After finishing, Eason is here to share. /Filter/FlateDecode Electromagnetic waves are related. Please answer the following questions: Question. The linear cavity is 30 cm long. Consider an optical pump at 940 nm for a Yb:YAG crystal placed in a laser cavity. Question. TYPES OF LASERS 301 570-640 nm (rhodamine 6G) and many others. 2. >> Solution of Problem 4.13 is expressed in radians and is equal to 100 10-3/500. . The length of the cavity is equal to 1 m. 1. The number of longitudinal modes is equal to the spectral band divided by the interval between the two longitudinal modes: Note: in general, 2 modes can successfully oscillate but, if one of the modes is perfectly in the centre of the transition, the number can rise to 3. Solution of Problem 4.12 Problem 4.13 A laser emitting at 0=850nm has a gain spectral width of = 32 nm and a peak gain of g(0) 50/cm , Plot g() equation 4.41. Qf� �Ml��@DE�����H��b!(�`HPb0���dF�J|yy����ǽ��g�s��{��. If from t =32.2 /cm , show the region where lasing takes place. $E}k���yh�y�Rm��333��������:� }�=#�v����ʉe x��Z͎�6��)��J�~�� A laser is a device that emits light (electromagnetic radiation) through a process called stimulated emission. Detailed solutions are given to Calculate the gap in frequency between two longitudinal modes in a linear cavity whose optic length, L, =300 mm. ��OU�S1z6��wM�,��7���](�i�yJӲ�i�w6�+�*���&��羸�+-B[��Y�`���1ΗrF��6?�%А᫕�@L��ra�3� |��� La�]��yW�����bX���`���3� �=��&�[�L�B�F��;���la��]�B�i3֏��9!�hcYD�ٿ�6��Ю�5H��6����h ֢�-6���6{a�S��0QS�8�)���q��*<5I��� �[������5)T��>\�h) ������1�7�M��Q����/��ɹxr΅�6��c���[�����"�@���Q���s� �zhQp�,Lr0u����bC�"Z���ɪMJ���3���bC��AP!�z"�n��OMT-ݭ�%��3 E�����z6��Cf.�+So�f���(�Q�g�)��L�7���F��c��?��3�*P�#wR���x��`�_����P�䮤��C�lJ���O��`�����)�@�_�'*�:�%&z���3X]P�߀S��a�8 x��͎� ��} If nothing is done, the laser is unlikely to oscillate. , where h is Planck's constant (6.62 10-34Js) and c is the speed of light in a vacuum (3.108ms-1). These dyes can be excited by optically with Argon lasers for example and emit at 390-435nm (stilbene), 460-515nm (coumarin 102), 7.3. /Length 810 43 0 obj The wavelength of ytterbium is 1030 nm. Problem; Problem. CO2 has a bandwidth equal to k�q��A����@���X ��9Z�QX{�;��VL۲l4�c�β�dY�@�섌fڕ�=�n9n)��� �YjEw��/�z��NRJ�\��Һ]�~Sb�J\)��Ɂ-o��ep�T&���λ�yqS��U��w��po�{�{�y�Ut}��ڦ�\���QT{�;���ie���ؾ-�E�8�=���VɱT�9�]�ĕ�=�n�~�T$F���-�Z$����}}�������a羳���H�Dˆ��ڑ������5/9�K�䥐�" �w�՞^�t!YCW�RHʎ�pձ�W��m����Avxӱg��@`�U��Ƒ�9��> �ZQ9�5ջ�V���j3�C��V.D>�Qwo��C>�1�j��9N|ަ[=��[�Ih��d���a�v��E���l9ɳջ,VRv����6��>�3���`�Zq����5V�Hi9�l�p����W��:�"'���8��>Z��l�GW +�;�� ڡ���r����l]N�˪a%i/�6=�g Calculate the average output power of the laser. endobj In addition, it is important to note that when cutting 5mm carbon steel plate with the laser cutting machine, it needs to replace 7.5 “focal length laser lens. << A Q-switched laser emits pulses of 10µJ of duration 1 ns. when laser oscillation occurs. 1. Problems and solutions Session 1. << ����rh�c��6��Ĩo�jl�4��n����;�]`��!��bH�g�ȳD�t��zo���KP�c�r2��y��i5�7�ނBV4��Lko)Q����H��җ����ܳ#8Jv�B=�kv�]�q ~�iH�����}P?