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Silindirik ve Küresel Optik Mikrokovukların Karakterizasyonunun İncelenmesi ve Karşılaştırılması

Yıl 2025, Cilt: 9 Sayı: 1, 35 - 44

Gökçe Dündar , Kerem Anar , Namık Akçay , Mustafa Eryürek

https://doi.org/10.29002/asujse.1650656

Öz

Bu çalışma, inceltilmiş optik fiberler kullanılarak silindirik ve küresel mikrokovukların optik uyarımı ve karakterizasyonuna odaklanmaktadır. Optik mikrokovuk teknolojileri, çok yüksek hassasiyet gerektiren optik algılama uygulamalarında önemli bir potansiyel sunmaktadır. Bu çalışmada, inceltilmiş fiber yapıların mikrokovuklarla etkileşim mekanizmaları detaylı bir şekilde incelenmiş ve rezonans modlarının (WGM) özellikleri çözülmüştür. Silindirik mikrokovuklar, basit geometrik yapıları sayesinde çevresel değişikliklere karşı duyarlı bir algılama platformu sunarken, küresel mikrokovuklar şekilsel simetrileri ve daha yüksek Q-faktörleri ile öne çıkmaktadır. Bu yapılar, optik algılamada spektral çözünürlüğü arttırmak ve daha hassas ölçümler yapmak için kritik bir rol oynar. Deneysel düzenekte, inceltilmiş optik fiberlerin üretiminde adyabatik inceltme teknikleri kullanılmış ve fiber-mikrokovuk etkileşiminin verimliliği optimize edilmiştir. Bu düzenek, hem rezonans modlarının çözülmesine hem de Q-faktörünün hassas bir şekilde ölçülmesine olanak tanımıştır. Silindirik mikrokovuklarda daha büyük serbest spektral aralıklar (FSR) elde edilirken, küresel mikrokovuklar daha yoğun mod spektrumları ile çok yüksek Q-faktörlerine ulaşmıştır. Sonuçlar, mikrorezonatörlerin geometrik özellikleri, üretim kalitesi ve hizalama hassasiyetinin optik performans üzerindeki kritik etkisini ortaya koymuştur. Bu çalışma, inceltilmiş fiber tabanlı mikrokovukların ileri algılama teknolojilerine entegrasyonu için önemli bir temel sunmaktadır. Gelecekte, üretim tekniklerinin ve system geometrilerinin optimize edilmesi ile mikrokovukların duyarlılığını ve performansını daha da artırmak mümkün olabilecektir.

Anahtar Kelimeler

Optik mikrokovuk Serbest spektral aralıklar (FSR) Kalite faktörü (Q-faktör) Fısıldayan galeri modları (WGM) İnceltilmiş fiber

Etik Beyan

Sunduğumuz makalenin orijinal olduğunu; herhangi bir başka dergiye yayınlanmak üzere verilmediğini, daha önce yayınlanmadığını garanti ederiz.

