions that cover frequency and spatial acceptance bandwidth for the second harmonic generation of the nonlinear crystal. It was assumed that each such part of the pump radiation could be treated as a coherent pump. However, this might not be very correct. Each such portion of the pump acts independently in second harmonics generation. The second harmonics are produced individually and assumed to be of random phases due to incoherent pump. Overall result is obtained by summing second harmonics power produced by all phase matched spatial portions of the pump. The present model utilizes only collinear second harmonic generation. Conversion efficiency obtained is approximately 105 times less than in the experiment. Conclusion can be made that frequency upconversion of an incoherent source is a complex process where second harmonics and all possible phase matched combinations of sum frequency generation at collinear and all possible combinations of non-collinear interactions take place simultaneously as predicted in the newly developed model [10]. The present simulation utilizes only a small part of all combinations, therefore difference with experiment is huge.
3. Practical application and discussion The benefit of the present work compared to the one made four decades earlier [3] is a demonstration of new possibilities to extend existing light characterization techniques, primary developed for coherent sources, for characterization of originally incoherent ones without laser use for boosting power of source. This is the only way to investigate distant light and properties of non-optically pumped sources. Practical application in metrology and astronomy may be expected as a result. Mixing of non-intense light of incoherent source with the light of one or a few powerful coherent sources might increase efficiency of the process and enhance visibility of the frequency up-converted incoherent radiation [12]. In addition to the awaited enhancement in power of the sum-frequency compared to the second harmonic, there may also be other benefits. Such design would have many similarities with popular ultra-short pulse shape and phase reconstructing cross-correlation method FROG (Frequency Resolved Optical Gating) [11], where investigated pulse is mixed with the reference pulse. Almost identical method may be used in Optical Frequency Comb [13] applications where nonlinear frequency mixing with incoherent sources may extend its use in spectroscopy and astronomy. There are various correlation techniques based on nonlinear frequency conversion developed for characterization of light pulses [11,14]. Lots of them might be adopted for characterization of incoherent sources if only nonlinear conversion could be realized. Attempts were made to demonstrate this possibility in real application.
G. Tamošauskas / Optics Communications 284 (2011) 5376–5380
a
2
1
0
2.5
to theoretically determined. Peak to background ratio of 4 times is seen in Fig. 4c in the numerically constructed autocorrelations of the incoherent radiation. Difference in peak to background ratios can be explained by different natures of the pump sources — coherent and incoherent. Coherent laser radiation consists of multiple longitudinal modes whose phases are locked. Therefore, they form periodic peaks and minimums as a result of beatings which are visible as pulsation of the laser radiation. Situation, when the delay difference in arms of the interferometer is such that the peak of one arm coincides with the minimum of the other, corresponds to steady background signal. Power produced by the nonlinear crystal, pumped by two noninteracting pulses from two arms of the interferometer, is eight times less compared to the case when the pulses coincide at the output of interferometer. Due to constructive interference, they produce four times higher intensity, compared to nonintersecting pulses. Both discussed models for incoherent radiation — of constant power beam and of intensity fluctuations, turn to the same result. Two beams of constant power, which overlap at the output of the interferometer, when the delay difference is much larger compared to the coherence time, are sent to the nonlinear crystal. It is obvious that power produced by nonlinear crystal is relatively twice as much as in the case of split and non-interacting pulses of the coherent radiation. As a result, peak to background ratio of the autocorrelation function decreases twice for incoherent radiation. The same is obtained for the model of intensity fluctuations because incoherent radiation of random phases does not produce periodic beatings and there is no such situation when the signal goes down or up on a certain delay. Chaotic beatings average over measurement time, which is much larger than coherence time, leading to the same result as discussed previously. Three ranges can be defined for this ratio: below two — nonlinear process may not be involved and possibly only first order autocorrelation may take place; above two and below four — nonlinear process takes place, range available for