�م��.M 峩�b�Q,�J��t@0 69 0 obj at 633 nm. I have to say that after reading all kinds of flower problems and solutions, I feel a lot of knowledge. For simplicity, the spectral profile is assumed to be rectangular. /Length 2594 72 0 obj Typically, lasers are thought of as emitting li… The peak power is the energy of the pulse divided by its duration: 2. The repetition rate of the pulses is equal to 10 kHz. Calculate the number of longitudinal modes that can oscillate in this cavity. �tq�X)I)B>==���� �ȉ��9. The period between each pulse is equal to, During this period, only one pulse is emitted. Case study: Diode-pumped Nd: YAG Laser; Lesson questions. Today’s theme is the high-frequency word in laser cutting-carbon steel. A helium-neon laser emitting at 633 nm makes a spot with a radius equal to 100 mm at 1/e2 at a distance of 500 m from the laser. stream ��xH���&�/?��KO: ^ S��S�r�Ԯ�۶�U=$��^�������6�i���\�h�3���Lj���?% laser, concentrated on a very small area, in order to cut or engrave a material. Calculate the peak power of the pulses. Chapter 1 is devoted to the methods of Mathematical physics and covers such topics which are relevant to subsequent chapters. �jN�jWma��]-`ȏl�D?��W@;��&�%�/}vIh�\��ņv�CD�N����湣-�|u_��2��u\d��i��7� �N�� Calculate the energy of each pulse. 2. 1. ���.P��Z1j�������Ծ�܃��Y�4��b��� � �E�>"�e1�[b�M�����#"^�+��3JD��-���u.qUg�{*��^rz��N�~Z�����ٌG�)s�����r� If all the photons emitted by the pump are absorbed by the crystal and used for the lasing process, calculate the maximum power output. )ɩL^6 �g�,qm�"[�Z[Z��~Q����7%��"� endobj The optic length of the cavity, L, is 1 m. The gap between two pulses from a mode-locked laser is defined by 2L/c. The laser cutting speed is too fast, and the linear velocity needs to be reduced. By considering the energy of the ground state to be zero and calling 0 the ground state and 1 the lower energy level: Thus 38% of the population is in the lower energy level. For simplicity, the spectral profile is assumed to be rectangular. The maximum output power is defined by 1. stream The calculation is the same as for the previous question: this time N=0.33! xڝ�wTT��Ͻwz��0�z�.0��. If an external electric field is applied to a dielectric (not conduct- ing) material the material will be polarized, resulting in a polarization P. The relation is then, E = D "0 P "0) D = "0E +P If P = 0, as in vacuum, E and D are in phase. No book on problems can claim to exhaust the variety in the limited space. Calculate the number of longitudinal modes that can oscillate in this cavity. An one milliwatt He-Ne laser is highly intense than the sun intensity. By taking into account the different wavelengths, the power is equal to. The energy (E) is therefore found from. A ring laser cavity is composed of 4 identical mirrors with a reflection coefficient equal to 0.99. It is also widely used in industrial production and processing. What is the radius of the beam at the waist (considering the waist and the laser are in the same plane)? Suppose when two photons each of amplitude are in phase with other, then young’s principle of superposition, the resultant amplitude of two photons is 2 and the intensity is 4 . Laser light is usually spatially coherent, which means that the light either is emitted in a narrow, low-divergence beam, or can be converted into one with the help of optical components such as lenses. The pump power is 1 W. At best, a pump photon gives a laser photon. 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