Destekleyen Kurum

TÜBİTAK BİLGEM UEKAE

Proje Numarası

121C216

Kaynakça

  • [1] Toropov, N., Cabello, G., Serrano M.P., Serrano, R.R., Rafti, M., Vollmer, F., (2021). Review of biosensing with whispering-gallery mode lasers, Light Sci Appl, 10,42. DOI: 10.1038/s41377-021-00471-3
  • [2] Notomi, M., Kuramochi, E., (2008). Large-scale arrays of ultrahigh-Q coupled nanocavities, Nature Photon, 2: 741-747. DOI: 10.1038/nphoton.2008.226
  • [3] Aoki, T., Dayan, B., Wilcut, E., Bowen, W.P., Parkins, A.S., Kippenberg, T.J., Kimble, H.J., (2006). Observation of strong coupling between one atom and a monolithic microresonator, Nature, 443: 671-674. DOI: 10.1038/nature05147
  • [4] Vahala, K.J., (2003). Optical microcavities. Nature, 424: 839-846. DOI: 10.1038/nature01939
  • [5] Yang, J., Guo, LJ., (2006). Optical sensors based on active microcavities. IEEE Journal of Selected Topics in Quantum Electronics, 12,1: 143–147. DOI: 10.1109/JSTQE.2005.862953
  • [6] Tang, G., Huang, Y., Chen, J., Li, Z., Liang, W., (2022). Controllable one-way add-drop filter based on magneto-optical photonic crystal with ring resonator and microcavities. Optics Express, 30, 28762-28773. DOI:10.1364/OE.460271.
  • [7] Strekalov, D.V., Marquardt, C., Matsko, A.B., Schwefel, H.G.L., Leuchs, G., (2016). Nonlinear and Quantum Optics with Whispering Gallery Resonators. Journal of Optics, 18, 123002. DOI: 10.1088/2040-8978/18/12/123002
  • [8] He, L., Özdemir, Ş.K., Yang, L., (2013). Whispering gallery microcavity lasers. Laser Photonics Reviews, 7-1: 60-82.
  • [9] Tureci, H.E., (2004). Wave Chaos in Dielectric Resonators: Asymptotic and Numerical Approaches. Doctoral Thesis. Corpus ID: 115383826
  • [10] Shioda, T., Yamazaki, T., (2012). Ultrafast optical frequency comb synthesizer and analyzer. Optic Letters. 1;37(17):3642-4. DOI: 10.1364/OL.37.003642
  • [11] Armani, A.M., Kulkarni, R.P., Fraser, S.E., Flagan, R.C., Vahala, K.J., (2007). Label-Free, Single-Molecule Detection with Optical Microcavities. Science, 317, 5839:783-787. DOI: 10.1126/science.1145002
  • [12] Ilchenko, V. S., Matsko, A. B., (2006). Optical resonators with whispering-gallery modes-part II: applications. IEEE Journal of selected topics in quantum electronics, 12(1), 15-32. DOI: 10.1109/JSTQE.2005.862943
  • [13] Xiao, Y. F., Vollmer, F., (2021). Special Issue on the 60th anniversary of the first laser-Series I: Microcavity Photonics-from fundamentals to applications. Light: Science & Applications, 10(1), 141. DOI: 10.1038/s41377-021-00583-w
  • [14] Eryürek, M., Karadag, Y., Ghafoor, M., Bavili, N., Cicek, K., Kiraz, A., (2017). Liquid refractometric sensors based on optical fiber resonators. Sensors and Actuators A: Physical, 265, 161-167. DOI: 10.1016/j.sna.2017.08.019
  • [15] Lončar, M., Yoshie, T., Scherer, A., Gogna, P., Qiu, Y., (2002). Low-threshold photonic crystal laser. Applied Physics Letters, 81(15): 2680-2682. DOI: 10.1063/1.1511538
  • [16] Maker, A.J., Armani, A.M., (2012). Fabrication of silica ultra high quality factor microresonator, Journal of Visualized Experiments, 65:1-6. DOI: 10.3791/4164
  • [17] Yan, M., Zhang, X., Wang, J., Hou, F., Yang, L., Sun, W., Yang, Y., Wang T., (2019). Effects of end surface and angle coupling on mode splitting and suppression in a cylindrical microcavity. Applied Optics, 58,7: 1752-1756. DOI: 10.1364/AO.58.001752.
  • [18] Ward, J., Benson, O., (2011). WGM microresonators: sensing, lasing and fundamental optics with microspheres. Lazer Fotonik Rev, 5, 4: 553–570. DOI: 10.1002/lpor.201000025
  • [19] Vollmer, F., Arnold, S., (2008). Whispering-gallery-mode biosensing: label-free detection down to single molecules. Nature Methods, 5(7): 591-596. DOI: 10.1038/nmeth.1221