coherent and incoherent radiation; above four indicates coherent radiation. Values close to four for incoherent and to eight for coherent radiation affirm a dominant second order process in the formation of the traces. A peak to background ratio of four is not achieved in the experiment, indicating the imperfection of the present design. Results of the halogen lamp and the Sun measurements are similar to each other as can be expected from the sources of similar spectra, but both differ a lot from the numerically constructed one. Although the demonstration was made, some difficulties still exist in precise interpretation. A second order autocorrelation function is assumed to be determined only by investigated signal. All spectral components of the signal should be equally transformed by a utilized nonlinear process. Otherwise, the magnitude of induced distortions can be estimated by analyzing imperfections of transformation. It is impossible to estimate the level of imperfection as well as to determine conditions for undistorted transformation because theory of incoherent light second harmonic generation is under development [10], therefore extended analysis is omitted. Despite the discussed drawbacks of present example, its main result is demonstration that 4
b
Normalized amplitude
3
Normalized amplitude
Normalized amplitude
The second order intensity autocorrelation measurement technique was chosen for demonstration purposes as the simplest one not requiring an assistant radiation. Existing application for lasing media measurement [15] may be an example of technique success in characterization of the source of low coherence. Experimental setup was modified by replacing mirror M2 with Michelson interferometer as shown in Fig. 1b. Broadband dielectric coating beam splitter BS is effective in all utilized spectral range. The setup did not achieve real interferometric quality because of long exposures and limited mechanical quality as a result of mobile design of the setup. Little attention was paid to precision, as the present measurement was not intended to produce new scientific data unavailable by other techniques. Autocorrelations of the Sun (Fig. 4a) and halogen lamp (its spatial spectrum was filtered down to the similar value as of the Sun) (Fig. 4b) were recorded using LiIO3 crystal oriented at θ = 35°. Autocorrelation of the LED was not recorded because the existing setup cannot deliver sufficient long-term interferometric stability required for detection of autocorrelation of such a weak pump. Experimental points represent normalized number of photoelectron (constant level at long delays normalized to one) counted over entire object image area. Three points at each delay are collected for the Sun as respond to slight wandering of the image. Unlike it was awaited from the second order function, the present autocorrelation traces lack of symmetry in time and suffer mainly from broad spatial spectra of sources, as well as from limited optical and mechanical interferometer quality. Autocorrelation of Gaussian function is shown as grey background for eye guide only. Peaks of recorded traces have constructive and destructive changes in magnitude similar to what can be expected from the autocorrelation process, as can be seen in comparison with the guide. The peak amplitude of the experimental traces exceed steady signal level by more than two times indicating that nonlinear process is involved in the formation of the traces. Two interpretations of the measurement's result may take place. One is that the trace is interferogram squared in amplitude due to nonlinear conversion if the measured light is treated as constant power and finite coherence time. The other is that the recorded trace is superposition of autocorrelation traces of power fluctuations, like for pulses, if to treat incoherent light consisting of power fluctuations predetermined by frequency spectra with certain phase relations. Both interference pattern and fluctuation statistics are functions of only source bandwidth in case of a random phase source such as thermal radiation. Second order autocorrelation traces for source of plane waves with random phases were numerically constructed by both methods (Fig. 4c) and they are undistinguishable, therefore either interpretationsare equally valid for the present case. The laser pulse measurement oriented theory of interferometric second order autocorrelation (see for example [11] pp. 84-88 and references therein) predicts 8 times ratio of the peak of the autocorrelation function to the steady background. Such ratio is obtained when phases of longitudinal modes of the source are locked. This value is used as the indicator of correctness of the measurements and it is required that the measured ratio would be as close as possible
2 1.5 1 0.5 0
-50
-25
0
Delay, fs
25
50
-40
5379
-20
0
Delay, fs
20
40
c
3 2 1 0 -40
-20
0
20
40
Delay, fs
Fig. 4. Autocorrelation traces of the Sun (a) and halogen lamp (b) recorded in LiIO3 crystal. Numerically constructed second order autocorrelation trace (c).