  • [20] Brambilla, G., Finazzi, V., Richardson, DJ., (2004). Ultra-low-loss optical fiber nanotapers. Optics Express, 12(10):2258-2263. DOI: 10.1364/OPEX.12.002258
  • [21] Tong, L., Gattass, RR., Ashcom, JB., He, S., Lou, J., Shen, M., Mazur, E., (2003). Subwavelength-diameter silicawires for low-loss optical waveguiding. Nature, 426: 816-819. DOI: 10.1038/nature02193
  • [22] Spillane, SM., Kippenberg, TJ., Painter, OJ., Vahala, KJ., (2002). Ideality in a fiber-taper-coupled microsphere resonator system for application to cavity quantum electrodynamics. Physical Review Letters, 91(4), 043902. DOI: 10.1103/PhysRevLett.91.043902.
  • [23] Braginsky, V.B., Gorodetsky, M.L., Ilchenko, V.S., (1989). Quality-factor and nonlinear properties of optical whispering-gallery modes. Physics Letters A, 137(7-8): 393-397. DOI: 10.1016/0375-9601(89)90912-2
  • [24] Matsko, A.B., Ilchenko, V.S., (2006). Optical resonators with whispering-gallery modes. Part II: Applications. IEEE Journal of Selected Topics in Quantum Electronics, 12(1): 3-14. DOI: 10.1109/JSTQE.2005.862952
  • [25] Birks, T.A., Li, Y.W., (1992). The shape of fiber tapers. Journal of Lightwave Technology, 10(4): 432-438, DOI: 10.1109/50.134196
  • [26] Cai, L., Pan, J., Hu, S., (2020). Overview of the coupling methods used in whispering gallery mode resonator systems for sensing. Optics and Lasers in Engineering , 127, 105968. DOI: 10.1016/j.optlaseng.2019.105968
  • [27] Eryürek, M., Karadag, Y., Taşaltın, N., Kılınç, N., Kiraz, A., (2015). Optical sensor for hydrogen gas based on a palladium-coated polymer microresonator. Sensors and Actuators B: Chemical, 212, 78-83. DOI: 10.1016/j.snb.2015.01.097
  • [28] Schiappelli, F., Kumar, R., Prasciolu, M., Cojoc, D., Cabrini, S., De Vittorio, M., Visimberga, G., Gerardino, A., Degiorgio, V., Di Fabrizio, E., (2004). Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling. Microelectronic Engineering, 73–74, 397-404. DOI: 10.1016/j.mee.2004.02.077.
  • [29] Savchenkov, A.A., Mahalingam, H., Ilchenko, V. S., Takahashi, S., Matsko, A. B., Steier, W. H., Maleki, L., (2017). Polymer Waveguide Couplers for Fluorite Microresonators. IEEE Photonics Technology Letters, 29(8): 667-670. DOI: 10.1109/LPT.2017.2675279.
  • [30] Taillaert, D., Van Laere, F., Ayre, M., Bogaerts, W., Van Thourhout, D., Bienstman, P., Baets, R., (2006). Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides. Japanese Journal of Applied Physics, 45, 6071. DOI: 10.1143/JJAP.45.6071
  • [31] Vogt, D. W., Jones, A.H., Schwefel, H.G.L., Leonhardt, R., (2018). Prism coupling of high-Q terahertz whispering-gallery-modes over two octaves from 0.2 THz to 1.1 THz. Optic Express, 26, 31190-31198. DOI: 10.1364/OE.26.031190
  • [32] Yariv, A., (2000). Universal relations for coupling of optical power between microresonators and dielectric waveguides. Electronics Letters, 36(4): 321-322. DOI: 10.1049/el:20000340.
  • [33] Ozel, B., Nett, R., Weigel, T., Schweiger, G., Ostendorf, A., (2010). Temperature sensing by using whispering gallery modes with hollow core fibers. Measurement Science And Technology, 21: 094015. DOI:10.1088/0957-0233/21/9/094015
  • [34] Kavungal, V., Farrell, G., Wu, Q., Mallik, A K., Semenova, Y., (2018). Studies of geometrical profiling in fabricated tapered optical fibers using whispering gallery modes spectroscopy. Optical Fiber Technology, 41:82-88. DOI: 10.1016/j.yofte.2018.01.007
  • [35] Chýlek, P., Kiehl, JT., Ko, M.K.W., (1978). Optical levitation and partial-wave resonances. Physical Review A, 18:2229-2233.
  • [36] Benner, H.E., Barber, P.W., Owen, F., Chang, B.K. (1980). Observation of Structure Resonances in the Fluorescence Spectra from Microspheres. Physical Review Letters, Vol 44, No 7.
  • [37] Armani, A.M., Vahala, K., (2006). Heavy water detection using ultra-high-Q microcavities. Optics Letters, 31:1896-1898.