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autocorrelation type measurements of incoherent light can be realized utilizing bulk crystals with second order nonlinearity for nonlinear transformations. Further research is needed in order to develop this and other potentially adoptable techniques up to the level of scientific instruments. Some sources are known to show higher conversion efficiency at low irradiance [16,17] and that may increase contrast over background radiation of, for instance, natural pure biphoton [18] sources. Some complex radiation sources, such as Cherenkov radiation [19] that emerge as bursts of light of specific directivity, wavelength and duration, may produce higher second harmonic signal and leave specific correlation traces, although this is not proved. Theoretical and experimental researches should be carried out to achieve real progress in applications capable to produce new data unavailable by other methods. Finally, an easily obtainable second harmonic image itself represents a peak of the second order autocorrelation, which can also be useful for analysis. Progress in generation of the second harmonic using incoherent sources may be expected not only in visible — near infrared electromagnetic wave region, but also in far infrared and terahertz region where newly developed metamaterials offer great progress in the near future [20]. This might be of interest for investigation of Space by means of measurements of spatial and time correlations, including high resolution phase resolving due to short wavelength and instant response of the nonlinear transformation. 4. Conclusion In conclusion, generation of well detectable second harmonic of continuous wave incoherent sources starting from microscopic size LED chip up to distant object such as the Sun was demonstrated. As a
result, intensity dependent nonlinear optics in crystals with second order nonlinearity, thanks to capabilities of modern experimental equipment, is downgraded from the strong field science usually associated with lasers to nonlinear process available with any light source. Present results are auspicious for a class of applications where new methods may be implemented for characterization of light sources beyond coherent ones and highly powerful laser initiated sources by means of direct correlation type measurements.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20]
T.H. Maiman, Nature 187 (1960) 493. P.A. Franken, A.E. Hill, C.W. Peters, G. Weinreich, Phys. Rev. Lett. 7 (1961) 118. D.H. McMahon, A.R. Franklin, J. Appl. Phys. 36 (1965) 2073. D.H. McMahon, J. Appl. Phys. 37 (1966) 4832. D.L. Weinberg, J. Appl. Phys. 41 (1970) 4239. M.F. Tompsett, G.F. Amelio, W.J. Bertram Jr., R.R. Buckley, W.J. McNamara, J.C. Mikkelsen Jr., D.A. Sealer, IEEE Trans. Electron Devices 18 (1971) 992. G. Tamošauskas, J. Galinis, A. Dubietis, A. Piskarskas, Opt. Express 18 (2010) 4310. F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V.G. Sala, D. Faccio, Phys. Rev. Lett. 105 (2010) 203901-1–203901-4. R.L. Sutherland, Handbook of nonlinear optics, second ed., Marcel Dekker, Inc., New York, 2003, p. 33. A. Stabinis, V. Pyragaitė, G. Tamošauskas, A. Piskarskas, unpublished results. R. Trebino, Frequency Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses, Kluver Academic Press, Boston, 2002. J. Midwinter, Appl. Phys. Lett. 12 (1968) 68. T.W. Hänsch, Rev. Mod. Phys. 78 (2006) 1297. G. Steinmeyer, J. Opt. A: Pure Appl. Opt. 5 (2003) R1. A.J. Bain, A. Squire, Opt. Commun. 135 (1997) 157. V.M. Petnikova, Sov. J. Quantum Electron. 9 (1979) 276. B. Dayan, A. Pe'er, A.A. Friesem, Y. Silberberg, Phys. Rev. Lett. 94 (2005) 043602-1– 043602-3. J. Gomez, A. Peimbert, J. Echevarria, Rev. Mex. Astron. Astrofis. 45 (2009) 279. M.F. Cawley, T.C. Weekes, Exp. Astron. 6 (1995) 7. M.W. Klein, Ch. Enkrich, M. Wegener, S. Linden, Science 313 (2006) 502.
Contents lists available at ScienceDirect
Optics Communications j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / o p t c o m
Observation of the second harmonic generation pumped by microscopic to extraterrestrial incoherent light sources Gintaras Tamošauskas ⁎ Department of Quantum Electronics, Vilnius University, Saulėtekio Ave. 9, Bldg. 3, LT10222 Vilnius, Lithuania
a r t i c l e
i n f o
Article history: Received 24 February 2011 Received in revised form 5 May 2011 Accepted 24 July 2011 Available online 6 August 2011
a b s t r a c t I report on the experimental demonstration of the second harmonic generation in bulk nonlinear crystals excited by light emitting diode, halogen lamp and the Sun. Practical application for measurement of autocorrelation functions of incoherent non-laser driven sources via second order nonlinearity is demonstrated for the first time. © 2011 Elsevier B.V. All rights reserved.
Keywords: Nonlinear optics Frequency conversion Harmonic generation Astronomical Space-research instrumentation Correlators
1. Introduction Recently optical community celebrated 50 years since the first laser was demonstrated in 1960 [1]. Development of coherent powerful source of light also stimulated the development of nonlinear optics and especially the one based on frequency conversions in crystals with second order nonlinearity. The very first experimental demonstration of the process was second harmonic generation in crystalline quartz published in 1961 [2]. Laser-based research of nonlinear optics was soon followed by attempts to implement incoherent sources for second harmonic, sum-frequency generation [3,4] and spontaneous parametric down-conversion [5]. Attempts of researches were focused on at least partial imitation of laser by incoherent sources. Atomic line emission sources and spatial spectra control were exploited in order to keep radiance and spectral radiance as high as possible, achieving parameters closer to the ones of the laser in both cases. Nevertheless these works did not find continuation and application for four decades. Lots of troubles were associated with low efficiency caused by extremely low spectral radiance of incoherent sources comparing with year-by-year improved lasers. Finally, ideas of incoherent excitation in contrast to laser use become inconsistent. Since that time only laser, laser initiated or stimulated
⁎ Tel.: + 370 5 2366023; fax: + 370 5 2366006. E-mail address: [email protected]. 0030-4018/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2011.07.056
emission (lasing media) sources were used for generation of the second harmonic. An important factor was also the absence of developed theoretical model for incoherent excitation, while, in contrast, all handbooks of nonlinear optics start with the definition of the pump of sinusoidal electromagnetic field. That is a direct attribute of highly coherent radiation. Decrease of the coherence of the pump is used for illustration of limitations and decreased process efficiency in handbooks. There is a well-developed theory and dozens of practical applications and scientific publications related to the process, published during half a century. Nevertheless, there is still no theory and practical application for second harmonic generation in nonlinear crystals excited by originally incoherent light sources. Present work relays on achievements made in experimental physics since the first attempts were made. A very important invention of CCD (charge coupled devices), from the point of view of light sensing, was made in 1971 [6]. It changed scientific methods dramatically and, for example, made a revolution in astronomy and high sensitivity microscopy. Present invention and its technological development took place when incoherent excitation in nonlinear optics had already lost its relevance. Recently, spontaneous parametric frequency down-conversion excited by the LED was investigated, showing high signal to noise contrast [7] as recorded with cooled CCD camera. While running that work, it was estimated that CW (continuous wave) signals resulted from the process with conversion efficiency as low as 10 − 15 could be recorded. The Hawking radiation detection [8] may also be an example of successful application of the CCD for recording signals from extremely low efficient nonlinear process.