Optical Characterization and Comparative Investigation of Cylindrical and Spherical Optical Microcavities

Yıl 2025, Cilt: 9 Sayı: 1, 35 - 44

Gökçe Dündar , Kerem Anar , Namık Akçay , Mustafa Eryürek

https://doi.org/10.29002/asujse.1650656

Öz

This study focuses on the optical excitation and characterization of cylindrical and spherical microcavities using tapered optical fibers. Optical microcavity technologies offer significant potential for optical sensing applications requiring ultra-high sensitivity. In this study, the interaction mechanisms between tapered fiber structures and microcavities were examined in detail, and the properties of so-called “whispering gallery mode” (WGM) resonances were analyzed. Cylindrical microcavities provide a sensitive sensing platform against environmental changes due to their simple geometric structures, while spherical microcavities stand out with their symmetrical shapes and higher quality factors (Q-factors). These structures play a critical role in enhancing spectral resolution and achieving precise measurements in optical sensing. In the experimental setup, adiabatic tapering techniques were employed to fabricate tapered optical fibers, and the efficiency of fiber-microcavity interactions was optimized. This setup allowed for resolving WGMs spectrally making precise measurement of Q-factors possible. Larger free spectral ranges (FSR) were obtained with cylindrical microcavities, whereas spherical microcavities achieved extremely high Q-factors with denser mode spectra. The results revealed the critical impact of geometric properties, fabrication quality, and alignment precision of microcavities on optical performance. This study provides a significant foundation for the integration of tapered fiber-based microcavities into advanced sensing technologies. In the future, optimizing fabrication techniques and system geometries could further enhance the sensitivity and performance of microcavities.

Anahtar Kelimeler

Optical microcavity Free spectral range (FSR) Quality factor (Q-factor) Whispering gallery mode (WGM) Tapered fiber

Etik Beyan

We guarantee that the submitted paper is original, has not been previously published, and has not been submitted to any other journal for publication.

Destekleyen Kurum

TÜBİTAK BİDEB

Proje Numarası

121C216

Teşekkür

This work was supported by TÜBİTAK BİDEB (Project Number: 121C216).