G. Tamošauskas / Optics Communications 284 (2011) 5376–5380
On the other hand, it is not clear how efficient the process of second harmonic generation is and how to simulate frequency upconversion of incoherent radiation. The existing theory [4] cannot simulate truly both incoherent frequency and spatially broadband pump such as tungsten bulb lamp. Modern widely accepted theory [9] and existing experimental demonstration [3,4] suggest that efficient coupling of incoherent CW light into ordinary nonlinear crystal is complicated, if not impossible. This is determined by either narrow frequency-spatial acceptance of a centimeter-long crystal or undetectable power conversion in a few microns long crystal. Simulations of spatial and frequency bandwidths of incoherent pump exceeding acceptance bandwidths of the centimeter-long crystal by hundreds of times and phase noise of the pump are rather complicated. This might be the reason why attempts to develop a general theory were not made until recently [10]. These conditions resulted in the decision to investigate the second harmonic generation (which is a threshold-less process) of truly incoherent CW sources experimentally, omitting theoretical analysis. The aim of the present work is to demonstrate well detectable generation of the second harmonic by various incoherent continuous wave sources in order to renew interest in this area of nonlinear optics. Practical application for adoption and development of correlation type [11] light characterization methods utilizing nonlinear transformations of incoherent light in bulk crystals are discussed and supported by demonstration of second order intensity autocorrelation measurements. Progress in this field may be important taking into account that majority of natural and artificial light sources are non-lasing incoherent. 2. Second harmonic generation Three different continuous wave sources of light were chosen for investigation: infrared light emitting diode (LED), halogen lamp and the Sun. All sources emit near infrared, therefore, second harmonics are expected to be in green-blue visible area. Mass production LED SFH4550 consists of miniature light emitting object with 300 μm edge
L1
length, relatively narrow emission bandwidth of 42 nm and low power. Original plastic collimator of the LED was polished out to decrease spherical distortions. Halogen lamp (Halostar 64440 S from OSRAM GmbH) is probably the best available analog to black body emission in the near infrared. The Sun is of highest spectral radiance among the used sources and its distant location makes it attractive for demonstration purpose. Named sources, compared to lasers, are of low spectral radiance and, for example, milliwatt laser exceeds them by a few orders of magnitude. These sources demonstrate a large variety of incoherent emitters available for investigation. The presented results were obtained by using mobile experimental setup designed to be capable to record the second harmonic generation of the introduced light sources. Simplified scheme of the setup for measurements of the Sun are presented in Fig. 1a and photo Fig. 1c. Setup consisted of objective L1 (different for various investigated sources), long wave pass filter F1, nonlinear crystal mounted on the rotation stage, long wave cut-off filter F2, imaging optics L2 and CCD camera ANDOR iDus420-OE as a light sensor. Reflection of the pump from the filter F2 is send to the guiding camera which is focused at the center of the nonlinear crystal. Guiding camera was used to visualize position of the light source and record images at approximately 0.9 μm wavelength shown in Fig. 2 a, c, e. Detection band approximately from 390 nm to 550 nm was set by filter F2 made of two blue glass filters CЗC-21 of 1.5 mm thickness and CЗC-22 of 2.5 mm thickness mounted at a 45° angle to the incident beam and transmittance of optics L2. The pump band of 0.73-1.2 μm was formed by the filter F1 made of two RG715 glass filters of 3 mm thickness mounted at a 45° angle to incident beam from the short wave side and the limit of reflection of the mirror M1 from the long wave side. Two nonlinear crystals were used. Most of the results were obtained using Lithium Iodate (LiIO3) crystal. Potassium Dihydrogen Phosphate (KDP) crystal was used for comparative measurements. Both crystals were 20 mm long and cut for Type I (o — ordinary polarized pump and e — extraordinary polarized second harmonic) interaction. Average wavelength acceptance bandwidth for the coherent second harmonic generation in the LiIO3 crystal is 0.45 nm and 5.3 nm in KDP. The setup worked as follows: objective imaged an object into the crystal where
Light source
a F1
Nonlinear crystal F2
L2
M2 Guiding camera
BS F1
Nonlinear crystal
F2
300 m
c
0
d
L2
Delay
M1
10
1 mm
e
Crystal location
30 20
CCD camera
c
0.8
0.4
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b
b
0
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Fig. 2. Images recorded in infrared by the guiding camera of the LED (a), halogen lamp (c) and the Sun (e). Second harmonic images of the LED (b), halogen lamp (d) and the Sun (f) recorded within 16 × 14 mm LiIO3 crystal area. Color bars indicate number of photoelectrons per second excited by the second harmonic radiation emitted from 1 mm2 area of the crystal.
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frequency doubling appeared, and newly generated radiation was imaged onto the CCD sensor. Such double imaging technique allowed not only to record the fact of frequency conversion, but also produced second harmonic images of the light emitting objects in acceptable quality. The main results of measured signal up-conversion are shown in Fig. 2. Images of the second harmonic, generated in LiIO3 crystal pumped by the LED, halogen lamp and the Sun (Fig. 2 b, d, f) are 16 × 14 mm in size. Spatial bandwidth of the pump is 0.05 rad for the LED, 0.14 rad for the halogen lamp and 0.04 rad for the Sun. Color bars indicate the number of photoelectrons per second excited by light emitted from 1 mm 2 area of the crystal recorded with approximately 25% quantum efficiency of detection. Images of the second harmonic are blurred in θ plane due to the spatial walk-off of the e polarized wave caused by the birefringence of the crystal. Second harmonic images, including the one made with only a few milliwatts power from the LED, are of similar shape as the images are recorded in infrared by the guiding camera and well recognizable. The presence of the second harmonic well recordable signal with pump irradiance of incoherent light well below 1 W/cm 2 is a promising result for application. Measurements of the Sun were performed by mounting optical-mechanical setup on an amateur altitude-azimuth astronomical mount. Sunlight, as the most powerful used, produced the strongest second harmonic signal (see Fig. 2f and 3). Power conversion efficiency is in order of 10− 11 (3· 10− 12 for the LED, 4.9 · 10 − 12 for the halogen lamp and 2.4 · 10− 11 for the Sun), but still can be effectively recorded with modern equipment. There are several experimental facts to prove that observed radiation is namely the second harmonic and not the other type of radiation. First of all, measurements without the crystal were performed and no light of similar power passing through optical filters was observed. Filters F1 and F2 provide sufficient power attenuation of straight light down to 5 · 10 − 15 as measured with halogen lamp. Also, the signal obtained in the crystal strongly depends on the polarization of the pump and can be canceled by rotating film polarizer mounted after the objective. This complies with the requirement of o polarized pump for Type I interaction. Also the power of the signal depends on nonlinear crystal orientation in phase matching θ plane. The narrow spatial spectrum of the signal excited by the LED was recorded by mounting the crystal close to the second lens L2 and placing CCD camera in the focal plane. This result confirmed that obtained signal was not a multi-photon absorption fluorescence with random directivity pattern. Finally, Raman anti-stokes generation should be excluded due to several reasons mentioned above. 10
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Listed arguments confirm that only the second harmonic generation occurred. Main properties of the second harmonic radiation excited by incoherent light source can be described in addition to the generation as experimental fact alone. Dependence of the second harmonic signal on pump power of halogen lamp, which was attenuated by neutral density glass filters, is presented in Fig. 3. LiIO3 and KDP crystals show good agreement with the second order dependence (lines in Fig. 3) on the pump power. The LED provided relatively the highest conversion efficiency compared to other sources taking into account lowest power and irradiance. This could be caused by narrow wavelength spectrum which relatively increases spectral radiance. Second harmonic conversion efficiency for the halogen lamp pump depends almost linearly on crystal length as recorded with various length KDP crystals starting from 4 mm up to 40 mm. An example of simplified numerical simulation for LiIO3 crystal was made to compare how a simple model based on theory of coherently pumped second harmonic generation matches experimental results. The pump was split into portions that cover frequency and spatial acceptance bandwidth for the second harmonic generation of the nonlinear crystal. It was assumed that each such part of the pump radiation could be treated as a coherent pump. However, this might not be very correct. Each such portion of the pump acts independently in second harmonics generation. The second harmonics are produced individually and assumed to be of random phases due to incoherent pump. Overall result is obtained by summing second harmonics power produced by all phase matched spatial portions of the pump. The present model utilizes only collinear second harmonic generation. Conversion efficiency obtained is approximately 105 times less than in the experiment. Conclusion can be made that frequency upconversion of an incoherent source is a complex process where second harmonics and all possible phase matched combinations of sum frequency generation at collinear and all possible combinations of non-collinear interactions take place simultaneously as predicted in the newly developed model [10]. The present simulation utilizes only a small part of all combinations, therefore difference with experiment is huge.