Kaynakça

  • [1] Toropov, N., Cabello, G., Serrano M.P., Serrano, R.R., Rafti, M., Vollmer, F., (2021). Review of biosensing with whispering-gallery mode lasers, Light Sci Appl, 10,42. DOI: 10.1038/s41377-021-00471-3
  • [2] Notomi, M., Kuramochi, E., (2008). Large-scale arrays of ultrahigh-Q coupled nanocavities, Nature Photon, 2: 741-747. DOI: 10.1038/nphoton.2008.226
  • [3] Aoki, T., Dayan, B., Wilcut, E., Bowen, W.P., Parkins, A.S., Kippenberg, T.J., Kimble, H.J., (2006). Observation of strong coupling between one atom and a monolithic microresonator, Nature, 443: 671-674. DOI: 10.1038/nature05147
  • [4] Vahala, K.J., (2003). Optical microcavities. Nature, 424: 839-846. DOI: 10.1038/nature01939
  • [5] Yang, J., Guo, LJ., (2006). Optical sensors based on active microcavities. IEEE Journal of Selected Topics in Quantum Electronics, 12,1: 143–147. DOI: 10.1109/JSTQE.2005.862953
  • [6] Tang, G., Huang, Y., Chen, J., Li, Z., Liang, W., (2022). Controllable one-way add-drop filter based on magneto-optical photonic crystal with ring resonator and microcavities. Optics Express, 30, 28762-28773. DOI:10.1364/OE.460271.
  • [7] Strekalov, D.V., Marquardt, C., Matsko, A.B., Schwefel, H.G.L., Leuchs, G., (2016). Nonlinear and Quantum Optics with Whispering Gallery Resonators. Journal of Optics, 18, 123002. DOI: 10.1088/2040-8978/18/12/123002
  • [8] He, L., Özdemir, Ş.K., Yang, L., (2013). Whispering gallery microcavity lasers. Laser Photonics Reviews, 7-1: 60-82.
  • [9] Tureci, H.E., (2004). Wave Chaos in Dielectric Resonators: Asymptotic and Numerical Approaches. Doctoral Thesis. Corpus ID: 115383826
  • [10] Shioda, T., Yamazaki, T., (2012). Ultrafast optical frequency comb synthesizer and analyzer. Optic Letters. 1;37(17):3642-4. DOI: 10.1364/OL.37.003642
  • [11] Armani, A.M., Kulkarni, R.P., Fraser, S.E., Flagan, R.C., Vahala, K.J., (2007). Label-Free, Single-Molecule Detection with Optical Microcavities. Science, 317, 5839:783-787. DOI: 10.1126/science.1145002
  • [12] Ilchenko, V. S., Matsko, A. B., (2006). Optical resonators with whispering-gallery modes-part II: applications. IEEE Journal of selected topics in quantum electronics, 12(1), 15-32. DOI: 10.1109/JSTQE.2005.862943
  • [13] Xiao, Y. F., Vollmer, F., (2021). Special Issue on the 60th anniversary of the first laser-Series I: Microcavity Photonics-from fundamentals to applications. Light: Science & Applications, 10(1), 141. DOI: 10.1038/s41377-021-00583-w
  • [14] Eryürek, M., Karadag, Y., Ghafoor, M., Bavili, N., Cicek, K., Kiraz, A., (2017). Liquid refractometric sensors based on optical fiber resonators. Sensors and Actuators A: Physical, 265, 161-167. DOI: 10.1016/j.sna.2017.08.019
  • [15] Lončar, M., Yoshie, T., Scherer, A., Gogna, P., Qiu, Y., (2002). Low-threshold photonic crystal laser. Applied Physics Letters, 81(15): 2680-2682. DOI: 10.1063/1.1511538
  • [16] Maker, A.J., Armani, A.M., (2012). Fabrication of silica ultra high quality factor microresonator, Journal of Visualized Experiments, 65:1-6. DOI: 10.3791/4164
  • [17] Yan, M., Zhang, X., Wang, J., Hou, F., Yang, L., Sun, W., Yang, Y., Wang T., (2019). Effects of end surface and angle coupling on mode splitting and suppression in a cylindrical microcavity. Applied Optics, 58,7: 1752-1756. DOI: 10.1364/AO.58.001752.
  • [18] Ward, J., Benson, O., (2011). WGM microresonators: sensing, lasing and fundamental optics with microspheres. Lazer Fotonik Rev, 5, 4: 553–570. DOI: 10.1002/lpor.201000025
  • [19] Vollmer, F., Arnold, S., (2008). Whispering-gallery-mode biosensing: label-free detection down to single molecules. Nature Methods, 5(7): 591-596. DOI: 10.1038/nmeth.1221
  • [20] Brambilla, G., Finazzi, V., Richardson, DJ., (2004). Ultra-low-loss optical fiber nanotapers. Optics Express, 12(10):2258-2263. DOI: 10.1364/OPEX.12.002258
  • [21] Tong, L., Gattass, RR., Ashcom, JB., He, S., Lou, J., Shen, M., Mazur, E., (2003). Subwavelength-diameter silicawires for low-loss optical waveguiding. Nature, 426: 816-819. DOI: 10.1038/nature02193
  • [22] Spillane, SM., Kippenberg, TJ., Painter, OJ., Vahala, KJ., (2002). Ideality in a fiber-taper-coupled microsphere resonator system for application to cavity quantum electrodynamics. Physical Review Letters, 91(4), 043902. DOI: 10.1103/PhysRevLett.91.043902.