3. Practical application and discussion The benefit of the present work compared to the one made four decades earlier [3] is a demonstration of new possibilities to extend existing light characterization techniques, primary developed for coherent sources, for characterization of originally incoherent ones without laser use for boosting power of source. This is the only way to investigate distant light and properties of non-optically pumped sources. Practical application in metrology and astronomy may be expected as a result. Mixing of non-intense light of incoherent source with the light of one or a few powerful coherent sources might increase efficiency of the process and enhance visibility of the frequency up-converted incoherent radiation [12]. In addition to the awaited enhancement in power of the sum-frequency compared to the second harmonic, there may also be other benefits. Such design would have many similarities with popular ultra-short pulse shape and phase reconstructing cross-correlation method FROG (Frequency Resolved Optical Gating) [11], where investigated pulse is mixed with the reference pulse. Almost identical method may be used in Optical Frequency Comb [13] applications where nonlinear frequency mixing with incoherent sources may extend its use in spectroscopy and astronomy. There are various correlation techniques based on nonlinear frequency conversion developed for characterization of light pulses [11,14]. Lots of them might be adopted for characterization of incoherent sources if only nonlinear conversion could be realized. Attempts were made to demonstrate this possibility in real application.
G. Tamošauskas / Optics Communications 284 (2011) 5376–5380
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to theoretically determined. Peak to background ratio of 4 times is seen in Fig. 4c in the numerically constructed autocorrelations of the incoherent radiation. Difference in peak to background ratios can be explained by different natures of the pump sources — coherent and incoherent. Coherent laser radiation consists of multiple longitudinal modes whose phases are locked. Therefore, they form periodic peaks and minimums as a result of beatings which are visible as pulsation of the laser radiation. Situation, when the delay difference in arms of the interferometer is such that the peak of one arm coincides with the minimum of the other, corresponds to steady background signal. Power produced by the nonlinear crystal, pumped by two noninteracting pulses from two arms of the interferometer, is eight times less compared to the case when the pulses coincide at the output of interferometer. Due to constructive interference, they produce four times higher intensity, compared to nonintersecting pulses. Both discussed models for incoherent radiation — of constant power beam and of intensity fluctuations, turn to the same result. Two beams of constant power, which overlap at the output of the interferometer, when the delay difference is much larger compared to the coherence time, are sent to the nonlinear crystal. It is obvious that power produced by nonlinear crystal is relatively twice as much as in the case of split and non-interacting pulses of the coherent radiation. As a result, peak to background ratio of the autocorrelation function decreases twice for incoherent radiation. The same is obtained for the model of intensity fluctuations because incoherent radiation of random phases does not produce periodic beatings and there is no such situation when the signal goes down or up on a certain delay. Chaotic beatings average over measurement time, which is much larger than coherence time, leading to the same result as discussed previously. Three ranges can be defined for this ratio: below two — nonlinear process may not be involved and possibly only first order autocorrelation may take place; above two and below four — nonlinear process takes place, range available for coherent and incoherent radiation; above four indicates coherent radiation. Values close to four for incoherent and to eight for coherent radiation affirm a dominant second order process in the formation of the traces. A peak to background ratio of four is not achieved in the experiment, indicating the imperfection of the present design. Results of the halogen lamp and the Sun measurements are similar to each other as can be expected from the sources of similar spectra, but both differ a lot from the numerically constructed one. Although the demonstration was made, some difficulties still exist in precise interpretation. A second order autocorrelation function is assumed to be determined only by investigated signal. All spectral components of the signal should be equally transformed by a utilized nonlinear process. Otherwise, the magnitude of induced distortions can be estimated by analyzing imperfections of transformation. It is impossible to estimate the level of imperfection as well as to determine conditions for undistorted transformation because theory of incoherent light second harmonic generation is under development [10], therefore extended analysis is omitted. Despite the discussed drawbacks of present example, its main result is demonstration that 4
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The second order intensity autocorrelation measurement technique was chosen for demonstration purposes as the simplest one not requiring an assistant radiation. Existing application for lasing media measurement [15] may be an example of technique success in characterization of the source of low coherence. Experimental setup was modified by replacing mirror M2 with Michelson interferometer as shown in Fig. 1b. Broadband dielectric coating beam splitter BS is effective in all utilized spectral range. The setup did not achieve real interferometric quality because of long exposures and limited mechanical quality as a result of mobile design of the setup. Little attention was paid to precision, as the present measurement was not intended to produce new scientific data unavailable by other techniques. Autocorrelations of the Sun (Fig. 4a) and halogen lamp (its spatial spectrum was filtered down to the similar value as of the Sun) (Fig. 4b) were recorded using LiIO3 crystal oriented at θ = 35°. Autocorrelation of the LED was not recorded because the existing setup cannot deliver sufficient long-term interferometric stability required for detection of autocorrelation of such a weak pump. Experimental points represent normalized number of photoelectron (constant level at long delays normalized to one) counted over entire object image area. Three points at each delay are collected for the Sun as respond to slight wandering of the image. Unlike it was awaited from the second order function, the present autocorrelation traces lack of symmetry in time and suffer mainly from broad spatial spectra of sources, as well as from limited optical and mechanical interferometer quality. Autocorrelation of Gaussian function is shown as grey background for eye guide only. Peaks of recorded traces have constructive and destructive changes in magnitude similar to what can be expected from the autocorrelation process, as can be seen in comparison with the guide. The peak amplitude of the experimental traces exceed steady signal level by more than two times indicating that nonlinear process is involved in the formation of the traces. Two interpretations of the measurement's result may take place. One is that the trace is interferogram squared in amplitude due to nonlinear conversion if the measured light is treated as constant power and finite coherence time. The other is that the recorded trace is superposition of autocorrelation traces of power fluctuations, like for pulses, if to treat incoherent light consisting of power fluctuations predetermined by frequency spectra with certain phase relations. Both interference pattern and fluctuation statistics are functions of only source bandwidth in case of a random phase source such as thermal radiation. Second order autocorrelation traces for source of plane waves with random phases were numerically constructed by both methods (Fig. 4c) and they are undistinguishable, therefore either interpretationsare equally valid for the present case. The laser pulse measurement oriented theory of interferometric second order autocorrelation (see for example [11] pp. 84-88 and references therein) predicts 8 times ratio of the peak of the autocorrelation function to the steady background. Such ratio is obtained when phases of longitudinal modes of the source are locked. This value is used as the indicator of correctness of the measurements and it is required that the measured ratio would be as close as possible
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Fig. 4. Autocorrelation traces of the Sun (a) and halogen lamp (b) recorded in LiIO3 crystal. Numerically constructed second order autocorrelation trace (c).
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autocorrelation type measurements of incoherent light can be realized utilizing bulk crystals with second order nonlinearity for nonlinear transformations. Further research is needed in order to develop this and other potentially adoptable techniques up to the level of scientific instruments. Some sources are known to show higher conversion efficiency at low irradiance [16,17] and that may increase contrast over background radiation of, for instance, natural pure biphoton [18] sources. Some complex radiation sources, such as Cherenkov radiation [19] that emerge as bursts of light of specific directivity, wavelength and duration, may produce higher second harmonic signal and leave specific correlation traces, although this is not proved. Theoretical and experimental researches should be carried out to achieve real progress in applications capable to produce new data unavailable by other methods. Finally, an easily obtainable second harmonic image itself represents a peak of the second order autocorrelation, which can also be useful for analysis. Progress in generation of the second harmonic using incoherent sources may be expected not only in visible — near infrared electromagnetic wave region, but also in far infrared and terahertz region where newly developed metamaterials offer great progress in the near future [20]. This might be of interest for investigation of Space by means of measurements of spatial and time correlations, including high resolution phase resolving due to short wavelength and instant response of the nonlinear transformation. 4. Conclusion In conclusion, generation of well detectable second harmonic of continuous wave incoherent sources starting from microscopic size LED chip up to distant object such as the Sun was demonstrated. As a
result, intensity dependent nonlinear optics in crystals with second order nonlinearity, thanks to capabilities of modern experimental equipment, is downgraded from the strong field science usually associated with lasers to nonlinear process available with any light source. Present results are auspicious for a class of applications where new methods may be implemented for characterization of light sources beyond coherent ones and highly powerful laser initiated sources by means of direct correlation type measurements.
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