  • [23] Braginsky, V.B., Gorodetsky, M.L., Ilchenko, V.S., (1989). Quality-factor and nonlinear properties of optical whispering-gallery modes. Physics Letters A, 137(7-8): 393-397. DOI: 10.1016/0375-9601(89)90912-2
  • [24] Matsko, A.B., Ilchenko, V.S., (2006). Optical resonators with whispering-gallery modes. Part II: Applications. IEEE Journal of Selected Topics in Quantum Electronics, 12(1): 3-14. DOI: 10.1109/JSTQE.2005.862952
  • [25] Birks, T.A., Li, Y.W., (1992). The shape of fiber tapers. Journal of Lightwave Technology, 10(4): 432-438, DOI: 10.1109/50.134196
  • [26] Cai, L., Pan, J., Hu, S., (2020). Overview of the coupling methods used in whispering gallery mode resonator systems for sensing. Optics and Lasers in Engineering , 127, 105968. DOI: 10.1016/j.optlaseng.2019.105968
  • [27] Eryürek, M., Karadag, Y., Taşaltın, N., Kılınç, N., Kiraz, A., (2015). Optical sensor for hydrogen gas based on a palladium-coated polymer microresonator. Sensors and Actuators B: Chemical, 212, 78-83. DOI: 10.1016/j.snb.2015.01.097
  • [28] Schiappelli, F., Kumar, R., Prasciolu, M., Cojoc, D., Cabrini, S., De Vittorio, M., Visimberga, G., Gerardino, A., Degiorgio, V., Di Fabrizio, E., (2004). Efficient fiber-to-waveguide coupling by a lens on the end of the optical fiber fabricated by focused ion beam milling. Microelectronic Engineering, 73–74, 397-404. DOI: 10.1016/j.mee.2004.02.077.
  • [29] Savchenkov, A.A., Mahalingam, H., Ilchenko, V. S., Takahashi, S., Matsko, A. B., Steier, W. H., Maleki, L., (2017). Polymer Waveguide Couplers for Fluorite Microresonators. IEEE Photonics Technology Letters, 29(8): 667-670. DOI: 10.1109/LPT.2017.2675279.
  • [30] Taillaert, D., Van Laere, F., Ayre, M., Bogaerts, W., Van Thourhout, D., Bienstman, P., Baets, R., (2006). Grating Couplers for Coupling between Optical Fibers and Nanophotonic Waveguides. Japanese Journal of Applied Physics, 45, 6071. DOI: 10.1143/JJAP.45.6071
  • [31] Vogt, D. W., Jones, A.H., Schwefel, H.G.L., Leonhardt, R., (2018). Prism coupling of high-Q terahertz whispering-gallery-modes over two octaves from 0.2 THz to 1.1 THz. Optic Express, 26, 31190-31198. DOI: 10.1364/OE.26.031190
  • [32] Yariv, A., (2000). Universal relations for coupling of optical power between microresonators and dielectric waveguides. Electronics Letters, 36(4): 321-322. DOI: 10.1049/el:20000340.
  • [33] Ozel, B., Nett, R., Weigel, T., Schweiger, G., Ostendorf, A., (2010). Temperature sensing by using whispering gallery modes with hollow core fibers. Measurement Science And Technology, 21: 094015. DOI:10.1088/0957-0233/21/9/094015
  • [34] Kavungal, V., Farrell, G., Wu, Q., Mallik, A K., Semenova, Y., (2018). Studies of geometrical profiling in fabricated tapered optical fibers using whispering gallery modes spectroscopy. Optical Fiber Technology, 41:82-88. DOI: 10.1016/j.yofte.2018.01.007
  • [35] Chýlek, P., Kiehl, JT., Ko, M.K.W., (1978). Optical levitation and partial-wave resonances. Physical Review A, 18:2229-2233.
  • [36] Benner, H.E., Barber, P.W., Owen, F., Chang, B.K. (1980). Observation of Structure Resonances in the Fluorescence Spectra from Microspheres. Physical Review Letters, Vol 44, No 7.
  • [37] Armani, A.M., Vahala, K., (2006). Heavy water detection using ultra-high-Q microcavities. Optics Letters, 31:1896-1898.
Toplam 37 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Fotonik, Optoelektronik ve Optik İletişim
Bölüm Araştırma Makalesi
Yazarlar

Gökçe Dündar 0000-0002-7876-5818

Kerem Anar 0009-0005-7168-5144

Namık Akçay 0000-0003-1660-213X

Mustafa Eryürek 0000-0001-8612-3164

Proje Numarası 121C216
Erken Görünüm Tarihi 28 Nisan 2025
Yayımlanma Tarihi
Gönderilme Tarihi 5 Mart 2025
Kabul Tarihi 21 Mart 2025
Yayımlandığı Sayı Yıl 2025Cilt: 9 Sayı: 1

Kaynak Göster

APA Dündar, G., Anar, K., Akçay, N., Eryürek, M. (2025). Optical Characterization and Comparative Investigation of Cylindrical and Spherical Optical Microcavities. Aksaray University Journal of Science and Engineering, 9(1), 35-44. https://doi.org/10.29002/asujse.1650656
Aksaray J. Sci. Eng. | e-ISSN: 2587-1277 | Period: Biannually | Founded: 2017 | Publisher: Aksaray University | https://asujse.aksaray.edu.tr